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断裂理论基础

现在大家比较一致的认识是，现代断裂理论大约是在１９４８ — １９５７年间形成，
· ii · 前言
它是在当时生产实践问题的强烈推动下，在经典 Griffith 理论的基础上发展起来的．上世纪６０年代是其大发展时期．从１９６５年下半年开始国内出现特殊的形势，上面提到的我国老一辈学者开创的断裂学科的较好势头也就丧失了，因而同国外的差距进一步拉大．在２０世纪７０年代初，受我国航空工业部门的委托，冶金部钢铁研究总院物理研究室陈箎同志领导的小组从材料断裂韧性测试开始，在十分困难的条件下，率先在我国开展了断裂力学的工作．显然，我国断裂力学工作起步至少比国外大约晚了２０多年．１９７２年，在敬爱的周恩来总理关怀下，包括力学在内的自然科学各基础学科举行了赶超世界先进水平的规划座谈会．当时力学学科的规划座谈会的预备会的纪要就引用了恩格斯的一句名言：“一个民族要想站在世界的高峰，就一刻也不能停止理论思维。”同时指出断裂力学是一门新学科，在理论上和实践上具有重要意义，建议尽快在我国开展该领域的工作．在冶金部钢铁研究总院物理研究室陈箎同志等工作和力学学科规划座谈会预备会纪要的激励下，尤其是众多实际问题需要的推动下，我国一些单位和科技工作者逐步开展了断裂力学的研究和应用工作．著者当时是作为一名业余爱好者参加到这项工作中去的．著者在当学生时，受到董铁宝教授的指导，读过一点经典断裂理论的文献，当时也得到王仁教授、张兴钤教授和钱临照教授的指教．在经过将近１０年中断并重新回到教学工作岗位时，获悉经典断裂理论已经发展成断裂力学这门新学科时，很振奋，但深感已经落后得太远了．枟断裂力学基础枠是著者学习断裂力学笔记整理出来的．当时著者对断裂力学的认识还很初步．该书出版至今已经超过了２０年，探索断裂现象规律的工作已从力学扩充到更广泛和深入的领域．考虑到这些情况的变化，需要对该书加以改写．

2010美国数学建模B题论文

Team#8254page1of16 Play your best hit:The mystery in baseball batMCM Contest Question ATeam#8254February22,2010Contents1Introduction (2)1.1Problem Restatement (2)1.2What is the sweet spot on earth? (2)1.3How to cork a bat? (2)1.4The material of baseball bat matters? (2)2Assumption (3)3A Simpliﬁed Model (3)3.1Model Description (3)3.2Finding the”sweet spot” (5)4An Augmented Model (6)4.1Model Description (6)4.2Why no corked bats and metal bats? (8)4.2.1Qualitative Analysis (8)4.2.2Quantitative Analysis (9)5Sensitivity (12)6Conclusion (13)6.1Strength (13)6.2Weakness (13)6.3Recommendation (13)7References (13)8Appendix (14)Team#8254page2of16 1Introduction1.1Problem RestatementEvery experienced hitter knows that there is a spot on the baseball bat that when hitting with this spot,the hand of the hitter feels no pain and the ball can be hit farther.This is the”sweet spot”.According to the theory of torque,this spot should be at the end of the bat,but the experience of the hitters proves it wrong.The location of”sweet spot”on a given baseball bat is approximately 6-1/2”from the end of the bat[1].Our purpose is to establish a model to give a scientiﬁc explanation.In addition,some players believe that drilling a cylinder in the end of the bat andﬁlling it with cork or rubber,namely,to cork the bat [2],enhances the”sweet spot”effect.We would like to found our model and use it to interpret it.What’s more,the question that whether the material of bats matters is also a part discussed in this paper.1.2What is the sweet spot on earth?There are many deﬁnitions of”sweet spot”[3].Here in this paper,we deﬁne it as the location where maximum energy is transferred to the ball.1.3How to cork a bat?”Corking”is to drill a1inch diameter hole6inches longitudinally into the bat’s barrel end.The structure of the real bat and the corked bat can be showed in Fig1.In our augmented model,we will analyze the effect of corking.1.4The material of baseball bat matters?Compared to the wood bats,aluminum bats is not easily be broke,and as the aluminum bats are hollow,the thickness of the shell can be manipulated so that the center of mass may be more closer to the handle,and consequently reducing the perceived weight while swinging.In this way,it increases the mobility of(a)Normal baseball bat(b)Corked baseball batFig1:Normal baseball bat and corked batTeam#8254page3of16 the hitter.What’s more,using aluminum bat can largely improve the energy of the ejecting ball,which may be too hard to catch or even dangerous for players. All those features lead to the prohibition of the using of aluminum bat[4].We will explain it in details later in this paper.Fig2:Cross section of aluminum bat2AssumptionAs the hitting process is too complex,we make the following assumptions in order to simplify the problems and establish our models:1.The better hitting effect means a larger exit speed of the ball and a shorteracceleration time of the bat.2.When the hitter swings,hitter-bat system rotates around a vertical axis that”penetrates”the hitter.3.The collision of the ball and the bat is one-dimensional.4.The hitter always hits the ball at the”sweet spot”.3A Simpliﬁed Model3.1Model DescriptionIn our simpliﬁed model,we omit the situations that the player might modify the baseball bat and concentrate on explaining why the”sweet spot”is not at the end of the bat but a few distances from the end.When you hit a ball,the bat vibrates in response.These vibrations travel in waves up and down the length of the bat.At one point,called”the node”, the waves always cancel each other out.If you hit the ball on the bat’s node, the vibrations from the impact will cancel out,and you won’t feel any stinging or shaking in your hand.Since little of the bat’s energy is lost to vibrations when this spot is hit,more can go to the ball[5].We will found a model based onTeam#8254page4of16 the characteristics showed as italics.In our model,we ignore the swing of the hitter’s arms when hit.We denote the spot where the hitter holds the bat as pivot, assuming that the pivot isﬁxed,and the bat is mounted on the pivot so that it can swing around the pivot freely.The parameters we use are given in the tabular Notation,and the force and motion diagram is showed in Fig3.NotationSymbols MeaningF ball the applied force in the collisionF px,F py the vertical and horizontal component forces of the force in the pivotcm the center of mass of the batp the impact pointpivot the spot where the hitter holds the batI pivot the moment of inertia of the bat with respect to pivotL x−y the distances between x and yαthe rotation angular acceleration of the batm bat the mass of the batL sum the whole length of the batFig3:The force and motion diagram of the batNext,we will analyze the model above with the knowledge of kinetics in order toﬁnd the”sweet spot”.Team #8254page 5of 163.2Finding the ”sweet spot”According to the theorem of moment of momentum we have:F ball ·L pivot =I pivot ·α(1)and based on the theorem of motion of center of mass:∑F =ma c we have:F ball +F px =m bat ·L pivot −cm ·α(2)Therefore,with equation (1)and (2)we have:F hand =F ball m bat ·L pivot −cm ·L pivot −p I pivot−1 Thus we know that the horizontal component force is 0whenL pivot −p =I pivotm bat L pivot −cmIn other words,when the distance between the pivot and the p is I pivot m bat ·L pivot −cm ,the p is the sweet spot.In order to ﬁnd the speciﬁc location of the ”sweet spot”on a certain bat,we quote the data from [6]and choose a C243wooden bat,thus we get the parame-ters L pivot −cm =0.42m ,I pivot =0.208kg ·m 2,L knob −pivot =0.15m ,m bat =0.905kg ,L sum =0.86m .Then we calculate L pivot −p =0.55m ,so that L knob −p =0.70m .From the re-sult we can obviously see that the ”sweet spot”is about 0.16m far from the end of the fat part of the bat.The forces on different location of the bat can be showed in Fig4.Fig 4:The rotation system in a hitting processIn this way,we have successfully demonstrated that the experience of the hitters is right.Team#8254page6of16 4An Augmented Model4.1Model DescriptionThe previous model fails to take the situation that some hitter may modify the bat into account.What’s more,in real baseball game it is impossible that the arms of the hitter are stationary when hit.So we augmented ourﬁrst model. In this augmented model,we assume that the hitter and the bat form a rotation system in which the hitter stays vertical and the bat stays horizontal.The hitting process can thus be modeled as:the system gets a torque T generated by the hitter and rotates around the axis which vertically”penetrates”the hitter and then hits a ball.After hitting process,the ball ejects out with a velocity of v f. The distance between the impact spot and the axis is r.The process is described in Fig5.Fig5:The rotation system in a hitting processWe notice that the ball gets maximum velocity after hitting means the effect of hitting is optimal,so we should focus on the exit speed of the ball.Two processes are displayed as follows:Process1:The hitter swings the bat and accelerates the bat to an angular velocity ofω.Process2:After the imperfect inelastic collision of bat and ball,the ball ejects out with a velocity of v f.In process1,the moment of inertia of bat and the air resistance will hamper the rotation of the system of hitter-bat.It is easy to calculate the liner velocity of any spot on the bat by the kinematics formula v=ωr,and according to the formulas given by Keith Koenig in reference[7],we know that the angular ve-Team#8254page7of16 locity and the linear velocity of the impact spot on the bat before the collision in process1are:ω=TK Dtanhcosh−1expK DI hitter+I batθv bat=rω(3) where•r is the rotation radius,equals the length from the impact spot to the axis.•T is the torque applied to the hitter-bat system which is generated by the hitter.•K D is an aerodynamic parameter,which is given byK D=12ρC D DL44(for more please read reference[7])•tanh is hyperbolic tangent function.•cosh−1is anti-hyperbolic cosine function.•exp is exponential function.•θis the angle that the bat rotates.•I hitter is the hitter’s moment of inertia with respect to the axis.•I bat is the bat’s moment of inertia with respect to the axis.In our case,we treat T,K D,I hitter,θas constant parameters while r and I bat are the only variables.In process2,we assume that the bat and ball have an one-dimensional col-lision and they both have some extent of deformation.The deformation trans-forms a small part of the kinetic energy(about25%,reference[8])into potential energy stored in bat and ball,while most part(about75%)of it dismisses due to the friction and the oscillation of the bat.And referring to reference[7]we havev f=COR−r M1+r Mv ball+COR+11+r Mv bat(4)where•COR is the coefﬁcient of restitution,it will be discussed in the next part.•v ball is the velocity of the ball right before the collision with the bat.Team #8254page 8of 16•v bat is the velocity of the bat right before the collision with the bat.by equation (3)and (4),we getv f =COR −r M 1+r M v ball +COR +11+r M r T K D tanh cosh −1 exp K D I hitter +I batθ (5)The parameters:COR ,I bat ,r M are explained in Appendix .4.2Why no corked bats and metal bats?In order to reveal the inﬂuence of each parameter on the velocity of the ball thus to ﬁgure out the effect of the corking behavior and predict different be-havior for wood and metal bats,we make some analysis about the application procedure of our augmented model.4.2.1Qualitative AnalysisWe assume that the velocity of the ball is constant before the collision with the bat,and the impact spots are on the same position of the bat,namely,r is a constant.The corking has two aspects of inﬂuences:one is the decrease of mass,the other is the deviation of the center of mass.1.Corked bat•The inﬂuence on v fDue to the lower density of material corked in the barrel,the whole mass of bat inclines and the center of mass moves to the rotation axis a little.On one hand,it will cause the decrease of I bat as I bat = r 2dm ,and according to the expression of v f :v f =COR −r M 1+r M v ball +COR +11+r M r T K D tanh cosh −1 exp K D I hitter +I batθ we know that the value of r T K D tanh cosh −1 exp K D I hitter +I batθ will increase.On the other hand,as we haver M =m ball (z −z p )2I cm +m bat L 2pivot −cmTeam#8254page9of16 we know that if m bat decreases and the center of mass deviates toknob,I cm and L pivot−cm will both decline,and that will make r M in-crease and lead to the decline of both COR−r M1+r M v ball and COR+11+r M.How-ever,it is impossible for us to ensure whether the value of v f willincrease or decrease without speciﬁc data.We will explain it later inthe Quantitative Analysis section.•The inﬂuence onﬂexibilityWe regard the procedure that the hitter-bat system is accelerated fromstationary situation to rotating with an angular velocity ofωas auniformly accelerated motion procedure.By kinematic formulas weknow that the acceleration time is t=2θω,and from the expression ofωmentioned in page6,section4.1,we know that as the I bat decreasesdue to corking,the value ofωwill increase,so that the accelerationtime will be shorten and in this way theﬂexibility develops.2.Metal bats vs.wood batsUsing our augmented model we are able to analyze the behavior of bats that have different composition material.•The inﬂuence on v fMetal bats(usually aluminum bats)have trampoline effect due togood elasticity,so that it has larger COR than wood bats(usually ashbats).In addition,as the aluminum bats have less mass,the inﬂuenceof material is just like that in discussing corked bats.It is obvious thatin order toﬁnd which kind of bat’s v f is larger we need the supportof data.•The inﬂuence onﬂexibilityThe aluminum bats are lighter than wood bats so that the inﬂuenceonﬂexibility is the same as corked bats.4.2.2Quantitative Analysis1.Data usingAs the qualitative analysis cannot show the exact differences between wood bats,corked wood bats(corked bats)and aluminum bats,we quote the data from reference[7][12][13][14]to verify our augmented model.Table1:Value of ConstantsTeam#8254page10of16Constants Valuem ball/(g)134.2v ball/(m/s)25(assumption)T316N·mK D/(N·m·s2)0.00544θ 2.36radr/(m)0.762R hitter−pivot/(m)0.305I hitter/(kg·m2)0.444Table2:Value of VariablesValues Wood bat Corked bat Aluminum batCOR0.500.500.58mass/(g)876834827I p/(kg·m2)0.2110.1950.17L cm−pivot/(cm)424039.5I bat/(kg·m2)0.5160.4760.446z−z p/(m)0.470.460.45r M0.14030.14540.1596 Using the data above we can calculate the three relative values of v f that are47.1m/s,47.6m/s and51.3m/s.The I bat is calculated based on parallel axis theorem.For a better compare of the hitting effects of the three bats,we use com-puter to make a hitting experiment simulation about theﬂying trajectories of the ball after hitting:Assuming that the ball dose a slanting parabolic motion and the launch angle of the ball after hitting with the bat isθ=30◦.Fig6shows the trajec-tories of balls that are hit by the three kinds of bats.2.The inﬂuence of three kinds of bats onﬂexibilityCombine the formula t=2θωwith the expression ofω,we have the expres-sion of the acceleration time t:t=2θTK Dtanhcosh−1expK DI hitter+I batθAfter using the values given in the table1and table2,we get:Kinds of bats t/(s)Wood Bats0.121Corked Bats0.118Aluminum Bats0.116Team#8254page11of16Fig6:The trajectories of the balls hit by the three kinds of bats It is easy to see that the acceleration time of corked bat is0.003s shorter than that of wood bat.During this time,the incoming ball moves0.075m farther,that is to say,theﬂying distance of the incoming ball from the ser-vice point to the collision point when using a corked bat is0.075m farther than that of wood bat,so that the hitter would feel more easy to deal with the incoming ball as he or she has more time to react and accelerate the bat when using a corked bat.In the same way we know that when usinga aluminum bat rather than a wood bat,the hitter has0.005s longer and0.125m farther to handle the bat.3.Summary of our analysisAt this point,we are able to answer the second and third questions about the corking behavior and the matters of different materials.•Why does Major League Baseball prohibit”corking”?From the analysis above we know that for a baseball bat used in ourmodel,if it is corked,the swinging velocity of bat right before hittingthe ball will increase0.5m/s and theﬂexibility of swinging can alsobe developed,as the mass of the bat decreases and the center of massof it deviates.•Why does Major League Baseball prohibit metal bats?According to our model,the hitting effect is closely linked with thematerials.We know from our qualitative veriﬁcation that the hittingvelocity of using a aluminum bat is4.2m/s more than that of woodbat,and the deviation of the center of mass further gains0.005s reac-tion time for the hitter.As the ball hit by aluminum bat has a muchbigger velocity,it makes the catching of the ball difﬁcult and evendangerous.Team#8254page12of16 5SensitivityAfter analyzing the application of our augmented model,weﬁnd it neces-sary to analyze the sensitivity of our model,aiming at implementing it more effectively.We choose to research the exit speed of normal wood bat with differ-ent parameters.1.The inﬂuence of massThe change of mass will inﬂuence both r M and I bat,but as the value of them are too hard to obtain by direct calculating,we make some simpliﬁcationsbelow:r M=m ball (z−z p)2I p=m ball(z−z p)2I cm+m bat L2pivot−cmIn this expression,as I cm is very small(about0.04kg·m2),we treat it as a constant one.It is the same to z−z p(about0.47m)and L pivot−cm(about 0.42m).Hence,the value of r M only correlates to m bat,and we haver M=0.1340.4720.04+m bat×0.422then in I bat=I cm+m bat·L2hitter−cm,we also treat L hitter−cm(about0.725m) as a constant,so we haveI bat=0.04+m bat×0.7252Relating to equation(5),we denote COR=0.5and get:m bat(kg)0.830.850.870.89v f(m/s)46.846.7646.7146.672.The inﬂuence of materialThe major inﬂuence of different materials is they have different COR s.When the mass is constant,we have I bat=0.516kg·m2,and r M=0.1403, andﬁnally we get:COR0.40.450.50.550.6v f/(m/s)42.344.747.149.551.9From the results above,we can see that COR seems a more prominent inﬂuence.Team#8254page13of16 6Conclusion6.1StrengthFirst of all,this paper solves the problem of”sweet spot”,and we give an easy formula to calculate the position of”sweet spot”.Secondly,we analyze the hitting process and divide it into two stages,and discuss the factors that affect the exit speed in details while giving a formula that can describe this stage.Then we answer the questions through qualitative analysis and quantitative calculation.Finally,we make a analysis about the sensitivity and prove the rationality by comparing the results.6.2WeaknessFirst of all,as the real hitting process is too complex to analyze,we make several simpliﬁcations in order to facilitate the founding of model.In model 1,we just regard the bat as a pendulum rod with one endﬁxed,which is a little different from the real situation.And in model2,we simplify the complex process of hitting into two stages.Secondly,the data weﬁnd are not precise,especially for the value of COR which we regard as constant.Additionally,the calculations in this paper are also simpliﬁed,thus the accu-racy of our results declines.6.3RecommendationThe biggest disadvantage of our model is lacking experiments,and if we have time and facilities to do some experiments,the result must be more reliable.For example,the equation(6)in Appendix can be used to measure COR,and in order to measure the value of I pivot,we could refer to[15]and use the method to obtain data.With this data we can verify our model in a better way.7References[1]/wiki/Sweet spot[2]/drussell/bats-new/corkedbat.html[3]/drussell/bats-new/sweetspot.html[4]/wiki/Aluminum Bats vs.Wood Bats[5]/baseball/sweetspot.htmlTeam#8254page14of16[6]/sysengr/slides/baseballBat.ppt[7]Keith Koenig,Nan Davis Mitchell,Thomas E.Hannigan,J.Keith Clutter.The inﬂuence of moment of inertia on baseball/softball bat swing speed.SportsEngineedng(2004)7,105-117.[8]Alan M.Nathana.Characterizing the performance of baseball bats.Am.J.Phys.,Vol.71,No.2,February2003134-143[9]/wiki/Coefﬁcient of restitution[10]Lv ZhongjieHuang Fenglei.Coefﬁcient of Restitution of a Circular PlateDuring Inelastic Collision.Transactions of Beijing Institute of Technology.Vol.28No.4.[11]P.J.Drane and J.A.Sherwood.Characterization of the effect of temperatureon baseball COR performance.[12]/sysengr/slides/baseballBat.ppt[13]/docs/621958/How-Does-a-Baseball-Bat-Work[14]/wiki/moment of inertia[15]/drussell/bats-new/bat-moi.html8AppendixParameters ExplanationIn expression(5),page8,section4.1,there are several parameters that will inﬂuence theﬁnal velocity of the ball:1.COR•What is COR?The coefﬁcient of restitution(COR),or bounciness of an object is afractional value representing the ratio of velocities after and before animpact[9].Fig7:The one-dimensional collision processTeam #8254page 15of 16The coefﬁcient of restitution is given byCOR =v 1f −v 2f v 1−v 2(6)where–v 1is the velocity of object 1before the collision.–v 2is the velocity of object 2before the collision.–v 1f is the velocity of object 1after the collision.–v 2f is the velocity of object 2after the collision.All the parameters above are scalars.In the ideal situations,we may have a so-called plastic collision when COR =0,namely the deformation of the material cannot re-store.And when COR =1,called perfectly elastic collision,is a situa-tion that the deformation can restore entirely.In general,the value of COR varies from (0,1).•What factors affect COR ?MaterialCOR represents the deformation recovery ability of the material.Gen-erally speaking,the more elastic the material is,the higher the value of COR will be.Impact velocityCOR decreases when the impact velocity increases.[10]The Temperature and Relative Humility of The EnvironmentCompared to the factors above,another two factors,the tempera-ture and relative humility have a relatively smaller inﬂuence.COR decreases when the temperature decreases and it decreases when the relative humility increases.[11]2.I bat•MOI (moment of inertia)[14]Moment of inertia is a measure of an object’s resistance to changes in its rotation rate.It is the rotational analog of mass,the inertia of a rigid rotating body with respect to its rotation.The moment of iner-tia plays much the same role in rotational dynamics as mass does in linear dynamics,determining the relationship between angular mo-mentum and angular velocity,torque and angular acceleration,and several other quantities.It is denoted asI = r 2dmwhere m is mass and r is the perpendicular distance to the axis of rotation.Team#8254page16of16•Parallel Axis TheoremI z=I cm+mL2where I cm is the moment of inertia of the rotor with respect to thecenter of mass,and the L is the distance from the center of mass toaxis z.•The factors affect MOIFigure:It inﬂuences the location of the center of mass,thereby affectsthe distance from the center of mass to rotation axis.Mass:Its increase is proportional to the increase of MOI.3.r MIn reference[8],Alan M.Nathan develops a formula relating v f to the initial speed of the ball v ball and the initial speed of the bat at the impact pointv bat as:r M=m ball (z−z p)2I pwhere•m ball and m bat are the ball and the bat’s mass respectively.•Z is the location of the impact point.•Z p is the location of the pivot point.•I p is the moment of inertia of the bat with respect to the pivot point. From the expression above we can see that reducing the mass of the bat m bat while keeping the other parameters constant will lead to a augment of r m.。

Some Recent Aspects of Differential Game Theory

Dyn Games Appl(2011)1:74–114DOI10.1007/s13235-010-0005-0Some Recent Aspects of Differential Game TheoryR.Buckdahn·P.Cardaliaguet·M.QuincampoixPublished online:5October2010©Springer-Verlag2010Abstract This survey paper presents some new advances in theoretical aspects of dif-ferential game theory.We particular focus on three topics:differential games with state constraints;backward stochastic differential equations approach to stochastic differential games;differential games with incomplete information.We also address some recent devel-opment in nonzero-sum differential games(analysis of systems of Hamilton–Jacobi equa-tions by conservation laws methods;differential games with a large number of players,i.e., mean-ﬁeld games)and long-time average of zero-sum differential games.Keywords Differential game·Viscosity solution·System of Hamilton–Jacobi equations·Mean-ﬁeld games·State-constraints·Backward stochastic differential equations·Incomplete information1IntroductionThis survey paper presents some recent results in differential game theory.In order to keep the presentation at a reasonable size,we have chosen to describe in full details three topics with which we are particularly familiar,and to give a brief summary of some other research directions.Although this choice does not claim to represent all the recent literature on the R.Buckdahn·M.QuincampoixUniversitéde Brest,Laboratoire de Mathématiques,UMR6205,6Av.Le Gorgeu,BP809,29285Brest, FranceR.Buckdahne-mail:Rainer.Buckdahn@univ-brest.frM.Quincampoixe-mail:Marc.Quincampoix@univ-brest.frP.Cardaliaguet( )Ceremade,UniversitéParis-Dauphine,Place du Maréchal de Lattre de Tassigny,75775Paris Cedex16, Francee-mail:cardaliaguet@ceremade.dauphine.frmore theoretic aspects of differential game theory,we are pretty much conﬁdent that it cov-ers a large part of what has recently been written on the subject.It is clear however that the respective part dedicated to each topic is just proportional to our own interest in it,and not to its importance in the literature.The three main topics we have chosen to present in detail are:–Differential games with state constraints,–Backward stochastic differential equation approach to differential games,–Differential games with incomplete information.Before this,we also present more brieﬂy two domains which have been the object of very active research in recent years:–nonzero-sum differential games,–long-time average of differential games.Theﬁrst section of this survey is dedicated to nonzero-sum differential games.Although zero-sum differential games have attracted a lot of attention in the80–90’s(in particular, thanks to the introduction of viscosity solutions for Hamilton–Jacobi equations),the ad-vances on nonzero-sum differential games have been scarcer,and mainly restricted to linear-quadratic games or stochastic differential games with a nondegenerate diffusion.The main reason for this is that there was very little understanding of the system of Hamilton–Jacobi equations naturally attached to these games.In the recent years the analysis of this sys-tem has been the object of several papers by Bressan and his co-authors.At the same time, nonzero-sum differential games with a very large number of players have been investigated in the terminology of mean-ﬁeld games by Lasry and Lions.In the second section we brieﬂy sum up some advances in the analysis of the large time behavior of zero-sum differential games.Such problems have been the aim of intense re-search activities in the framework of repeated game theory;it has however only been re-cently investigated for differential games.In the third part of this survey(theﬁrst one to be the object of a longer development) we investigate the problem of state constraints for differential games,and in particular,for pursuit-evasion games.Even if such class of games has been studied since Isaacs’pioneer-ing work[80],the existence of a value was not known up to recently for these games in a rather general framework.This is mostly due to the lack of regularity of the Hamiltonian and of the value function,which prevents the usual viscosity solution approach to work(Evans and Souganidis[63]):Indeed some controllability conditions on the phase space have to be added in order to prove the existence of the value(Bardi,Koike and Soravia[18]).Following Cardaliaguet,Quincampoix and Saint Pierre[50]and Bettiol,Cardaliaguet and Quincam-poix[26]we explain that,even without controllability conditions,the game has a value and that this value can be characterized as the smallest supersolution of some Hamilton–Jacobi equation with discontinuous Hamiltonian.Next we turn to zero-sum stochastic differential games.Since the pioneering work by Fleming and Souginidis[65]it has been known that such games have a value,at least in a framework of games of the type“nonanticipating strategies against controls”.Unfortunately this notion of strategies is not completely satisfactory,since it presupposes that the players have a full knowledge of their opponent’s control in all states of the world:It would be more natural to assume that the players use strategies which give an answer to the control effectively played by their opponent.On the other hand it seems also natural to consider nonlinear cost functionals and to allow the controls of the players to depend on events of the past which happened before the beginning of the game.The last two points have beeninvestigated in a series of papers by Buckdahn and Li[35,36,39],and an approach more direct than that in[65]has been developed.Theﬁrst point,together with the two others,will be the object of the fourth part of the survey.In the last part we study differential games with incomplete information.In such games, one of the parameters of the game is chosen at random according to some probability mea-sure and the result is told to one of the players and not to the other.Then the game is played as usual,players observing each other’s control.The main difference with the usual case is that at least one of the players does not know which payoff he is actually optimizing.All the difﬁculty of this game is to understand what kind of information the informed player has interest in to disclose in order to optimize his payoff,taking thus the risk that his opponent learns his missing information.Such games are the natural extension to differential games of the Aumann–Maschler theory for repeated games[11].Their analysis has been developed in a series of papers by Cardaliaguet[41,43–45]and Cardaliaguet and Rainer[51,52].Throughout these notes we assume the reader to be familiar with the basic results of dif-ferential game theory.Many references can be quoted on this subject:A general introduction for the formal relation between differential games and Hamilton–Jacobi equations(or sys-tem)can be found in the monograph Baçar and Olsder[13].We also refer the reader to the classical monographs by Isaacs[80],Friedman[67]and Krasovskii and Subbotin[83]for early presentations of differential game theory.The recent literature on differential games strongly relies on the notion of viscosity solution:Classical monographs on this subject are Bardi and Capuzzo Dolcetta[17],Barles[19],Fleming and Soner[64],Lions[93]and the survey paper by Crandall,Ishii and Lions[56].In particular[17]contains a good introduc-tion to the viscosity solution aspects of deterministic zero-sum differential games:the proof of the existence and the characterization of a value for a large class of differential games can be found there.Section6is mostly based on the notion of backward stochastic differential equation(BSDE):We refer to El Karoui and Mazliak[60],Ma and Yong[96]and Yong and Zhou[116]for a general presentation.The reader is in particular referred to the work by S.Peng on BSDE methods in stochastic control[101].Let usﬁnally note that,even if this survey tries to cover a large part of the recent literature on the more theoretical aspects of differential games,we have been obliged to omit some topics:linear-quadratic differential games are not covered by this survey despite their usefulness in applications;however,these games have been already the object of several survey ck of place also prevented us from describing advances in the domain of Dynkin games.2Nonzero-sum Differential GamesIn the recent years,the more striking advances in the analysis of nonzero-sum differential games have been directed in two directions:analysis by P.D.E.methods of Nash feedback equilibria for deterministic differential games;differential games with a very large number of small players(mean-ﬁeld games).These topics appear as the natural extensions of older results:existence of Nash equilibria in memory strategies and of Nash equilibria in feedback strategies for stochastic differential games,which have also been revisited.2.1Nash Equilibria in Memory StrategiesSince the work of Kononenko[82](see also Kleimenov[81],Tolwinski,Haurie and Leit-mann[114],Gaitsgory and Nitzan[68],Coulomb and Gaitsgory[55]),it has been knownthat deterministic nonzero-sum differential games admit Nash equilibrium payoffs in mem-ory strategies:This result is actually the counterpart of the so-called Folk Theorem in re-peated game theory[100].Recall that a memory(or a nonanticipating)strategy for a player is a strategy where this player takes into account the past controls played by the other play-ers.In contrast a feedback strategy is a strategy which only takes into account the present position of the system.Following[82]Nash equilibrium payoffs in memory strategies are characterized as follows:A payoff is a Nash equilibrium payoff if and only if it is reach-able(i.e.,the players can obtain it by playing some control)and individually rational(the expected payoff for a player lies above its min-max level at any point of the resulting trajec-tory).This result has been recently generalized to stochastic differential games by Buckdahn, Cardaliaguet and Rainer[38](see also Rainer[105])and to games in which players can play random strategies by Souquière[111].2.2Nash Equilibria in Feedback FormAlthough the existence and characterization result of Nash equilibrium payoffs in mem-ory strategies is quite general,it has several major drawbacks.Firstly,there are,in general, inﬁnitely many such Nash equilibria,but there exists—at least up to now—no completely satisfactory way to select one.Secondly,such equilibria are usually based on threatening strategies which are often non credible.Thirdly,the corresponding strategies are,in general, not“time-consistent”and in particular cannot be computed by any kind of“backward in-duction”.For this reason it is desirable toﬁnd more robust notions of Nash equilibria.The best concept at hand is the notion of subgame perfect Nash equilibria.Since the works of Case[54]and Friedman[67],it is known that subgame perfect Nash equilibria are(at least heuristically)given by feedback strategies and that their corresponding payoffs should be the solution of a system of Hamilton–Jacobi equations.Up to now these ideas have been successfully applied to linear-quadratic differential games(Case[54],Starr and Ho[113], ...)and to stochastic differential games with non degenerate viscosity term:In theﬁrst case,one seeks solutions which are quadratic with respect to the state variable;this leads to the resolution of Riccati equations.In the latter case,the regularizing effect of the non-degenerate diffusion allows us to useﬁxed point arguments to get either Nash equilibrium payoffs or Nash equilibrium feedbacks.Several approaches have been developed:Borkar and Ghosh[27]consider inﬁnite horizon problems and use the smoothness of the invari-ant measure associated to the S.D.E;Bensoussan and Frehse[21,22]and Mannucci[97] build“regular”Nash equilibrium payoffs satisfying a system of Hamilton–Jacobi equations thanks to elliptic or parabolic P.D.E techniques;Nash equilibrium feedbacks can also be built by backward stochastic differential equations methods like in Hamadène,Lepeltier and Peng[75],Hamadène[74],Lepeltier,Wu and Yu[92].2.3Ill-posedness of the System of HJ EquationsIn a series of articles,Bressan and his co-authors(Bressan and Chen[33,34],Bressan and Priuli[32],Bressan[30,31])have analyzed with the help of P.D.E methods the system of Hamilton–Jacobi equations arising in the construction of feedback Nash equilibria for deter-ministic nonzero-sum games.In state-space dimension1and for theﬁnite horizon problem, this system takes the form∂V i+H i(x,D V1,...,D V n)=0in R×(0,T),i=1,...,n,coupled with a terminal condition at time T(here n is the number of players and H i is the Hamiltonian of player i,V i(t,x)is the payoff obtained by player i for the initial condition (t,x)).Setting p i=(V i)x and deriving the above system with respect to x one obtains the system of conservation laws:∂t p i+H i(x,p1,...,p n)x=0in R×(0,T).This system turns out to be,in general,ill-posed.Typically,in the case of two players(n= 2),the system is ill-posed if the terminal payoff of the players have an opposite monotonicity. If,on the contrary,these payoffs have the same monotony and are close to some linear payoff (which is a kind of cooperative case),then the above system has a unique solution,and one can build Nash equilibria in feedback form from the solution of the P.D.E[33].Still in space dimension1,the case of inﬁnite horizon seems more promising:The sys-tem of P.D.E then reduces to an ordinary differential equation.The existence of suitable solutions for this equation then leads to Nash equilibria.Such a construction is carried out in Bressan and Priuli[32],Bressan[30,31]through several classes of examples and by various methods.In a similar spirit,the papers Cardaliaguet and Plaskacz[47],Cardaliaguet[42]study a very simple class of nonzero-sum differential games in dimension1and with a terminal payoff:In this case it is possible to select a unique Nash equilibrium payoff in feedback form by just imposing that it is Pareto whenever there is a unique Pareto one.However,this equilibrium payoff turns out to be highly unstable with respect to the terminal data.Some other examples of nonlinear-quadratic differential games are also analyzed in Olsder[99] and in Ramasubramanian[106].2.4Mean-ﬁeld GamesSince the system of P.D.Es arising in nonzero-sum differential games is,in general,ill-posed,it is natural to investigate situations where the problem simpliﬁes.It turns out that this is the case for differential games with a very large number of identical players.This problem has been recently developed in a series of papers by Lasry and Lions[87–90,94] under the terminology of mean-ﬁeld games(see also Huang,Caines and Malhame[76–79] for a related approach).The main achievement of Lasry and Lions is the identiﬁcation of the limit when the number of players tends to inﬁnity.The typical resulting model takes the form⎧⎪⎨⎪⎩(i)−∂t u−Δu+H(x,m,Du)=0in R d×(0,T),(ii)∂t m−Δm−divD p H(x,m,Du)m=0in R d×(0,T),(iii)m(0)=m0,u(x,T)=Gx,m(T).(1)In the above system,theﬁrst equation has to be understood backward in time while the second one is forward in time.Theﬁrst equation(a Hamilton–Jacobi one)is associated with an optimal control problem and its solution can be regarded as the value function for a typical small player(in particular the Hamiltonian H=H(x,m,p)is convex with respect to the last variable).As for the second equation,it describes the evolution of the density m(t)of the population.More precisely,let usﬁrst consider the behavior of a typical player.He controls through his control(αs)the stochastic differential equationdX t=αt dt+√2B t(where(B t)is a standard Brownian motion)and he aims at minimizing the quantityET12LX s,m(s),αsds+GX T,m(T),where L is the Fenchel conjugate of H with respect to the p variable.Note that in this cost the evolving measure m(s)enters as a parameter.The value function of our average player is then given by(1-(i)).His optimal control is—at least heuristically—given in feedback form byα∗(x,t)=−D p H(x,m,Du).Now,if all agents argue in this way,their repartition will move with a velocity which is due,on the one hand,to the diffusion,and,one the other hand,to the drift term−D p H(x,m,Du).This leads to the Kolmogorov equation(1-(ii)).The mean-ﬁeld game theory developed so far has been focused on two main issues:ﬁrstly,investigate equations of the form(1)and give an interpretation(in economics,for instance)of such systems.Secondly,analyze differential games with aﬁnite but large num-ber of players and interpret(1)as their limiting behavior as the number of players goes to inﬁnity.Up to now theﬁrst issue is well understood and well documented.The original works by Lasry and Lions give a certain number of conditions under which(1)has a solution,discuss its uniqueness and its stability.Several papers also study the numerical approximation of this solution:see Achdou and Capuzzo Dolcetta[1],Achdou,Camilli and Capuzzo Dolcetta[2], Gomes,Mohr and Souza[71],Lachapelle,Salomon and Turinici[85].The mean-ﬁeld games theory has been used in the analysis of wireless communication systems in Huang,Caines and Malhamé[76],or Yin,Mehta,Meyn and Shanbhag[115].It seems also particularly adapted to modeling problems in economics:see Guéant[72,73],Lachapelle[84],Lasry, Lions,Guéant[91],and the references therein.As for the second part of the program,the limiting behavior of differential games when the number of players tend to inﬁnity has been understood for ergodic differential games[88].The general case remains mostly open.3Long-time Average of Differential GamesAnother way to reduce the complexity of differential games is to look at their long-time be-havior.Among the numerous applications of this topic let us quote homogenization,singular perturbations and dimension reduction of multiscale systems.In order to explain the basic ideas,let us consider a two-player stochastic zero-sum dif-ferential game with dynamics given bydX t,ζ;u,vs =bX t,ζ;u,vs,u s,v sds+σX t,ζ;u,v,u s,v sdB s,s∈[t,+∞),X t=ζ,where B is a d-dimensional standard Brownian motion on a given probability space (Ω,F,P),b:R N×U×V→R N andσ:R N×U×V→R N×d,U and V being some metric compact sets.We assume that theﬁrst player,playing with u,aims at minimizing a running payoff :R N×U×V→R(while the second players,playing with v,maximizes). Then it is known that,under some Isaacs’assumption,the game has a value V T which is the viscosity solution of a second order Hamilton–Jacobi equation of the form−∂t V T(t,x)+Hx,D V T(t,x),D2V T(t,x)=0in[0,T]×R N,V T(T,x)=0in R N.A natural question is the behavior of V T as T→+∞.Actually,since V T is typically of linear growth,the natural quantity to consider is the long-time average,i.e.,lim T→+∞V T/T.Interesting phenomena can be observed under some compactness assumption on the un-derlying state-space.Let us assume,for instance,that the maps b(·,u,v),σ(·,u,v)and (·,u,v)are periodic in all space variables:this actually means that the game takes place in the torus R N/Z N.In this framework,the long-time average is well understood in two cases:either the dif-fusion is strongly nondegenerate:∃ν>0,(σσ∗)(x,u,v)≥νI N∀x,u,v,(where the inequality is understood in the sense of quadratic matrices);orσ≡0and H= H(x,ξ)is coercive:lim|ξ|→+∞H(x,ξ)=+∞uniformly with respect to x.(2) In both cases the quantity V T(x,0)/T uniformly converges to the unique constant¯c forwhich the problem¯c+Hx,Dχ(x),D2χ(x)=0in R Nhas a continuous,periodic solutionχ.In particular,the limit is independent of the initial condition.Such kind of results has been proved by Lions,Papanicoulaou and Varadhan[95] forﬁrst order equations(i.e.,deterministic differential games).For second order equations, the result has been obtained by Alvarez and Bardi in[3],where the authors combine funda-mental contributions of Evans[61,62]and of Arisawa and Lions[7](see also Alvarez and Bardi[4,5],Bettiol[24],Ghosh and Rao[70]).For deterministic differential games(i.e.,σ≡0),the coercivity condition(2)is not very natural:Indeed,it means that one of the players is much more powerful than the other one. However,very little is known without such a condition.Existing results rely on a speciﬁc structure of the game:see for instance Bardi[16],Cardaliaguet[46].The difﬁculty comes from the fact that,in these cases,the limit may depend upon the initial condition(see also Arisawa and Lions[7],Quincampoix and Renault[104]for related issues in a control set-ting).The existence of a limit for large time differential games is certainly one of the main challenges in differential games theory.4Existence of a Value for Zero-sum Differential Games with State Constraints Differential games with state constraints have been considered since the early theory of differential games:we refer to[23,28,66,69,80]for the computation of the solution for several examples of pursuit.We present here recent trends for obtaining the existence of a value for a rather general class of differential games with constraints.This question had been unsolved during a rather long period due to problems we discuss now.The main conceptual difﬁculty for considering such zero-sum games lies in the fact that players have to achieve their own goal and to satisfy the state constraint.Indeed,it is not clear to decide which players has to be penalized if the state constraint is violated.For this reason,we only consider a speciﬁc class of decoupled games where each player controls independently a part of the dynamics.A second mathematical difﬁculty comes from the fact that players have to use admissible controls i.e.,controls ensuring the trajectory to fulﬁlthe state constraint.A byproduct of this problem is the fact that starting from two close initial points it is not obvious toﬁnd two close constrained trajectories.This also affects the regularity of value functions associated with admissible controls:The value functions are,in general,not Lipschitz continuous anymore and,consequently,classical viscosity solutions methods for Hamilton–Jacobi equations may fail.4.1Statement of the ProblemWe consider a differential game where theﬁrst player playing with u,controls aﬁrst systemy (t)=gy(t),u(t),u(t)∈U,y(t0)=y0∈K U,(3) while the second player,playing with v,controls a second systemz (t)=hz(t),v(t),v(t)∈V,z(t0)=z0∈K V.(4)For every time t,theﬁrst player has to ensure the state constraint y(t)∈K U while the second player has to respect the state constraint z(t)∈K V for any t∈[t0,T].We denote by x(t)= x[t0,x0;u(·),v(·)](t)=(y[t0,y0;u(·)](t),z[t0,z0;v(·)](t))the solution of the systems(3) and(4)associated with an initial data(t0,x0):=(t0,y0,z0)and with a couple of controls (u(·),v(·)).In the following lines we summarize all the assumptions concerning with the vectorﬁelds of the dynamics:⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩(i)U and V are compact subsets of someﬁnitedimensional spaces(ii)f:R n×U×V→R n is continuous andLipschitz continuous(with Lipschitz constant M)with respect to x∈R n(iii)uf(x,u,v)andvf(x,u,v)are convex for any x(iv)K U={y∈R l,φU(y)≤0}withφU∈C2(R l;R),∇φU(y)=0ifφU(y)=0(v)K V={z∈R m,φV(z)≤0}withφV∈C2(R m;R),∇φV(z)=0ifφV(z)=0(vi)∀y∈∂K U,∃u∈U such that ∇φU(y),g(y,u) <0(vii)∀z∈∂K V,∃v∈V such that ∇φV(z),h(z,v) <0(5)We need to introduce the notion of admissible controls:∀y0∈K U,∀z0∈K V and∀t0∈[0,T]we deﬁneU(t0,y0):=u(·):[t0,+∞)→U measurable|y[t0,y0;u(·)](t)∈K U∀t≥t0V(t0,z0):=v(·):[t0,+∞)→V measurable|z[t0,z0;v(·)](t)∈K V∀t≥t0.Under assumptions(5),the Viability Theorem(see[9,10])ensures that for all x0= (y0,z0)∈K U×K VU(t0,y0)=∅and V(t0,z0)=∅.Throughout the paper we omit t0in the notations U(t0,y0)and U(t0,y0)whenever t0=0.We now describe two quantitative differential games.Let us start with a game with an integral cost:Bolza Type Differential Game Given a running cost L:[0,T]×R N×U×V→R and aﬁnal costΨ:R N→R,we deﬁne the payoff associated to an initial position(t0,x0)= (t0,y0,z0)and to a pair of controls(u,v)∈U(t0,y0)×V(t0,z0)byJt0,x0;u(·),v(·)=Tt0Lt,x(t),u(·),v(·)dt+Ψx(T),(6)where x(t)=x[t0,x0;u(·),v(·)](t)=(y[t0,y0;u(·)](t),z[t0,z0;v(·)](t))denotes the solu-tion of the systems(3)and(4).Theﬁrst player wants to maximize the functional J,while the second player’s goal is to minimize J.Deﬁnition1A mapα:V(t0,z0)→U(t0,y0)is a nonanticipating strategy(for theﬁrst player and for the point(t0,x0):=(t0,y0,z0)∈R+×K U×K V)if,for anyτ>0,for all controls v1(·)and v2(·)belonging to V(t0,z0),which coincide a.e.on[t0,t0+τ],α(v1(·)) andα(v2(·))coincide almost everywhere on[t0,t0+τ].Nonanticipating strategiesβfor the second player are symmetrically deﬁned.For any point x0∈K U×K V and∀t0∈[0,T]we denote by A(t0,x0)and by B(t0,x0)the sets of the nonanticipating strategies for theﬁrst and the second player respectively.We are now ready to deﬁne the value functions of the game.The lower value V−is deﬁned by:V−(t0,x0):=infβ∈B(t0,x0)supu(·)∈U(t0,y0)Jt0,x0;u(·),βu(·),(7)where J is deﬁned by(6).On the other hand we deﬁne the upper value function as follows:V+(t0,x0):=limε→0+supα∈A(t0,x0)infv(·)∈V(t0,z0)Jεt0,x0;αv(·),v(·)(8)withJεt0,x0;u(·),v(·):=Tt0Lt,x(t),u(t),v(t)dt+Ψεx(T),where x(t)=x[t0,x0;u(·),v(·)](t)andΨεis the lower semicontinuous function deﬁned byΨε(x):=infρ∈R|∃y∈R n with(y,ρ)−x,Ψ(x)=ε.The asymmetry between the deﬁnition of the value functions is due to the fact that one assumes that the terminal payoffΨis lower semicontinuous.WhenΨis continuous,one can check that V+can equivalently be deﬁned in a more natural way asV+(t0,x0):=supα∈A(t0,x0)infv(·)∈V(t0,z0)Jt0,x0;αv(·),v(·).We now describe the second differential game which is a pursuit game with closed target C⊂K U×K V.Pursuit Type Differential Game The hitting time of C for a trajectory x(·):=(y(·),z(·)) is:θCx(·):=inft≥0|x(t)∈C.If x(t)/∈C for every t≥0,then we setθC(x(·)):=+∞.In the pursuit game,theﬁrst player wants to maximizeθC while the second player wants to minimize it.The value functions aredeﬁned as follows:The lower optimal hitting-time function is the mapϑ−C :K U×K V→R+∪{+∞}deﬁned,for any x0:=(y0,z0),byϑ−C (x0):=infβ(·)∈B(x0)supu(·)∈U(y0)θCxx0,u(·),βu(·).The upper optimal hitting-time function is the mapϑ+C :K U×K V→R+∪{+∞}de-ﬁned,for any x0:=(y0,z0),byϑ+ C (x0):=limε→0+supα(·)∈A(x0)infv(·)∈V(z0)θC+εBxx0,αv(·),v(·).By convention,we setϑ−C (x)=ϑ+C(x)=0on C.Remarks–Note that here again the deﬁnition of the upper and lower value functions are not sym-metric:this is related to the fact that the target assumed to be closed,so that the game is intrinsically asymmetric.–The typical pursuit game is the case when the target coincides with the diagonal:C= {(y,z),|y=z}.We refer the reader to[6,29]for various types of pursuit games.The formalism of the present survey is adapted from[50].4.2Main ResultThe main difﬁculty for the analysis of state-constraint problems lies in the fact that two trajectories of a control system starting from two—close—different initial conditions could be estimated by classical arguments on the continuity of theﬂow of the differential equation. For constrained systems,it is easy to imagine cases where the constrained trajectories starting from two close initial conditions are rather far from each other.So,an important problem in order to get suitable estimates on constrained trajectories,is to obtain a kind of Filippov Theorem with ly a result which allows one to approach—in a suitable sense—a given trajectory of the dynamics by a constrained trajectory.Note that similar results exist in the literature.However,we need here to construct a constrained trajectory in a nonanticipating way[26](cf.also[25]),which is not the case in the previous constructions.Proposition1Assume that conditions(5)are satisﬁed.For any R>0there exist C0= C0(R)>0such that for any initial time t0∈[0,T],for any y0,y1∈K U with|y0|,|y1|≤R,。

Design of Railway Track for Speed and High-speedRailways(3)

P rocedia Engineering 91 ( 2014 )256 – 2611877-7058 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license(/licenses/by-nc-nd/3.0/).Peer-review under responsibility of organizing committee of the XXIII R-S-P seminar, Theoretical Foundation of Civil Engineering (23RSP)doi: 10.1016/j.proeng.2014.12.056ScienceDirectAvailable online at XXIII R-S-P seminar, Theoretical Foundation of Civil Engineering (23RSP) (TFoCE 2014) Design of Railway Track for Speed and High-speed RailwaysStanislav Hodas a *a University of Žilina, Fac. of Civil Engineering, Dept. of Railway Engineering, Univerzitná 8215/1, SK-01026 Žilina, Slovak RepublicAbstractThe design of railway lines under the current standard STN 73 6360 [1] including the comparison of railway line parameters to the European Standard EN 13803-1 and a new proposal in accordance to the new prepared standard STN 73 6360-1 [2] of Slovak Railways (ŽSR). Specifications of the basic design parameters of these standards: designing minimum radius values of horizontal and vertical alignment radii within these standards, for example at speeds: V = 160 km/h, V = 200 km/h and V = 250/300 km/h. The routes shown in the 3D model terrain surface. Dynamic spatial design of railway lines and their routing designs in 3D drawings, their development in the terrain and comparison according to the selected speed parameters.© 2014 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of organizing committee of the XXIII R-S-P seminar, Theoretical Foundation of Civil Engineering (23RSP). Keywords: railway track design; comparison of parameters; high-speed lines; 3D model.1. IntroductionA designer that designs reconstruction, modernization or newly built railway tracks must consider the 3D design of digital design documentation and design parameters of the currently valid standards. In the European countries there are valid railway track design standards for the CEN members, for example EN 13803-1, adopted by the EU Member States as STN EN 13803-1 [2]. Besides this, some countries have adopted regional standards that regulate design parameters with regard to the conditions of a particular country, while respecting the basic framework criteria of the European standards. For example, the currently valid STN 73 6360 [1] in the Slovak Republic which will be replaced by the new STN 73 6360-1 [3] in 2014. The new standard [3] will have to consider new higher speed limits of RP5 and RP6 (in Slovak standards referred to as RP) for the speed and high-speed tracks for V 300 km/h also using the other standards for buildings that are parts of the railway tracks (tunnels, bridges, catenary, safety and signaling equipment, railway superstructure and railway subgrade, etc.).The current standard [1] contains the speed limits RP1 to RP4 for V 160 km/h, the new standard proposal [3] will modify these design criteria and complete them with other limits, RP5 for V 230 km/h and RP6 V 300 km/h.* Corresponding author. Tel.: +421-41-513-5847.E-mail address: stanislav.hodas@fstav.uniza.sk© 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (/licenses/by-nc-nd/3.0/).Peer-review under responsibility of organizing committee of the XXIII R-S-P seminar, Theoretical Foundation of Civil Engineering (23RSP)257S tanislav Hodas / P rocedia Engineering 91 ( 2014 )256 – 261 The higher the speed, the more stringent design criteria of the track geometry and also of the deformation resistance of the railway subgrade body [7, 8] are required.The final project documentation for the construction of railway track must be elaborated in a very high quality of processing, not only graphics but also software solutions utilized for its creation. The design documentation stand-ards for project documentation drawings are required as prior mandatory criteria for their form and content.In the Slovak Republic the modernization of main railways corridors for V 160 km/h is now being performed. The railway lines for V > 250 km/h are worldwide considered high-speed in all new constructions or when the existing rail corridors are reconstructed for V 200 km/h. In the upcoming STN [3] and the existing STN EN [2] these speed limits are also included, but common practice in Slovakia is different, i.e. the modernization takes place only at V 160 km/h and new buildings such as tunnels and bridges are designed for V 200 km/h (for example, the double track railway tunnel “Turkish Hill - Turecký vrch” on the main corridor of the track Žilina - Bratislava at the railway station Tren þianske Bohuslavice), [6]. On the upgraded railway corridors it will be possible to drive at V 200 km/h using passenger train sets with tilting bodies, as they allow driving through curves at higher speed. In Slovakia we are currently limited by the maximum permissible track speed V max 160 km/h stated by railway traffic regulations.2. Basic design parameters of curves of railway tracksThe design parameters of the railway line project and the optimized location of this track body are closely related. The more difficult conditions of complicated terrain or dense area (population, objects and industrial parks), the more difficult is to satisfy the criteria of parameters for designing the railway line and there is also a reduction in driving comfort (especially in the case of passenger transport). Therefore, in the proposal we exclude the minimum design radius r min (designated as R lim in EN 13803-1) despite the allowed values of the norm and we aim to maxim-ize the optimization criteria and reduce the energy intensity of lines in future operations (adjustment of horizontal and vertical curvature of track line, new train sets, propulsion systems of train sets, etc.).If the railway line is only used by passenger trains, for example in the speed limit RP6 (230 < V 300 km/h), it is possible to use maximum longitudinal gradients of vertical alignment of the lines and maximum cant of rails in curves. The passenger trains are light, short, have a low center of gravity of wagons, aerodynamic shape etc. On these tracks freight trains and heavy trains would not be able to run. In the case of mixed traffic, the line is also used by slower trains (e.g. freight trains) and these trackage parameter values would not be suitable for them. Therefore it is necessary to make a compromise between the assumed fastest and slowest trains of the particular designed rail line, for example this implies the proposed radius r between r min and r max according to (1), also the cant p [mm] of the track can be calculated from (1) (designated as D in STN EN [2]) the cant deficiency I max [mm] or cant excess E max [mm] and other parameters such as longitudinal gradient [‰], etc.2min max 2max max 8.118.11V E p r V I p d d (1)The track designer must also consider the weight which will be transported on the track. We consider the sum of weights of all the powered railway vehicles (PRV) and transported vehicles (TV) and their load weight: brutto = tarra + netto . To transfer the values between longitudinal gradient of the track sections, towable mass of vehicles and their speeds we can use the tables of technical normative weights for the particular PRV. The tables of towable masses are developed for various types of driving resistance (types R, S, T, U, details are in the regulation SR 1013[4]), which take into account the analytical calculations and load diagrams (Koref´s nomogram) for the particular operated PRV.The axis alignment of the route with large radius values requires increased investment costs and complicated structural and engineering solutions (large number of tunnels, bridges, walls, etc.).Nowadays, the proposals of rail tracks are only developed in digital 3D format using computer technology and software products specialized in railway engineering [11, 12]. The development of the railway route depends on the type of railway track with its different specified standard parameters for the design of the route of the speed and high-speed lines.258 S tanislav Hodas / P rocedia Engineering 91 ( 2014 ) 256 – 261In the case of reconstruction, the railway track follows the original body and only improves certain elements of the track, but in the case of modernization, e.g. for V = 160 km/h, the track route usually leaves the original body in some sections of the new railway track, as there is the axis alignment of the route under ŽSR Z10 [5]. The speed and high-speed tracks have their own specified criteria of design parameters [2] and are typically designed on a new body or with certain completely redesigned sections of the original route (according to [2] - large values of radii r min = C .V max 2/(D + I lim ), where C = 11.8 mm.m.h 2/km 2, cant D = 160 mm, possibly limit of D = 180 mm, cant deficiency I lim = 100; 130 mm for V max = 300 km/h, but for tilting railway cars running at V 260 km/h the values are I lim = 275; 306 mm).If the terrain is mountainous, it is appropriate to consider the optimal location of the route in the terrain. In a mountain area the route requires a lot of bridges, tunnels, supporting and retaining walls and other objects. It is not necessary to circumvent mountains and valleys, as it was in the past.A possible development of the railway route is presented by basic examples in Fig. 1 as two typical options for rout-ing. The pictures can be viewed as construction of two routes for speeds of V = 140; 100 km/h and V = 300 km/h, where various structural and technological solutions will be applied. Or we can consider that the original track for V = 140; 100 km/h was rebuilt to a track of higher quality, in this case to a high-speed track for V 300 km/h.In Fig. 1a the route is built for V = 140 km/h as a hillside route and circumvents transverse mountain ridge or moun-tain range. For the above mentioned speed according to [1] the minimum radius r min is proposed for mixed traffic as (2).85033.8491401505.65.622max max 2min | V p r d m (2) The proposed radii are greater r 1 = 2500 m, r 2 = 1250 m and r 3 = 900 m, thus the particular cants will be in the new curves smaller than the ones considered in the calculation for r min in (2). The high-speed tracks require r min as (3) in [2].450062.40843001001608.1122max max min | V I p C r m (3) The design of the track axis radius is greater than (3) and has value of r = 6000 m (whole 500 m above).a) b)Fig. 1. Railway track - (a) mountain range; (b) valley, transverse valley. 60.60411601001508.1122min max max V E p C r m (4) If the track is going to be used by slower trains such as freight trains running at V min = 160 km/h, it is necessary to consider the design of the radius with respect to the cant excess E max of the slowest train in (4) for r max of [2], where cant p = 160 mm, in [3] p = 150 mm.These values are valid for the recommended limits which secure the driving comfort of passengers and also the safety of goods transport. Maximum permissible limit values are also acceptable by the standard [2], but in this way the driving comfort is reduced. The route requires the tunnel advancement through the rock mass.In Fig. 1b the route development across the valley or transverse valley is presented. The railway route for V = 140; 100 km/h follows the contours around the hillside and the track for V = 300 km/h passes through a compulsory259S tanislav Hodas / P rocedia Engineering 91 ( 2014 )256 – 261 bridge object and then leads to the tunnel tube. If the speed is V = 100 km/h (for the speed limit RP3) for mixed traffic, the minimal radius r min is designed according to [2] for the relevant speed limit (5), other values from Fig. 1.47533.4731001501.71.722max max 1min | V p r d m (5) The smallest designed radius of the reconstructed track route is r 3 = 475 m in Fig. 1b. Then the present design values of the cants of the particular curves p 1, p 2 and p 3 are calculated.The principle and basic differences of particular tracks are shown in Fig. 2, where the track is reconstructed for V 140 km/h (RP4), the modernized track for V 160 km/h, the speed track for V 200 km/h (RP5) and the high-speed track for V 300 km/h (RP6). Some technologically advanced countries in Europe and in the world are able to operate high-speed lines at V = 320 to 360 km/h (the world record is V = 574.8 km/h on the conventional railway corridor TGV - LGV East in France, dated 3.4.2007).Fig. 2. Railway tracks - comparison of route development by speed limits RP i .When designing curves, grade lines with continuous height shape, i.e. non-linear grade lines or lines with constant line shape (Table 1), are inserted between the non-canted part of rail and the canted part of the same rail (due to climbing of the cant p ). In Slovakia, we may design cosine spiral with non-linear grade line for speed limit zones RP5 and RP6 in accordance with [3] for the speed of V > 160 km/h up to V 300 km/h. Under restricted conditions with speed 80 < V 300 km/h we may design Bloss spiral with non-linear grade line for RP3 to RP6. The standard [3] recommends cubic parabola with linear grade line for RP1 to RP6.Table 1. Transition spirals and grade lines for speed limits RP1 to RP6 in accordance with [3].Types of spirals andgrade linesSpeed limit zone Equations of the transition spirals Shapes of grade lines Cubic parabolawith lineargrade line*RP1 to RP6 0 > V 300 km/h p l r x y 63 Bloss spiralwith non-lineargrade line*RP3 to RP6 80 > V 300 km/h r l x r l x y p p 3524104Cosine spiralwith non-lineargrade line* RP5 and RP6 200 > V 300 km/h ¸¸¹·¨¨©§ 1cos 24222p p l x r l r x y S S3. Dynamic design of spatial position of railway trackThe directional curvature of railway track including basic specifications of its structural elements such as curve radii (blue), shape and length of transition spirals (green), straight sections between the curves (red), etc., must be consistent with the design values of railway track according to STN [1] or STN EN [2]. Consequently, the principles of dynamic track design are characterized in the graphical environment with 3D terrain, using software tools260 S tanislav Hodas / P rocedia Engineering 91 ( 2014 ) 256 – 261accepted by railway practice [11, 12] etc. The values of the radii and transition spirals can be selected directly in the design of the tangent polygon either sequentially or we can design a minimum radius with the length of the transition spiral for all the curves and within the final solutions we modify the values in the software database tables (the whole 3D line model will be automatically modified after each modification of the basic parameters).In the drawing with 3D contours in Fig. 3 the tangent polygon (gray) will be designed, including the following minimum radii for RP4 V = 160 km/h (orange line), for RP5 V = 200 km/h (green line), for RP6 V = 300 km/h (blue line) according to (9) to (10). The presentation of the speed limit zones of railway lines is shown in Fig. 2.For rail route with V = 160 km/h according to STN [1] for cant p max = 150 mm:125032.12081600472.00472.022max min | u V r m (6)120033.11091501605.65.6222max min | u d p V r m (7) Compared to the values in accordance with EN STN [3] for cant p = 150 mm, I max = 100 mm, C = 11.8:125032.12081601001508.1122max max min | V I p C r m (8) The result is a design of all the radii above the value r i 1250 m of the track for V = 160 km/h in Fig. 4 (orange). The tangent polygon route can be modified by moving its top points VB i and by changing the parameter values r i , l iand other design elements by shifting them directly in the drawing in Fig. 3.Fig. 3. Railway track - dynamic solution design in 3D.For the track RP6 V max = 250 km/h according to Standard [3], supplemented by Standard [1], p max = 150 mm, where the slow trains run at the speed of V min =140 km/h:for the speed V max = 250 km/h, cant p = 150 mm and cant deficiency I max = 100 mm:300000.29502501001508.1122max max min | V I p C r m (9) for V min = 140 km/h, cant p = 150 mm and cant excess E max = 110 mm:550000.57821401101508.1122min max max | V E p C r m (10) The result is a design of the radius 3000 m r i 5500 m of the track curves for V = 250 km/h (RP6) in Fig. 4. During the designing we are supposed to check that all the radii r i values are in the interval r min r i r max , (1). The design of the minimum radius in our example for V = 160 km/h is according to (6) to (8) and for V = 250 km/h according to (9) applying (10). It must be considered whether the freight and slow passenger trains will be allowed on high-speed lines, because the high-speed line requires quality and stable geometric position and height of the track and these freight trains would have a significant influence on the track and increase the costs of the trackage261S tanislav Hodas / P rocedia Engineering 91 ( 2014 )256 – 261maintenance during its operation. The final designs of both railway lines are shown in Fig. 4.Fig. 4. Railway tracks - layout design.4. ConclusionThe design works include complicated procedures, while the railway track components must comply with all de-sign criteria of the currently applicable standards and regulations. In principle the route design of slow tracks such as RP1 to RP4 is equally challenging to prepare as for the speed and high-speed lines of RP4 and RP6 speed limits, but the internal basic design parameters are different for each particular project. With increasing track speed we must also increase and secure its safety during operation which is much more expensive.Nowadays the development of quality and precise design documentation is not possible without computer technology using 3D variant solutions. The project design documentation contains many complex structural objects required for the railway operation and crossing with other modes of transport (bridges, tunnels, railway stations, terminals, intermodal terminals, humps and others [6]) and all of them must have an exact spatial position [8 to 10] given by the coordinate and height system (ETRR/89, S-JTSK, etc.).References[1] STN 73 6360 Geometric position and arrangement of the track standard gauge railways, 1999, update No.1 2003.[2] STN EN 13803-1 Railway applications. Track. Track alignment design parameters. Track gauge 1435 mm and wider. Part 1: Plain line, SK,(In accordance with EN 13803-1), 2010.[3] STN 73 6360-1 Geometric position arrangement of 1435 mm gauge Railways, Research and development institute of Railways, SlovakRailways - ŽSR, http://www.zsr.sk, Slovakia, before issuing 2014/2015.[4] SR 1013 Technical specifications of traction rolling stocks, ŽSR, 2006, SK, update No.11 2013.[5] Z10 Rules of technical operation of the railway infrastructure (PTPŽI), SK, 2014.[6] L. Ižvolt, S. Hodas, Modernisation of railway infrastructure in the Slovak Republic, COMPRAIL XIII - Computer system design and opera-tion in the railway and other transit systems, New Forest, UK, organised by WESSEX Institute of Technology, , , Southampton, United Kingdom, 2012, ISBN 978-1-845564-616-5, e-ISBN 978-1-84564-617-2, pp. 211-223 [7] S. Hodas, L. Ižvolt, Modelling of temperature regime of railway track structure and its comparison with the results of experimental meas-urements, COMPRAIL XIV - Railway engineering design and optimization, Rome, Italy, organised by WESSEX Institute of Technology, , , Southampton, United Kingdom, 2014, ISBN 978-1-84564-766-7, eISBN 978-1-84564-767-4, pp. 253-265.[8] L. Ižvolt, P. Dobeš, M. Meþár, Contribution to the methodology of the determination of the thermal conductivity coefficients Ȝ of materialsapplied in the railway subbase structure, Communications, Scientific letters of the University of Žilina, http://svf.uniza.sk/kzsth, Žilina, Slo-vakia, ISSN 1335-4205, Vol. 15, No. 4 (2013), pp. 9-17.[9] J. Ižvoltová, A. Villim, Identification of observations errors by Gauss-Jacobi algorithm, Civil and environmental engineering, Scientifictechnical journal, ISSN 1336-5835, Vol. 8, No. 1 (2012), Faculty of Civil Engineering, ŽU Žilina, Žilina, Slovakia, 2012, pp. 13-17.[10] J. Ižvoltová, Coordinate and datum transformation, Analele universităĠii din Oradea, Fascicula construcĠii úi instalaĠii hidroedilitare, ISSN1454-4067, Vol. 13, (2010), Oradea, Romania, 2010, pp. 201-206.[11] A utoCAD Civil 3D 2015 CZ EDU, Software, AUTODESK, .[12] R ailCAD, Software for arrangement and design of the track geometry, VÚT Brno, http://www.railcad.cz, Brno, Czech Republic, 2003-2014.。

Suwon University, Gyeonggi-do, Korea SPONSORED BY

FINAL PROGRAMTHE 2007 ACM SIGAPPSYMPOSIUM ON APPLIED COMPUTING/conferences/sac/sac2007Seoul, Korea March 11 - 15, 2007Organizing CommitteeRoger L. Wainwright Hisham M. Haddad Sung Y. ShinSascha Ossowski Ronaldo MenezesLorie M. Liebrock Mathew J. Palakal Jaeyoung Choi Tei-Wei Kuo Jiman HongSeong Tae Jhang Yookun Cho Yong Wan KooH OSTED BYSeoul National University, Seoul, Korea Suwon University, Gyeonggi-do, KoreaSPONSORED BYSAC 2007 I NTRODUCTIONSAC 2007 is a premier international conference on applied com-puting and technology. Attendees have the opportunity to hear from expert practitioners and researchers about the latest trends in research and development in their fields. SAC 2007 features 2 keynote speakers on Monday and Wednesday, from 8:30 to 10:00. The symposium consists of Tutorial and Technical programs. The Tutorial Program offers 3 half-day tutorials on Sunday March 11, 2007, starting at 9:00am. The Technical Program offers 38 tracks on a wide number of different research topics, which run from Monday March 12 through Thursday March 15, 2007. Regular sessions start at 8:30am and end at 5:00pm in 4 parallel sessions. Honorable ChairsYookun Cho, Honorable Symposium ChairSeoul National University, KoreaYong Wan Koo, Honorable Program ChairUniversity of Suwon, KoreaOrganizing CommitteeRoger L. Wainwright, Symposium ChairUniversity of Tulsa, USAHisham M. Haddad, Symposium Chair, Treasurer, Registrar Kennesaw State University, USASung Y. Shin, Symposium ChairSouth Dakota State University, USASascha Ossowski, Program ChairUniversity Rey Juan Carlos, Madrid, SpainRonaldo Menezes, Program ChairFlorida Institute of Technology, Melbourne, FloridaJaeyoung Choi, Tutorials ChairSoongsil University, KoreaTei-Wei Kuo, Tutorials ChairNational Taiwan University, ChinaMathew J. Palakal, Poster ChairIndiana University Purdue University, USALorie M. Liebrock, Publication ChairNew Mexico Institute of Mining and Technology, USAJiman Hong,Local Organization ChairKwangwoon University, KoreaSeong Tae Jhang,Local Organization ChairUniversity of Suwon, KoreaSAC 2007 Track OrganizersArtificial Intelligence, Computational Logic, and Image Analysis (AI)C.C. Hung, School of Computing and Soft. Eng., USAAgostinho Rosa, LaSEEB –ISR – IST, PortugalAdvances in Spatial and Image-based Information Systems (ASIIS)Kokou Yetongnon, Bourgogne University, FranceChristophe Claramunt, Naval Academy Research Institute, France Richard Chbeir, Bourgogne University, FranceKi-Joune Li, Prusan National University, KoreaAgents, Interactions, Mobility and Systems (AIMS)Marcin Paprzycki, SWPS and IBS PAN, PolandCostin Badica, University of Craiova, RomaniaMaria Ganzha, EUH-E and IBS PAN, PolandAlex Yung-Chuan Lee, Southern Illinois University, USAShahram Rahimi, Southern Illinois University, USAAutonomic Computing (AC)Umesh Bellur, Indian Institute of Technology, IndiaSheikh Iqbal Ahamed, Marquette University, USABioinformatics (BIO)Mathew J. Palakal, Indiana University Purdue University, USALi Liao, University of Delaware, USAComputer Applications in Health Care (CACH)Valentin Masero, University of Extremadura, SpainPierre Collet, Université du Littoral (ULCO), France Computer Ethics and Human Values (CEHV)Kenneth E. Himma, Seattle Pacific University, USAKeith W. Miller, University of Illinois at Springfield, USADavid S. Preston, University of East London, UKComputer Forensics (CF)Brajendra Panda, University of Arkansas, USAKamesh Namuduri, Wichita State University, USAComputer Networks (CN)Mario Freire, University of Beira Interior, PortugalTeresa Vazao, INESC ID/IST, PortugalEdmundo Monteiro, University of Coimbra, PortugalManuela Pereira, University of Beira Interior, PortugalComputer Security (SEC)Giampaolo Bella, Universita' di Catania, ItalyPeter Ryan, University of Newcastle upon Tyne, UKComputer-aided Law and Advanced Technologies (CLAT) Giovanni Sartor, University of Bologna, ItalyAlessandra Villecco Bettelli, University of Bologna, ItalyLavinia Egidi, University of Piemonte Orientale, ItalyConstraint Solving and Programming (CSP)Stefano Bistarelli, Università degli studi "G. D'Annunzio" di Chieti-Pescara, ItalyEric Monfroy, University of Nantes, FranceBarry O'Sullivan, University College Cork, IrelandCoordination Models, Languages and Applications (CM) Alessandro Ricci, Universita di Bologna, ItalyBernhard Angerer, Michael Ignaz Schumacher, EPFL IC IIF LIA, SwitzerlandData Mining (DM)Hasan M. Jamil, Wayne State University, USAData Streams (DS)Jesus S. Aguilar-Ruiz, Pablo de Olavide University, SpainFrancisco J. Ferrer-Troyano, University of Seville, SpainJoao Gama, University of Porto, PortugalRalf Klinkenberg, University of Dortmund, GermanyDatabase Theory, Technology, and Applications (DTTA) Ramzi A. Haraty, Lebanese American University, LebanonApostolos N. Papadopoulos, Aristotle University, GreeceJunping Sun, Nova Southeastern University, USADependable and Adaptive Distributed Systems (DADS)Karl M. Göschka, Vienna University of Technology, AustriaSvein O. Hallsteinsen, SINTEF ICT, NorwayRui Oliveira, Universidade do Minho, PortugalAlexander Romanovsky, University of Newcastle upon Tyne, UK Document Engineering (DE)Rafael Dueire Lins, Universidade Federal de Pernambuco, Brazil Electronic Commerce Technologies (ECT)Sviatoslav Braynov, University of Illinois at Springfield, USADaryl Nord, Oklahoma State University, USAFernando Rubio, Universidad Complutense de Madrid, Spain Embedded Systems: Applications, Solutions and Techniques (EMBS)Alessio Bechini, University of Pisa, ItalyCosimo Antonio Prete, University of Pisa, ItalyJihong Kim, Seoul National University, KoreaEvolutionary Computation (EC)Bryant A. Julstrom, St. Cloud State University, USA Geoinformatics and Technology (GT)Dong-Cheon Lee, Sejong University, KoreaGwangil Jeon, Korea Polytechnic University, KoreaGeometric Computing and Reasoning (GCR)Xiao-Shan Gao, Chinese Academy of Sciences, ChinaDominique Michelucci, Universite de Bourgogne, FrancePascal Schreck, Universite Louis Pasteur, FranceHandheld Computing (HHC)Qusay H. Mahmoud, University of Guelph, CanadaZakaria Maamar, Zayed University, UAEInformation Access and Retrieval (IAR)Fabio Crestani, University of Strathclyde, UKGabriella Pasi, University of Milano Bicocca, ItalyMobile Computing and Applications (MCA)Hong Va Leong, Hong Kong Polytechnic University, Hong KongAlvin Chan, Hong Kong Polytechnic University, Hong KongModel Transformation (MT)Jean Bézivin, University of Nantes, FranceAlfonso Pierantonio, Università degli Studi dell’Aquila, ItalyAntonio Vallecillo, Universidad de Malaga, SpainJeff Gray, University of Alabama at Birmingham, USAMultimedia and Visualization (MMV)Chaman L. Sabharwal, University of Missouri-Rolla, USAMingjun Zhang, Agilent Technologies, USAObject-Oriented Programming Languages and Systems (OOP) Davide Ancona, DISI - Università di Genova, ItalyMirko Viroli, Università di Bologna, ItalyOperating Systems and Adaptive Applications (OSAA)Jiman Hong, Kwangwoon University, KoreaTei-Wei Kuo, National Taiwan University, TaiwanOrganizational Engineering (OE)José Tribolet, Technical University of Lisbon, PortugalRobert Winter, University of St. Gallen, SwitzerlandArtur Caetano, Technical University of Lisbon, Portugal Programming for Separation of Concerns (PSC)Corrado Santoro, Catania University, ItalyEmiliano Tramontana, Catania University, ItalyIan Welch, Victoria University, New ZealandYvonne Coady, Victoria Univeristy, CanadaProgramming Languages (PL)Chang-Hyun Jo, California State University at Fullerton, USAMarjan Mernik, University of Maribor, SloveniaBarrett Bryant, University of Alabama at Birmingham, USAReliable Computations and their Applications (RCA)Martine Ceberio, University of Texas at El Paso, USAVladik Kreinovich, University of Texas at El Paso, USAMichael Rueher, Universite de Nice ESSI, FranceSemantic Web and Application (SWA)Hyoil Han, Drexel University, USASemantic-Based Resource Discovery, Retrieval and Composition (SDRC)Eugenio Di Sciascio, SinsInfLab Politecnico di Bari, ItalyFrancesco M. Donini, University of Tuscia, ItalyTommaso Di Noia, SinsInfLab Politecnico di Bari, ItalyMassimo Paolucci, DoCoMo Euro-Labs, GermanySoftware Engineering (SE)W. Eric Wong, University of Texas at Dallas, USAChang-Oan Sung, Indiana University Southeast, USASoftware Verification (SV)Zijiang Yang, Western Michigan University, USALunjin Lu, Oakland University, USAFausto Spoto, Universita di Verona, ItalySystem On Chip Design and Software Supports (SODSS) Seong Tae Jhang, Suwon University, KoreaSung Woo Chung, Korea University, KoreaTrust, Recommendations, Evidence and other Collaborative Know-how (TRECK)Jean-Marc Seigneur, University of Geneva, SwitzerlandJeong Hyun Yi, Samsung Advanced Institute of Technology, South Korea Ubiquitous Computing: Digital Spaces, Services and Content (UC)Achilles Kameas, Hellenic Open University, GreeceGeorge Roussos, University of London, UKWeb Technologies (WT)Fahim Akhter , Zayed University, UAEDjamal Benslimane, University of Lyon, FranceZakaria Maamar, Zayed University, UAEQusay H. Mahmoud, University of Guelph, CanadaLocal SupportLocal support for SAC 2007 is provided by the Seoul National University in Seoul, Suwon University in Gyeonggi-do, Ministry of Education and Human Resources Development, Samsung, mds technology, KETI, MIC, CVB, and ETRI. The SAC organizing committee acknowledges and thanks the local supporters for their generous contributions to SAC 2007. Their support has been essential to the success of Symposium, and is greatly appreciated. ACM SIGAPPThe ACM Special Interest Group on Applied Computing is ACM's primary applications-oriented SIG. Its mission is to further the interests of the computing professionals engaged in the development of new computing applications and applications areas and the transfer of computing technology to new problem domains. SIGAPP offers practitioners and researchers the opportunity to share mutual interests in innovative application fields, technology transfer, experimental computing, strategic research, and the management of computing. SIGAPP also promotes widespread cooperation among business, government, and academic computing activities. Its annual Symposium on Applied Computing (SAC) provides an international forum for presentation of the results of strategic research and experimentation for this inter-disciplinary environment. SIGAPP membership fees are: $30.00 for ACM Non-members, $15.00 for ACM Members, and $8.00 for Student Members. For information contact Barrett Bryant at bryant@. Also, checkout the SIGAPP website at /sigapp/M ESSAGE FROM THE S YMPOSIUM C HAIRSRoger WaiwrightUniversity of Tulsa, USAHisham M. HaddadKennesaw State University, USASung Y. ShinSouth Dakota State University, USAOn behalf of the Organization Committee, it is our pleasure to welcome you to the 22nd Annual ACM Symposium on Applied Computing (SAC 2007). This year, the conference is hosted by Seoul National University and Suwon University in Gyeonggi-do, Korea. Many thanks for your participation in this international event dedicated to computer scientists, engineers, and practitioners seeking innovative ideas in various areas of computer applications. The sponsoring SIG of this Symposium, the ACM Special Interest Group on Applied Computing, is dedicated to further the interests of computing professionals engaged in the design and development of new computing applications, interdisciplinary applications areas, and applied research. The conference provides a forum for discussion and exchange of new ideas addressing computational algorithms and complex applications. This goal is reflected in its wide spectrum of application areas and tutorials designed to provide variety of discussion topics during this event. The conference is composed of various specialized technical tracks and tutorials. As in past successful meetings, talented and dedicated Track Chairs and Co-Chairs have organized SAC 2007 tracks. Each track maintains a program committee and group of highly qualified reviewers. We thank the Track Chairs, Co-Chairs, and participating reviewers for their commitment to making SAC 2007 another high quality conference. We also thank our invited keynote speakers for sharing their knowledge with SAC attendees. Most of all, special thanks to the authors and presenters for sharing their experience with the rest of us and to all attendees for joining us in Seoul, Korea.The local organizing committee has always been a key to the success of the conference. This year, we thank our local team from Seoul National University and Suwon University. In particular, we thank Dr. Jiman Hong, from Kwangwoon University, and Dr. Seong Tae Jhang, from Suwon University, for chairing the local organization effort. We also thank Dr. Jaeyoung Choi, from Soongsil University, and Dr. Tei-Wei Kuo, from National Taiwan University, for organizing the Tutorials Program. Other committee members we also would like to thank are Lorie Liebrock for her tremendous effort putting together the conference proceedings, Mathew Palakal for coordinating another successful Posters Program, and Sascha Ossowski and Ronaldo Menezes for bringing together the Technical Program. Finally, we extend outthanks and gratitude to our honorable Symposium and Program Chairs Drs. Yookun Cho of Seoul National University and Dr. Yong Wan Koo of Suwon University. Many thanks for hosting the conference and coordinating governmental and local support. Again, we welcome you to SAC 2007 in the lively city of Seoul. We hope you enjoy your stay in Seoul and leave this event enriched with new ideas and friends. Next year, we invite you to participate in SAC 2008 to be held in the costal city of Fortaleza, Brazil. The symposium will be hosted by the University of Fortaleza (UNIFOR) and the Federal University of Ceará (UFC). We hope to see there!M ESSAGE FROM THE P ROGRAM C HAIRSSascha OssowskiUniversity Rey Juan Carlos, SpainRonaldo MenezesFlorida Institute of Technology, USAWelcome to the 22nd Symposium on Applied Computing (SAC 2007). Over the past 21 years, SAC has been an international forum for researchers and practitioners to present their findings and research results in the areas of computer applications and technology. The SAC 2007 Technical Program offers a wide range of tracks covering major areas of computer applications. Highly qualified referees with strong expertise and special interest in their respective research areas carefully reviewed the submitted papers. As part of the Technical Program, this year the Tutorial Program offers several half-day tutorials that were carefully selected from numerous proposals. Many thanks to Jaeyoung Choi from the Soongsil University and Tei-Wei Kuo from the National Taiwan University for chairing the Tutorial Program. Also, this is the fourth year for SAC to incorporate poster papers into the Technical Program. Many thanks to Mathew Palakal from Indiana University Purdue University for chairing the poster sessions. SAC 2007 would not be possible without contributions from members of the scientific community. As anyone can imagine, many people have dedicated tremendous time and effort over the period of 10 months to bring you an excellent program. The success of SAC 2007 relies on the effort and hard work of many volunteers. On behalf of the SAC 2007 Organizing Committee, we would like to take this opportunity to thank all of those who made this year's technical program a reality, including speakers, referees, track chairs, session chairs, presenters, and attendees. We also thank the local arrangement committee lead by Jiman Hong from the Kwangwoon University and Seong Tae Jhang from Suwon University. We also want to thank Hisham Haddad from Kennesaw State University for his excellent job again as the SAC Treasurer, Webmaster, and Registrar.SAC's open call for Track Proposals resulted in the submission of 47 track proposals. These proposals were carefully evaluated by the conference Executive Committee. Some proposals were rejected on the grounds of either not being appropriate for the areas that SAC covers traditionally or being of rather narrow and specialized nature. Some others tracks were merged to form a single track. Eventually, 38 tracks were established, which then went on to produce their own call for papers. In response to these calls, 786 papers were submitted, from which 256 papers were strongly recommended by the referees for acceptance and inclusion in the Conference Proceedings. This gives SAC 2007 an acceptance rate of 32.5% across all tracks. SAC is today one of the most popular and competitive conferences in the international field of applied computing.We hope you will enjoy the meeting and have the opportunity to exchange your ideas and make new friends. We also hope you will enjoy your stay in Seoul, Korea and take pleasure from the many entertainments and activities that the city and Korea has to offer. We look forward to your active participation in SAC 2008 when for the first time SAC will be hosted in South America, more specifically in Fortaleza, Brazil. We encourage you and your colleagues to submit your research findings to next year's technical program. Thank you for being part of SAC 2007, and we hope to see you in sunny Fortaleza, Brazil for SAC 2008.O THER A CTIVITIESReview Meeting: Sunday March 11, 2007, from 18:00 to 19:00 in Room 311A. Open for SAC Organizing Committee and Track Chairs and Co-Chairs.SAC 2008 Organization Meeting: Monday March 12, 2007, from 18:00 to 19:00 in Room 311A. Open for SAC Organizing Committee.SAC Reception: Monday March 12, 2007 at 19:00 to 22:00. Room 402. Open for all registered attendees.Posters Session: Tuesday March 13, 2007, from 13:30 to 17:00 in the Room 311C. Open to everyone.SIGAPP Annual Business Meeting: Tuesday March 13, 2007, from 17:15 to 18:15 in Room 311A. Open to everyone.SAC Banquet: Wednesday March 14, 2007. Rooms 331-334. Open for Banquet Ticket holders. See your tickets for full details. Track-Chairs Luncheon: Thursday April 27, 2006, from 12:00 to 13:30. Hosu (Lake) Food-mall. Open for SAC Organizing Committee, Track Chairs and Co-Chairs.SAC 2008SAC 2008 will be held in Fortaleza, Ceará, Brazil, March 16 – 20, 2008. It is co-hosted by the University of Fortaleza (UNIFOR) and the Federal University of Ceará (UFC). Please check the registration desk for handouts. You can also visit the website at /conferences/sac/sac2008/.M ONDAY K EYNOTE A DDRESSA New DBMS Architecture for DB-IRIntegrationDr. Kyu-Young WhangDirector of Advanced Information Technology Research Center, Korea Advanced Institute ofScience and Technology, Daejeon, Korea M ONDAY M ARCH 12, 2007, 9:00 – 10:00ROOM 310 A, B AND CABSTRACTNowadays, there is an increasing need to integrate the DBMS (for structured data) with Information Retrieval (IR) features (for unstructured data). DB-IR integration becomes one of major challenges in the database area. Extensible architectures provided by commercial ORDBMS vendors can be used for DB-IR integration. Here, extensions are implemented using a high-level (typically, SQL-level) interface. We call this architecture loose-coupling. The advantage of loose-coupling is that it is easy to implement. But, it is not preferable for implementing new data types and operations in large databases when high performance is required. In this talk, we present a new DBMS architectureapplicable to DB-IR integration, which we call tight-coupling. In tight-coupling, new data types and operations are integrated into the core of the DBMS engine in the extensible type layer. Thus, they are incorporated as the "first-class citizens" within the DBMS architecture and are supported in a consistent manner with high performance. This tight-coupling architecture is being used to incorporate IR features and spatial database features into the Odysseus ORDBMS that has been under development at KAIST/AITrc for over 16 years. In this talk, we introduce Odysseus and explain its tightly-coupled IR features (U.S. patented in 2002). Then, we demonstrate excellence of tight-coupling by showing benchmark results. We have built a web search engine that is capable of managing 20~100 million web pages in a non-parallel configuration using Odysseus. This engine has been successfully tested in many commercial environments. In a parallel configuration, it is capable of managing billons of web pages. This work won the Best Demonstration Award from the IEEE ICDE conference held in Tokyo, Japan in April 2005.W EDNESDAY K EYNOTE A DDRESS The Evolution of Digital Evidence asa Forensic ScienceDr. Marc RogersChair of the Cyber Forensics Program,Department of Computer and InformationTechnology, Purdue University, USAW EDNESDAY M ARCH 14, 2007, 9:00 –10:00ROOMS 310 A, B AND CABSTRACTThe field of Digital Evidence while garnering significant attention by academia, the public, and the media, has really just begun its journey as a forensic science. Digital Forensic Science (DFS) in general is an immature discipline in comparison to the other more traditional forensic sciences such as latent fingerprint analysis. Digital Evidence, which falls under the larger umbrella of DFS, truly encompasses the notion of being an applied multi-disciplinary science. The areas of Computer Science, Technology, Engineering, Mathematics, Law, Sociology, Psychology, Criminal Justice etc. all have played and will continue to play a very large role in maturing and defining this scientific field. The presentation will look at the history of Digital Forensic Science and Digital Evidence, the current state of the field, and what might be in store for the future.S EOUL R EPRESENTATIVE A DDRESSKoran IT policy - IT839Dr. Jung-hee SongAssistant MayorChief of Information OfficerInformation System Planning DivisionSeoul Metropolitan Government, KoreaW EDNESDAY M ARCH 14, 2007, 18:30 – 19:00ROOMS 331-334(DURING BANQUET)ABSTRACTKorean IT policy initiated by Ministry of Information and Communication called IT839 Strategy will be introduced. By defining government role in the u-Korea vision pursuit, it removes uncertainties for IT industry and increases its active participation. As capital of Korea, Seoul presented a grand plan to be u-Seoul. An overview of u-Seoul masterplan will be delivered with introduction of 5 specific projects.SAC 2007 S CHEDULES UNDAY M ARCH 11, 200709:00 – 17:00 L OBBYR EGISTRATION09:00 – 10:30 R OOMS 310 A AND BAM T UTORIALS IT1: Introduction to Security-enhanced Linux(SELinux)Dr. Haklin Kimm, Professor, omputer Science Department, ast Stroudsburg University of Pennsylvania, USAT2: Similarity Search - The Metric Space Approach Pavel Zezula, Masaryk University, Brno, Czech RepublicGiuseppe Amato, ISTI-CNR, Pisa, ItalyVlastislav Dohnal, Masaryk University, Brno, Czech Republic10:30 – 11:00 L OBBYC OFFEE B REAK11:00 – 12:30 R OOMS 310 A AND BAM T UTORIALS IIT1: Introduction to Security-enhanced Linux(SELinux)Dr. Haklin Kimm, Professor, omputer Science Department, ast Stroudsburg University of Pennsylvania, USAT2: Similarity Search - The Metric Space Approach Pavel Zezula, Masaryk University, Brno, Czech RepublicGiuseppe Amato, ISTI-CNR, Pisa, ItalyVlastislav Dohnal, Masaryk University, Brno, Czech Republic 12:00 – 13:30 H OSU (L AKE) F OOD-MALL,1ST F LOORL UNCH B REAK13:30 – 15:00 R OOM 310 APM T UTORIAL IT3: Introduction to OWL Ontology Developmentand OWL ReasoningYoung-Tack Park, Professor, School of Computing, SoongsilUniversity,Seoul, Korea15:00 – 15:30 L OBBYC OFFEE B REAK15:30 – 17:00 R OOM 310 APM T UTORIAL IIT3: Introduction to OWL Ontology Developmentand OWL ReasoningYoung-Tack Park, Professor, School of Computing, SoongsilUniversity,Seoul, Korea18:00 – 19:00 R OOM 311A SAC 2007 R EVIEW M EETINGM ONDAY M ARCH 12, 200708:00 – 17:00 L OBBYR EGISTRATION08:30 – 09:00 R OOM 310O PENING R EMARKS09:00 – 10:00 R OOM 310K EYNOTE A DDRESSA New DBMS Architecture for DB-IRIntegrationDr. Whang, Kyu-YoungDirector of Advanced Information TechnologyResearch CenterKorea Advanced Institute of Science andTechnologyDaejeon, Korea10:00 – 10:30 L OBBYC OFFEE B REAK10:30 – 12:00 R OOM 310A(DS) Data StreamsJoao Gama, University of Porto (UP), Portugal RFID Data Management for Effective ObjectsTrackingElioMasciari, CNR, ItalyA Priority Random Sampling Algorithm for Time-based Sliding Windows over Weighted StreamingDataZhang Longbo, Northwestern Polytechnical University, China Li Zhanhuai, Northwestern Polytechnical University, ChinaZhao Yiqiang, Shandong University of Technology, ChinaMin Yu, Northwestern Polytechnical University, China Zhang Yang, Northwest A&F University, ChinaOLINDDA: A Cluster-based Approach forDetecting Novelty and Concept Drift in DataStreamsEduardo Spinosa, University of Sao Paulo (USP), BrazilAndré Carvalho, University of Sao Paulo (USP), Brazil Joao Gama, University of Porto (UP), PortugalA Self-Organizing Neural Network for DetectingNoveltiesMarcelo Albertini, Universidade de Sao Paulo, BrazilRodrigo Mello, Universidade de São Paulo, Brazil10:30 – 12:00 R OOM 310B (AI) Artificial Intelligence, ComputationalLogic and Image AnalysisChih-Cheng Hung, Southern Polytechnic State University, USA Toward a First-Order Extension of Prolog'sUnification using CHRKhalil Djelloul, University of Ulm, GermanyThi-Bich-Hanh Dao, University d'Orléans, FranceThom Fruehwirth, University of Ulm, GermanyA Framework for Prioritized Reasoning Based onthe Choice EvaluationLuciano Caroprese, University of Calabria, ItalyIrina Trubitsyna, University of Calabria, ItalyEster Zumpano, University of Calabria, ItalyA Randomized Knot Insertion Algorithm for Outline Capture of Planar Images using CubicSplineMuhammad Sarfraz, King Fahd University of Petroleum andMinerals, Saudi ArabiaAiman Rashid, King Fahd University of Petroleum and Minerals,Saudi ArabiaEstraction of Arabic Words from Complex ColorImagesRadwa Fathalla, AAST, EgyptYasser El Sonbaty, AAST College of Computing, Egypt Mohamed Ismail, Alexandria University, Egypt10:30 – 12:00 R OOM 310C (PL) Programming LanguagesMarjan Mernik, University of Maribor, Slovenia Implementing Type-Based Constructive Negation Lunjin Lu, Oakland University, USATowards Resource-Certified Software: A Formal Cost Model for Time and its Application to anImage-Processing ExampleArmelle Bonenfant, University of St Andrews, UKZehzi Chen, Heriot-Watt University, UKKevin Hammond, Univestiy of St Andrews, UKGreg Michaelson, Heriot-Watt University, UKAndy Wallace, Heriot-Watt University, UKIain Wallace, Heriot-Watt University, UK。

骨性Ⅲ类错牙合牙弓、基骨弓的特点及其矫治

骨性Ⅲ类错牙合牙弓、基骨弓的特点及其矫治摘要目的骨性Ⅲ类错牙合畸形家族遗传倾向显著，乳牙早失或滞留、口腔不良习惯等因素也可引起，Ⅲ类骨面型影响患者咀嚼、言语功能，不利于颜面美观。

骨性Ⅲ类错牙合牙弓与基骨弓的协调性对正畸疗效的稳定及侧貌美观极其重要。

本文就骨性Ⅲ类错牙合畸形牙弓与基骨弓的特点及临床矫治作一综述。

关键词骨性Ⅲ类错牙合牙弓基骨弓一、骨性Ⅲ类错牙合牙弓、基骨弓形态特点既往国内外学者对骨性Ⅲ类错牙合与Ⅰ类错牙合患者模型对比分析两者牙弓形态特点，所得结果有所差异。

孙留振等人发现：骨性Ⅲ类错牙合患者上颌牙弓前段长度发育不足。

范向飞等人的研究结果表明骨性Ⅲ类错牙合患者下颌尖牙区牙弓宽度大于正常牙合，上颌尖牙区牙弓宽度小于正常牙合。

Slaj等人研究发现Ⅲ类错牙合患者尖牙区及前磨牙区牙弓宽度最大。

Suk等人发现下颌尖牙间牙弓宽度及磨牙间牙弓宽度大于正常牙合。

Chen等测量Ⅲ类错牙合患者与Ⅰ类错牙合患者模型，发现Ⅲ类错牙合患者上颌基骨弓宽度窄于Ⅰ类错牙合患者,下颌基骨弓宽度两者无明显差异。

二、骨性Ⅲ类错牙合牙弓与基骨弓形态的协调牙弓形态与基骨弓形态的协调性与正畸疗效的稳定性，咀嚼功能及微笑美学息息相关。

受遗传因素、口周肌肉等因素影响。

既往研究用曲线形态对牙弓及基骨弓形态进行描述，研究结果发现牙弓形态与基骨弓形态高度相关，特别是尖牙及磨牙区，且尖牙区变异系数较磨牙区高。

刘颖等测量成人骨性Ⅲ类错牙合牙弓及基骨弓宽度的各项指标，结果显示骨性Ⅲ类错牙合患者上、下颌尖牙区牙弓宽度差小于正常牙合对应区域牙弓宽度差，上、下颌双尖牙区及磨牙区基骨弓宽度差小于正常牙合对应区域基骨弓宽度差。

孙留振等人发现该类错牙合患者上颌牙弓与基骨弓长度小于与正常牙合，双尖牙及第一磨牙区差异显著；下颌牙弓与基骨弓长度大于正常牙合，第一前磨牙及第一磨牙区差异显著；下颌牙弓、基骨弓宽度大于正常牙合，第一磨牙区差异显著。

三、骨性Ⅲ类错牙合畸形的矫治骨性Ⅲ类错牙合表现为上颌后缩，下颌发育过度，或两者兼有；侧貌软组织特征主要表现为面下1/3凹陷，下颌及颏部前突，颏唇沟浅。

3t-2阶Steiner三连系构造的一种方法

第31卷第4期吉首大学学报(自然科学版)Vol.31No .42010年7月Journ al of Ji shou Universit y (Nat ural Science Edit ion)July.2010文章编号:1007-2985(2010)04-0001-043t-2阶Steiner三连系构造的一种方法侴万禧1,霍玉洪2,李晓毅3(1.安徽理工大学土木建筑学院,安徽淮南232001;2.淮南师范学院数学与计算科学系,安徽淮南232038;3.沈阳师范大学数学与系统科学学院,辽宁沈阳110034)摘要:阐明了v 阶Steiner 三连系构造的基本思路,给出边矩阵的定义.提出3t-2阶Steiner 三连系构造的一种方法,介绍25阶Steiner 三连系构造的全过程,最后讨论了3t-2阶Steiner 三连系不同构的个数问题.关键词:Steiner 三连系;构造;完全图;边矩阵;阶中图分类号:O157.5文献标志码:A区组设计理论是组合数学的一个重要分支,它在试验设计、竞赛安排及数字通讯等许多领域中均有重要作用.早在1850年,Kir kman 提出了一个有趣的15名女生问题,并于同年做出解答.1971年,D.R.Ray Chaudhur i 与R.M.Wilson 共同发表论文!Kir kman 女生问题的解以阐明6n+3阶Kirkman 三连系的构造[1-6].百余年来,就是否对每个n=0,1,2,3,#总是存在6n+3阶Steiner 三连系,一直是个难题.1961年,中国数学家陆家羲提出了BIBD 设计可分解的充要条件.1基本思路设G(V,E)为一个v 阶完全图K v ,若完全图K v 的阶数满足v =3t- 2.t 为已有阶Steiner 三连系的阶数,则v 阶Steiner三连系的构造等价于一个完全图K v 的v(v-1)/6个完全图K 3的分解.但是,当完全图K v 的阶数较高时,无法将完全图K v直接分解出v(v-1)/6个完全图K 3,倘若将完全图K v 先分解出3个t 阶完全图K (1)t ,K (2)t ,K (3)t及1个完全三分图K t-1,t-1,t-1,则3个t 阶完全图K (i)t 中的3t (t -1)/6个完全图K 3及1个完全三分图K t -1,t-1,t-1中的(t-1)(t-1)个完全图K 3将构成v =3t -2阶Steiner 三连系中的v(v-1)/6个完全图K 3,而将完全图K v 分解出3个t 阶完全图K (i)t 和1个完全三分图K t-1,t-1,t-1的有力工具是完全图K v 的边矩阵K v %.定义1设G(V,E)为一个完全图K v ,若将完全图K v 中的v(v-1)/2个边按自然顺序排成上三角阵,使得任意边V i V j分别与顶V i ,V j 相关联,则所得到的上三角阵就称为完全图K v 的边矩阵,并记为K v %[7-8],v 2v 3v 4v 5v 6#v n K v %=1213141516#1n 23242526#2n 343536#3n 4546#4n 565n(n -1)n v 1v 2v 3v 4v 5v n -1.2Steiner 三连系的构造设Steiner 三连系的阶数满足v =3t -2,若令t =9,则v =3t -2=25阶Steiner 三连系的构造可被视为一个完全图*收稿日期:2010-04-18基金项目国家自然科学基金资助项目(6);安徽省年高等学校省级自然科学研究资助项目(K B 6Z);淮南师范学院年度青年科研基金计划资助项目(LK 5)作者简介侴万禧(3),男,辽宁大连人,安徽理工大学土木建筑学院教授,主要从事图论研究:10471092009J20082920072007P0:190-.K25的v(v-1)/6=2524/6个完全图K3的分解.v(v-1)/6个完全图K3的分解的具体步骤如下:v2v3v4#v9v10v11#v17v18v19#v25K25%=121314#19110111#117118119#125 2324#29210211#217218219#225 34#39310311#317318319#32589810811#817818819#825910911#917918919#9251011#101710181019#102511251617#17181719#17251819#182519252425&v1v2v3v8v9v10v11v17v18v19v24St ep1将完全图K25总的v(v-1)/2=2524/2个边按自然顺序排成上三角阵边矩阵K v%.St ep2将边矩阵K v%分解出3个完全图K(i)9及1个完全三分图K8,8,8或3个完全二分图K(1,2)8,8,K(1,3)8,8和K(2,3)8,8(K8,8,8=K(1,2)8,8(K(1,3)8,8(K(2,3)8,8)有25种选择,下面拟用25个方案当中的第9个方案进行完全图K25的子图的分解,所得到的3个完全图K(1)9,K(2)9和K(3)9及3个完全二分图K(1,2)8,8,K(1,3)8,8和K(2,3)8,8如下:v2v3v4v5v6v7v8v9K(1)9=121314151617181923242526272829343536373839454647484956575859676869787989v1v2v3v4v5v6v7v8,v10v11v12v13v14v15v16v17K(2)9=9109119129139149159169171011101210131014101510161017111211131114111511161117121312141215121612171314131513161317141514161417151615171617v9v10v11v12v13v14v15v16, v18v19v20v21v22v23v24v25K(3)9=9189199209219229239249251819182018211822182318241825192019211922192319241925202120222023202420252122212321242125222322242225232423252425v9v18v19v20v21v22v23v24,v10v11v12v13v14v15v16v17K(1,2)8,8=110111112113114115116117210211212213214215216217310311312313314315316317410411412413414415416417510511512513514515516517610611612613614615616617710711712713714715716717810811812813814815816817v1v2v3v4v5v6v7v8,2吉首大学学报(自然科学版)第31卷v 18v 19v 20v 21v 22v 23v 24v 25K (1,3)8,8=118119120121122123124125218219220221222223224225318319320321322323324325418419420421422423424425518519520521522523524525618619620621622623624625718719720821722723724725818819820921822823824825v 1v 2v 3v 4v 5v 6v 7v 8,v 18v 19v 20v 21v 22v 23v 24v 25K (2,3)8,8=1018101910201021102210231024102511181119112011211122112311241125121812191220122112221223122412251318131913201321132213231324132514181419142014211422142314241425151815191520152115221523152415251618161916201621162216231624162517181719172017211722172317241725v 10v 11v 12v 13v 14v 15v 16v 17,K %(1,3)8,8=118119120121122123124125219220221222223224225218320321322323324325318319421422423424425418419420522523524525518519520521623624625618619620621622724725718719720821722723825818819820921822823824,K %(2,3)8,8=1018111912201321142215231624172510191120122113221423152416251718102011211222132314241525161817191021112212231324142515181619172010221123122413251418151916201721102311241225131814191520162117221024112512181319142015211622172310251118121913201421152216231724.St ep 3将2个完全二分图的边矩阵K (1,3)8,8,K (2,3)8,8各自的88个边重新排列形成2个新的方阵K %(1,3)8,8,K %(2,3)8,8,再将2个新方阵K %(1,3)8,8,K %(2,3)8,8与完全二分图的边矩阵K (1,2)8,8相叠加,得由88个完全图K 3构成的三连系矩阵完全三分图K (1,2,3)8,8,8的边矩阵K %(1,2,3)8,8,8,K %(1,2,3)8,8,8=1,10,181,11,191,12,201,13,211,14,221,15,231,16,241,17,252,10,192,11,202,12,212,13,222,14,232,15,242,16,252,17,183,10,203,11,213,12,223,13,233,14,243,15,253,16,183,17,194,10,214,11,224,12,234,13,244,14,254,15,184,16,194,17,205,10,225,11,235,12,245,13,255,14,185,15,195,16,205,17,216,10,236,11,246,12,256,13,186,14,196,15,206,16,216,17,227,10,247,11,257,12,187,13,197,14,207,15,217,16,227,17,238,10,258,11,188,12,198,13,208,14,218,15,228,16,238,17,24.St ep 4将3个完全图K (i)9各分解出12个完全图K 3,得3个9阶Steiner 三连系ST (1)(9),ST (2)(9)和ST (3)(9)如下:ST (1)(9)={1,2,3,1,4,7,1,5,6,1,8,9,2,4,5,2,6,8,2,7,9,3,4,8,3,5,9,3,6,7,4,6,9,5,7,8};ST (2)(9)={9,10,11,9,12,15,9,13,14,9,16,17,10,12,13,10,14,16,10,15,17,11,12,16,11,13,17,11,14,15,12,14,17,13,15,16};ST (3)(9)={9,18,19,9,20,23,9,21,22,9,24,25,18,20,21,18,22,24,18,23,25,19,20,24,19,21,25,19,22,23,20,22,25,21,23,24}.再求ST (1)(9),ST (2)(9),ST (3)(9)和K %(1,2,3)8,8,8之并,即得25阶Steiner 三连系ST (9)(25),ST (9)(25)={1,2,3,1,4,7,1,5,6,1,8,9,1,10,18,1,11,19,1,12,20,1,13,21,1,14,22,1,15,23,1,16,24,1,17,25,2,4,5,2,6,8,2,7,9,2,10,19,2,11,20,2,12,21,2,13,22,2,14,23,2,15,24,2,16,25,2,17,18,3,4,8,3,5,9,3,6,7,3,10,20,3,11,21,3,12,22,3,13,23,3,,,3,5,5,3,6,,3,,,,6,,,,,,,,,,3,,3,,,,5,,5,,,6,,,,,5,,,5,,,5,,3,5,,,5,3,5,5,,,5,5,,5,6,,3第4期侴万禧,等:3t-2阶Steiner 三连系构造的一种方法1424121181719494102141112412241244142411841194172078102211212241214181191204吉首大学学报(自然科学版)第31卷5,17,21,6,10,23,6,11,24,6,12,25,6,13,18,6,14,19,6,15,20,6,16,21,6,17,22,7,10,24,7,11,25,7,12,18,7,13,19,7,14,20,7,15,21,7,16,22,7,17,23,8,10,15,8,11,18,8,12,19,8,13,20,8,14,21,8,15,22,8,16,23,8,17,24,9,10,11,9,12,15,9,13,14,9,16,17,9,18,19,9,20,23,9,21,22,9,24,25,10,12,13,10,14,16,10,15,17,11,12,16,11,13,17,11,14,15,12,14,17,13,15,17,18,20,21,18,22,24,18,23,25,19,20,24,19,21,25,19,22,23,20,22,25,21,23,24}.33t-2阶Steiner三连系的计数3t-2阶Steiner三连系的个数N取决于3t-2阶完全图K v的1个完全三分图K t-1,t-1,t-1和3个完全图K(i)t的分解方案数N(1),以及完全三分图K(1,2,3)t-1,t-1,t-1的(t-1)(t-1)个完全图K3的分解方案N(2)=t-1,K v的子图分解方案数N(1)=3t-2,K(1,2,3)t-1,t-1,t-1的完全图K3的分解方案数N(2)=t-1,故3t-2阶Steiner三连系的不同构的个数N=N(1)N(2)= (3t-2)(t-1),25阶Steiner三连系ST(25)的个数N=258=200个.4结语(1)给出了任意完全图K v的边矩阵的定义,使得边矩阵K%v成为完全图K v分解为v(v-1)/6个完全图K3的有效工具;(2)提出了3t-2阶Steiner三连系构造的一种方法;(3)解决了3t-2阶Steiner三连系的计数问题.参考文献:[1]VANLINT J H,WILSON R M.A Coar se in Combinatorics[M].Beijing:China Machine Pr ess,2004.[2]ROBERTS F RED S,BAR RY TESM AN.Applied Combinator ics[M].Beijing:China Pr ess,2007.[3]DOUGLAS B WEST.Introduction to Graph Theor y[M].Beijing:China Machine Pr ess,2004.[4]FOULDS L R.Graph T heory Applicat ion[M].NewYork:Springer Ver lag,1992.[5]杨骅飞,王朝瑞.组合数学及其应用[M].北京:北京理工大学出版社,1992.[6]康庆德.斯坦纳和柯克曼三元系及大集问题[J].自然杂志,1984,8(6):459-465.[7]侴万禧.r t阶Kirkman三连系构造的一种方法[J].数学的实践与认识,2004,34(9):144-145.[8]侴万禧.高阶Steiner三连系及其构造方法[J].安徽理工大学学报:自然科学版,2004,24(3):76-80.A Method of Constructing S teiner Triple Systems of Order3t-2CH OU Wan xi1,H U O Yu hong2,LI Xiao yi3(1.School of Civil Engineering and Architecture,Anhui University of Science and Technology,H uainan232001,AnhuiChina;2.School of Mathemat ics and Computational Science,Huainan Normal Univer sity,Huainan232038,Anhui China;3.School of Mathematics and Systems Science,Shenyang NormalUniversity,Shenyang110034,China)Abstr act:The basic concept of constructing Steiner triple systems of order v is described.T he definition of edges matrix is given.A method of constructing Steiner triple systems of or der3t-2is proposed.The en tire procedure of constructing Steiner triple systems of or der25is presented.The enumeration problem of disjoint Steiner triple systems of or der25is discussed.Key words:Steiner tr iple systems;construction;complete graph;edges matrix;order(责任编辑向阳洁)。

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2009-02-25-ON-LINE_PARTIAL_DISCHARGE_MONITORING_AND_DIAGNOSIS_AT_POWER_CABLES

ON-LINE PARTIAL DISCHARGE MONITORING AND DIAGNOSISAT POWER CABLESMatthias Boltze1, Sacha. Michel Markalous1, Alain Bolliger2, Omar Ciprietti3, Javis Chiu4 LDIC GmbH1, LDIC AG2, Brugg Kabel AG3, Chan-Ching-Electric Technique Consulting CO.LTD4KEYWORDSQuality control, Maintenance, Power Cable, High Voltage- and Partial Discharge- Commissioning Test, Sensing, On-line Monitoring, Diagnosis and Trend-AnalysisABSTRACTMost defects observed in today’s EHV cable systems causes partial discharges (PD) under AC stress in the accessories. Combining AC testing and sensitive PD measurements results in best test efficiency. The condition-based maintenance of power cables required reliable significant diagnosis methods for the integrity of operation of power cable systems.This paper describes experiences with Partial Discharge measurements during installation tests of high voltage XLPE insulated single core underground cable systems tested with AC series resonant voltages. Considering the importance of installations in power stations permanent PD monitoring have been performed at GIS- and outdoor cable terminations after commissioning.Non-conventional partial discharge methods have been established for condition assessment of power cable insulations. A new system applying UHF sensors and acquisition was developed, suitable for any kinds of HV XLPE cable terminations like transformer sealing ends, cable terminations for metal-clad substations and outdoor sealing ends based on past experiences during investigations on site.This paper reports on present successful efforts to measurements as well as monitoring PD in the accessories after jointing in the EHV-XLPE cable systems and describes the UHF- PD measurement method.INTRODUCTIONMethods that allow the condition of transmission, distribution and generation power networks to be monitored have been developed and extensively researched. Monitoring, in relation to power cable systems and other system components of the electric power supply, describes measuring methods to allow continuously and periodic observation of operating states and properties with no interruption of the power supply – online-monitoring.Targets of the power cable monitoring are prevention, increasing the operational availability respectively reduction down times of the systems and their loading optimization. Following table is listing the possible monitoring methods for power cable systems and their objects:© 2009 Doble Engineering Company -76th Annual International Doble Client ConferenceAll Rights Reserved© 2009 Doble Engineering Company -76th Annual International Doble Client ConferenceAll Rights ReservedTABLE 1Possible monitoring methods for power cable systemMeasured quantityObject, target Axial Distribution of the cable temperature - Hot Spot Recognition- Prediction of the temperature trending by overload- Optimized thermal loadingWater permeability under the cable shield (polymer-insulated power cable) - Localization of leakages- Prevention for Water Treeing and cable shield corrosion- Substitution of the cable sheath testPD-Monitoring on power cable accessories - Early recognition, localization and assessment of failures at powercable accessories- Scheduling of shutdowns and repairs- Damage limitationLeakage-Monitoring on oil-insulated power cables- Prevention of contamination- Scheduling of shutdowns and repairs SF 6-Monitoring In power cable systems (sealing ends) - Early recognition and assessment of leakages at cable terminations in switchgears- Scheduling of shutdowns and repairs- Damage limitationOperating current and operating voltage- Loading optimization for the networkToday’s widely deployed monitoring methods are: monitoring of cable temperature, detection of water in the cable as well as the measurement of partial discharges in polymer-insulated power cables or their accessories.Of more important interest becomes the partial discharge monitoring methods for HV- and EHV-XLPE cable systems over the last few years to check the insulation condition. All power cables with polymer isolation are tested in the factory according to IEC60840 and IEC62067 with the best methods and with calibrated PD-measuring systems in the screened test room with high sensitivity.After transport and laying the sheath- and corrosion protection- test are performed on power cables using high DC voltage between metal sheath or screen and ground. If the sheath is in undamaged condition can be also confirmed that the polymer isolation is intact, no mechanical damages when transport and laying. The isolation of cable is still in the good PD-free condition like the routine test on the manufacture.However, for the assembly of the terminations and joints on the cable ends directly on the isolation one works again. Here error can occur. Therefore a partial discharge test is very important on the termination and joints after jointing. This requirement leaded to a development of new measurement systems for PD-On-Site-Tests on HV- and EHV-XLPE cable systems especially designed for termination and joints.This paper describes the concept for the UHF-PD-monitoring system from the instrumentation side and provides case studies about AC- and PD commissioning tests, quality- and inspection- checks where the effectiveness such kind of tests are presented.© 2009 Doble Engineering Company -76th Annual International Doble Client ConferenceAll Rights ReservedInstrumentation for Testing Power Cable Accessories The test procedures recommended in the relevant standards IEC 60270 and IEC 60885-3 are not qualified for all site PD tests to get sensitive measuring results due to the pure signal-to-noise (S/N) ratio. This is mainly caused by the limitation of the upper measuring frequency below 500 kHz and the site noise conditions as well.From a physical point of view, however, the S/N ratio can essentially be improved by increasing the measuring frequency much above 500 kHz and by using either a frequency selective signal processing or ultra wide band signal processing. Therefore the UHF PD measuring technology is increasingly used as an alternative.Due to the strong attenuation of the higher frequency spectrum of PD pulses if traveling trough long power cables it seems obvious that this technology works selective, i.e. the PD coupler has to be installed as close as possible to the supposed PD source.Therefore the UHF method is advantageously applicable for checking the correct assembling work of power cables accessories, such as joints and terminations.The UHF-PDM system is consisting of the PD measuring instrument, the Pre-amplifier and the UHF-PD-Sensor. A schematic diagram of the complete set-up is reported in figure 1. The attachment of the UHF-sensor to the GIS-cable termination is evident from figure 1.HV Termination with Decoupling LoopPD testing circuit acc. non-conventional measuring method. UHF-PD-Sensor connected at theHV- and EHV- Termination (Crossing Area: GIS - Power Cable)FIGURE 1In order to capture the very fast electromagnetic transients of PD events the lower section of the GIS-cable termination has been bridged by a measuring loop which is attached to the UHF sensor. Therefore PD defects close to the PD decoupling loop may well be recognized, whereas noises and even PD events far from the decoupling point are strongly attenuated, which ensures an excellent S/N ratio.This arrangement can be considered as a short circuit between the grounded parts of the GIS enclosure and the cable termination, if only the lower frequency range is considered. In the UHF range, however, the resulting impedance becomes about 50 Ω, which ensures an excellent S/N ratio and thus a high PD detection sensitivity even under noisy on-site condition.The output of the UHF sensor is connected via a coaxial measuring cable to a high-pass filter, which limits the measuring frequency range between about 300 MHz. A pre-amplifier installed at the UHFsensor is increasing the S/N ratio.For PD pulse processing an UHF-Processing Unit with functionality similar to a spectrum analyzer as both ’ultra-wideband mode’ and ’zero-span mode’ is plugged-in in the PDM instrument.The measuring frequency range of the ultra-wideband mode (UWB) is limited by the lower cut-off frequency f C,L = 100 MHz and the higher cut-off frequency f C,H = 1 GHZ. The PD instruments the PD Guard/UHF as permanent monitoring device and the LDS-6/UHF as periodic monitoring device are working in the UWB-mode.The measuring frequency in the zero span mode of the UHF Processing Unit is adjustable with a frequency bandwidth of 8 MHz in the frequency range of 110 MHz to 1700 MHz. The LDS-6/UHF configured in the zero-span-mode is used as periodic monitoring device.The acquisition as well as the storage and the visualization of the PD data are performed by means of a computer-based PD monitoring system.The results of the PD monitoring are further evaluated with different software tools which can easily be upgraded. For continuous monitoring the PD parameter (PD magnitude as peak value or as average value) is displayed and transmitted in real-time-mode.All functions run in real-time and it is easy to analyze and evaluate the acquired RAW PD data with functions like: q(phase), H(q, phase), q(t), n(t), I(t), H(phase), qpeak(phase), qmean(phase) and H(q). The windows-based control and analyzing software and the standard windows based. TCP/IP network allows an easy operation of the PD monitoring system.It is possible to do continuous PD monitoring with an extreme high measuring dynamics well as phase resolved PD measurements. Also a PD signal representation, storage and evaluation of the PD pulses in combination with corresponding test voltage information can be performed.The permanent monitoring system is able to evaluate the signal trend of the partial discharges in a very high range. The measuring sensitivity is automatically controlled using the preamplifiers and the amplifiers. The communication system transmits the monitored data and alarm messages to a main control server via Ethernet TCP/IP network communications.The resolution of the A/D-converter is 12 bit bipolar. The computer is able to store the partial discharge signals and the voltage signals by its internal memory and the control system can access this data frequently.The control and monitoring program shows scope mode, trend mode, monitoring mode and setup mode. It allows easy operation by plant personnel on a daily basis (monitoring mode) and sophisticated evaluation by specialists in case of alarm (trend mode, scope mode and setup mode).© 2009 Doble Engineering Company -76th Annual International Doble Client ConferenceAll Rights ReservedCase StudiesThe following case studies, for which representative PD measurements data are available, demonstrate the potential advantage of the UHF-PD-sensing at HV- and EHV-XLPE cable accessories.Case Study 1: AC- and PD- Commissioning Test of 400 KV XLPE cable systemUHF-PD-Monitoring and on-site-commissioning-test of 400 KV XLPE-insulated cable circuits at Jebel Ali / United Arab EmiratesSystem configurationBrugg Kabel AG, Switzerland, has successfully commissioned 400 KV cable project in Dubai. The project consists of (figure 2):- Six 400 KV XLPE cable systems for connections between the HV-side of the Unit Step-up Transformers and the 400 KV Substation bays with different cable lengths (120…320 m), - 36 pcs GIS-sealing ends with pre-fabricated and pre-tested stress-cones manufactured from silicone,- 18 pcs UHF-PD sensors with ground-connexion and TNC connector,- 18 pcs UHF-PD sensors without ground-connexion and TNC connector,- One complete On-line UHF-PD Monitoring System, type PD Guard/UHF, supplied by LDIC GmbHSystem layout for the installed monitoring system as well as the PD sensor application for theAC- and PD- commissioning test.FIGURE 2Test procedure and test application for the AC- and PD- commissioning testThe electrical quality check on the complete installed cable system has been performed with a mobile power-frequency resonance testing station under the following test procedure (figure 3).© 2009 Doble Engineering Company -76th Annual International Doble Client ConferenceAll Rights Reserved© 2009 Doble Engineering Company -76th Annual International Doble Client ConferenceAll Rights ReservedTest condition for on-site AC test combined with a selective on-site PD test at Jebel Ali. ACresonance test set connected to the power cable under test.FIGURE 3The PD commissioning has been performed with the instrument LDS-6/UHF as periodic monitoring instrument. Prior to the AC and PD test the instrumentation an instrument-performance-check of the PD measuring system has been perform by injecting of the voltage signal at the UHF-PD-Sensor. Increase the voltage in steps of 50 KV and observe the PD pattern at each voltage level. At Uo= 230 KV take a PD-measurement recording during 1 minute and afterwards increase the voltage in further steps of 50 KV until 320 KV. At each step note the measured PD value. Once reaching 320 KV leave this voltage applied for 1 hour and observe if there is a change in the recorded PD pattern and value, just before the 1 hour test period elapse take another recording of the PD measurement for 1 minute. While ramping the test voltage down, take another PD measurement for 1 minute at U o = 230 KV.Measuring instrumentation to perform the PD commissioning test, PD measuring instrument LDS-6/UHF as periodic monitoring system as well as the voltage generator LDC-7/UHF connected over the UHF-PD-Sensor to inject the voltage step as instrument-performance-checkFIGURE 4Test resultsDuring the applied high voltage to the power cables the PD level has been observed continuously. The following both screen shots are showing exemplary for one power cable the measured PD signals, near and remote sealing end, during the on-site commissioning test (figure 5).© 2009 Doble Engineering Company -76th Annual International Doble Client ConferenceAll Rights ReservedNear End Remote EndReal-time measured-data acquisition during the AC and PD commissioning test of the power cable under test displayed with the front-end software LDS-6/UHF. The measured PD signals at 230 KVtest voltage are not above the baseline.FIGURE 5 Recordings at 230KV test voltage - near & remote end:For the data evaluation and reporting the replay function of LDS-6/UHF Analysis Mode has been used. Phase-correlated pulses, which are a typical signature for real PD events, could not be observed, i.e. thehere recorded signal level is only due to baseline / basic background noises in the measuring surroundings (figure 6). Near End Remote EndRecording at 230KV test voltage, no significantly PD appearances above the baselineFIGURE 6Recordings at 320 KV test voltage (one-hour-test):Other further diagnosis methods, such as based on expert systems, were not necessary because replay mode was sufficient in this particular case to recognize jittering of the noise pulses caused by the power electronics of the resonance test set. Please refer to the screenshot of replay mode with pulse plots in figure 7.© 2009 Doble Engineering Company -76th Annual International Doble Client ConferenceAll Rights ReservedNoise Identification: Clearly assigned noise signal caused by electronicsof the HV resonance test systemFIGURE 7. All tested 18 power cables has been tested successfully with a recorded average background signal level ranges up to 75 mV. Based on these PD test results the investigated cables have been assessed PD-free under operation voltage considered to the recorded background noise level.Since one year ago the AC- and PD commissioning test has been performed the sealing ends of the power cable systems are monitored with the PDM system PD Guard/UHF. No conspicuousness has been observed during the one-year-period.Case Study 2 - AC and PD Commissioning Test of 345 KV XLPE cable systemUHF-PD-Monitoring and on-site-commissioning-test of 345 KV XLPE-insulated cable circuits at EHV Substation Wufong / TaiwanSystem Configuration and Test ApplicationBrugg Kabel AG, Switzerland, has been awarded and has successfully commissioned 325 KV cable project in Taiwan. The project consists of (figure 8):-Four 325 KV XLPE cable systems for connections between the Overhead-Line and GIS of the 325 KV Substation lines with different short cable length -Additional 3 power cable systems between GIS and Power Transformer -Outdoor-sealing ends as well as GIS-sealing ends pre-fabricated and pre-tested stress-cones manufactured from silicone -Complete 56 pcs installed UHF-PD sensors for permanent and periodic Monitoring, -One complete On-line UHF-PD Monitoring System for the Outdoor-sealing end supplied by LDIC GmbH (24 UHF-PD sensors at two Overhead-Line Towers)© 2009 Doble Engineering Company -76th Annual International Doble Client ConferenceAll Rights ReservedSensor- and Instrumentation- Arrangement for PD Monitoring of the 345 KV SubstationFIGURE 8The PD monitoring system has been designed to monitor the PD signals continuously at the outdoor-sealing ends both overhead-line towers as permanent monitoring. The indoor GIS-sealing ends will be monitored periodic annually once. Within the first two years after system energization the GIS-sealing ends will be monitored twice the year.Test procedure and test application for the AC- and PD- commissioning testIn agreement with the end-user the test procedure for power cables has been performed as follow (figure9):Increase the voltage in steps of 50 KV and observe the PD signals as well as the PD pattern at each voltage level. At the voltage level 120KV, 199KV (U 0), 260KV, 345KV (1.7U 0) takes PD-recordings during 10-15 minutes. At each voltage level the PD pattern have been observed to check the power cable accessories under test concerning PD phenomena.Test condition for on-site AC test combined with a selective on-site PD test at Wufong ACresonance test set connected to the power cable under test.FIGURE 9© 2009 Doble Engineering Company -76th Annual International Doble Client ConferenceAll Rights ReservedThe PD commissioning test has been performed with the monitoring instruments PD Guard/UHF as installed permanently at the outdoor sealing-ends (figure 10). The indoor GIS-sealing ends have been checked with temporary measuring instrumentation. All measured PD signals, max. 6 measuring signals during the commissioning test of each cable phase separately, have been monitored and observed at the data acquisition server located in the control room.Application layout for permanent PD Monitoring at EHV substation, Wufong. Temporarymeasuring instrumentation at the GIS-sealing ends.FIGURE 10 Test ResultsDuring the AC- and PD commissioning tests at the 345 KV substation abnormal discharge appearances has been recognized at two GIS-sealing ends (figure 11). Increased phase correlated pulses have been observed on the terminations GIS A+ and GIS B- at one phase. Phase-resolved PD Pattern, which have a typical signature for real PD events, could be observed.Due to the short link connection via busbar, 4 m distance, between GIS A+ and GIS B- sealing ends the PD signals coupled over from one to another one. To confirm the cross-over coupling and to isolate the PD phenomena the link from the GIS B- sealing end has been opened. It could be clearly assigned that the typical PD appearances have the origin at the GIS A+ sealing end. The phase-resolved PD Pattern are showing significantly PD behaviour with triangular and symmetrically PD appearances.Recordings at 199 KV test voltage:GIS A+ GIS B-Phase resolved PD pattern recorded at 199 KV test voltage. Clearly assigned PD phenomena at GIS A+, cross-over coupling at GIS BFIGURE 11 Due to the observed typically PD pattern during the AC- and PD- commissioning test it has been decided to open the sealing end at GIS A+ to inspect the termination assembly. After de-assembly of the sealing end tracking path on the cable insulation has been discovered caused by improper termination assembling work (figure 12). Foreign matter, a small piece of tape layer, initiated discharges with the tracking path in the insulation as result.Tracking path as reason for partial discharges caused by foreign matter in the high voltage insulation system FIGURE 12 After re-assembling of the GIS A+ sealing end the AC- and PD commissioning test has been repeated with no relevant discharges above the baseline. All tested power cable accessories have been assessed PD-free under operation voltage.© 2009 Doble Engineering Company -76th Annual International Doble Client Conference All Rights ReservedCase Study 3 – Periodic PD Monitoring as Inspection Test Periodic UHF-PD-Monitoring- and inspection-test of 161 kV GIS-sealing end in Taiwan System Configuration, Test Sequence and Instrumentation A set of GIS-sealing ends, three sealing ends, of 161 KV XLPE power cable system has been inspected as routine test. The PDM system including three UHF-PD-sensors as described previously has been set up in energized condition of the power cable system. PD recordings have been taken at each phase of the investigated power cable system. At one phase abnormal conspicuousness in the partial discharge measuring readings has been observed during the routine inspection measurement. Based on the initial result it has been decided to perform periodic monitoring once the month to check the PD trending as well as to observe changes in the phase resolved PD pattern. Test Results During the routine inspection strong partial discharge activities have been measured at the cable termination of S-phase, the phase-resolved-pattern is shown in figure 13. The measured partial discharge signals are not similar to the typical PD pattern appearance, 0°~90° and 180°~270° of the applied test voltage, due to the outlet voltage as reference voltage has been not taken from the cable under test.Phase resolved PD Pattern at GIS-sealing end, phase S - Initial measurement as start of the periodic monitoring FIGURE 13 The origin of the partial discharge source has been located by comparing the measuring results, the partial discharge magnitudes as well as the phase resolved PD pattern, all three tested cable terminations. As shown in figure 13 the phase-resolved-pattern is indicating the discharges based on true PD-nature from the insulation of the GIS-sealing end arrangement at phase S. Moreover, the time domain signal and the frequency spectrum have been used to figure out the partial discharge source, as shown in figure 14. The measurement results shows that the partial discharge signal is suspected from the S-phase cable termination than from outside. Therefore, the S-phase cable termination has been considered that there is a defect inside the insulation arrangement, and a suggestion has been proposed to perform periodic PD monitoring once the month.© 2009 Doble Engineering Company -76th Annual International Doble Client Conference All Rights ReservedFig 14 Time domain signal of the decoupled PD signal at GIS-sealing end, phase S, and his correlated frequency spectrum FIGURE 14 The first review of on-line PDM is done one month later. The measured partial discharge signals have been increased as indicated in figure 15 (left). Comparing with initial measurement, the partial discharge magnitudes are slightly increased, the phaseresolved PD pattern is similar and the repetitive rate is almost the same. Figure 15 is showing that partial discharge area is shifted by 180 degree, and this is resulting from taking different outlet as reference voltage, the real synchronized voltage derived from phase S. It has been confirmed that the partial discharge source is inside the cable termination.Phase-resolved-pattern of 1st review, phase-resolved-pattern of 2nd review recorded each at phase S FIGURE 15 The second review of on-line PDM is done on Dec. 12th 2007. The measured partial discharge is stabilized at the PD level measured before, and the partial discharge still remains. Abnormal behavior has been assigned at the investigated cable system, discharges based on random noise or resulting from unexpected switching transients has been excluded. Therefore, the internal partial discharge of cable termination has been validated, the cable termination has been replaced, and the details are as following:© 2009 Doble Engineering Company -76th Annual International Doble Client Conference All Rights ReservedDisassembling of the GIS-sealing end. No abnormal condition observed at the surface of cable termination (left). After further disassembling serious trace path as result of partial discharge activities has been found (right). FIGURE 16Case Study 4 – Periodic Monitoring as Quality CheckPeriodic UHF-PD-Monitoring and inspection-test of 230 KV XLPE-insulated power cable accessories in a substation in Saudi Arabia System Configuration Two sets of GIS-sealing ends of 230 KV XLPE power cable system has been inspected and monitored during a one-year-period: - Six 230 KV GIS-sealing end at two circuits side by side (circuit A and circuit B) Test instrumentation and -sequence The used instruments to perform the quality check consist of the PD measuring Instrument LDS-6/UHF configured in zero-span- and ultra- wideband mode, Pre-Amplifier LDA-5/GIS, Voltage Generator LDC-7/UHF, UHF-PD-sensor (figure 17).Measuring setup for the power cable accessories insulation check by using PD monitoring instrumentation (frequency selective- as well as ultra wideband- measuring method): the PD instrument LDS-6/UHF as portable version and the UHF-PD-senor are displayed. FIGURE 17© 2009 Doble Engineering Company -76th Annual International Doble Client Conference All Rights ReservedThe PD-recordings has been taken during the GIS is in service condition. The UHF-PD-sensor has been installed with no outage as the GIS is in service. The test sequence has been performed at each sealing end as follow. 1. Setup of the PDM system LDS-6/UHF incl. the UHF-PD-sensor Note: Voltage synchronization by using the external Trigger, real synchronized voltage derived from the investigated circuit, of the PD Instrument performed at all circuits 2. Frequency analysis for determination of the measuring frequency (only for zero-span-mode measurement required) 3. Instrument performance check by using the voltage generator LDC-7/UHF 4. Recording of the measuring signals for the measuring cycle of 120 seconds Note: Ultra-wideband-mode measurements and zero-span-mode measurements have been performed at all circuits 5. For localization purposes and confirmation of UHF-PD-measuring series 2: recordings of acoustic signals captured by the acoustic insulation analyzer AIA100 (using the R3α-Sensor) at six measuring points according picture per phase (figure 18) 6. Evaluation of the measuring recordings by using the LDS-6/UHF analysis software: PD pattern recognition and replay-mode for signal evaluationSchematic Overview of the investigated GIS, GIS-sealing ends both circuits A and B. FIGURE 18© 2009 Doble Engineering Company -76th Annual International Doble Client Conference All Rights ReservedThe following table is reporting the measuring sequences both test series within the one-year-monitoringperiod: TABLE 2 Test configurations to perform the periodic PD monitoringSwitchin g No. 1 Measuring series as part of the periodic monitoring Initial measurement (quality check) Status Measuring method Electrical InstrumentationCircuit A energized Circuit B energized Circuit A: deenergized (circuit breaker and disconnector open, disconnector closed) Circuit B: in serviceLDS-6/UHF (zero-span-mode, UWB) LDS-6/UHF (zero-span-mode, UWB) AIA100 LDS-6/UHF (zero-span-mode, UWB) AIA1002Nine-month laterElectrical busbar circuit Acoustic Electrical busbar circuit3Nine-month laterCircuit A in service Circuit B: deenergized (circuit breaker and disconnector open, disconnector closed)AcousticFirst test series, quality check after system assembling of the GIS-sealing ends Based on the below reported test results it can be concluded, that the GIS-sealing ends both investigated circuit at each phase L2 have critical PD levels above the detection sensitivity of about 20 mV. Noises appearing either stochastically or phase-correlated could clearly be identified as external disturbances, due to further investigative site measurements and deeper analysis of the captured data by the ’Replay-Mode’ of the digital PD measuring system LDS-6/UHF. It could be excluded the origin of these PD pattern are not generated by the power transformers connected to the power cable via the GIS and not from the GIS-busbar system connected from the GIS sealing ends to the power transformer.© 2009 Doble Engineering Company -76th Annual International Doble Client Conference All Rights Reserved。

中橡协轮胎分会2010年会员大会在山东威海召开

［ｏ１］蒋修治．白炭黑／烷填料体系的化学与橡胶补强性［］橡硅Ｊ．
胶参考资料，０６３（）３－１２０，６４：６４．
收稿日期：０００ — ４２１ — １１
ＣｈｎｅｎｃｏｓｉｋｓｒｃｕｅａｄｄｎｍｉｉｃｅａｔｃｔｆＥＳａｇｓｉｒｓｌｎｔｕｔｒｎｙａｃＶｓｏｌｓｉｉｙｏＢＲ
１７９９．
下降，白炭黑胶料的Ｐｙｅ应明显减小。ａｎ效（）种填充体系构成的网络打破与重建的５两应变依赖性相似，ａｃ的应变依赖性相差不大。ｔｎ￣
参考文献：
［］韩慧，大为，志宏．炭黑／黑并用比对轿车轮胎胎１李陈白炭
ｖｌａｉａｅｄｒｎｅｉｅｆｔｇｅｕｃｎｚｔｕｉｇｔｎｓｌａｉｕ
ＳＵＮｏｇ，ＩＧｎ，ＣｈｎＤＮＬｉＺＨＡＮＧｉｇＰｎ
（ｎａｎｖｒｉｆＳｃｅｅａｃｎｌｇＱｉｇａ２６４Ｃｈｎ）ＱｉｇｄｏＵｉｅｓｔｏｉｎｃｎｄＴｅｈｏｏｙ，ｎｄｏｙ６０２，ｉａ
［］赵青松，友平，素合．炭黑增强ＳＢ和ＥＢ复合材２吴赵白ＳＲＳＲ料结构性能的比较口］特种橡胶制品，０７２（）１４．２０，８２：－．
［］周风柱，智端，慧贞，．聚乳聚丁苯橡胶基本工艺性３贺胡等溶能与分子参数的关系［］橡胶工业，９１３（０：８ —８．Ｊ．Ｉ９，８１）５０５４

945-1781-1-PB

INERTIAL AND VIBRATIONAL CHARACTERISTICS OF SOFTBALL AND BASEBALL BATS: RESEARCH AND DESIGN IMPLICATIONSLarry Noble, Kansas State University, Manhattan, USA INTRODUCTION: The design of baseball and softball bats has been an ongoing process since the inception of the game in the early 19th century. Until the early 1970's, the only material to be used was wood and the potential for design improvements was limited because they involved changing the physical dimensions of the bat. Also, most of the changes were initiated by the player and were carried out by local craftsmen in wood shops. However, with the introduction of hollow-wall aluminum bats in the 1970's and other metal alloys as well as composite materials since then, the potential for applying relevant mechanical principles to improve the performance characteristics of bats has improved dramatically. In recent years a plethora of bats with innovative features have become available to the consumer. Some of these innovations are a result of the research and development efforts of the bat manufacturing industry, often in collaboration with scientists not directly affiliated with the industry, while others are a result of flawed ideas that are not completely thought through. Braham (1997) provides a recent, up-to-date summary of recent innovations by the leading bat manufacturers, but an evaluation of the claims of these products using relevant criteria is lacking. The purpose of this paper is to provide a scientific basis and a focus for examining and developing new bat design features. The paper will provide an overview of the factors that are relevant to the design of baseball and softball bats, including related theoretical and empirical studies.Factors relevant to the design of baseball and softball batsWhen developing or evaluating a design feature of a baseball or softball bat, the following factors must be considered: (1) the manner in which the bat is swung and forces are transmitted to the bat during the swing, (2) the constraints resulting from rules in the particular sport, and (3) the relevant properties of the bat. I will review each of these general factors in detail, making reference to related scientific literature.Characteristics of batting relevant to bat designBaseball and softball batting is a two-handed sidearm striking skill with the bat held near one end and swung as a physical pendulum. Power hitters attempt to impart maximum velocity to the impacted ball in the desired direction by generating maximum linear velocity of the impacting part of the bat to the ball. The motion of the bat is predominantly in the horizontal plane and the rotation axis ranges from .15 to.20 m off the knob end of the bat toward the hitter’s body during the swing. During the swing, the maximum linear (COP) and rotational velocity of the bat is approximately 33 m/s and 36 r/s, respectively, for college females and 38 m/s and 44 r/s, respectively, for college males. Because the primary goal of the power swing is to maximize bat velocity on impact, it is somewhat surprising that maximum bat velocity has repeatedly been found at from .01 to .05 s prior to impact (Shapiro, 1974; McIntyre & Pfautsch, 1982; Messier & Owen, 1984; Spragg, 86 ISBS'98 –Proceedings II1986). While this finding has been reported in the scientific literature frequently, a plausible explanation of the reason has not been found. A review of the elastic properties of the bat (appearing later in this paper) and the characteristics of the swing may provide a tenable hypothesis. It is possible that, at the beginning of the swing, torque applied to the bat handle to rotate the bat toward the incoming ball and the inertia of the barrel end of the bat cause the bat to bend, with the barrel of the bat lagging behind. This bending mode, usually referred to as the diving board mode , would begin to release when the rotational acceleration of the bat begins to drop. It is conjectured that the elite hitter learns through trial and error to adopt a bat and swing that are matched such that the velocity of the impact point of the bat is maximized at impact. To accomplish this end, accelerating forces would be reduced quickly at either 1/4 or 1 3/4 of the period of oscillation of the diving board mode. For example, if the fundamental, diving board mode of a bat is 25 Hz, then the period of oscillation is 40 ms. For the hitter to take advantage of this elastic behavior, this bending mode would need to be …released“ at approximately 10 or 70 ms prior to impact. While this characteristic of the skilled golf swing has been empirically verified (Cochran & Stobbs, 1986), no empirical data in support of this hypothesis applied to softball or baseball bats have been found.Rules most relevant to bat designThe rules regarding baseball bat characteristics are different from those regarding softball bats. Also, rules are different for different genders and different levels of play. For adult males, the maximum baseball and softball bat barrel size is 2.25 and 2.75 in (.057 and .070 m), respectively. The maximum bat length is 42 and 34 inches (1.067 and .864 m) for baseball and softball, respectively, while the maximum softball bat weight is 38 oz (10.569 N). There is no maximum baseball bat weight. All bats used in professional baseball must be made of wood. The most recent rule, which places an upper limit on the coefficient of restitution (Bat Performance Factor) for bats at different levels and types of play, is having a tremendous impact on the direction of bat design activity. Bat performance factor will be discussed in greater detail later in this paper.Inertial and vibrational properties relevant to bat designSeveral inertial and vibrational properties of the bat are relevant to its effective use: (1) mass, (2) moment of inertia, (3) coefficient of restitution, (4) location of node of the fundamental vibration node, and (5) center of percussion location.Mass and moment of inertia determine the amount of effort required to swing the bat. There is an inverse relationship between bat linear and angular acceleration and mass and moment of inertia, respectively, for a given linear and angular impulse (integral of force/torque and time). Thus, the more mass and/or moment of inertia, the more impulse required to produce a given change in bat speed or direction. In other words, greater mass and moment of inertia compromise the hitter’s ability to control the path of the bat as it moves toward the ball as well as to generate bat velocity during the swing. Theoretical models of the relationship between mass and impact parameters indicate that lighter bats than have been used by most skilled players would be more effective (Kirkpatrick, 1963; Adair, 1990). In a study which sought to empirically determine an individual’s ideal bat, this concept was supported (Bahill & Karnavas, 1991). Furthermore, bats now used by elite softball and baseball players are much lighter than they were 10 years ago. ISBS'98 – Proceedings II 87Bat manufacturers and retailers do not provide moment of inertia measurements with their products; however, moment of inertia is a critical design parameter and is also used to develop bat selection guidelines.When the ball and bat are impacted, during impact the bat behaves in some respects as a physical pendulum and in some respects as an elastic body. Taking both rigid-body and elastic properties into consideration, the best part of the bat on which to hit the ball is called the …sweet spot“. The …sweet spot“ is a general, nonscientific term, that means that the best overall results are obtained from impacts on this point. In other words, impacts on the sweet spot feel best to the hitter and results in imparting velocity to the ball are best. Or, in more precise terms, the sweet spot is the impact location where the transfer of energy from the bat to the ball is maximal while the transfer of energy to the hands is minimal. On closer examination, four parameters have been identified as having an effect on the …sweetness“ (liveliness) and location of the sweet spot: (1) center of percussion (COP), (2) node of the fundamental vibrational mode, (3) coefficient of restitution, and (4) the maximum …power“ point.Center of percussion. When the ball hits the bat at the center of percussion (COP), there is no reaction impulse (shock) at the axis. The impact axis for bats has been shown to be the point under the first knuckle of the top hand (Plagenhoef, 1971; Noble, 1983). Thus, COP impacts are more comfortable than at other locations because there is no painful impact …shock“ that is experienced during impacts at other locations. The distance from the impact axis to the COP of a bat can be found from the following equation:COP dist = T2g/4π2 = .2483877*T2 (units in meters)where T is the period of one oscillation when the bat is suspended from the axis, and g is the gravitational constant in meters. The COP has been demonstrated to be the impact location producing the greatest post-impact velocity with stationary bats (Weyrich, Messier, Ruhmann, & Berry, 1989). Another empirical study involving 18 elite slow-pitch softball hitters reported a correlation of .58 between the perceived location of the sweet spot and the COP. Thus, COP location explained 33% of the variability in perceived sweet spot impact location (Noble, 1983). Brody developed a theoretical construct for determining the impact location of a swinging bat with a pitched ball that would result in greatest postimpact ball velocity (Brody, 1986). This location was not on the COP, but was a function of the relative velocity and mass of the ball and bat as well as the inertial properties of the bat.In an early study (Bryant, Bryant, Chen, & Krahenbuhl, 1977) comparing the dynamic and performance characteristics of aluminum and wood bats, data were reported showing an impact area of several cm in length on hollow-wall aluminum bats where there was zero-order reaction impulse while reaction impulse on wood bats was a direct linear of function of distance from the COP. However, a later study by Noble and Eck (Noble & Eck, 1986) presented a theoretical construct and empirical data demonstrating that, assuming the bat is rigid during impact, reaction impulse is a direct linear function of the distance of the impact from the COP (Figure 1). Also, the slope of the regression line of impact reaction impulse on impact-COP distance is a direct linear function of the distance of the COP from the impact axis (Figure 2). In other words, the greater the distance of the COP from the 88 ISBS'98 –Proceedings IIISBS'98 – Proceedings II 89 hands, the smaller the reaction impulse resulting from an impact of a given distance from the COP. This study also demonstrated thatthe distance of the COP from the axis was:COP = I/Mrwhere I = moment of inertia about the axis, M = the totalbat mass, and r = distance from the axis to the center ofmass. Strategies were later presented for systematicallydisplacing the location of the COP (Noble & Eck, 1985) by placing mass at various locations along the longitudinalaxis of the bat. While these strategies were effectivein displacing the COP to a more distal location on the bat,this …improvement“ did not enjoy wide acceptance by theplayers because of the greater excitation of thefundamental vibrational mode resulting from COP impacts(Noble & Walker, 1994b).Figure 1. Mechanical system describing center of percussion (COP)location as a function of impact location. (Legend: P = impact impulse, P 1= impact reaction impulse, A = impact location, a p = distance from COMto COP, O = impact axis, M = mass, S = axis-COM distance, I o = momentof inertia about impact axis). Note. From …Effects of Selected Softball BatLoading Strategies on Impact Reaction Impulse“ by L. Noble and J. Eck(1986). Medicine and Science in Sports and Exercise 18, 51. Copyright1986 by the American College of Sports Medicine. Adapted with permission.Figure 2. Theoretical relationship between impact reaction impulse and impact location. (Legend: P = impact impulse, P 1 = impact reaction impulse, a p = COP location, a = distance from impact axis to impact, M = mass, S = axis-COM distance, I o = moment of inertia about impact axis). Note. From …Effects of Selected Softball Bat Loading Strategies on Impact Reaction Impulse“ by L. Noble and J. Eck (1986). Medicine and Science in Sports and Exercise 18, 51. Copyright 1986 by the American College of Sports Medicine. Adapted with permission.90 ISBS'98 –Proceedings II Vibrational properties. The above discussion relates to the rigid body behavior of the bat during impact. The bat also exhibits important and relevant elastic properties during impact as well as during the swing because the bat is not completely rigid. The vibrational behavior of a bat approximates that of a uniform beam, described in detail in most engineering textbooks on vibrations (Thompson, 1993). If we assume, for simplicity, that a bat can be represented by a uniform rod rigidly suspended at the point of contact with the hands, then the various normal vibrational modes are only those for a rigid clamped rod. Figure 3a illustrates the approximate length (modeled after a uniform rod), node locations, and relative amplitude of these modes. The lowest frequency mode, commonly called the diving board mode, corresponds to a vibration where the axis is at a nodal point and the barrel end is at a maximum. This node has a wavelength (λ0)of approximately 4H, where H is the distance from the axis to the barrel end of the bat. This fundamental mode only has one node and it is located at the clamped point. The next highest frequency mode has a node at the handle and another at 3/4H. If the ball strikes the bat at a node of a given vibrational mode, then thatmode will not be excited. Since all modes have an anti-node at theFigure 3. Vibrational modes of bat as (a) a uniformed rod clamped at the axis, and (b) as a free-free rod. (λi = approximate wavelength of i th harmonic modeled as a uniform rod). Note: Part a from …Effects of Selected Softball Bat Loading Strategies on Impact Reaction Impulse“ by L. Noble and J. Eck (1986). Medicine and Science in Sports and Exercise 18, 51. Copyright 1986 by the American College of Sports Medicine. Part b from …Baseball Bat Inertial and vibrational Characteristics and Discomfort Following Ball-Bat Impacts“ by L. Noble and H. Walker (1994). Journal of Applied Biomechanics 10,134. Copyright 1994 by Human Kinetics, Inc. Adapted with permission.unclamped, or barrel end of the bat, all modes of vibration can be excited when striking the bat at the barrel end. The frequency of the diving board mode has been reported to be 27 Hz for an aluminum softball bat and 18 Hz for a wood softball bat (Brody, 1990) and that of the first overtone mode was 317 and 209 Hz, respectively. Both of these bats were 34 inches (.864 m) in length. Shorter bats and bats with greater strength/mass ratios will have higher fundamental frequencies. It is likely that this mode is excited during the swing, as has been demonstrated during the swinging of golf clubs (Cochran & Stobbs, 1986); however, this low-frequency mode is not excited by the impacting ball (Brody, 1990; Noble & Walker, 1994a; Noble & Walker, 1994b).During impact, the vibration behavior of the bat corresponds to that of a free, non-supported bat whether irregardless of the firmness of the grip. Figure 3b illustrates the lowest (fundamental) and first harmonic modes, approximate wavelengths and node locations of the free, unsupported bat. The approximate locations of the two nodes for the first mode are 29% of the bat length from each end. The next highest mode has three nodes with approximate locations as depicted in Figure 3b. The number of nodes for each successively higher mode increases by one at each step. Also, the amplitude associated with each mode decreases as the frequency increases and increases as the distance from the node increases.The node locations and frequency of the fundamental and first harmonic modes can be measured by, first, supporting the bat in a horizontal position by threads attached to the ceiling. A vibration exciter and velocity sensor are horizontally oriented and placed as indicated in Figure 4. Specific placement of the exciter and sensor is not critical as long as they are not placed on one of the nodes. A resister is put in series with the exciter coil, and the voltage displayed on the horizontal axis of an oscilloscope. This voltage is proportional to the current through the resister and exciter coil which is proportional to the force applied by the exciter. The output of the velocity sensor is displayed on the vertical axis of the oscilloscope. This display is generally an ellipse whose axes are oriented at an angle determined by the gain setting of the oscilloscope, the phase relationship of the two signals, and the location of the velocity sensor. The input is gradually increased in frequency until resonance is achieved. At resonance, the exciting force and velocity are in phase and the ellipse is reduced to a straight line. The straight line changes slope as the velocity sensor is moved along the long axis of the bat. The slope changes from positive to negative as the sensor passes over a node and is horizontal when the sensor is located at a node.ISBS'98 – Proceedings II 91The fundamental frequency (free condition) of 34-inch (.864m) aluminum softball bats is usually within the range of 180-360 Hz and can be varied throughout this range by changing the shape of the bat and strategic redistribution of mass (Noble & Walker, 1993). The easiest way to change the fundamental frequency is to modify the diameter of the bat in the taper region, which is near the antinode of theFigure 4. Vibration measurement system. From …Baseball Bat Inertial and vibrational Characteristics and Discomfort Following Ball-Bat Impacts“ by L. Noble, H. Walker (1994). Journal of Applied Biomechanics10, 134. Copyright 1994 by Human Kinetics, Inc. Adapted with permission. fundamental mode. Node locations of the fundamental mode can also be strategically displaced as much as .06 mm using similar strategies. The distal node of the fundamental mode has been identified as one of the determinants of the sweet spot. Impacts on the node do not excite the low-frequency, fundamental mode, resulting in a higher-frequency sound and smaller, higher frequency vibrations of the bat handle. Thus, it is reasonable to expect that nodal impacts would be more comfortable for the hitter. Fortunately, in most bats the location of this node and the COP are less than .02 m apart, approximately 25 per cent of the bat length from the barrel end. When using bats with the node and COP close together, impacts at both locations are more comfortable than at other locations (Noble & Walker, 1994a) with no significant difference between the two. However, strategies developed to strategically displace the COP toward the barrel end were found to significantly increase the distance (.06 m) between the node and COP. Impacts at the node on these bats were found to be more comfortable than impacts at any other location, including the COP (Noble & Walker, 1994b). This is consistent with results from a study investigating the sweet spot location of tennis racquets indicating the node as the predominant predictor of sweet spot location (Hatze, 1994). Furthermore, the node-COP distance has been found to be one of the most powerful predictors of player’s perception of bat performance and preference (Noble & Dzewaltowski, 1994).No empirical studies have been found investigating the effects of impact location relative to the location of the distal node of the fundamental mode on post-impact ball velocity. However, an excellent theoretical presentation of this effect has been developed, but unfortunately it remains unpublished (Van Zandt, 1991). This paper applied the theory of the elastic behavior of an irregularly shaped, cylindrically92 ISBS'98 –Proceedings IIsymmetric object to a wood baseball bat (frequency of diving board mode and first harmonic - 27 Hz and 137 Hz, respectively). The node-COP distance was .01 m. A set of equations was developed and used to find the first 20 normal modes of vibration and calculate each mode’s effect on the recoil of the ball. Figure 5 illustrates estimates of the post-impact ball velocity as a function of impact point along the length of the bat. The impact ball and bat velocities were 40 m/sec and 16 m/sec, respectively. The solid curve shows the expected result, the dashed curve shows the effect of suppressing all modes above the fundamental for the free condition (137 Hz), and the starred curve shows the performance expected for an infinitely rigid club having otherwise identical properties. Two observations relative to the effect of impact location and post-impact ball velocity are notable: (1) post-impact velocity is significantly lower for impacts not on the node, especially as the impact location moves toward the handle of the bat; and (2) the higher-frequency modes serve to increase post-impact ball velocity. For a collision only .10 m toward the bat handle from the node, post-impact ball velocity is expected to decrease by 5%. The effect of this loss in ball velocity would cost a distance in ball flight of 10%, or 42 ft (12.8 m). The higher elastic modes play an important role in bat performance, restoring approximately 50% of the loss in ball velocity. This degradation in bat performance would be less with stiffer bats with higher natural frequencies, such as those made from composites, aluminum, and other metal alloys. The loss in bat performance would be eliminated if the fundamental frequency of the bat was …tuned“ to the ball-bat contact, or dwell, time. To obtain impact frequency tuning, the fundamental frequency should equal the reciprocal of twice the dwell time. For example, the dwell time of a softball and bat collision (velocity = 31 m/s) has been measured at .0035 sec (Plagenhoef, 1971). For this case, the frequency-matched bat would have a fundamental frequency of 143 Hz. This procedure would be difficult to effectively apply with precision because the dwell time is a function of collision velocity, which is not entirely under the control of the hitter, as well as the hardness of the ball. Coefficient of restitution. The coefficient of restitution (COR) of two colliding objects, such as the ball and bat, is the ratio of the difference between their velocities immediately after impact compared to the difference between their velocities prior to impact. This ratio has been shown to be a function of collision velocity as well as temperature. For simplicity, the COR of balls and bats are evaluated separately. Ball COR is usually determined by impacting the balls with a wooden wall backed by concrete. Rules for different levels of play for softball and baseball have been established setting an upper limit for the COR, usually determined by impacting the balls with a steel plate at 60 mph (26.4 m/s). The COR is now often stamped on the cover of the ball. For most adult softball competition, the maximum COR is .55. The COR of bats has been shown to be a weak function of impact location along the barrel of the bat where the diameter is constant. Thus, it does not play a significant role in determining the location of the sweet spot. If a given ball impacts with a ball with these conditions held constant, the bat with the higher coefficient of restitution will produce the greatest post- impact ball velocity. Improving the COR of bats has been the primary focus of the research and development efforts of the major bat manufacturers during the past decade. The COR has been significantly improved through the use of materials of higher strength/mass ratios and strategic manipulation of the wall thickness of the ISBS'98 – Proceedings II 93barrel of the bat. These dramatic increases in COR have caused great concern on the part of coaches and officials associated with all levels of play. This concern relates to the safety of the participants and to the changes in the nature and integrity of the games that those associated with the game identify with. An outgrowth of this concern is the adoption of a standard for evaluating theFigure 5. Theoretical estimates of the degradation of post-impact ball velocity at different impact locations due to bat vibrations. From The Dynamical Theory of the Baseball Bat, by L. L. Van Zandt (1991). Unpublished manuscript. W. Lafayette, IN: Purdue University.…liveliness“ (COR) of bats and implementing rules placing an upper limit on this aspect of bat performance. A standard method of testing to measure the COR of bats has recently been adopted by most of the baseball and rules committees in the USA (ASTM, 1995). This procedure involves impacting a ball with a known COR with a stationary bat with a fixed axis (free to rotate) at the bat’s COP at a ball speed of 88 ft/sec (26.8 m/s). The COR is calculated by the standard method of comparing the difference between the velocity of the bat and ball before impact to that following impact. A Bat Performance Factor (BPF) is then calculated from the ratio of bat and ball COR to the ball COR. For example, if the predetermined ball COR is .5 and the measured COR of the ball-bat collision is .55, then the BPFof the bat would be 1.1. The BPF of most wood bats is between .9 and 1.0 whilethat of the latest aluminum alloy bats is typically above 1.1. Maximum bat94 ISBS'98 –Proceedings IIperformance standards have now been adopted by most levels of play for both baseball and softball. For example, the maximum BPF allowed for most adult slow pitch softball is 1.2 and that established for collegiate baseball is 1.15. The adoption of this standard has changed the recent trend in bat design from focusing on increasing COR to improving other performance characteristics that comply with the rules.Maximum …power“ point. The impact point along the longitudinal axis of the bat that will result in the greatest post-impact ball velocity, or maximum power point, is another important performance characteristic of the bat. Brody (1986) developed a theoretical framework and estimates of the maximum power point for a bat that is swung and impacts with a pitched ball, behaving as a free-free body during impact. Estimates of the location of the distance from the maximum power point to the bat COM (PPTDIST) were found to increase as the mass and moment of inertia of the bat increases and as the ratio of bat/ball mass increases. Furthermore, PPTDIST increases as the ratio of bat angular velocity to ball linear velocity increases. Thus, PPTDIST was estimated to be less for baseball than for fastpitch softball. PPTDIST was calculated for an aluminum softball bat and ball with varying bat/ball velocity and mass ratios and found the location of the maximum power point to be located between the COM and COP. No empirical data relative to these estimates was reported. Weyrich, Messier, Ruhmann (1989) provided empirical data on the effects of impact location on postimpact ball velocity. Bats were not swung, but held stationary by either clamps or strings mounted to the ceiling while balls were propelled against the bat at 27 m/s. Impacts on the COP produced greater postimpact ball velocities than impacts on the COM and impacts near the barrel end. While these results are apparently contradictory to the theoretical work of Brody(1986), these bats were not swung, as Brody’s estimates assume, and no impacts were studied in the area between the COM and COP. The empirical data provided by Noble (1983) in an earlier study does, however, appear to conflict with Brody’s estimates. In this study, the location of 52 self-perceived …sweet spot“ impacts of 12 elite male softball players and 5 highly skilled college male baseball players was examined using cinematographic methods (200 f/s). The …sweet spot“ location, the point where the results were best, coincided very closely with the COP location. Furthermore, sweet spot location relative to the COP did not appear to be different for softball and baseball impacts. If it can be assumed that these elite players’ perception of sweet spot is synonymous with the maximum power point, then these results do not seem to support Brody’s 1986) theoretical estimates of maximum power point location. However, because COP location only accounted for 33 per cent of the variability in sweet spot location in the empirical study (Noble, 1983), other characteristics of the bat, ball, hitter-bat interface and of the swing probably affected these results. Further empirical research is necessary to clarify this issue. CONCLUSIONS: Several important factors relevant to the design of baseball and softball bats were identified.: (1) how is the bat swung and how forces are transmitted to the bat during the swing, (2) what are the constraints resulting from rules in the particular sport, and (3) what mechanical properties are relevant. The most important mechanical properties of the bat are: (1) mass, (2) moment of inertia, (3) coefficient of restitution (COR), (4) vibrational properties, (5) center of ISBS'98 – Proceedings II 95。

含正交各向异性夹层的Kirsch问题的弹性解

第 39 卷第 6 期2023 年12 月结构工程师Structural Engineers Vol. 39 ， No. 6Dec. 2023含正交各向异性夹层的Kirsch问题的弹性解AHEHEHINNOU OUGBE ANSELME1，2高梦园1，2，*（1.浙江大学土木工程系，杭州 310058； 2.浙江大学平衡建筑研究中心，杭州 310007）摘要针对含有正交各向异性圆环的Kirsch问题，利用级数展开求解材料内部的弹性控制方程，获得了两种不同荷载下各向异性圆环嵌入无限基体的位移/应力解析表达式，其中圆环材料的形态分别考虑为径向各向异性、环向各向异性、横观各向同性。

在该理论退化验证良好的基础上，对各向异性材料进行力学分析。

结果表明：不同形态的圆环对孔口周围的应力分布有较大的影响。

另外，随着各向异性圆环的厚度增大，圆环和基体之间界面处的应力值也增大。

关键词拓展Kirsch问题，正交各向异性材料，二维弹性解，应力集中Elastic Solutions of Kirsch Problem with OrthogonalAnisotropic InterlayerAHEHEHINNOU　OUGBE ANSELME1，2GAO　Mengyuan1，2，*（1.School of Civil Engineering，Zhejiang University， Hangzhou 310058， China；2.Center for Balance Architecture，Zhejiang University， Hangzhou 310007， China）Abstract The elastic governing equations within the material are solved through the utilization of a series expansion for the Kirsch problem，incorporating an orthogonal anisotropic hollow layer. Analytical expressions for the displacement/stress of anisotropic hollow layers embedded in an infinite matrix are obtained for two different loads.The material morphology of the hollow layer is considered to be radially anisotropic，circumferentially anisotropic，and transversely isotropic.A mechanical analysis of the anisotropic materials is performed based on the well-verified theoretical degradation. The results show that the various configurations of the hollow layers have a great effect on the stress distribution around the orifice.In addition，as the thickness of the anisotropic circular hole increases，the stress value at the interface between the circular hole and the substrate increases.Keywords expanding the kirsch problem，orthotropic materials，two-dimensional elastic solution，stress concentration0 引言钻井工程中井壁失稳问题是比较棘手的井下事故，井壁失稳通常表现为井眼漏失和井壁坍塌［1-2］。

metal foams

On the compressive strength of open-cell metal foams with Kelvin and random cell structuresWen-Yea Jang a ,Stelios Kyriakides a ,*,Andrew M.Kraynik ba Research Center for Mechanics of Solids,Structures and Materials,The University of Texas at Austin,United States bSandia National Laboratories,Albuquerque,NM 87185,United Statesa r t i c l e i n f o Article history:Received 20January 2010Received in revised form 15June 2010Available online 23June 2010Keywords:FoamsAluminumElastic properties Strengtha b s t r a c tTwo families of ﬁnite element models of anisotropic,aluminum alloy,open-cell foams are developed and their predictions of elastic properties and compressive strength are evaluated by direct comparison to experimental results.In the ﬁrst family of models,the foams are idealized as anisotropic Kelvin cells loaded in the <100>direction and in the second family more realistic models,based on Surface Evolver simulations of random soap froth with N 3cells are constructed.In both cases the ligaments are straight but have nonuniform cross sectional area distributions that resemble those of the foams tested.The lig-aments are modeled as shear deformable beams with elasto-plastic material behavior.The calculated compressive response starts with a linearly elastic regime.At higher stress levels,inelastic action causes a gradual reduction of the stiffness that eventually leads to a stress maximum,which represents the strength of the material.The periodicity of the Kelvin cell enables calculation of the compressive response up to the limit stress with just a single fully periodic characteristic cell.Beyond the limit stress,deforma-tion localizes along the principal diagonals of the microstructure.Consequently beyond the limit stress the response is evaluated using ﬁnite size 3-D domains that allow the localization to develop.The random models consist of 3-D domains of 216,512or 1000cells with periodicity conditions on the compressed ends but free on the sides.The compressive response is also characterized by a limit load instability but now the localization is disorganized resembling that observed in experiments.The foam elastic moduli and strengths obtained from both families of models are generally in very good agreement with the cor-responding measurements.The random foam models yield 5–10%stiffer elastic moduli and slightly higher strengths than the Kelvin cell models.Necessary requirements for this high performance of the models are accurate representation of the material distribution in the ligaments and correct modeling of the nonlinear stress–strain response of the aluminum base material.Ó2010Elsevier Ltd.All rights reserved.1.IntroductionOpen-cell foams have a complex microstructure consisting of an interconnected network of ligaments that form along the edges of randomly packed cells that evolve during the foaming process.As reported in Matzke’s pioneering work on soap froth [1946],the cells are irregular polyhedra with anywhere from 11to 17faces when the foam is nearly monodisperse.In the case of solid foams,the material is concentrated in the nearly straight edges of the polyhedra and in the nodes where they intersect,usually four at a time.This microstructure gives such foams unique mechanical,thermal,acoustical and other properties (e.g.,see Hilyard andCunningham,1994;Gibson and Ashby,1997;Weaire and Hutzler,1999;Ashby et al.,2000).Connecting the microstructure to these properties is an enabling step in the design of solid foams.These objectives have been pursued by detailed studies of a class of poly-meric open-cell foams (Gong et al.,2005a;Gong and Kyriakides,2005,2006)and more recently of metallic foams (Jang and Kyriak-ides,2009I,II –referred to as J &K-09I and J &K-09II henceforth).Here we will present additional results for metallic foams.The foams under study are Aluminum (Al-6101-T6)Duocel Òopen-cell foams manufactured by ERG with relative densities of about 8%.A typical image of the microstructure of such foams gen-erated with computed X-ray tomography is shown in Fig.1.This type of foam is thought to be made using polymeric foams as tem-plates to generate a mold in which aluminum alloy is cast (see Sec-tion 2.5Ashby et al.,2000).Consequently it retains characteristics such as cell size uniformity,type of polyhedra,ligament length dis-tribution,etc.,exhibited by commercially available polymeric0020-7683/$-see front matter Ó2010Elsevier Ltd.All rights reserved.doi:10.1016/j.ijsolstr.2010.06.014*Corresponding author.Address:Research Center for Mechanics of Solids,Structures and Materials,WRW 110,C0600,The University of Texas at Austin,Austin,TX 78712,United States.E-mail address:skk@ (S.Kyriakides).foams(see comparison of geometric characteristics of polymeric and Al foams in Jang et al.(2008)).The typical compressive stress-(r11=force/undeformed area)displacement(d1/H1)response of such a foam is shown in Fig.2.It consists of a nearly linear elastic regime that terminates into a limit load(r I).This is followed by a load plateau that extends to an average strain of about50–55%,fol-lowed by a second stiff branch(densiﬁcation).The low initial stress peak and extended load plateau are responsible for the superb en-ergy absorption characteristics of such foams.In our most recent work(J&K-09I and J&K-09II)the foam microstructure was idealized using the14-sided regular cell of Kel-vin(Thompson,1887).It was demonstrated that most aspects of compressive response,such as the one in Fig.2,can be reproduced using suitable domains of this model foam.This was achieved by assigning ligament and cell geometric properties representative of those of the actual foam studied,along with the elasto-plastic properties of the Al alloy base material,to the Kelvin cell foam. The present results are a continuation of this work in which ran-dom soap froth microstructures generated using the Surface Evolv-er software(Brakke,1992)are similarly modeled.The random foam models are used to establish the elastic properties and the ‘‘strength”of such foams.The results are evaluated by direct com-parison to measured properties and are also critically compared to corresponding results from the Kelvin cell models.2.Background2.1.Review of the morphology of aluminum foamsComputed X-ray tomography was used to characterize the foam microstructure including cell size,distribution,anisotropy,liga-ment length and cross sectional area distributions as described in Jang et al.(2008).Here we will summarize theﬁndings that are re-quired in the modeling effort that follows.Three foams of the same alloy and heat treatment with nominal cell sizes of10-,20-and40-ppi and respective average relative densities(q*/q)of8.23%,7.50% and7.54%were analyzed.As can be seen in the foam image in Fig.1,the polyhedral cells are elongated in the rise direction of the polymeric foam template.Average anisotropy values k=h1/h2 of1.27,1.24and1.18are reported in Table1(h1and h2deﬁned in cell image below Table1and h1is the average height of the cells).Given in the table is also a measure of polydispersity based on the ratio of one standard deviation of the average cell height ðR h1Þnormalized by h1.The results range from0.0707to0.0754 indicating that cell size variation is small in these foams(i.e., nearly monodisperse).Furthermore,from comparisons of the microstructures of the three foams it was concluded that at least toﬁrst order they scale with cell size(Fig.5in J&K-09I).The irregular polyhedral nature of the cells is illustrated in Fig.1.As reported earlier the ligaments of these foams have round-er convex boundaries(see Fig.11in Jang et al.(2008)).The areas of many ligament cross sections A(n)were measured digitally as a function of the axial position n=x/‘and the results wereﬁtted with the following symmetric expression(Fig.14of Jang et al. (2008)):AðnÞ¼A o fðnÞ¼A o36n4þn2þ1ÀÁð1ÞA o in turn was found to vary with ligament length in the manner shown in Fig.15of Jang et al.(2008).(The normalizing values o and ‘for each foam and their standard deviations are listed in Ta-ble1.)The measurements wereﬁtted as follows:A oðgÞ¼o gðgÞ¼o0:6633þ0:2648gÀ2:5963ÀÁ;g¼‘= ‘ð2Þpression experiments2.0Â2.0Â2.0in(51Â51Â51mm)specimens were extracted from large blocks of foam using a computer operated wire EDM system.The process minimizes distortion along the cut edges and improves the parallelity of the two loaded surfaces.In order to minimize the inﬂuence of the edges on the initial response,Al alloy plates were bonded to the two surfaces that were subse-quently loaded.The specimens were compressed between parallel platens in a stiff electromechanical testing machine run under dis-placement control.The typical displacement rate was_d=H¼8:3Â10À4sÀ1(corresponds to the strain rate when the deformation is homogeneous;H=height of the specimen).Because the foam den-sity varied slightly within the mother foam blocks the relative den-sities of individual specimens will be reported(see Tables2and3).Fig.3shows the early parts(d/H60.12)of a pair of representa-tive stress–displacement responses obtained from rise and trans-verse direction compression tests on10-ppi foam specimens.The rise direction response is seen to exhibit an initial nearly linear part during which the deformation is essentially homogeneous. At approximately a stress of300psi(2.07MPa)bending andSolids and Structures47(2010)2872–28832873stretching cause plastiﬁcation in some of the ligaments and the material stiffness becomes progressively smaller.Indeed a stress maximum develops at a stress of 396psi (2.73MPa)after which the stress drops to a local minimum and then follows a relatively ﬂat stress plateau until the crushing has consumed the whole spec-imen or the material has densiﬁed (see Fig.2).The stress maxi-mum,henceforth called initiation stress (r I 1)or the foam strength ,represents the onset of localized deformation associated with buckling of ligaments in localized bands.This is demonstrated in Fig.4that shows the undeformed ({)and two deformed images obtained using X-ray tomography.The images show a slice of the material approximately 6mm thick in a neighborhood that devel-ops an inclined band of initially buckled ligaments that later lead to the collapse of the affected cells.Image r was taken at d /H =10%in order for the ligament buckling and cell crushing inTable 1Table 2Measured mechanical properties of Al-6101-T6foams in the rise direction.Exp.No.q Ã=q (%)E Ã1=E (%)r I 1psi (MPa)(a)10ppi,k =1.27R10–18.330.865396(2.73)R10–28.790.857456(3.14)R10–38.630.863446(3.08)R10–48.480.871396(2.73)(b)20ppi,k =1.24R20–18.260.705352(2.43)R20–27.470.677283(1.95)R20–38.430.779379(2.61)R20–48.370.857369(2.54)(c)40ppi,k =1.18R40–17.980.660339(2.34)R40–28.200.746360(2.48)R40–38.240.780393(2.71)R40–48.180.733406(2.80)E =104ksi (69GPa),m =0.3.Table 3Measured mechanical properties of Al-6101-T6foams in the transverse direction.Exp.No.q Ã=q (%)E Ã2=E (%)r I 2psi (MPa)(a)10ppi,k =1.27T10–18.560.466290(2.00)T10–28.480.493298(2.05)T10–38.740.527333(2.30)(b)20ppi,k =1.24T20–17.360.459297(2.05)T20–27.670.426308(2.12)T20–37.700.479309(2.13)(c)40ppi,k =1.18T40–18.220.570294(2.03)T40–28.030.506323(2.23)T40–38.030.538289(1.99)E =104ksi (69GPa),m =0.3.2874W.-Y.Jang et al./International Journal of Solids and Structures 47(2010)2872–2883ilar plots of the elastic moduli EÃ1and EÃ2appear in Figs.14(a)and21(a)of J&K-09I respectively).3.Modeling of the foamsThe Al foams studied will be modeledﬁrst by adopting the per-fectly ordered structure,based on Kelvin’s14-sided cell shown in Fig.7loaded in the<100>and<010>directions,henceforth re-ferred to as‘‘Kelvin”(also used in J&K-09II and previously by Gong and Kyriakides(2005)and Gong et al.(2005b)in the modeling of polymeric foams).The second model used consists of clusters of Kelvin cells with randomly perturbed vertices;it will be referred to as‘‘perturbed Kelvin.”Here the coordinates of all the nodes of aﬁnite size do-4.The initial and two deformed conﬁgurations corresponding to the direction compressive response R10–4shown in Fig.3.Note the bending buckling of ligaments in conﬁgurations r and s.main of Kelvin cells are perturbed as follows.The position vector in the perturbed conﬁguration,x,is given by:x¼x oþp n‘;06n i60:5;i¼1;3ð3Þwhere x o is the initial position vector of a node,x is the perturbation and p is a normally distributed random number betweenÀ0.5and 0.5(in the results that follow n i=n o,i=1,3).The disturbance ap-plied to the nodes on opposite faces of the domain is chosen so as to accommodate periodic boundary conditions(see Jang et al., 2008for more details).The most realistic models analyzed are based on the micro-structure of random spatially periodic soap froth simulated with Brakke’s Surface Evolver(1992)(Kraynik et al.,2003),and is re-ferred to as‘‘random.”As reported in Jang et al.(2008),the process generates a foam skeleton that is very representative of actual foam microstructures as demonstrated in the cluster of cells shown in Fig.8(a).In other words,the types of polyhedra present in the model,the distribution of different polygonal cell faces,and the distribution of ligament lengths compare very well with measure-ments made in polymeric foams.(Appendix A presents an outline of the numerical steps involved in generating such random foams). Details of the main geometric characteristics of the models follow.3.1.Ligament geometryThe ligaments in all models will be assumed to have circular cross sections(radius R)with the area distribution given in(1) (see J&K-09II for justiﬁcation).3.2.AnisotropyAnisotropy is introduced to the three model foams as follows. All ligaments with a projection in the x1-direction are elongated so that this projection is ampliﬁed by the factor k while the projec-tions in the x2-and x3-directions remain the same.Thus,for exam-ple,the Kelvin cell height becomes h1¼2ﬃﬃﬃ2p‘tan a while the width remains h2¼2ﬃﬃﬃ2p‘,whereh1h2¼tan a¼kð4Þas shown in Fig.7(see also Dement’ev and Tarakanov,1970b;Gong and Kyriakides,2005).Fig.8(b)shows how an anisotropy of k=1.3 alters the cluster of random cells shown in Fig.8(a).3.3.Correction for the volume of material in the nodesWhen ligaments are modeled as beams that connect four to each node,the ends of the beams overlap.Jang et al.(2008)re-moved the overlap material by cutting the ends of the beams (see Refs.for details).With this correction,the relative density re-lates to the ratio of the radius at mid-span of ligaments,R o,and the length,‘,throughqÃq¼kR onð5Þwhere n depends on the anisotropy(n–2).Table4lists k and n for anisotropy values16k61.3.For a foam of a required density and anisotropy R o is evaluated from Eq.(5)using the ligament length of the initial isotropic Kelvin cell.A o depends on‘,which is introduced in the following approx-imate manner.The average length of all ligamentsð ‘Þin any model isﬁrst calculated.The lengths are then grouped into those longer and those shorter than ‘,and the average length of each category ð ‘1; ‘2Þis established.The two average lengths are then used in Eq.(2)to establish corresponding values for A o.The effect of this change on the foam density,if any,is not considered.2876W.-Y.Jang et al./International Journal of Solids and Structures47(2010)2872–28833.4.DiscretizationThe ligaments are discretized withﬁnite elements within the nonlinear code ABAQUS using the B32,3-node quadratic space beam element.Each ligament is represented by8elements of uni-form cross sectional area that is based on A=A o f(n)as deﬁned in the empiricalﬁt of the measurements in Eq.(1).The values of f(n)used are listed in Table5.B32elements are shear deformable as they include the strain energy due to transverse shear as follows (see ABAQUS manual for details):U s¼Z1=2À1=2bV2ðnÞ‘d n where b¼AIyZzQ2ðzÞdzð6ÞThe second integral is over the cross section of the ligament(Fig.5 in J&K-09II)with Q being theﬁrst moment of area about the y-axis and b(z)the width;for circular cross sections b=10/9(V is the shear force and U s the strain energy due to shear).4.ResultsWe now use the three models outlined in Section3to predict the initial compressive response in the rise and transverse direc-tions.The calculations will be terminated soon after the expected initial load maximum that represents the strength of the foam is reached.The material is elasto-plastic with the stress–strain re-sponse of the Al-6101-T6alloy measured in a tensile test on a rod cast together with the foams tested(Ramberg–Osgoodﬁt parameters E=104ksi(69GPa),r y=28ksi(193MPa),n=48;see also Fig.2in J&K-09I).4.1.Kelvin cell modelAs has been shown in the past,because of the regularity of this idealized microstructure several of the mechanical properties of interest can be evaluated by considering just the characteristic cell(e.g.,Dement’ev and Tarakanov,1970a;Warren and Kraynik,1997; Zhu et al.,1997;Laroussi et al.,2002;Gong and Kyriakides,2005; Gong et al.,2005b;Mills,2007;Jang et al.,2008).It is thus natural to start by compressing the fully periodic characteristic cell shown in Fig.9in which the ligaments have been assigned the geometric characteristics described in Section3.Furthermore,in theﬁrst cal-culations a generic foam is considered with a relative density of q*/q=0.08and an anisotropy of k=1.2both of which approxi-mately represent the average values of the three foams tested.The cell isﬁrst compressed in the rise direction by prescribing incrementally the relative displacement(D d1)between the upper and lower periodic boundaries.The average stress r11required to produce this deformation is the force divided by the initial cross sectional area of the cell(h2Âh2).Fig.10(a)shows the calculated stress-displacement response.The stress is normalized by the ini-tial elastic modulus of the foam,EÃ1,and the shortening,d1,by the height of the domain Nh1(N=1for this case).The initial part of theresponse is nearly linear with modulus EÃ1which is in very good agreement with measured values.The ligaments experience com-bined axial compression and bending that eventually cause the material to yield.Thus,in the neighborhood of point a inelastic ac-tion causes the response to become progressively softer.The pro-gressive reduction in stiffness eventually results in a load maximum at point b(normalized stress and strain values {5.06Â10À3,0.0161}).Beyond this point(bc’),the single cell re-sponse has a negative slope indicating that localization may be possible in a larger domain.The corresponding cell response for a linearly elastic material is drawn in theﬁgure with a dashed line(oab’).It bifurcates into a long wave mode at a stress of r1Ce¼0:163EÃ1and strain of0.262, values that are much higher than those of the limit stress(see Fig.7in J&K-09-II).By contrast,when the actual elasto-plastic stress–strain re-sponse of the Al alloy is used in the calculations no bifurcationisdetected between point a and the load maximum at b (the Bloch-wave method is used to check for possible bifurcations—Gong et al.,2005b ).A limit load instability in the response of a character-istic cell implies that in a larger domain localized modes of defor-mation may be preferred.This possibility is investigated by considering a larger domain that is one characteristic cell thick and has 5Â6cells in the x 1Àx 2plane.The domain has periodic boundaries at the top and bottom as well as the front and back but the two vertical sides are left free.The response of this domain,drawn in red 1color in Fig.10(a),coincides with that of the unit cell up to the local load maximum (point b ).At higher displacements it traces a lower trajectory associated with localized shear buckling of two diagonal bands as shown in the deformed conﬁguration in Fig.10(b)(i)that corresponds to d 1/5h 1=0.05(see similar results in Luxner et al.(2007)).Although always along the diagonals,theTable 4Fit parameters for correcting the relative density of Al foams with Eq.(5).k n k 1.00 1.7072 2.02631.10 1.7131 1.95431.20 1.7189 1.89851.301.72501.8561Table 5Cross-sectional area of beam elements in the foam ligaments.n af (n )06j n j 60.210.2<j n j 60.3 1.1720.3<j n j 60.4 1.6630.4<j n j 60.53.227aÀ1/26n (=x /‘)61/2.1For interpretation of colour in ﬁgures,the reader is referred to the Web version of this article.localization patterns were shown in J&K-09II to depend on the do-main size.Fig.10(b)(ii)shows the deformed conﬁguration at the same displacement(d1/6h1=0.05)for a6Â9cells domain.Clearly the localization patterns are different from those of the smaller do-main in image(i).This difference does not affect the response up to the limit load but was shown to affect to some degree the part of the crushing response that immediately follows it.The behavior observed has similarities to that of laterally loaded polymeric honey-combs reported in Papka and Kyriakides(1998).A difference is that in that problem the limit load was induced by a plastic bifurcation that led to localized collapse of horizontal rows of cells(see also Tri-antafyllidis and Schraad,1998).The unit cell was used to perform similar calculations for vari-ous foam densities in the range of interest keeping the anisotropy at k=1.20which is close to the average of the values of the foams tested(see Table1).Predictions of the strength(r I1)are included in Fig.6(a)where they are seen to be in good agreement with the measured values.Similar calculations were performed for compression in the transverse direction.Because of the anisotropy the material stiff-ness and strength are lower than those in the rise direction.How-ever,the nature of the response is very similar and the strength can again be predicted using the unit cell.Numerical values of the transverse direction strength(r I2)are plotted in Fig.6(b)where they are seen to be in good agreement with the experimental re-sults.In summary,as reported in J&K-09II,the strengths of this Al foam can be evaluated with accuracy using the characteristic Kelvin cell.In such calculations the strength of the material ap-pears as an initial load maximum in the compressive response. 4.2.Perturbed Kelvin cell modelThe perturbed Kelvin cell models that will be considered have three-dimensional domains with{6Â5Â6}cells with periodic boundaries at the top and bottom but free lateral sides.Such a do-main isﬁrst generated using regular Kelvin cells with the required anisotropy.The nodes of the cells are then perturbed randomly (amplitude n o)in the manner described in Section3.Three-dimen-sionality does not change the behavior in the early part of the re-sponse but,as we reported in J&K-09II,affects the onset of densiﬁcation,which is beyond the scope of the current work.Cal-culations were performed for models with the generic values of relative density and anisotropy of q*/q=0.08and k=1.2,and three values of the perturbation amplitude n o=0.05,0.10,0.15.The cal-culated rise direction stress-displacement responses are shown in Fig.11(a)together with the one from the perfect microstructure. The responses are similar to those of the perfect structure.Interest-ingly,the limit stress is quite insensitive to this geometric imper-fection but the trough that follows and the subsequentstressUnit Cell(i)(ii)Solids and Structures47(2010)2872–28832879undulation are inﬂuenced by n o.Increasing n o reduces the depth of theﬁrst trough as well as the amplitude of the undulations.(It is pointed out that because of the randomness of the applied pertur-bation,responses corresponding to the same n o can differ slightly.)A possible explanation for this change can be seen in the compar-ison of the initial and two deformed conﬁgurations of the perfect case with ones from a case with n o=0.15in Fig.11(b).The pertur-bation of the nodes tends to break up the symmetry of the banded collapse localization of the perfect case.Instead,cell buckling and collapse are more randomly distributed and this tends to‘‘smooth”the response.Compression of perturbed domains in the transverse direction has similar effects on the calculated responses and consequently speciﬁc responses will not be presented.Perturbed Kelvin domains with n o=0.15were used to evaluate the elastic moduli and strengths of foams in both directions.It should be noted that be-cause of the randomness of the perturbation such results vary slightly from case to case.For this reason,the values that will be quoted represent averages of10sets of calculations.The predicted elastic moduli are slightly higher than the values predicted by the regular Kelvin model(see comparisons in Jang et al.(2008)).Pre-dictions of the strengths in the two directions are included in Fig.6(a)and(b).In both directions they are just slightly higher than the regular Kelvin model strengths.4.3.Random foam modelThe main random foam model that will be used has a cubical domain with{8Â8Â8}cells.Anisotropy is introduced by elongat-ing all cells in the x1-direction in the manner described in Sec-tion3.2.The ligaments are then‘‘dressed”with solid beams in the manner described in Section3.4.For chosen values of density and anisotropy and the average length of all ligaments in the mod-el,the cross sectional area A o at mid-span of each ligament is cal-culated from Eq.(5).Subsequently the length dependence of A o is introduced using Eq.(2)and the scheme described in the last par-agraph of Section3.3.Guided by the behavior observed in the Kel-vin cell model in calculations of the response including the anticipated load maximum,the two surfaces of the block that are compressed are made to be periodic while the four sides are left free.2880W.-Y.Jang et al./International Journal of Solids and Structures47(2010)2872–2883The model isﬁrst evaluated by direct comparison to the re-sponse from Exp.R40–4in which the foam had a relative density of0.082and an anisotropy of1.18.Fig.12(a)shows a comparison of the measured stress–displacement response and the one calcu-lated up to a value of d1/H1=10%(H1is the height of the domain). The predicted response follows the experimental one quite closely. It exhibits a limit load at a stress and strain of{423psi,1.64%}, which compare with{406psi,1.65%}from the experiment.The two responses also agree quite well beyond the limit load although at values of average strain corresponding to the local minimum and beyond the numerical results are no longer dependable as con-tact of ligaments in the collapsing cells commences which is not in-cluded in the random model calculations.Fig.12(b)shows two deformed conﬁgurations of the skeletal version of the compressed model.The deformation measure found to best represent the localization that develops is the magnitude of the‘‘rotation”of the beam ligaments.The rotation is calculated in each node of the beams while between two nodes the values are interpolated.The code stores the three components of a rotation vector/for all nodes.The vector/is deﬁned by amplitude/ =k/k and a rotation axis P=//k/k.The rotation vector/then con-sists of a rotation/(radians)around the axis P.Drawn in color in the deformed conﬁgurations is the magnitude of/.Conﬁguration r is a frontal view of the foam block analyzed at d1/H1=4.58%. The rotation distribution indicates that localized deformation along inclined directions has developed.The localization is more pronounced in conﬁguration s that corresponds to d1/H1=9.03% (shown for illustrative purposes only as some ligament contact would have commenced by this point).The localization is seen to form along inclined directions but the patterns are disorganized and vary through the depth of the block.The patterns seen differ signiﬁcantly from those in the Kelvin cell domain in Fig.11(b);in-deed they much more resemble crushing patterns seen in the experiments reported in J&K-09I.Since the vertical sides of the domain analyzed are free,the sen-sitivity of such responses to the domain size must be considered.To this end cubical random microstructure domains of different sizes were generated in approximately the same manner.The skeletal domains wereﬁrst elongated in the x1-direction to an anisotropy of k=1.2and made into foams with relative density of8.0%by dressing them with appropriate beams as described earlier.The models were then compressed in the same manner as the case de-scribed above.It must be pointed out that no two such random microstructures are the same.Consequently,the responses of any two such models of the same size are never the same.For this rea-son several models of the same size were considered in order to establish the trend.Fig.13shows a comparison of the compressive responses from three representative models with{10Â10Â10}, {8Â8Â8}and{6Â6Â6}cells.The results show that there is a stiffening effect as the domain size increases primarily because the role of the free edges becomes less important as the domain vol-ume increases.For the results shown,the elastic modulus EÃ1for the 103model is3.1%higher than the83model while the value for the 63model is7.4%lower.The stress maximum,r I1,increases with size also,so for the larger domain it is5.6%higher than the83model and for the smaller one it is5.1%smaller.As pointed out these re-sults can be viewed as averages of several runs for each domain size.83cell models are now used to conduct a limited parametric study of random foams.In an effort to best represent an inﬁnite foam medium,when calculating the elastic moduli the cubical do-main is made to be fully periodic(as was done in Jang et al.(2008)). Thus,for example for q*/q=8.0%this scheme yields EÃ1and EÃ2val-ues that are respectively10.9%and12%higher than the corre-spondingﬁnite size domains.This difference tends to decrease as the domain size considered increases.Predictions for the rise-and transverse direction moduli for various relative density values in the range of interest are included in Fig.29of Jang et al.(2008). They are somewhat higher than the predictions from the Kelvin cell model for both directions but lie within the scatter of the experimental results.Calculations of the initiation stresses were performed using the same83cell models with the four lateral sides were left free.W.-Y.Jang et al./International Journal of Solids and Structures47(2010)2872–28832881。

VS2010自动化整理代码（1）

VS2010自动化整理代码（1）展开全文VS2010 自动化整理代码（1）--- VS 正则表达替换 PK Vim自从开始在VS2010的IDE 中开始用正则表达式修改最近为了给Fortran 找个好一点的编辑器，又开始使用Vim 了。

Vim 是久负盛名的编辑器之神，可我们习惯了Visual Studio 的智能提示等方便的操作，就总在琢磨要是VS1. VS 正则表达替换 PK Vim这是善用佳软中的一篇教程：《普通人的编辑利器——Vim 》挺简单易懂的/s/blog_46dac66f010005kw.html###挺老的文章，例子是整理“八荣八耻”的文本，恩，06年的。

测试的文本在这 /pcedu/soft/gj/photo/0609/pic/test .txt1 坚持以热爱祖国为荣、以危害祖国为耻，以服务人民为荣、以背离人民为耻，以崇尚科学为荣、以愚昧无知为耻，以辛勤劳动为荣、以好逸恶劳为耻，以团结互助为荣、以损人利己为耻，以诚实守信为荣、以见利忘义为耻，以遵纪守法为荣、以违法乱纪为耻，以艰苦奋斗为荣、以骄奢淫逸为耻。

Vim 的整理方式在善用佳软中有详细的介绍，Ok ，看看VS2010下怎么快速整理。

一排字没有分行，先给每句话分行。

Ctrl+F 到查找，快速替换--勾选：使用正则表达式1 2 3 为..替换为：\0\n1 好了，看到效果了，瞬间全部替换成竖排了为.. 表示“为“后面跟着2个单个字符\0 表示被替换的全部内容，也就是”为..”,\n 是换行不用说了。

其实单击右面的小箭头常用的替换格式就会列出来，最下面还有微软完整的替换帮助然后替换标点什么的就不用说了。

列操作可以 Alt+鼠标左键，也非常方便。

按下Ctrl+R，Ctrl+W 显示空格和换行（再次按下关闭显示），我们添加注释符号再向后平移几个空格那条蓝线就是同时为下面选中的一列同时添加。

为了在不同的编辑器中能够良好的注释对齐，可以在VS中自动用空格表示Tab工具--选项--文本编辑-- 选择对应的语言--制表符这样按Tab键就能缩进指定的空格数。

BZOJ2007LG2046「NOI2010」海拔平面图最小割转对偶图最短路

BZOJ2007LG2046「NOI2010」海拔平⾯图最⼩割转对偶图最短路问题描述题解发现左上⾓海拔为 0 ，右上⾓海拔为 1 。

上坡要付出代价，下坡没有收益，所以有坡度的路越少越好。

所以海拔为 1 的点，和海拔为 0 的点，⼀定能够在这个⽹格图中由⼀条连续的线划分为两个集合。

将⼀个图中的所有结点划分为两个集合，显然为最⼩割模型。

⼜发现是⽹格图，所以平⾯图最⼩割转化为对偶图最短路。

Code不删调试见祖宗#include<bits/stdc++.h>using namespace std;const int maxn=500*500+3;int n,S,T;int Head[maxn],to[maxn*5],Next[maxn*5],w[maxn*5],tot=1;int fr[maxn*5];void add(int x,int y,int z){fr[++tot]=y,to[tot]=x,Next[tot]=Head[y],Head[y]=tot,w[tot]=z;}int id(int x,int y){return (x-1)*n+y;}void Init(void){scanf("%d",&n);}void WestToEast(void){for(int i=1,x;i<=n;i++){scanf("%d",&x);add(id(1,i),S,x);}for(int i=2;i<=n;i++){for(int j=1,x;j<=n;j++){scanf("%d",&x);add(id(i,j),id(i-1,j),x);}}for(int i=1,x;i<=n;i++){scanf("%d",&x);add(T,id(n,i),x);}}void NorthToSouth(void){for(int i=1,x;i<=n;i++){scanf("%d",&x);add(T,id(i,1),x);for(int j=2;j<=n;j++){scanf("%d",&x);add(id(i,j-1),id(i,j),x);}scanf("%d",&x);add(id(i,n),S,x);void EastToWest(void){for(int i=1,x;i<=n;i++){scanf("%d",&x);add(S,id(1,i),x);}for(int i=2;i<=n;i++){for(int j=1,x;j<=n;j++){scanf("%d",&x);add(id(i-1,j),id(i,j),x);}}for(int i=1,x;i<=n;i++){scanf("%d",&x);add(id(n,i),T,x);}}//n lines//n+1 every-linevoid SouthToNorth(void){for(int i=1,x;i<=n;i++){scanf("%d",&x);add(id(i,1),T,x);for(int j=2;j<=n;j++){scanf("%d",&x);add(id(i,j),id(i,j-1),x);}scanf("%d",&x);add(S,id(i,n),x);}}void debug(){printf("\n### S = %d\n",S);printf("### T = %d\n\n",T);for(int i=2;i<=tot;i++){printf("*** From %d To %d , val = %d\n",fr[i],to[i],w[i]); }}void Graph_build(void){S=n*n+1,T=S+1;WestToEast();NorthToSouth();EastToWest();SouthToNorth();}int dis[maxn];bool vis[maxn];#define pii(x,y) make_pair(x,y)void dijkstra(void){memset(dis,0x3f,sizeof(dis));priority_queue<pair<int,int> >q;q.push(pii(0,S));dis[S]=0;while(!q.empty()){int x=q.top().second;q.pop();if(vis[x]) continue;vis[x]=1;if(x==T) return;for(int i=Head[x];i;i=Next[i]){int y=to[i];if(dis[y]>dis[x]+w[i]){dis[y]=dis[x]+w[i];q.push(pii(-dis[y],y));}}void Work(void){Graph_build();#ifndef ONLINE_JUDGE// debug();#endifdijkstra();printf("%d\n",dis[T]);}int main(){#ifndef ONLINE_JUDEG// freopen("hzlbn.in","r",stdin); #endifInit();Work();return 0;}Processing math: 100%。

屈服与破坏准则

Z-P准则在p-q子午面屈服曲线
C-M准则的形状函数为：
g( ) 2(
3 sin 3 cos sin sin )
满足这些条的 g( )设置为：
g (
)
(1
K)
2K (K 1) sin
3
--(4-3-5)
1
式4-3-5
两者在偏平面上的图（图3）可见设置 g( )
就是将C-M准则在偏平面上的六角抹去。
2. 评价结果
表4-1 Mises屈服破坏准则评价结果
表4-2 D-P屈服破坏准则评价结果
五． Mises 准则与 Drucker-Prager准则
Coulomb-Mohr条件
smooth Z-P准则
Mises准则
Tresca准则
拟合C-M得系数
D-P准则
广义Tresca准则
图1-1 典型岩土应力-应变曲线
图1-2 屈服曲面、加载曲面和破坏曲面
提问：那为什么本章屈服准则没有破坏面？
2. 三个主应力或三个应力不变量都对屈服或破坏有影响。在弹性力学和传统塑性理论中，只有应力偏量与塑性部分有关。但岩土试验表明，塑性变形既与应力偏量有关，也与应力球张量有关，岩土的球应力与偏应力之间存在着交叉影响。
图1-7 单向拉压时的硬化模型
结论：S-D校应是岩土材料的固有属性，包辛格改变了材料的内部结构。在经过拉伸塑性变形后改变了材料内部的微观结构，使拉伸屈服应力提高压缩屈服应力降低；同样经过压缩塑性变形后压缩应力提高，拉伸应力降低的现象叫包辛格（Bauschinger）效应。当然这是以金属材料为试验标本。
本节重点:
各屈服破坏准则的评价标准，评价结果；各屈服破坏准则之间的相互关系。

一种基于混沌映射的抗剪切的数字水印算法

一种基于混沌映射的抗剪切的数字水印算法
高婷婷;廖晓峰;桑军
【期刊名称】《计算机科学》
【年(卷),期】2005(32)1
【摘要】本文提出了一种基于混沌映射的空域数字水印算法.利用混沌系统产生的混沌信号在载体图像中随机选取要嵌入水印的点,考虑人类视觉系统(HVS)的特性,并结合这些点的自身特征,在这些点上自适应地嵌入水印.本文的水印是由Logistic 映射产生的一个随机序列.由于算法是在空域上进行水印嵌入的,因此计算较快,实时性较好.同时又充分利用了HVS特性,水印的不可见性得到了很好的保证.实验结果表明该算法对剪切攻击具有较好的鲁棒性.
【总页数】3页(P116-117,124)
【作者】高婷婷;廖晓峰;桑军
【作者单位】重庆大学计算机学院,重庆,400044;重庆大学计算机学院,重
庆,400044;重庆大学计算机学院,重庆,400044
【正文语种】中文
【中图分类】TP391.41
【相关文献】
1.一种抗剪切的DWT域多重音频数字水印算法 [J], 谢斌;肖玲玲;吴君钦
2.一种基于混沌映射和奇异值分解的数字图像水印算法 [J], 焦问;丁文霞
3.基于混沌映射的抗剪切鲁棒水印算法 [J], 唐国坪;廖晓峰
4.一种基于共轭混沌映射的数字水印算法研究 [J], 张伟;廖晓峰;韦鹏程;杨华千;黄松
5.一种基于混沌映射与SVD的数字水印算法 [J], 张有矿;杨峰
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2010年国家公务员考试申论真题省级以上（含副省级）综合管理类给定资料：1．全球海洋面积大约3.6亿平方公里，占地球面积的71%。

一般认为海洋资源包括旅游、可再生能源、油气、渔业、港口和海水六大类。

根据国务院2003年5月9日颁布的《全国海洋经济发展规划纲要》，我国有海洋生物两万多种，其中，海洋鱼类3000多种。

天然气资源量14万亿立方米，滨海砂矿资源储量31亿吨。

海洋可再生能源理论贮藏量6.3亿千瓦，海洋石油资源量约240亿吨。

联合国亚洲及远东经济委员会对包括钓鱼岛列岛在内的我国东部海底资源进行勘察，得出的结论是：东海大陆架可能是世界上最丰富的油田之一。

据我国科学家估计，钓鱼岛周围海域石油储量大约30亿到70亿吨。

据有关部门测算，整个南海发现的石油地质储量大约230亿至3000亿吨，约占我国总资源量的三分之一，有第二个“波斯湾”之城。

南海海域是世界上尚待开发的大型油藏之一，其中一半以上的储量分布在应归中国管辖的海域。

国家海洋局某负责通知指出，要看过我国海洋资源这些数字相对于我国庞大的人口规模来说是非常有限的。

他说，衡量一个国家的海洋资源优势通常有三个指标：第一个指标是人均管辖海域面积。

从这个指标上来看，我国在世界的排名大概是120名左右；第二个指标是海陆面积比。

我国这个比值是0.31︰1，世界排名大概100多一点；还有一个指标是海岸线长度和国土面积比。

这个比值我国在世界的排名90多位。

渤海是我国唯一的半封闭型内海，总面积7.7万平方公里，海岸线3784公里，素有我国“鱼仓”、“盐仓”和：“海洋公园”的美誉。

渤海是中国北方经济社会发展的生命线，上世纪80年代以来，随着环渤海地区经济的快速发展和开发力度加大，渤海的污染日益加剧。

濒临渤海的二界沟是某市最大的渔港，过去成立的海鲜商贩和饭店伙计基本上都到这里来上海货。

可眼下，尽管离休渔期还有一个月，但很多穿都停靠在码头没有出海。

“去年上冻之前，船上坞，一直停到现在。

”一位码头管理人员告诉记者，因为污染，渤海的鱼越来越少，许多渔民都不愿出海了。

有些大船一停就是半年，只有零星几条小船还出海打渔。

正说话间，一条出海的渔船回来了。

记者：“出去多长时间了？弄到啥了？”船老大：“哪有鱼啊，两天就那点虾爬子。

”记者：“是不是你这船不行，不能到远的地方去？”船老大：“这船能跑十多海里呢，远处也没什么货，油用的多，赔的更多嘛。

”船老大告诉记者，出去两天，走了5海里，打上来的东西也就卖个几百块钱。

可工钱、油钱、再加吃喝，一天就得一千块钱，倒赔。

船老大：“三四年前这个季节，我一网下去就能上来四五百斤虾爬子，真能致富啊！可好景太短啦。

眼前这些小的可怜的海货只配作饲料，卖不上价钱。

”根据某水产研究所的调查，1983年渤海鱼类有63种，2004年只有30种，带鱼、鳓鱼、真鲷、银鲳等几乎绝迹。

2007年，渤海实施监测的100个入海排污口中，有91个排污口超标排污，超标排污所占比例居渤海、黄海、东海、南海四大海域之首。

调查显示，2003年至2007年，渤海全海域未达到清洁海域水质标准的面积年均2.25万平方公里，约占总面积的29%。

主要污染物位无机氮、活性磷酸盐和石油类。

污染物主要来源于陆源排污、河流输入和海上养殖业。

近年来，渤海海域赤潮发生的频率和规模逐年上升。

2000年至2007年，发生赤潮87次，累计赤潮面积2.05万平方公里，赤潮已经成为渤海海域主要海洋灾害之一。

权威部门指出，如果不采取果断措施，渤海将在十几年后变成“死海”。

那时，即使不向渤海输入一滴污水，单靠其与外界水体交换恢复清洁，至少也要200年。

实际上，从世界范围看，海洋及其资源的破坏，波及面积相当大，其原因不单是污染，还包括过度捕捞、天海造地、盲目攫取海底能源等等。

海洋的污染将毁灭鱼儿的家园，但让人类不寒而栗的毁灭绝非仅此而已！008年11月，国务院批准了《渤海环境保护总体规划（2008-2020年）》，规划确定了加强重点环节和关键领域保护与防治，建立渤海污染防治与生态保护系统：面源点源制防联动，建立陆域污染源控制和综合治理系统；全面实施节水治污战略，建立流域水资源和水环境综合管理与整治系统等五大主要建设任务，体现了渤海环境保护任务的综合性、战略性与长期性，并强调在海洋开发过程中，全面推进节水、节能、节地、节才和综合以用，确保引进项目为低消耗、低排放、低污染和高效益的企业和产品，促进海洋环境的可持续利用。

2．2009年4月，中共中央总书记，国家主席胡锦涛在视察沿海某省时提出“要大力发展海洋经济，科学开发海洋资源，培育海洋优势产业，打造搬到蓝色经济区。

”截止2008年，我国海洋经济总产值接近3万亿元，占GDP总量的9.87%，并且提供了数以千万计的就业岗位。

我国沿海已初步形成包括环渤海、长三角、珠三角在内的“三大五小”的经济区域整体布局，为进一步发展海洋经济奠定了坚实基础。

据预测，到2010年，我国海洋生产总值占国内生产总值比重有可能达到11.11%，2020年将达到15.84%。

与传统海洋经济相比，承载蓝色经济发展的经济区，是以海洋、临港、涉海产业发达为特征，以科学开发海洋资源、保护生态环境为导向，以优势区域产业为特色，以经济社会生态协调发展为前提，既有较强综合竞争力的经济功能区。

格局《实施集中集约用海打造半岛蓝色经济区草案》，蓝色经济区将被打造成为黄河流域出海大通道经济引擎、环渤海经济圈南部隆起带、贯穿东北老工业基地与长三角经济区的枢纽、中日韩自由贸易先行区。

但是，该省目前存在着实施“集中集约用海”的障碍，所谓“诸侯经济”发展态势明显，沿海各地申请的用海项目大都局限于本地区经济社会发展的需求，“诸侯经济”催生的“诸侯港口、诸侯电厂”遍地开花，重复建设及海岸线资源浪费严重，打造半岛蓝色经济区则有望打破这一瓶颈。

该省知名专家W分析：“如果从全国乃至全球发展的大格局上来审视，需要明确一个在国内外具有核心竞争力的重大战略；放在黄河流域来定位，则需要一个便捷的出海大通道和能带动整个流域发展的龙头。

”他认为：“把半岛蓝色经济区建设成为黄河流域的大港口、大交通、大钢铁、大能源、大电力、大石化、大造船基地，将拉动整个黄河流域社会经济迅猛崛起……半岛蓝色经济区的战略定位并非仅仅成为黄河流域经济发展的龙头，要争取把半岛蓝色经济区纳入国家发展战略。

”目前，环渤海地区的天津滨海新区、河北曹妃甸工业区等都陆续进入国家战略。

曹妃甸地处唐山市南部沿海，它依托唐山雄厚的产业基础和京津等大城市的区位、人才优势，发展潜力极大。

根据国家批准的《曹妃甸循环经济示范区产业发展总体规划》，其工业区确定的功能定位是：能源、矿石等大宗货物的集疏港、新型工业化基地、商业性能源储备基地和国家级循环经济示范区。

W呼吁；“我省也必须积极争取国家重大政策支持，为今后的经济发展定位一个高起点。

另一方面，环渤海地区的产业集聚能力已经相当高，为我省环渤海区域经济发展带来了不可多得的机遇。

有识之士都赞成把原来分散的海洋经济区域整合起来，打造一个产业集聚区，最大程度地实现资源优势互补，在半岛地区形成具有核心竞争力的产业集群。

据悉，该省拟打造蓝色经济区主体区“两城七区”，包括两个海上新崛以及重化工集聚区、机械制造业集聚区、海洋装备业集聚区、海洋化工业集聚区、海洋高新科技产业集聚区、海洋新能源产业集聚区、石油产业集聚区等7个工业区。

“两城七区”的功能定位有交集，但是主导产业在其原有发展的基础上各有所异，海洋高科技产业在半岛蓝色经济去产业中的比重将得到大幅提高，以实现开发与保护并重的目的。

3．日本濑户内海是半封闭的内海，曾是天然的鱼仓，日本列岛最富足的海湾。

上世纪40年代末，日本为权全力发展经济，将濑户内海沿岸选为最重要的工业基地，此后，这里便逐渐成为工业部门的下水道，工厂把未经处理的工业废水随意排入内海。

1955年以后，濑户内海的污染日甚一日，原来十几年一次的赤潮，后来发展到一年几百次，鱼虾绝迹。

在这个过程中，发生了震惊世界的水俉病，熊本县水俉湾的老百姓吃了从濑户内海中捕捞的被高毒性的汞污染的海产品，导致痴呆麻痹、精神失常，只有4万居民的水俉县，竟有一万人的了这种病，更可怕的是水俉病还具有遗传性。

水俉病震惊了世界。

上世纪70年代开始，日本下决心着手治理濑户内海，首先，颁布实施《水质污染防止法》、《海洋污染及海上灾害防止法》、还针对濑户内海特别制定了《濑户内海环境保护临时措施法》，还决定对排入濑户内海及其邻近海域的工业废水负荷量减少一半，并规定3年之内，逐步将与工业废水有关的污染负荷量减少到规定程度。

该《措施法》实施了三年，又延长了两年，事实证明它对恢复海域的良好环境起到很大的作用，为不使前功尽弃，日本国会通过决议，将《濑户内海环境保护临时措施法》改为永久性法律，更名为《濑户内海环境保护特别措施法》。

为了切断污然源头，政府将污染严重的化工厂迁离濑户内海，并大大减少天海造地的面积，濑户内海的大部分区域都被规划为国家公园，建立了800多个野生动物自然保护区。

政府还协调建立了该海区沿岸13个府县和5个市的知事、市场参加的环境保护工作会议制度。

在治理海洋污染的过程中，这种联席会议发挥着非常重大的作用。

同时，有关部门大力加强内海环境调查与监视、监测的投资，各种自动化监测设备可以一年到头连续在海上观测，并多次开展大规模的海洋污染综合调查，对濑户内海的污染现状、如何治理了然于胸。

通产省成立了防止濑户内海水质污染研究会、海洋生物环境研究所等科研机构，其他许多省厅和地方政府的研究所及大学和民间团体也都从事着与治理海洋污染有关的环境科学研究工作。

半官方的濑户内海环境保护协会也扮演了重要角色，民间环保组织更是大量诞生，规模之大居世界之首。

社会各阶层都在宣传保护濑户内海的重要性和必要性。

经过30年社会各界的共同努力，濑户内海水质已基本恢复到良好状态，海洋渔获量明显增加。

现在，“综合性海域管理”已经成为世界诶学者都很重视和关注的课题，一些国际学者最担忧的情况是对海洋的无序开发，希望各国政府能以此未见，因为无序开发将给海洋环境带来难以估量的严重后果。

4．2009年10月，荷兰内阁批准一项“退耕环海”方案，位于荷兰南部西斯海尔德水道两岸的部分堤坝被推倒，一片围海造田得来的3平方公里“开拓地”将再次被海水淹没，恢复为可供鸟类栖息的湿地。

这项“退耕环海”计划是对西斯海尔德水道疏浚工程的“补偿”，西斯海尔德水道位于荷兰南部，是比利时重要港口普、安特卫普港的出海通道，由于湾长水浅，进出安特卫蒲港的大型油轮只能在海水涨潮时通过西斯海尔德水道，据称，因此每年给安特卫蒲港造成损失7000万欧元。

疏浚西斯海尔德水道对于荷兰、比利时两国无疑都具有重要的经济意义。

但是，要疏浚水道，必然拓宽水岸，岸边的湿地面积就会受到侵占。