2011年国际数模资料 Evolution of Graphene Growth on Ni and Cu by Carbon Isotope Labeling

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2011年美国大学生数学建模竞赛优秀作品

2011年美国大学生数学建模竞赛优秀作品

AbstractThis paper presents one case study to illustrate how probability distribution and genetic algorithm and geographical analysis of serial crime conducted within a geographic information system can assist crime investigation.Techniques are illustrated for predicting the location of future crimes and for determining the possible residence of offenders based on the geographical pattern of the existing crimes and quantitative method,which is PSO.It is found that such methods are relatively easy to implement within GIS given appropriate data but rely on many assumptions regarding offenders’behaviour.While some success has been achieved in applying the techniques it is concluded that the methods are essentially theory-less and lack evaluation.Future research into the evaluation of such methods and in the geographic behaviour of serial offenders is required in order to apply such methods to investigations with confidence in their reliability.1.IntroductionThis series of armed robberies occurred in Phoenix,Arizona between13September and5December1999and included35robberies of fast food restaurants,hotels and retail businesses.The offenders were named the“Supersonics”by the Phoenix Police Department Robbery Detail as the first two robberies were of Sonic Drive-In restaurants.After the35th robbery,the offenders appear to have desisted from their activity and at present the case remains unsolved.The MO was for the offenders to target businesses where they could easily gain entry,pull on a ski mask or bandanna, confront employees with a weapon,order them to the ground,empty the cash from a safe or cash register into a bag and flee on foot most likely to a vehicle waiting nearby. While it appears that the offenders occasionally worked alone or in pairs,the MO, weapons and witness descriptions tend to suggest a group of at least three offenders. The objective of the analysis was to use the geographic distribution of the crimes to predict the location of the next crime in an area that was small enough to be suitable for the Robbery Detail to conduct stakeouts and surveillance.After working with a popular crime analysis manual(Gottleib,Arenberg and Singh,1994)it was found that the prescribed method produced target areas so large that they were not operationally useful.However,the approach was attractive as it required only basic information and relied on simple statistical analysis.To identify areas that were more useful for the Robbery Detail,it was decided to use a similar approach combined with other measurable aspects of the spatial distribution of the crimes.As this was a“live”case, new crimes and information were integrated into the analysis as it came to hand.2.AssumptionIn order to modify the model existed,we apply serial new assumptions to the principle so that our rectified model can be much more practical.Below are the assumptions:1.C riminals prefer something about the locations where previous crimes werecommitted committed..We supposed the criminals have a greater opportunity to ran away if they choose to crime in the site they are familiar with.In addition,the criminals probably choose previous kill sites where their target potential victims live and work.2.Offenders regard it safer to crime in their previous kill site as time went by.This is true that the site would be severely monitored by police when a short term crime happened and consequently the criminal would suffer a risk of being arrested in that site.And as mentioned above ,the police would reduce the frequency of examining the previous kill sites as time went by.3.Criminals are likely to choose the site that have optimal distance .This is a reasonable assumption since it is probably insecure to crime in the site that stays far away and that costs an amount of energy to escape and adds the opportunity to be arrested in such an unfamiliar terrain.And it is also impossible to crime in the site nearby since it increases the probability of being recognized or being trapped.As a result,we can measure a optimal distance in series perpetrations.4.Crimes are committed by individual.We assume that all the case in the model are committed by individuals instead of by organized members.In this way the criminal is subject to the assumptions mentioned above due to his insufficient preparation.5.Criminals Criminals''movements unconstrained.Because of the difficulty of finding real-world distance data,we invoke the “Manhattan assumption”:There are enough streets and sidewalks in a sufficiently grid-like pattern that movements along real-world movement routes is the same as “straight-line”movement in a space be discrete into city blocks.It is demonstrated that across several types of serial crime,the Euclidean and Manhattan distances are essentially interchangeable in predicting anchor points.3.The prediction of the next crime site3.1The measure of the optimal distanceDue to the fact that the mental optimal distance of the criminal is related to whether he is a careful person or not,it is impossible for him to make a fixed constant.Besides,the optimal distance will change in different moment.However,such distance should be reflected on the distances of the former crime sites.Presume that the coordinates of the n crime sites is respectively ),(11y x 、),(22y x 、……、),(n n y x ,and define the distance between the th i crime site and the th j one as j D ,i .The distance above we first consider it as Euclid distance,which is:22,)()(j i j i j i y y x x D −+−=With that,we are able to measure the distance between the th n crime site and the th 1-n one respectively.According to the assumption 2,the criminal believes that the earlier crime sites have became saferfor him to commit a crime again,so we can define his mental optimal distance,giving the sites the weights from little to much according to when the offenses happened in time sequence,as:∑−==11,n i ni i D w SD Satisfying 121......−<<<n w w w ,111=∑−=n i i w .Presuming the th i crime happens in i t ,whichis measured by week,we can have ∑−==11n i i kk t t w .SD can reflect the criminal's mental condition to some extent,so we can use it to predict the mental optimal distance of the criminal in the th n 1+case.While referring to the th n crime site,the criminal is able to use SD to estimate the optimal distance in the next time,and while referring to the rest crime sites,the optimal distances reduce as time goes back.Thus,the optimal security of the th i crime site can be measured as the following:n ni i SD t t SD *=3.2The measure of the probability distributionGiven the crime sites and location,we can estimate tentatively the probability density distribution of the future crimes,which equals to that we add some small normal distribution to every scene of crime to produce a probability distribution estimate function.The small normal distribution uses the SD mentioned above as the mean,which is:∑=−−=n i i i SD r n y x f 122)2)(exp(211),(σσπi r is defined as the Euclid distance between the site to the th i crime site,and the standard difference of the deviation of the criminal's mental optimal distance is defined as σ,which also reflects the uncertainty of the deviation of the criminal's mental optimal distance,involves the impacts of many factors and can not be measured quantitatively.The discussion of the standard difference is as following:3.3The quantization of the standard differenceThe standard difference is identified according to the following goal,which is,every prediction of the next crime site according to the crime sites where the crimes were committed before should have the highest rate of success.When having to satisfying such optimization objective,it isimpossible to make the direct analysis and exhaustivity.Instead,we have to use the optimized solutions searching algorithm,which is genetic algorithm.\Figure1:The Distribution of the Population of the Last GenerationAccording to the figure,the population of the last generation is mostly concentrated near80, which is used as the standard distance and substituted to the*formula.With the*formula,we are able to predict the probability density of Whether the zones will be the next crime site.Case analysis:5crime site according to the4ones happened before Figure2:The prediction of theth6crime site according to the5ones happened before Figure3:The prediction of theth6crime site according to the5ones happened before Figure4:The prediction of thethAccording to the predictions happened before,the predictions of the outputs based on the models are accurate relatively,and they are able to be the references of the criminal investigations to some extent.However,when is frequency of such crime increases,the predictions of the outputs23crime site according deviated the actual sites more and more,such as the prediction of thethto the22ones happened before,which is:23crime site according to the22ones happened before Figure5:the prediction of thethConclusion according to analysis:It may not be able to predict the next crime site accurately if we use Euclid distance to measure the probability directly.So,we should analyze according to the actual related conditions.For example,we can consider the traffic commutes comprehensively based on the conveniences of the escapes,such as the facilities of the express ways network and the tunnels.According to the hidden security of the commitments,we should consider the population of the area and the distance from the police department.Thus,we should give more weights to the commute convenience,hidden security and less population.In addition,when the commitments increases,the accuracy of the model may decrease,resulted from the fact that when the criminal has more experience,he will choose the next crime sites more randomly.4.Problems and further improvementsWith23crimes in the series the predictions tended to provide large areas that included the target crime but were too large to be useful given the limited resources the police had at their disposal.At this stage,a more detailed look was taken at the directionality and distances between crimes.No significant trends could be found in the sequential distance between crimes so an attempt was made to better quantify the relationship between crimes in terms of directionality.The methodology began by calculating the geographic center of the existing crimes. The geographic center is a derived point that identifies the position at which the distance to each crime is minimized.For applications of the geographic center to crime analysis.Once constructed,the angle of each crime from the north point of the geographic center was calculated.From this it was possible to calculate the change indirection for the sequential crimes.It was found that the offenders were tending to pattern their crimes by switching direction away from the last crime.It appears that the offenders were trying to create a random pattern to avoid detection but unwittingly created a uniform pattern based upon their choice of locations.This relationship was quantified and a simple linear regression used to predict what the next direction would be.The analysis was once again applied to the data.While the area identified was reduced from previous versions and prioritized into sub-segments,the problem remained that the areas predicted were still too large to be used as more than a general guide to resource deployment.A major improvement to the methodology was to include individual targets.By this stage of the series,hotels and auto parts retailers had become the targets of choice.A geo-coded data set became available that allowed hotels and retail outlets to be plotted and compared to the predicted target areas.Ideally those businesses falling within the target areas could be prioritized as more likely targets.However,in some cases the distribution of the likely businesses appeared to contradict the area predicted.For example,few target hotels appeared in the target zone identified by the geographic analysis.In this case,more reliance was placed upon the location of individual targets. From this analysis it was possible to identify a prioritized list of individual commercial targets,which was of more use operationally.Maps were also provided to give an indication of target areas.Figure6demonstrates a map created using this methodology.It is apparent from the above discussion that the target areas identified were often too large to be used as more than a general guide by the Robbery Detail.However,by including the individual targets,it was possible to restrict the possible target areas to smaller,more useful areas,and a few prioritized targets.However,such an approach has the danger of being overly restrictive and it is not the purpose of the analysis to restrict police operations but to suggest priorities.This problem was somewhat dealt with by involving investigators in the analysis and presenting the results in an objective manner,such that investigators could make their own judgments about the results.To be more confident in using this kind of analysis a stronger theoretical background to the methods is required.What has been applied here is to simply exploit the spatial relationships in the information available without considering what the connection is to the actual behaviour of the offenders.For example,what is the reason behind a particular trend observed in the distance between crimes?Why would such a trend be expected between crimes that occur on different days and possibly involve different individuals?While some consideration was given to identifying the reason behind the pattern of directionality and while it seems reasonable to expect offender’s to look for freeway access,such reasoning has tended to follow the analysis rather than substantiate it.Without a theoretical background the analysis rests only on untested statistical relationships that do not provide an answer to the basic question:why this pattern?So next we will apply a quantitative method,which is PSO,based on a theoretical background,to locate the residence of the criminal's residence.5.The prediction of the residenceParticle Swarm Optimization is a evolutionary computation,invented by Dr.Eberhart and Dr.Kennedy.It is a tool of optimization based on iteration,resulted from the research on the behaviors of the bird predation.Initiating a series of random number,the PSO is able to catch the optimization with iteration.Like PSO,the resolution of our residence search problem is the criminal,whose serial crime sites have been abstracted into 23particles without volume and weight and extended to the 2-D space.Like bird,the criminal is presumed to go directly home when he committed a crime.So,there are 23criminals who commit the crimes in the 23sites mention before and then they will go home directly.The criminals are defined as a vector,so are their speed.All criminals have a fittness decided by the optimized functions,and every of them has a according speed which can decide their direction and distance.All the criminals know the best position (pbest,defined as the residence known by the individual),which has been discovered so far,and where they are now.Besides,every criminals also know the best position which has been found by the group (gbest,defined as the residence known by the group).Such search can be regarded as the experience of other criminals.The criminals are able to locate the residence by the experience of itself and the whole criminals.PSO computation initiates the 23criminals and then the offenders will pursue the optimized one to search in the space.In other words,they find the optimized solutions by iteration.Presume that in the 2-D space the location and speed of the ith crime site is relatively ),(2,1,i i i x x X =and ),(2,1,i i i v v V =.In every iteration,the criminals will pursue the two best positions to update themselves.The two best positions are relatively the individual peak (pbest),),(2,1,i i i p p P =,which is found by the criminal himself,and the group optimized solution (gbest),g P ,which has been found to be the optimized solution by the whole group so far.When the criminals found the two optimized solutions,they will update their speed and new position based on the following formulas.2,1),1()()1()]([)]([)()1(,,,,,22,,11,,=++=+−+−+=+j t v t x t x t x p r c t x p r c t wv t V j i j i j i j i j g j i j i j i j i In the above,the w is inertial weighted factor,21c andc are positive learning factors,21r andr are random number which are distributed uniformly between 0and 1.The learning factor can make the criminals have self-conclude ability and ability of learning from others.Here we make both of them be 2,as what they always are in PSO.The inertial weighted factor w decides the extent of the inheritance of the current speed of the crime sites.The appropriate choice can make them have balanced searching and exploring ability.For balancing the global searching ability and the local improving ability of the criminal in the PSO algorithm,here we adopt one of the self-adapted methods,which is Non-linear Dynamic Inertial Weight Coefficient to choose the inertial weight.The expression is as following:⎪⎩⎪⎨⎧=≤−−−−>avg avg avg f f f f f f w w w f f w w ,))*((,minmin min max min max In the above,the max w and min w are defined respectively as the maximum and minimum of w,f means the current functional value of the criminal,and the avg f and min f respectively means the average value and minimum value of all the current criminals.In addition,the inertial weight will change automatically according to the objective value,which gives the name self-adapted method.When the final values,which are estimations of the criminal's residence,become consistent,it will make the inertial weight increase.When they become sparser,it will make the inertial weight decrease.In the meantime,referring to the criminals whose final values are worse than the average value,its according inertial weighted factor will become smaller,which protect the crime site.Oppositely,when referring to the criminals whose final values are better than the average value,its according inertial weighted factor will become bigger,which makes the criminal nearer to the searching zone.So now,with the PSO of Non-linear Dynamic Inertial Weight Coefficient,we can calculate the minimum value of22,)()(j j j i y y x x R −+−=,j=1,2,3 (23)In the above,j ,i R is the residence of the criminal.Thus,we have the output (x,y)as(2.368260870656715,3.031739124610613).We can see the residence in the figure 7.Figure7:The residence in the map6.ConclusionThis paper has presented one case study to illustrate how probability distribution and geographical analysis of serial crime conducted can assist crime investigation. Unfortunately,in the Supersonic armed robbery investigation the areas identified were too large to have been of much use to investigators.Further,because of the number of assumptions applied the method does not inspire enough confidence to dedicate resources to comparing its results to the enormous amount of suspect data collected on the case.While the target areas predicted tended to be large,the mapping of individual commercial targets appears to offer a significant improvement to the method.However,as they stand,these methods lack a theoretical basis that would allow the results to be judged and applied in investigations.Limitations such as these can be offset to some degree by the involvement of investigators in the analysis.In the end,we used a quantitative method to locate the residence of the criminal to make the identified areas smaller.So,due to the advantages and drawbacks of the above methods,we suggest that we should use different methods to help us fight again the crimes comprehensively.。

2011数学建模国赛A题优秀获奖论文

2011数学建模国赛A题优秀获奖论文

我们参赛选择的题号是(从 A/B/C/D 中选择一项填写) : 我们的参赛报名号为(如果赛区设置报名号的话) : 所属学校(请填写完整的全名) : 参赛队员 (打印并签名) :1. 2. 3. 指导教师或指导教师组负责人 (打印并签名): 日期: 2012 西安电子科技大学 欧阳照玮 李娟 王小磊
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2011 高教社杯全国大学生数学建模竞赛



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Materials and Manufacturing Processes-2011-649

Materials and Manufacturing Processes-2011-649

This article was downloaded by: [East China University of Science and Technology]On: 23 November 2012, At: 00:44Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UKMaterials and Manufacturing ProcessesPublication details, including instructions for authors and subscription information:/loi/lmmp20Mullite Fibers Prepared by Sol-Gel Method UsingAluminum Chloride Aluminum Isopropoxide andTetraethylorthosilicateYabin Zhang a , Yaping Ding a , Yong Li a , Jiqiang Gao a , Jianfeng Yang a & Litong Guo ba State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an,Chinab Material Science and Engineering College, China University of Mining and T echnology,Xuzhou, ChinaVersion of record first published: 22 Apr 2011.PLEASE SCROLL DOWN FOR ARTICLEMaterials and Manufacturing Processes ,26:649–653,2011Copyright ©Taylor &Francis Group,LLC ISSN:1042-6914print/1532-2475online DOI:10.1080/10426910903124787Mullite Fibers Prepared by Sol-Gel Method Using Aluminum Chloride Aluminum Isopropoxide and TetraethylorthosilicateYabin Zhang 1,Yaping Ding 1,Yong Li 1,Jiqiang Gao 1,Jianfeng Yang 1,and Litong Guo 21State Key Laboratory for Mechanical Behavior of Materials,Xi’an Jiaotong University,Xi’an,China 2Material Science and Engineering College,China University of Mining and Technology,Xuzhou,ChinaMullite fibers with good flexibility were prepared from an aqueous water solution of aluminum chloride (AC),aluminum isopropoxide (AIP),tetraethylorthosilicate (TEOS)by the sol-gel process.Aluminosilicate spinnable sol (pH =2)with the stoichiometric mullite composition Al:Si =3:1 AIP/AC =2:1 was prepared.The removal of organic and chlorine was completed at 800 C.The complete transformation to mullite was observed at 1200 C by X-ray diffraction (XRD).The lateral and circumferential cracks were showed in the results of scanning electron microscopy (SEM)when fibers were sintered at 10 C min −1.It was useful for preparation of fibers with smooth surface and uniform diameter by controlling the sintering schedule.Keywords AlCl 3·6H 2O;Drying;Fiber;Mullite;Process;Reaction;Sintering;Sol-gel.IntroductionMullite fibers were used widely for their excellent high-temperature strength,creep resistance,thermal and chemical stability,low thermal expansion coefficient,and good dielectric properties [1–6].They are mainly used as reinforcement of metals or ceramics and as high-temperature or electrical insulating materials.Conventionally,ceramic fibers are prepared by drawing the melt through the orifice at high temperature [7,8].This method makes the raw materials to a homogeneous high melt with certain viscosity.However,it is difficult to prepare the fibers with high melting points of start materials.The sol-gel technique applied to fiber preparation overcomes the difficulties [9–13].The sol is hydrolyzed and then condensed or polymerized at certain temperature until an appropriate viscosity for spinning is achieved for the production of fipared to high temperature melt,the sol-gel method not only makes the start materials homogeneous,but also lowers the sintering temperature because of its fine grains and homogeneous composting.Some successful methods for preparing mullite fibers by the sol-gel method have been reported.Ki Chang Song [14,15]prepared the mullite fiber with the aluminum isopropoxide (AIP),aluminum nitrate,tetraethylorthosilicate (TEOS).Kiyoshi Okada et al.studied the effect of different Al source on the mullite fiber [16]and found some cracks due to decomposition of nitrates.Long cracks along the fiber axis were also seen.In most of starting materials,aluminum nitrate was selected as Al source [14–18]because of its good solubility in water or ethanol.However,the decomposition of nitrate took placeReceived March 2,2009;Accepted June 2,2009Address correspondence to Yabin Zhang,State Key Laboratory for Mechanical Behavior of Materials,Xi’an Jiaotong University,Xi’an 710049,China;E-mail:zhyab@when mixing solution was condensed to sol using a water bath,resulting into the formation of bubbles of yellowish nitrogen-dioxide gas.Consequently,the spinnability of sol was influenced by the microbubbles,although mullite fibers with smooth surface and uniform diameter were obtained finally.In this work,mullite fibers with smooth surface and no cracks were fabricated from using water solvent system of AlCl 3·6H 2O (AC),AIP,and TEOS.The process of mullite fibers,including rheological behavior and viscosity of sol,drying temperature,drying time,and sintering schedule are presented in this article.ExperimentalAluminosilicate gel with the stoichiometric mullite composition Al:Si =3:1 was prepared as follows.An aqueous solution of AC (Chemical grade,Xi’an reagent factory,Xi’an,China)and AIP (chemical grade,Shanghai chemical reagent Co.Ltd.,Shanghai,China)was used as an alumina source,and AIP/AC in molar ratio was 2:1.The silicon was introduced by the TEOS (chemical grade,Xi’an reagent factory,Xi’an,China).AC was dissolved into distilled water at room temperature with vigorously stirring for 0.5h.A solution with a pH value of 2was obtained.Then TEOS was added to the solution further stirring for 1h.The value of TEOS/H 2O was 1:3in volume ratio.To this solution,AIP was added slowly with vigorously stirring at 80 C.The distilled water was added into the solution with stirring until the solution was transparent.The solution was condensed at around 80 C using a water bath.After appropriate condensation of the solution,the viscosity of solution with a pH value of 1was suitable for spinning.Subsequently,gel fibers were drawn at room temperature 25 C by a hand drawing method.The gel fibers were then dried around 10minutes at 40 C.The dried fibers were sintered in air at different temperature at the rate of 5 C and 10 C.649D o w n l o a d e d b y [E a s t C h i n a U n i v e r s i t y o f S c i e n c e a n d T e c h n o l o g y ] a t 00:44 23 N o v e m b e r 2012650Y.ZHANG ET AL.Rheological measurement and viscosity measurement of as-prepared and spinning sols were carried out by using a NDJ-1viscometer (Shanghai Balance Tech.Co.,Ltd.,Shanghai,China)at room temperature at different shear rate (6rmin −1,12rmin −1,30rmin −1,and 60rmin −1 .The average values of viscosity at different shear rate were calculated.The prepared fibers were characterized by Fourier transform infrared (FTIR)spectroscopy,thermo-gravimetric analysis/differential scanning calorimetry (TG/DSC),X-ray diffraction (XRD),and scanning electron microscopy (SEM).The FTIR spectroscopy was detected on Prestige-21(Shimadzu,Tokyo,Japan).The TG/DSC was measured on SDT Q600(TA,USA)with a heating rate 10 C min −1and sample weights about 15mg.The XRD patterns were obtained on D/max-3c diffractometer (Rigaku Co.,Ltd.,Japan)at 40kV and 100mA using Cu K radiation,a step width of 0 02 and a counting time of 0.3s.The SEM observation was done on JSM-35C instrument (JEOL,Japan).Results and discussionThe effect of time in 80 C water bath on viscosity of sol is presented in Fig.1(a).The viscosity of as-prepared sol was about 150mPa ·s.It increased with time when it was condensed in 80 C water bath.The sol viscosity increased slowly before 1000mPa ·s,and it was considered that AIP and TEOS was hydrolyzed and condensed slowly according to Eqs.(1)and (2),and the fiber length was only 2–4cm at this time.Subsequently,water evaporation took place accompanied with chemical reaction until the sol viscosity was up to 1600mPa ·s.The spinning fibers length was an excess of 20cm,which was due to the good spinnability of sol.However,the spinnability of sol became worse when the sol viscosity increased to 3000mPa ·s,while fiber length was short and fibers diameter was asymmetric.This could be explained by the condensation reaction among hydroxyl groups and formation of Si-O-Si and Al-O-Al oxide network because of the polymerization of raw materials [19–23].The dehydration reactions can occur not only between molecules (intermolecular self-condensation)but also within one molecule (intramolecular self-condensation)according to Eqs.(3)–(6).Figure 1(b)shows the rheological behavior of spinning sol which was bathed at 80 C for 105minutes.It can be seen that the shear rate had no effect on sol viscosity.The spinning sol behaved as Newtonian fluid at 80 C water bath aged for 105minutes.It could be attributed to the large amount of linear polymers rather than network structures included in Newtonian flow.The sol viscosity was influenced by the quantity and length of linear polymers.Thus the sol that behaved like Newtonian fluid showed good spinnability,whereas the sol that included large amounts of network structures showed badspinnability.Figure 1.—Viscosity change (a)and flow behavior (b)of sol at 80 C using a water bath.D o w n l o a d e d b y [E a s t C h i n a U n i v e r s i t y o f S c i e n c e a n d T e c h n o l o g y ] a t 00:44 23 N o v e m b e r 2012MULLITE FIBERS PREPARED BY SOL-GEL METHOD651Figure 2.—FTIR spectra of spinnable sol.The spinnable sol was also studied through FTIR analysis in the wave number region of 4000–400cm −1,as shown in Fig.2.The absorption peak at 3415cm −1and 1635cm −1are assigned to the OH stretching and bending modes of water.The band at 1436cm −1corresponded to the stretching vibration of CH 2and CH 3from residual reaction products according to Eqs.(1)and (2).It may be noted that the bands assigned to Al-O and Si-O groups were in the region of 1200–400cm −1.The band appeared at 1080cm −1was attributed to the Si-O-Si stretching vibration of SiO 4.In addition,bands at 979cm −1and 600cm −1were observed,which were due to the Al-O-Al vibration.Figure 3shows the weight loss of fibers when dried at 40 C.The fibers lost the majority of their weight during the first 8minutes,which was chiefly attributed to the evaporating of solvent.Little change in weight can be seen above 10minutes.Figure 3.—The weight loss of fibers which were dried at 40C.Figure 4.—TG and DSC curves of mullite sol.Figure 4shows the TG and DSC curves of mullite sol.The mass decreased drastically up to 800 C,which was chiefly due to the removal of chlorine and the decomposition of organic materials.No peak before 100 C could be seen because water was evaporated partly during drying procedure.The endothermic peak at ∼200 C corresponded to combustion of organic materials.The small exothermic peak at around 770 C was considered as removal of residual chlorine [see Fig.4(b)].So the weight decreased quickly before 300 C and slowly between 300 C and 800 C.The total amount of weight loss was also around 60mass%before 800 C,while the mass of sol became almost constant above 800 C.A sharp exothermic peak was shown at about 980 C in the TG/DSC curves,which was assigned to crystallization of mullite.Figure 5shows the XRD patterns of mullite fiber sintered at 1000 C,1100 C,and 1200 C.The main phase insamplesFigure 5.—XRD patterns of mullite fiber sintered at different temperature.D o w n l o a d e d b y [E a s t C h i n a U n i v e r s i t y o f S c i e n c e a n d T e c h n o l o g y ] a t 00:44 23 N o v e m b e r 2012652Y.ZHANG ETAL.Figure 6.—SEM photograph of fibers sintered at 1200 C for 1h using different rate:(a)and (b)10 C min −1,(c)5 C min −1,and (d)fibers showed flexibility.sintered at 1000 C was mullite phase.An amorphous phase was simultaneously observed at 1000 C,which was considered as the amorphous SiO 2and Al 2O 3(see the endothermic peak at ∼1000 C as shown in Fig.3).The mullite peaks showed higher intensity at 1100 C than 1000 C.It was shown that large amount of mullite phase was formed and amorphous phase plete transformation to mullite was observed at 1200 C.The mixing scale of Al and Si components was considered to be the factor that affected the mullization temperature.The mixing of Al and Si at molecular level was helpful to low transformation temperature,and the fiber achieved complete mullization temperature at 1200 C.Martin Schmücker et al.[24]explained the mullite grain microstructure developed from mosaic-type to facetted at the first stage of mullization.According to their conclusions,the grain growth exponent increased with firing temperature.So fiber mullization was remarkably slow between 1000 C and 1100 C,and subsequently grain growth exponent increased until the complete mullization at 1200 C.Figure 6shows the SEM photograph of fiber sintered at 1200 C for 1h using different rate.The diameter of sintered fibers was 20–40 m whereas average diameter of green fibers was 100 m.It showed the diameter shrinkage of the fibers was up to 50%at least,which corresponds well with the weigh loss observed in the TG curve.Figures 6(a)and (b)shows the fibers which were sintered at 10 C min −1.Figure 6(a)shows the lateral cracks running to the elongated direction of the fiber and circumferential cracks.Because of the fast drying and sintering speed of fibers,the amount of evaporation inside the fiber was different from that around fiber surface.So cracks occurred when fibers were sintered,which was due to the different expansion coefficient.Fibers after sintering showed surfaceroughness,as shown in Fig.6(b).As mentioned in the TG/DSC curve,evaporation of Cl −ions and removal of organic lead to rough surface of fibers.Although Cl −ions began to evaporate at ∼650 C,minor amounts of Cl −were present in the fibers when the fibers were calcined up to 1100 C [25].Chlorine as hydrochloric acid was removed when mullization transformation developed,which result in the rough surface.The sintered fibers at 5 C min −1were showed in Fig.6(c).It was showed that the fibers had uniform diameter and smooth surface.Defects were not found on the surface of fiber.The fiber which was sintered at 1200 C showed good flexibility,as shown in Fig.6(d).ConclusionsMullite fibers with good flexibility were prepared by sol-gel method using AC,AIP,and TEOS as start materials.The total amount of weight loss was also around 50mass%,whereas the diameter shrinkage of the fibers was also 50%at least.Spinnability was good when the sol included linear polymers,and Newtonian flow was obtained when viscosity was up to 1000mPa ·plete transformation to mullite was achieved at 1200 teral and circumferential cracks were found when fibers were sintered at 10 C min −1.However,it showed uniform diameter and smooth surface with no defects on the fiber surface when fibers were sintered at 5 C min −1slowly.The fiber also showed good flexibility when it was sintered at 1200 C.References1.Kanka,B.;Schneider,H.Aluminosilicate fiber/mullite matrix composites with favorable high-temperature properties.Journal of the European Ceramic Society 2000,20,619–623.2.Kaya,C.;Butler,E.G.;Selcuk,A.;Boccaccini,A.R.;Lewis,M.H.Mullite (Nextel™720)fibre-reinforced mullite matrix compositesD o w n l o a d e d b y [E a s t C h i n a U n i v e r s i t y o f S c i e n c e a n d T e c h n o l o g y ] a t 00:44 23 N o v e m b e r 2012MULLITE FIBERS PREPARED BY SOL-GEL METHOD653exhibiting favourable thermomechanical properties.Journal of the European Ceramic Society 2002,22,2333–2342.3.Boccaccini,A.R.;Atiq,S.;Boccaccini,D.N.;Dlouhy,I.;Kaya,C.Fracture behaviour of mullite fibre reinforced–mullite matrix composites under quasi-static and ballistic impact posites Science and Technology 2005,65,325–333.4.Deléglise, F.;Berger,M.H.;Bunsell, A.R.Microstructural evolution under load and high temperature deformation mechanisms of a mullite/alumina fibre.Journal of the European Ceramic Society 2002,22,1501–1512.5.Kriven,W.M.;Palko,J.W.;Sinogeikin,S.;Bass,J.D.;Sayir,A.;Brunauer,G.;Boysen,H.;Frey, F.;Schneider,J.High-temperature single crystal properties of mullite.Journal of the European Ceramic Society 1999,19,2529–2541.6.Mileiko,S.T.Single crystalline oxide fibres for heat-resistant posites Science and Technology 2005,65(15–16),2500–2513.7.Pan,W.;Li,R.T.Crystallization kinetics of the aluminum silicate glass fiber.Materials Science and Engineering A-Structure 1999,271(1–2),298–305.8.Bunsell,A.R.;Berger,M.H.Fine diameter ceramic fibres.Journal of the European Ceramic Society 2000,20(13),2249–2260.9.Yoon,W.;Sarin,P.;Kriven,W.M.Growth of textured mullite fibers using a quadrupole lamp furnace.Journal of the European Ceramic Society 2008,28(2),455–463.10.Venkatesh,R.;Chakrabarty,P.K.;Siladitya,Chatterjee,B.M.;Ganguli, D.Preparation of alumina fibre mats by a sol-gel spinning technique.Ceramics International 1999,25(6),539–543.11.Chatterjee,M.;Naskar,M.K.;Chakrabarty,P.K.;Ganguli,D.Sol-gel alumina fibre mats for high-temperature applications.Materials Letters 2002,57(1),87–93.12.Gotoh,Y.;Fujimura,K.;Ohkoshi,Y.;Nagura,M.;Akamatsu,K.;Deki,S.Preparation of transparent alumina film and fiber from a composite of aluminum polynuclear complex/methyl cellulose.Materials Chemistry and Physics 2004,83(1),54–59.13.Chandradass,J.;Balasubramanian,M.Effect of magnesium oxide on sol–gel spun alumina and alumina–zirconia fibres.Journal of the European Ceramic Society 2006,26(13),2611–2617.14.Song,K.C.Preparation of mullite fibers from aluminumisopropoxide–aluminum nitrate–tetraethylorthosilicate solutions by sol–gel method.Materials Letters 1998,35(5–6),290–296.15.Song,K.C.Preparation of mullite fibers by the sol-gel method.Journal of Sol-Gel Science and Technology 1998,13(1–3),1017–1021.16.Okada,K.;Yasohama,S.;Hayashi,S.;Yasumori,A.Sol-gelsynthesis of mullite long fibres from water solvent systems.Journal of the European Ceramic Society 1998,18(13),1879–1884.17.Chen,X.T.;Gu,L.X.The sol-gel transition of mullite spinningsolution in relation to the formation of ceramic fibers.Journal of Sol-Gel Science and Technology 2008,46(1),23–32.18.Chen,X.T.;Gu,L.X.Effect of solid content on formation ofsol-gel derived mullite fibres.Materials Science and Technology 2008,24(10),1179–1182.19.Rüdiger,S.;Eltanany,G.;Gro ß,U.;Kemnitz,E.Real sol-gelsynthesis of catalytically active aluminium fluoride.Journal of Sol-Gel Science and Technology 2007,41(3),299–311.20.Akihiko,M.;Hui, C.;Kazuo,T.;Michael,G.;Klaus,U.Novel route in the synthesis of MCM-41containing framework aluminum and its characterization.Microporous and Mesoporous Materials 1999,32(1–2),55–62.21.Hossein,A.D.;Mohammadsadegh,Y.;Burtron,H.D.An XRDand fourier-transformed infrared spectroscopy investigation of single and mixed -alumina and thorium oxide.Journal of Molecular Catalysis A:Chemical 2005,238(1–2),72–77.22.Sungseen, C.;Boyoung, C.;Seunggoo L.;Sungwook,L.;Sungsoon,I.;Seonghun,K.;Jongkyoo,P.Titania-doped silica fibers prepared by electrospinning and sol-gel process.Journal of Sol-Gel Science and Technology 2004,30(3),215–221.23.Masashi,I.;Minoru,K.;Tomoyuki,I.Alkoxyalumoxanes.Chemistry of Materials 2000,12(1),55–61.24.Marin,S.;Hartmut,S.;Thomas,M.;Bernd,C.Temperature-dependent evolution of grain growth in mullite fibres.Journal of the European Ceramic Society 2005,25(14),3249–3256.25.Ramanan,V.;Sutapa,R.R.Effect of organic additives on theproperties of sol-gel spun alumina fibres.Journal of the European Ceramic Society 2000,20(14–15),2543–2549.D o w n l o a d e d b y [E a s t C h i n a U n i v e r s i t y o f S c i e n c e a n d T e c h n o l o g y ] a t 00:44 23 N o v e m b e r 2012。

2011年美赛真题优秀论文

2011年美赛真题优秀论文

中继站的协调方案摘要(Abstract )中继站是将信号进行再生、放大处理后,再转发给下一个中继站,以确保传输信号的质量。

低功耗的用户,例如移动电话用户,在不能直接与其他用户联系的地方可以通过中继站来保持联系。

然而,中继站之间会互相影响,除非彼此之间有足够远的距离或通过充分分离的频率来传送。

为了排除信号间的干扰,实现某一区域内(题中以40英里为半径的圆形区域)通信设备正常的发射和接收信号,需要利用PL 技术对中继站作合理的协调和分配。

首先本文结合香农理论的相关算法,考虑了信号供给系统的损耗、天线增益、信号的传播损耗、辐射效率因素的影响,得到中继站的辐射范围半径公式为:,10,10log ()37.23282010r outr inp P d -=在供给对象为低功率消耗设备,查资料一般发射功率为3.2W ,中继站能接收到的最弱的信号1W μ,代入数据得到每个中继站的辐射半径为15.28m iles 。

同时本文在不考虑其他因素(包括:地形、大雾、山川、建筑物等)对辐射范围和辐射强度的影响下,结合相关知识和题目中给出的条件,在不引入PL 技术时得出每个中继站所服务的用户数量为39个。

对于问题一, 我们首先定义了均衡覆盖、覆盖效率,在均衡覆盖中即用圆覆盖圆形区域,我们根据式子2(2)n k n ππ-=,得出(,)k n 的可能值有(3,6),(4,4),三种,即等效三角形、正方形、正六边形覆盖,并通过覆盖效率的比较,最终得出正六边形覆盖是最好的覆盖方法,即蜂窝拓扑网络。

在这种覆盖情况下我们,我结合中继站覆盖半径15.28m iles ,根据式子m i n 3(1)1,0,1,2,3,N K K K =++=……,求出最少需要19个中继站,并在满足单位面积覆盖同时在线人数的情况下引入PL 技术,得出此时中继站在该区域可同时服务在限人数为1292人。

对于问题二,我们在问题一模型基础上从提高中继站服务人数和减少中继站半径两方面考虑,得出在将PL 分为18层,即中继站同时在线服务人数为702的情况下,结合单位面积同时在线服务人数,得出在中继站最少的情况下,中继站半径在[]11.094,,11.68范围内都可,我们为了让同时在线服务人数最大,取11.094英里,得出服务人数为11305。

2011全国数模竞赛A题

2011全国数模竞赛A题

承诺书我们仔细阅读了中国大学生数学建模竞赛的竞赛规则.我们完全明白,在竞赛开始后参赛队员不能以任何方式(包括电话、电子邮件、网上咨询等)与队外的任何人(包括指导教师)研究、讨论与赛题有关的问题。

我们知道,抄袭别人的成果是违反竞赛规则的, 如果引用别人的成果或其他公开的资料(包括网上查到的资料),必须按照规定的参考文献的表述方式在正文引用处和参考文献中明确列出。

我们郑重承诺,严格遵守竞赛规则,以保证竞赛的公正、公平性。

如有违反竞赛规则的行为,我们将受到严肃处理。

我们参赛选择的题号是(从A/B/C/D中选择一项填写): A我们的参赛报名号为(如果赛区设置报名号的话): 20111663 所属学校(请填写完整的全名):南京邮电大学参赛队员 (打印并签名) :1. 刘超舟2. 刘立亿3. 董睿指导教师或指导教师组负责人 (打印并签名):日期: 2011 年 9 月12 日赛区评阅编号(由赛区组委会评阅前进行编号):编号专用页赛区评阅编号(由赛区组委会评阅前进行编号):全国统一编号(由赛区组委会送交全国前编号):全国评阅编号(由全国组委会评阅前进行编号):A题城市表层土壤重金属污染分析一.摘要二.问题重述三.符号约定四.基本假设五.建模与求解5.1问题(1)的建模与求解5.1.1问题分析根据采样的坐标,我们可以得到一个大概的区域分布散点图,如下图:图5.1.1 功能区采样点分布散点图图中各功能区得分布无规律,采样间隔比较大,很难建立各重金属测量值与样本采集点坐标的平滑函数,故采用等高线图来描述各种重金属在该城区的空间分布。

附件中给了采样点的三维坐标和各重金属元素的含量值,由于我们只需要考虑该区域的污染程度,因此不需要考虑坐标,只用知道采样地点位于某一区即可。

我们从采集样本的样本值中可以分析出每一区域的污染程度。

由于重金属分子的相对分子质量较大,取样时只对表层土壤0~10厘米深度进行取样,从收集的资料来看,可对取样值污染程度采用地积累指数分析法进行评级分析。

2011数学建模D题

2011数学建模D题

天然肠衣搭配问题摘要本文研究的是天然肠衣搭配问题,目的是在满足规格要求的条件下,选择使成品捆数最多的优化方案。

共建立了3个模型。

对题中给出的要求逐个考虑,并运用Lingo和Matlab软件编程求解。

模型1 在给定一批原料的情况下,装出的成品捆数越多方案越好。

对各种不同规格的原料,根据每捆成品的总长度和根数建立整数规划模型,得出三种规格的最大捆数分别为14捆, 34捆,129捆。

总数量为177捆。

模型2 根据要求2,在模型1捆数最大的基础上,得出各规格捆数最大时的不同搭配方案,选出最优方案(详见表27,30,47)。

模型3 针对要求3,允许总长度有5.0的误差,各规格成品每捆的根数可以比标准少一根,明显条件放宽,可能会增加成品捆数。

运用Matlab和Lingo软件求解得到三种规格的捆数增加了6捆,总捆数为183捆,具体搭配方案见表48。

针对要求4,后一规格完成搭配后若材料有剩余,剩余材料可降级到前一规格使用,计算出三种规格的捆数增加3,最终最大捆数为186捆。

最后,选用合理的数据对模型进行模拟检验,把相应的数字输入流程,采用计算机搜索法,得出的方案时间不超过30分钟。

关键词:整数规划模型Lingo Matlab1 问题重述1.1 题目背景天然肠衣(以下简称肠衣)制作加工是我国的一个传统产业,出口量占世界首位。

肠衣经过清洗整理后被分割成长度不等的小段(原料),进入组装工序。

传统的生产方式依靠人工,边丈量原料长度边心算,将原材料按指定根数和总长度组装出成品(捆)。

1.2 题目条件1 原料按长度分档,通常以0.5米为一档,如:3-3.4米按3米计算,3.5米-3.9米按3.5米计算,其余的依此类推。

表1是几种常见成品的规格,长度单位为米,∞表示没有上限,但实际长度小于26米。

2 为了提高生产效率,公司计划改变组装工艺,先丈量所有原料,建立一个原料表。

表2为某批次原料描述(见附录A)。

1.3 题目要求1 对于给定的一批原料,装出的成品捆数越多越好;2 对于成品捆数相同的方案,最短长度最长的成品越多,方案越好;3 为提高原料使用率,总长度允许有± 0.5米的误差,总根数允许比标准少1根;4 某种规格对应原料如果出现剩余,可以降级使用。

2011年数学建模A题参考答案

2011年数学建模A题参考答案

城市表层土壤重金属污染分析摘要随着人们生活质量的提高和城市人口的增加,城市土壤的污染日益加剧。

通过对某城区土壤中的重金属元素含量的测定,分析污染情况。

根据所给数据,用MATLAB做出散点图及浓度的等值线图,找到各重金属元素的分布区。

然后,用单因子污染指数法和内梅罗综合污染指数法对采样地区土壤重金属污染程度作出分析,并根据重金属污染物的传播特征,利用聚类分析法建模,以确定污染源的位置。

重金属的分布在不同地区有所差异,并且距离污染源的位置越远其含量越少。

据此,用MATLAB作出浓度的等值线,即可看出As、Cd、Cr、Hg主要分布在工业区,Cu、Zn、Pb主要分布在主干道区。

用单因子污染指数法和内梅罗综合污染指数法,计算各元素的平均值与其环境背景值的比值,求得污染指数。

依据污染指数标准,可得污染程度由大到小依次为:工业区、主干道路区、生活区、公园绿地区、山区。

每个样品的重金属元素组成并不是独立、互不相干的,来自同一种源的成分之间存在较强的相关性。

因此可以通过主成分分析法缩减分析变量,找出主因子。

用SPSS进行因子分析,采用主成分分析法进行主因子的提取。

从输出数据中得到因子载荷量和累计贡献率,因子载荷量大的元素Cr,Ni,Cu,即为污染源的主要因素,累计贡献率大的为第一主因子,可代表主要污染源,即主要来源于工业污染和交通污染。

进入土壤中的重金属元素大部分通过渗透向外扩散(汞除外),从高浓度到底浓度,高海拔到低海拔逐层扩散。

重金属的分布在同一污染源周围有一定的规律,相似性高;不同的污染源在其周围的污染程度不同,相似性低。

所以通过对选取样本数据进行筛选,用聚类分析法分出相似性高的点,并求出其类中心,即求得各重金属的污染源。

考虑到地势、恶劣的气候、自然灾害、过度的获取地下水、重金属的污染、水环境的演化和人类工程活动等因素都对城市地质环境的演变产生不同的影响,收集以上相关数据,采用层次分析法,分析得出各因素对环境演变的主次关系,找到解决问题的途径。

2011数学建模c题

2011数学建模c题

2011 高教社杯全国大学生数学建模竞赛承诺书我们仔细阅读了中国大学生数学建模竞赛的竞赛规则。

我们完全明白,在竞赛开始后参赛队员不能以任何方式(包括电话、电子邮件、网上咨询等)与队外的任何人(包括指导教师)研究、讨论与赛题有关的问题。

我们知道,抄袭别人的成果是违反竞赛规则的, 如果引用别人的成果或其他公开的资料(包括网上查到的资料),必须按照规定的参考文献的表述方式在正文引用处和参考文献中明确列出。

我们郑重承诺,严格遵守竞赛规则,以保证竞赛的公正、公平性。

如有违反竞赛规则的行为,我们将受到严肃处理。

我们参赛选择的题号是(从A/B/C/D 中选择一项填写): C我们的参赛报名号为(如果赛区设置报名号的话):sxxxxx所属学校(请填写完整的全名):xxx xxx xxx参赛队员(打印并签名) :1.2.3.指导教师或指导教师组负责人(打印并签名):日期: 2011 年9 月12 日赛区评阅编号(由赛区组委会评阅前进行编号):2011高教社杯全国大学生数学建模竞赛编号专用页赛区评阅编号(由赛区组委会评阅前进行编号):赛区评阅记录(可供赛区评阅时使用):全国统一编号(由赛区组委会送交全国前编号):全国评阅编号(由全国组委会评阅前进行编号):企业退休职工养老金制度的改革摘要针对企业退休职工养老金的改革问题,本文建立了差分阻滞模型模型以解决该类问题。

对于问题1,我们采用差分阻滞模型,先根据我国的经济发展战略目标和目前我国职工工资的实际发放情况以及现阶段中等发达国家的职工年平均工资,利用经验估计方法确定工资最大值T=20万元,再利用差值作图求出方程系数k ≈0.0000007,即求得差分方程式,最后利用方程式和matlab预测出的2011—2035年山东省职工历年平均工资与我国的国情基本吻合。

在此模型的检验图中我们可发现1978—2010年的工资预测值与实际值无太大差别。

对于问题2,先根据附件2求各年龄段职工工资与该企业平均工资之比作为职工缴费指数的参考值,再根据问题1中2011—2035年所预测的年平均工资、附件3中所给的养老金计算方法及个人账户养老金和本人指数化月平均缴费工资的计算公式,并利用matlab软件计算出6种情况下的养老金和养老金替代率。

数模选拔题:2011年

数模选拔题:2011年

A题教学楼的快速疏散问题近年来,诸如地震、火灾等突发事件时有发生。

虽然人们在很多情况下还不能准确预报这些突发事件,但当灾难发生时,尽可能减少伤亡人数是人们应对突发事件的首选。

在突发事件中,身处灾难环境的人员快速疏散可以有效减少伤亡人数。

本着居安思危的态度,假设某一天上午,学生正在主教学楼上课,突然该楼发生火灾,请你完成如下任务:1.用数学建模的方法,给出一种使学生快速疏散的方案;2.针对该教学楼,用你的方案给出其第二、三层学生快速撤离的具体方案和所用时间;3.建模研究你认为值得研究的其他相关问题;4.为学校管理层提供相关建议。

B题水资源短缺风险综合评价水资源,是指可供人类直接利用,能够不断更新的天然水体。

主要包括陆地上的地表水和地下水。

风险,是指某一特定危险情况发生的可能性和后果的组合。

水资源短缺风险,泛指在特定的时空环境条件下,由于来水和用水两方面存在不确定性,使区域水资源系统发生供水短缺的可能性以及由此产生的损失。

近年来,我国、特别是北方地区水资源短缺问题日趋严重,水资源成为焦点话题。

以北京市为例,北京是世界上水资源严重缺乏的大都市之一,其人均水资源占有量不足300m3,为全国人均的1/8,世界人均的1/30,属重度缺水地区,附表中所列的数据给出了1979年至2000年北京市水资源短缺的状况。

北京市水资源短缺已经成为影响和制约首都社会和经济发展的主要因素。

政府采取了一系列措施, 如南水北调工程建设, 建立污水处理厂,产业结构调整等。

但是,气候变化和经济社会不断发展,水资源短缺风险始终存在。

如何对水资源风险的主要因子进行识别,对风险造成的危害等级进行划分,对不同风险因子采取相应的有效措施规避风险或减少其造成的危害,这对社会经济的稳定、可持续发展战略的实施具有重要的意义。

《北京2009统计年鉴》及市政统计资料提供了北京市水资源的有关信息。

利用这些资料和你自己可获得的其他资料,讨论以下问题:1.评价判定北京市水资源短缺风险的主要风险因子是什么?影响水资源的因素很多,例如:气候条件、水利工程设施、工业污染、农业用水、管理制度,人口规模等。

2011年国际大学生数学竞赛试题解答第二天

2011年国际大学生数学竞赛试题解答第二天

1
Solution. (a) Let M be the set of males, F the set of females, and E the set of emales. Consider the (tripartite) graph G with vertices M ∪ F ∪ E and edges for likes. A 3-cycle is then a possible family. We’ll call G the graph of likes. First, let k = n 2 . Then n has to be even and we need to construct a graph of likes with no 3-cycles. We’ll do the following: divide each of the sets M , F , and E into two equal parts and draw all edges between two parts as shown below:
n b) Show that if k ≥ 34 , then it is always possible to create n disjoint married triples, thus marrying all of the expedition members.
Fedor Duzhin and Nick Gravin, Singapore
What are the possible values of lim xn ? Can such a sequence diverge? Johnson Olaleru, Lagos Solution 1. We prove by induction that 0 < 1 − xn < Then we will have (1 − xn ) → 0 and therefore xn → 1. The case n = 0 is true since

2011年美国大学生数学建模竞赛培训课件

2011年美国大学生数学建模竞赛培训课件

2011年美国大学生数学建模竞赛培训课件内容:2010年研究生数学建模竞赛D题题目特殊工件磨削加工的数学建模某科研单位和工厂研制了一种大型精密内外圆曲线磨床,用来加工具有复杂母线旋转体的特殊工件,如导弹天线罩等,这些工件具有硬度高、尺度大、加工精度高和母线为连续光滑曲线等特点。

图1是几类加工工件示例,工件1的内外母线均为凸的,工件2的内母线是非单调凸的。

这些工件的最后精密成形工艺采用磨削加工。

图1 几类特殊加工工件示例该磨床主要由机床底座,下工作台,中工作台,上工作台(简称下台、中台和上台),工件工作箱和砂轮机箱等组成(见图2,其中仅画出砂轮而未显示砂轮机箱)。

下台、中台可分别沿着设在底座和下台上的直导轨作直线运动,这两组导轨相互垂直;上台能沿中台上的圆导轨作转动。

驱动砂轮高速旋转的砂轮机箱安装在机床底座上,砂轮的旋转轴线与底座导轨方向保持平行,且与工件工作箱的旋转主轴等高(即两旋转轴线位于同一水平面)。

各工作台的移动量均可在机床控制面板上自动显示。

图2所示为磨削工件外表面时的情况,更换砂轮后可加工内表面。

图2 大型数控精密内外圆磨床的结构示意图工件工作箱固装在上台上,它通过专用夹具装夹工件,使工件绕工件工作箱主轴以较慢的转速旋转,同时随三个工作台的复合运动改变待加工工件与砂轮的相对位置。

三个台的运动必须相互配合,使工件与砂轮相切磨削,加工出满足要求的旋转体。

三个工作台的运动分别由三组步进电机控制。

步进电机是一种精密数控电动机,每输入一个控制脉冲,电机主轴转动一个精确的步进角度(正向或反向),它的大小与方向由电机结构和控制电路确定(改变电机诸绕组的通电顺序就可改变其旋转方向);既可输入适当个数的脉冲控制电机主轴的角位移量;也可通过控制某时段中的脉冲频率或脉冲的分布使电机主轴转动速度达到某种要求:若某时段中的脉冲频率为常数(即脉冲为均匀分布),则电机主轴的转动可视为匀速,否则为变速,从而实现调速。

2011年美国数学建模大赛论文

2011年美国数学建模大赛论文

dimension reduction(MDR) model to maximize vertical air, twist and flip. The MDR analysis model is proposed. And we define as a tradeoff fac tor to develop a “practical” course.
In requirement 3, we take key factors, including s lope angle angar radius
and the
into consideration to implement the “practical” multiple-factor
Accordingly, by setting up an objective function and using the simulation, we get the conclusion
Team # 9561
Page 1 of 28
that the optimal value of
is
and
Team Control Number For office use only T1 ________________ T2 ________________ T3 ________________ T4 ________________
9561
Problem Chosen
For office use only F1 ________________ F2 ________________ F3 ________________ F4 ________________
.
Keywords: half-pipe snowboard, variant force differential-integration model, semi-spiral track decomposition model, multi-factor dimension reduction model, vertical air, twist, flip

2011年美国数学建模C题汉语版

2011年美国数学建模C题汉语版

电动汽车作为一个普遍的手段交通Rick BaileyBrenda HowellZachary StankoHumboldt State UniversityArcata, CAAdvisor: Brad Finney摘要我们适应一个Lotka-Volterra生态竞争模型来描述汽车(和轻型卡车)市场。

我们假设汽油内部内燃机车辆(ICE),插电式混合动力车(PHEV),和电池动力汽车杆状执行像生物竞争一个共享的但有限的资源。

对于生物,这个资源可能是一个食品供应;在汽车市场,制造商争夺消费者的钱。

这个方程描述利率变化的三个因变量,每种类型的汽车的数量。

该模型参数描述增长利率,种间竞争,和承受能力,也间接的联系对消费者偏好、经济条件下,政府的影响,在汽车技术和改进。

变量和参数模型中使用的表1中列出。

我们假设内在增长速率常数,但兼容模型可以描述它们作为函数的时候,市场力量,或随机变量。

我们假设承载能力以1%的速度增长,一致的与人类的人口增长率为美国[世界银行集团2011]。

我们将一起模型参数,以确定的变量反映各方面影响消费者的选择。

我们调查的5个场景变化影响汽车市场。

一个基本场景使用当前的年度增长率和当前的人口;其他调查高油价的影响,提高电池的性能。

政府投资和高电价。

UMAP杂志的32(2)(2011)165 - 178。

c 2011年版权届时系统公司。

保留所有权利。

许可,将数字或硬拷贝的部分或全部这项工作为个人或课堂使用授予没有费只要副本没有制造或分布式的利润或商业优势,此通知副本熊。

抽象与信贷是允许的,但版权组件的这项工作由其他人拥有比届时系统必须遵守的。

复制否则,全文转载,发布服务器上,或重新分配到列表需要事先同意届时系统。

我们比较了两种车型的现值目前可用的,来检查这些汽车的竞争力。

没有目前的政府补贴,尼桑Leaf有较低的现值比本田思域和因此处于不利地位对公民。

Leaf将竞争没有补贴与线性上升在天然气价格5美元/加仑,增加数十亿效率(kWh /英里驱动),和更高的转售价值。

2011年数学建模A题答案

2011年数学建模A题答案

一、问题重述城市是受人类活动影响最强烈的区域,矿山开采、金属冶炼、交通活动和城市生活等极易造成城市土壤中重金属的富集。

土壤是人类不可或缺的生产资料,重金属污染是破坏土壤生态环境的主要因素,土壤中的有毒重金属能通过食物链直接危害人体健康,所以重金属对人类的危害必须引起我们的高度重视。

本文要研究的是某城市城区表层土壤重金属污染问题,该城市城区主要分为五个区:生活区、工业区、山区、交通区及公园绿地区等,该城市要分析的8中重金属元素是:As(砷)、Cd(镉)、Cr(铬)、Cu(铜)、Hg(汞)、Ni(镍)、Pb(铅)、Zn(锌)。

附录中给出了采样点的位置、所属功能区、8种主要重金属元素在采样点处的浓度及其的背景值等信息。

现对该城市城区土壤地质环境进行调查取样,将所考察的城区划分为间距1公里左右的网格子区域,按照每平方公里1个采样点对表层土(0~10厘米深度)进行取样、编号,并用GPS记录采样点的位置。

应用专门仪器测试分析,获得了每个样本所含的多种化学元素的浓度数据。

另一方面,按照2公里的间距在那些远离人群及工业活动的自然区取样,将其作为该城区表层土壤中元素的背景值。

因此,为了该城区的生态平衡,以及了解重金属在土壤中的形态分布,我们需要利用题目所给的已知条件和数据研究以下问题:(1)给出8种主要重金属元素在该城区的空间分布,并分析该城区内不同区域重金属的污染程度。

(2)通过数据分析,说明重金属元素污染的主要原因。

(3)分析重金属污染物的传播特征,由此建立模型,确定污染源的位置。

(4)分析你所建立模型的优缺点,为更好地研究城市地质环境的演变模式,还应收集什么信息?有了这些信息,如何建立模型解决问题?二、模型的基本假设假设1:重金属元素可看作介质中某一连续点源向四周等强度地传播,在向无穷空间传播的过程中不发生性质变化假设2:重金属元素的传播服从扩散定律,即单位时间通过单位法向面积的流量与它的浓度梯度成正比假设3:重金属元素向四周传播过程中没有发生化学反应假设4:假设5:三、符号说明四、模型的分析、建立和求解4.1问题一:给出8种主要重金属元素在该城区的空间分布,并分析该城区内不同区域重金属的污染程度。

2011年国际生物奥林匹克竞赛理论试题B

2011年国际生物奥林匹克竞赛理论试题B

All IBO examination questions are published under the following Creative Commons license:CC BY-NC-SA (Attribution-NonCommercial-ShareAlike) -https:///licenses/by-nc-sa/4.0/The exam papers can be used freely for educational purposes as long as IBO is credited and new creations are licensed under identical terms. No commercial use is allowed.22nd INTERNATIONAL BIOLOGY OLYMPIADJuly 10-17, 2011Taipei, TaiwanTHEORETICAL TEST: PART BDuration: 150 minutesDear participants,●Check your Student Code on the Answer Sheet before starting the test.●The questions in Part B may have more than one correct answer. Fill your answers in theAnswer Sheet. The marks, numbers, or characters to answer questions in Part B vary depending on questions. Mark the correct answers with “○” and incorrect answers with “—” on the Answer Sheet clearly, as shown below.●Write down your results and answers in the Answer Sheet. Answers written in the QuestionPaper will not be evaluated.●Some of the questions may be marked “DELETED”. DO NOT answer these questions.●The maximal points of Part B is 120 (3 points for each question)●All answers must be correct in each question. Then you will get the points.●Stop answering and put down your pencil IMMEDIATELY after the end bell rings.:Good Luck!!I. Cell biologyProblem set: Figure 1 depicts the cross-section of a certain cell surface structure observed by electron microscope. Answer questions 1 and 2.B1. Which of the following possess the above structure?(A) Paramecium(B) Escherichia coli(C) Tracheid of gymnosperm(D) Sieve tube element of angiosperm(E) Human tracheal cell(F) Human intestinal epithelial cellB2. What is/are the functions and what is the major chemical composition of the structure?Function options:(A) Attachment(B) Locomotion(C) Transportation(D) Secretion(E) AbsorptionComposition options:(P) Cellulose(Q) Protein(R) Mucin(S) Lipid(T) Nucleic acidB3.Some pathogens produce exotoxins that can cause human diseases. One type of exotoxins consists of two polypeptides, subunits A and B. Subunit B can bind to surface receptors on the target cells and cause the transport of the subunit A or associated molecules across the plasma membrane into the cell. Once the subunit A enters the cell, it inhibits protein synthesis and destroys the cells. Which of the following statements regarding exotoxins is/are correct?(A) Subunit A alone can cause disease.(B) Subunit B alone can bind to target cells.(C) Subunit A may carry other molecules to kill target cells.(D) Subunit B may carry other molecules and assist these molecules to enter target cells.(E) When conjugated with an antibody against breast cancer cells, subunit A can kill breastcancer cells.Problem set: Some leucocytes can ingest invaded pathogens by phagocytosis. Digestive enzymes that kill pathogens only function in acidic conditions. Please answer questions 4 and 5.B4. Based on the information provided in the following table, complete the synthesis process of digestive enzymes during phagocytosis:(1) mRNA-ribosome complex is transferred to a to continue b .(2) Synthesized enzymes enter c and d for modification.(3) The modified enzymes are stored in e .(A) a: ④b: ①c: ⑥d: ⑦e: ④(B) a: ⑦b: ②c: ⑦d: ⑧e: ⑤(C) a: ⑧b: ③c: ⑥d: ⑧e: ⑥(D) a: ⑤b: ②c: ⑤d: ⑧e: ⑦(E) a: ⑥b: ①c: ⑤d: ⑦e: ⑧B5. Tom isolated phagocytes from a blood sample. He cultured these phagocytes in a test tube fora period of time. To observe phagocytosis, E. coli was co-cultured with phagocytes. Whatwill be the consequence if an antacid is added to the culture?(A) Phagocytes can ingest and kill E. coli.(B) Ingestion of E. coli by phagocytes is inhibited.(C) E. coli is viable in phagolysosome.(D) If phagolysosomes are formed, the digestive enzymes in them are inactive.(E) Phagocytes can secrete ingested debris out of the cells.Problem set: Jessica is dissecting a signal transduction pathway (depicted in the following figure) that leads to oncogenesis in cancer cells, in the hope that she can find inhibitors to block the signaling pathway and use them as chemotherapy drugs for cancer treatment. Please answer questions B6-B8.ponents of signal transduction, including A, B and C, usually are activated through phosphorylation or dephosphorylation reactions. What are the mechanisms by which proteins A , B and C are phosphorylated or dephosphorylated?(A) Receptors may contain enzyme domains which can catalysephosphorylation/dephosphorylation reactions.(B) Enzymes that participate in phosphorylation/dephosphorylation reactions may exist inthe cytoplasm.(C) Proteins A, B and C may contain enzyme domains which can catalysephosphorylation/dephosphorylation reactions.(D) Phosphorylation or dephosphorylation may not be mediated through enzymaticreactions.(E) A phosphate group is transferred from the receptor to protein A.(F) The phosphate group can only be provided by H3PO4.B7. Which of the following experiment can prove that the signal transduction pa thway is B→C, but not C→B?(A) Adding an A antagonist will activate B.(B) Adding an A agonist will activate C.(C) Adding a B agonist will activate C.(D) Adding a B antagonist will activate C.(E) Increasing the expression level of B will generate more active C molecules.(F) Cell response can be observed when B antagonist and active C molecules are added tothe cell.B8.If this is a highly activated signal transduction pathway in cancer cells, which of the following processes does the signaling pathway involve?(A) Inhibiting cell division(B) Inhibiting cell differentiation(C) Hypomethylation of some tumor suppressor genes(D) Activating the transcription of an oncogene(E) Arresting the cell cycle at S phase(F) Inhibiting the expression of some DNA repair genesB9. In protein synthesis, there are 64 codons, 61 codons specify the 20 amino acids and the other3 for termination “STOP” (Table). The following sequence of amino acids occurred in thestructure of a polypeptide found in a wild-type organism:Ser-Arg-Ile-Leu-Ala-Ala-Lys-Tyr. Which of the following may generate the mutant amino acid sequence Ser-Arg-Ile-Trp-Arg-Gln-Lys-Tyr?(A) 1 nucleotide mutation(B) 1 nucleotide insertion(C) 1 nucleotide deletion(D) 2 nucleotide mutation(E) 2 nucleotide insertion(F) 3 nucleotide mutationII. Plant anatomy and physiologyB10. At the time of pollination, the living pollen grain typically consists of only the tube cell and the generative cell. During the germination of pollen grain, a pollen tube is produced and the nucleus of generative cell divides and forms two sperms. Directed by a chemical attractant (such as GABA) produced by the synergids, the tip of pollen tube enter the ovule through the micropyle. Then in the embryo sac, double fertilization occurs by the two sperms. Which of the followings are correct as concerning the pollination and double fertilization?(A) Tube cell, sperm, and synergid are haploid, while generative cell and zygote arediploid.(B) During the pollination, a gradient in GABA content is formed from the stigma (low) tothe ovary (high).(C) The two sperms fertilize two eggs, but only one forming zygote.(D) After fertilization, one zygote and one endosperm initial are formed.(E) Germinated pollen grain is male gametophyte, while embryo sac is femalegametophyte.B11. Mary divided 30 pots of plant X of similar condition into 10 plants per group, with each group being treated with different types of light regime. After a month, the flowering phenotypes of each group are shown in the table below:Light DarknessAccording to the information above, which of the following descriptions of plant X are correct?(A) Plant X is a short day plant(B) The critical dark-length required by plant X for flowering is less than 10 hours(C) If group III i s given an “one-minute dark treatment” in the middle of the light period,after one month, most plants in this group will flower(D) If group II is given an “one-minute red light treatment” in the middle of the dark period,most plants in this group will not flower right after one month(E) If the apical buds of group I plants are removed before giving the light regime treatment,then most plants will not produce florigen required for flowering after giving lightregime treatment.B12 and B13 are a problem setDr. Wang carried out experiments with the model organism Arabidopsis thatliana, and identified the two proteins Phototropin 1 and Phototropin 2 as regulators of stomata opening. His experimental results are depicted in the following figure, illustrating the stomata of plants during the day.B12. Which of the following pathways potentially depicts the relationship of Phototropin 1 and Phototropin 2 on a molecular level?B13. Which of the following processes could be regulated and/or mediated by Phototropin 1 and2?(A). K + ion efflux (B). K + ion influx(C). Na + ion influx(D). H 2O efflux(E). H +-ATPase activity (F). Blue light sensingB14. Phytochromes exist in two isoforms, Pr and Pfr. In darkness, they are synthesized as Pr form,then turned into Pfr form after absorbing red light (most effective at 666 nm). When irradiated with far red light, Pfr transforms back to Pr. According to the description above, which of the following are likely to be the absorption spectra of phytochrome?(B)(A)(C)(D)(E)B15. The AGAMOUS(AG) gene is involved in flower development. Plant mutants without a functional AG would produce flowers with only sepals and petals. A scientist generated a transgenic plant harboring a green fluorescence protein (GFP) gene driven by the AG promoter in a wild type background that produces normal flowers. In which of the following flower parts, you are likely to observe strong GFP fluorescent signals?(A) Receptacle(B) Sepal(C) Petal(D) Stamen(E) CarpelIII. Animal anatomy and physiologyB16 to B18 are a problem setB16. In the following figure, the structure of fish gills and the direction of water flow in the ventilation are illustrated. Answer the questions.Which of the following statements are correct?(A) Vessel A carries oxygenated blood(B) Vessel B carries deoxygenated blood(C) Vessel A is an arteriole(D) Vessel B is a venule(E) Vessel A and B are portal vesselsB17. During evolution, the gas exchange in gills has become more effective by(A)A decrease in the thickness of the structure C(B)A decrease in the number of cell layers in structure C(C)An increase in the metabolic rate of the structure C(D)An increase in the cell volume of the structure C(E)An increase in the surface area of the structure CB18. Scientists found a kind of epithelial cell (X cell) in the structure of D with which fish can maintain body fluid osmolarity. Consequently, X cells are supposed to(A) Absorb salt actively in freshwater fish(B) Excrete salt actively in seawater fish(C) Excrete water actively in freshwater fish(D) Absorb water actively in seawater fish(E) be rich in mitochondriaB19. The following image represents a gastric fold from the interior surface of the stomach. The different structures are indicated by roman numerals:The list below describes the function for each structure.a. Secretes hydrochloric acidb. Secretes mucus which lubricates and protects the cells that cover the stomach.c. Contains a series of ridges or deep pits which lead to the glandsd. Secretes pepsinogene. Contains three different types of cells that secrete the components of gastric acid.Please indicate the correct set of answers relating structure with corresponding function.B20. The graph below depicts the different pulmonary volumes and capacities:Below, you will find two charts, please correlate with each other and with the graph above:B21. Which of the following statements about thermo-adaption in animals are correct?(A) Blue-fin tuna is able to raise their core temperature. Therefore, it is an endothermicanimal.(B) Some icefish are able to survive in the freezing ice-laden water and maintain a verystable body temperature. Therefore, icefish are homeothermic animals.(C) Shivering can help mammals to generate heat, and it is regulated by hypothalamus inmammals.(D) Brown adipose tissues help mammals to generate heat by supplying energy to skeletalmuscles.(E) Brown adipose cells are rich in mitochondria for heat generation.B22. Maintenance of the blood glucose level is important for normal physiological function. It is modulated by both neural and endocrine systems. The diagram below shows two different situations resulting from physiological stress or low blood glucose level. Complete the table in the answer sheet by using appropriate letters shown below.B23 and B24 are a problem setB23.Normal spermatognesis and androgen secretion are delicately regulated by hormones in males. The occurrence of infertility in the male could be resulted from the disturbance of hormonal regulation. The following figure partly illustrates the cross interactions among hypothalamus, pituitary gland, and male gonads. The symbols “(-)” indicate negative feedback inhibitions. As shown in the table below, some hormones, cells, or tissues are tried to match to the terms in this figure (a to h).B24. The application of available and suitable hormonal therapy to the male patients with gonad failure is very important. Consider how the following case may be improved by a hormonal treatment.Patient A suffered from testicular cancer and had both testis removed.According to the figure of Q22, select the most appropriate letter to patient A.B25 and B26 are a problem setB25. A to E in the diagram below represents the five major steps of synaptic transmission.Scientists study drug effects on synaptic transmission by using electrophysiological recording. Briefly the postsynaptic current will be recorded and used to determine the possiblemechanism which may account for the drug effects. Figure 1 is the typical tract of postsynaptic current before drug administration. Match the figure number with the correct drug effects below(I) (IV)A. Release of neurotransmitter.B. Activation of presynaptic calcium channel.C. Activation of postsynaptic sodium channel.D. Re-uptake of neurotransmitter.(II) (V)(III)B26. Epilepsy is a common neurological condition. Patients suffer convulsions which result from hyperactivity of certain cerebral areas. Symptoms can be reduced by using antiepileptic drugs. If the receptor activated in the above figure was a chloride channel instead of a sodium channel, which of the following mechanism(s) may form the basis for an antiepileptic drug?B27. The following diagram indicates the basic structure of a sarcomere.Choose and fill in the appropriate answering code shown below to each statement in the following table. The statements are about a muscle fiber undergoing an isotonic contraction.IV. EthologyB28. There are two types of bird hatchlings: precocial and altricial. In general, precocial birds are covered with feathers when they hatch, and can find their own food with help and instructions from their mothers. In contrast, altricial hatchlings require feeding and caring for from the parents. Based on this, which of the following statements are correct?(A) Precocial hatchlings usually take longer to hatch than altricial hatchlings.(B) Altricial hatchlings usually develop imprinting earlier than precocial hatchlings.(C) Parents invest more in precocial hatchlings than in altricial hatchlings during nestlingperiod.(D) For a group of young birds that hatch at the same time, altricial hatchlings tend todevelop the ability to fly earlier than precocial hatchlings.(E) Parents of precocial and altricial hatchlings have the same level of investment inreproduction during the breeding season.B29. An entomologist found that a species of cockroach use the dramatic change of light intensity at dusk (given as 6:00 pm) to reset its biological clock. He also found out that the circadian (daily) rhythm is 25 hrs. If a student cages a cockroach of this species into a dark box at 6:00 pm, at what time the cockroach will be active after 12 days? Fill in the time in the given space, then circle “am” or “pm” in the Answer Sheet.B30. A biologist discovered that a species of moth is capable of flying in a straight line at night because it keeps a constant angle (80°) between its body axis and the direction of moon lightusing photoreceptors as a tool. If the moth encounters a bright light in a dark night, what kind of flight path of the moth one will expect to see in relation with the light source?B31. A researcher monitored 10 pairs of adult birds during the breeding season. For each of the pairs, he recorded body lengths of the male and female, and their nesting date (Table 1).Table 1. The body lengths of the males and females, and the nesting dates for the 10 pairs of birds (A to J)Based on the data in Table 1, the mean body length is 26.65 cm for the females, and 28.99 cm for the males. In comparison with the mean body length of 26.10 cm in females and 27.60 cm in males in the total adult ( breeders + non-breeders) population (N=30) of the study area, which of the following statements are correct?(A) All males in this species are larger than females.(B) Females tend to pair with males that are larger than themselves.(C) Male body lengths do not affect female mate choices.(D) Nesting dates are linked to male body lengths.(E) The chance of breeding of this species is most likely affected by the body size.V. Genetics and EvolutionB32. The black, brown and white coat colors of mice are determined by the interaction of B/b andC alleles. B and b alleles control the synthesis of black and brown pigments, respectively. Inthe presence of the C allele, black and brown pigments are deposited in the fur. In a crossing between BbCc and bbCc, which of the following statements are correct?(A) The coat colors of parental mice are black and brown respectively.(B) The ratio of black and brown offspring is 1:1.(C) 3/4 of the offspring are black.(D)1/4 of the offspring are brown.(E) 1/4 of the offspring are white.(F) Alleles C and B/b are co-dominant.B33. Fur of Guinea pigs can have different colors (black and white).Hairs can be rough and smooth. Alleles Q and q are coding forcolor, alleles R and r for type of hair. A number of cavias withexactly the same genotype (parents group) are allowed to mate and the result is a big F1 offspring. Most of these have a black rough fur. A small number has white smooth fur.Besides about the same number of offspring is white and rough, or black and smooth.ing the given letters, indicate the genotype of the guinea pigs in the parents group: .B33.2.If 1024 F1 offspring were born, how many of them are black and smooth? .B33.3. Guinea pigs often have a fur spot pattern. According to a simplified model spot pattern is determined by one gene with two alleles: G and g. If G is present the guinea pig is spotted.Students investigate the population Guinea pigs in a territory and find out that 84 % was spotted. Presuming this population is in (Hardy Weinberg) equilibrium. Calculate the frequency of G. Give your answer in one decimal. .B33.4. At one day all unspotted guinea pigs are caught and transported to another territory. What will be the number of unspotted guinea pigs in the next generation? Give your answer as a percentage without decimals. .B34.It is believed that “land plan t s” are evolved from charophytes. Which of the following statements support this hypothesis?(A) Both have alternation of generation in life cycles(B) Both contain chlorophyll a and chlorophyll b(C) Both have peroxisomes that contain photorespiration related enzymes(D) Both can form phragmoplasts during cytokinesis(E) Both contain cellulosic cell walls(F) Both have the cellulose synthase arranged on the plasma membrane in a rosette patternQuestions B35a-B35c are a problem setDr. Chen was investigating the function of gene X in rice by using a mutant with a T-DNA inserted in the exon 2 as diagrammed below. The size of the T-DNA is approximately 5 kilo base pairs (Kbp). She used PCR analysis for genotyping of five individual plants (A, B, C, D, E ) with primers I, II, and III as indicated in the diagram. The gel on the right shows the PCR result. The DNA molecular size markers are shown in lane M. Lane A-E are the PCR products from leaf samples of the plant A-E, respectively. It is known that the polymerase being used is unable to effectively amplify DNA fragments above 5 Kbp.Based on the above information, answer questions B34a-B34b :B35a . Which pair of primers (I+II, I+III, or II+III) amplified the DNA band in lane B? B35b . Which plant(s) (A, B, C, D, or E) is/are homozygous mutant(s)?B35c. Which plant(s) (A, B, C, D, or E) is/are the F1 offspring of homozygous mutant crossedto the wild type?B36. Doctor Lin isolated a rice mutant with a late flowering time phenotype. The mutant alleleresponsible for this phenotype was identified by map-based cloning technique and named LFT m . When Doctor Lin sequenced the whole LFT m gene, including the promoter region, she could not find any difference in the nucleotide sequence as compared to the wild-type allele. Which of the following phenomena are likely to be responsible for this observation?(A) The mRNA level of LFT in the mutant is the same as that in the wild-type at the samedevelopmental stage(B) The LFT protein found in the wild type plants cannot be detected or is lower in the mutant primerprimerprimer(C)The DNA methylation patterns on LFT are altered in the mutant(D)The levels of histone proteins are dramatically altered in the mutant(E)Introducing the cloned LFT m into the wild-type plant generates a transgenic plant withlate flowering phenotypeVI. EcologyB37. The population size of a dragonfly in a pond was estimated to be 50,000 during a survey.Their sex ratio is 1:1. Each female lays approximately 400 eggs. A second survey of the next generation revealed that the population size is still 50,000 and the sex ratio is still 1:1.What is the average survival rate (surviving to adult stage) of the eggs?(A)0.2%(B)0.25%(C)0.5%(D)1%(E)5%B38. Biologists found that the threshold temperature for development of a mosquito species is 15℃. They also found that the product of (1) the number of days it takes to complete development, and (2) the difference between the temperature during development and threshold temperature, is a constant. That is, the result of multiplying (1) and (2) is a constant. It is known that this mosquito requires 15 days to complete development at 30℃, and given that there was an unusually warm May in India this year with an average temperature of 40℃, how many days it should take this mosquito to complete development this May in India?B39. Assuming human, birds, and fish respectively have Type I, II, and III survival curves (thevertical axis is survival rate, and horizontal axis is time), which of the following figures most accurately describes mortality curves (obtained by replacing survival rate with mortality rate) for these three groups of organisms (Type I’, II’ and III’)?B40. The figure below shows a nutrient cycle, and the six groups of organisms (A to F) involved in this cycle.Which of the following descriptions are correct?(A) C and F are carnivores.(B) C and E are carnivores.(C) A and B are herbivores.(D) D includes bacteria and fungi.(E) F includes bacterivores and fungivores.B41. When comparing closely-related bird species, mortality of breeding individuals appears to be higher for species in temperate regions than in tropical regions. Therefore, predation risks to parents themselves, their young and eggs are given different priorities for species in different regions. In an experiment where specimen of three different predators (crows, owls, and hawks) were placed at close distances to the nests during the day in the breeding period, which of the following responses from the parents can be expected? Note that crows are predators of the young and eggs, owls are nocturnal predators, and hawks are diurnal predators of adult birds.(A) The owl specimen is more strongly avoided by the parents than the hawk specimen.(B) With the crow specimen, the parents of tropical species reduce the frequency ofreturning to the nests and feeding the young to a lesser degree than parents of temperatespecies.(C) With the hawk specimen, the parents of tropical species reduce the frequency ofreturning to the nests and feeding the young to a lesser degree than parents oftemperature species.(D) With the hawk specimen, the parents of tropical species reduce the frequency ofreturning to the nests and feeding the young to a greater degree than parents oftemperature species.(E) The degree to which the parents reduce their frequency of returning to the nests andfeeding the young when predator specimen is present is not affected by the type ofpredators or the latitudes in which the species is distributed.B42.The figure below shows a scheme of the assimilation efficiency (A/I) and production efficiency (P/A) of two groups of mammals in a meadow ecosystem.Which of the following descriptions are correct?(A) Digestion of plant materials costs relatively less energy than digestion of animalmaterials.(B) Plant materials that are reabsorbed have less organic contents than animal materials thatare reabsorbed.(C) R ranges between 40 and 60 J in carnivores.(D) R ranges between 40 and 60 J in herbivores.(E) R is lower in Bull frogs than in mammals.B43. Some fungi form symbiotic associations with the roots of vascular plants, which are called mycorrhizae. In such associations, mycorrhizae help plants to absorb water, phosphate salt and other mineral nutrients. Depending on whether the fungus colonizes the roots extracellularly or intracellularly, mycorrhizae can be grouped into ectomycorrhizae or arbuscular mycorrhizae. Which of the following descriptions of mycorrhizae are correct?(A) Seedlings with mycorrhizae grow more rapidly than seedlings without mycorrhizae inlow-phosphorus soils.(B) Hyphae of arbuscular mycorrhizae can penetrate the cortical cells of the roots and cellmembranes to form symbiotic associations intracellularly.(C) Hyphae of ectomycorrhizae can penetrate the cortical cells of the roots, and form hyphalsheaths around the roots.(D) Mycorrhizae have similar functions as root hairs of plants, and therefore, plants withmycorrhizae have less-developed root hairs.(E) Each mycorrhiza forms symbiotic associations with the roots of specific plants.VII. BiosystematicsB44. Eggleton et al (2007) studied the phylogeny of Dictyoptera, as shown below. According to the proposed phylogeny, determine whether the following statements are true (T) or false (F).(A) Mantids’ sister group is cockroaches.(B) Cockroaches form a paraphyletic group.(C) Termites should be viewed as highly modified cockroaches.(D) Mantids should be viewed as highly modified cockroaches.(E) Termites evolved from mantids.。

2011年数学建模C题(国二)

2011年数学建模C题(国二)

承诺书我们仔细阅读了中国大学生数学建模竞赛的竞赛规则.我们完全明白,在竞赛开始后参赛队员不能以任何方式(包括电话、电子邮件、网上咨询等)与队外的任何人(包括指导教师)研究、讨论与赛题有关的问题。

我们知道,抄袭别人的成果是违反竞赛规则的, 如果引用别人的成果或其他公开的资料(包括网上查到的资料),必须按照规定的参考文献的表述方式在正文引用处和参考文献中明确列出。

我们郑重承诺,严格遵守竞赛规则,以保证竞赛的公正、公平性。

如有违反竞赛规则的行为,我们将受到严肃处理。

我们参赛选择的题号是(从A/B/C/D中选择一项填写): C 我们的参赛报名号为(如果赛区设置报名号的话):所属学校(请填写完整的全名):四川文理学院参赛队员 (打印并签名) :1. 刘姣2. 冯德琼3. 何招才指导教师或指导教师组负责人 (打印并签名):张瑞日期: 2011 年 9 月 11 日赛区评阅编号(由赛区组委会评阅前进行编号):编号专用页赛区评阅编号(由赛区组委会评阅前进行编号):全国统一编号(由赛区组委会送交全国前编号):全国评阅编号(由全国组委会评阅前进行编号):企业退休职工养老金制度改革的探究摘 要本文针对我国企业退休职工养老保险基金收支平衡的问题,根据2005年颁发的《国务院关于完善企业职工基本养老保险制度的决定》,建立养老保险基金收支平衡模型[1],即缴存的养老保险金E 与得到的养老保险金F 保持一致;和对养老金替代率讨论模型58.5%u ε=±。

分析了在该政策背景下,当已知基金收益率和缴费率时,各个因素对基金收支平衡的影响。

对问题一采用阻滞增长模型[2]0()1(1)m rtm x x t x e x -=+-,用曲线拟合[3]的方法预测从2011年至2035年山东省职工的年平均工资。

对于问题二计算出各年龄段职工工资与该企业平均工资之比,再使用加权平均得出缴费指数参考值。

针对问题三根据一个职工他所交的养老保险金和他退休后总共领取到的养老金的差值来计算其缺口,最后找到该职工领取养老金到多少岁时,达到收支平衡。

生物多样性评价模型

生物多样性评价模型

2011年第四届“互动出版杯”数学中国数学建模网络挑战赛论文2011年第四届“互动出版杯”数学中国数学建模网络挑战赛题目生物多样性的评价指标摘要2010年是联合国大会确定的国际生物多样性年。

保护地球上的生物多样性已经越来越被人类所关注。

生物多样性包括物种多样性、遗传多样性、生态系统多样性,影响生物多样性的因素也相当的多,因此,对生物多样性的评定时一个相当复杂的问题。

为提出一种全面而有效的生物多样性评定指标,我们建立数学线性模型。

根据科学性、代表性、实用性的原则,提出了生物多样性综合评价的7个指标:野生维管束植物丰富度、野生高等动物丰富度、生态系统多样性、植被垂直层谱的完整性、物种特有型、外来物种入侵度、物种受威胁程度。

利用归一化模型处理以上7个指标,按照经过研究归结的各指标所占权重,得到评价生物多样性指标系数。

在此过程中,利用样线法、样方法等采集群落数据,利用数学思想、图表、函数等形式将调查所得数据进行处理,得到一系列关于生物多样性的指标系数。

再利用规定的生物多样性状况等级图表,从而能够得到生物多样性状况的分布情况。

文中也提到物种丰富度、shannon多样性指数,这些都对生物多样性的评定有一定影响。

然而这一切的指数都需要用合理的数据,因此,我们选取重庆、四川的生物多样性为本次研究的主要对象。

本文通过科学的计算和阅读大量的资料以及样地调查等野外调查方法进行评测,建立了一个用数学知识解决受多因素影响的生物多样性指标的回归模型。

关键词:生物多样性评价指标野生维管束植物丰富度野生高等动物丰富度生态系统多样性植被垂直层谱的完整性物种特有性外来物种入侵度物种受威胁程度归一化处理问题重述当前,作为人类生存基础的生物多样性受到越来越严重的威胁,世界自然保护联盟(IUCN)发布的“2004年濒危物种红色名录”表明,113种的两栖类动物,二分之一以上的龟类,八分之一的鸟类和四分之一的哺乳动物正在面临生存威胁。

所以,保护地球上的生物多样性越来越被人类社会所关注。

研究生数学建模2011年C题

研究生数学建模2011年C题

2011年全国研究生数学建模竞赛C题小麦发育后期茎秆抗倒性的数学模型小麦高产、超高产的研究始终是小麦育种家关注的热点问题。

随着产量的增加,小麦的单茎穗重不断增加。

但穗重的增加同时使茎秆的负荷增大,导致容易倒伏。

倒伏不但造成小麦减产,而且影响小麦的籽粒品质。

因此要实现小麦高产优质的跨越,就必须解决或尽量减少小麦的倒伏问题。

小麦倒伏从形式上可分为“根倒”和“茎倒”,一般都发生在小麦发育后期。

“根倒”主要与小麦种植区域的土壤品种与结构特性有关,本题不做讨论。

“茎倒”是高产小麦倒伏的主要形式,尤其是发生时间较早的“茎倒”,往往造成大幅度的减产。

“茎倒”的原因是茎秆与穗的自重和风载作用的迭加超过了小麦茎秆的承受能力。

解决倒伏问题的方法之一就是针对不同的产量,寻找小麦抗倒伏能力最佳的茎秆性状(包括株高、茎长、各节间长、各节茎外径、壁厚、茎秆自重、穗长、穗重等)。

各方面的专家通过分析影响小麦倒伏的各种因素,目前已经得到了一些结果,但是对抗倒伏能力最佳的茎秆性状还没有定论。

通过物理力学类比研究小麦抗倒伏性是一个新方向,已有一些工作。

值得我们进行探讨。

困难在于缺乏相关试验参考数据,我们只能在作较多假设下先进行粗略研究,为进一步试验提供根据。

题目的附件中收集了一批各个品种小麦的茎秆性状、产量、倒伏情况的数据。

显然还不够完整,各年参数选取不一致,也有数据缺漏。

但农业数据一年只有一次,短期内无法做到完整、全面、详尽,期望以后能逐渐完善。

请你们就已有数据解决以下几个问题:(1) 依据有些论文中判断茎秆抗倒性的抗倒伏指数公式:茎秆抗倒伏指数=茎秆鲜重×茎秆重心高度/茎秆机械强度对提供的数据,建立各品种小麦的茎秆抗倒指数公式。

对于缺乏有关参数的年份,可进行合理的假设,如通过已知数据求茎秆机械强度与茎秆粗厚的关系。

(2) 研究抗倒伏指数与茎秆外部形态特征之间的关系。

即给出抗倒伏指数与株高、穗长、各节间长、节间长度比、各节壁厚、穗重、鲜重等茎秆性状在最易引起倒伏期的相关性指标。

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Evolution of Graphene Growth on Niand Cu by Carbon Isotope LabelingXuesong Li,†Weiwei Cai,†Luigi Colombo,*,‡and Rodney S.Ruoff*,†Department of Mechanical Engineering and the Texas Materials Institute,1Uni V ersityStation C2200,The Uni V ersity of Texas at Austin,Austin,Texas78712-0292,andTexas Instruments Incorporated,Dallas,Texas75243Received August3,2009ABSTRACTLarge-area graphene growth is required for the development and production of electronic devices.Recently,chemical vapor deposition(CVD) of hydrocarbons has shown some promise in growing large-area graphene or few-layer graphenefilms on metal substrates such as Ni and Cu.It has been proposed that CVD growth of graphene on Ni occurs by a C segregation or precipitation process whereas graphene on Cu grows by a surface adsorption process.Here we used carbon isotope labeling in conjunction with Raman spectroscopic mapping to track carbon during the growth process.The data clearly show that at high temperatures sequentially introduced isotopic carbon diffuses into the Nifirst,mixes,and then segregates and precipitates at the surface of Ni forming graphene and/or graphite with a uniform mixture of12C and 13C as determined by the peak position of the Raman G-band peak.On the other hand,graphene growth on Cu is clearly by surface adsorption where the spatial distribution of12C and13C follows the precursor time sequence and the linear growth rate ranges from about1to as high as6µm/min depending upon Cu grain orientation.This data is critical in guiding the graphene growth process as we try to achieve the highest quality graphene for electronic devices.Graphene,a monolayer of sp2-bonded carbon atoms or one monolayer of graphite,has attracted interest in part because of its unique transport properties.1The surface science community has published extensively on what is referred to as“monolayer graphite”,that is,graphene,as grown on various metalfilms that are epitaxially well matched to graphene.2To date,devices have been fabricated mostly on exfoliated graphene,1chemically reduced graphite oxide,3-6 graphene formed by ultrahigh vacuum(UHV)annealing of single crystal SiC,7,8and that grown on metal substrates.9-15 However,exfoliated graphene still shows superior transport properties compared to all other sources.Graphene obtained on SiC single crystals has good mobility,but this material may be limited to devices on SiC only,since transfer to other substrates such as SiO2/Si has not been demonstrated yet and might be difficult.There have been a number of reports on the growth of graphene on metal substrates such as Ni, Co,Ru,Ir,Cu,etc.,by UHV-chemical vapor deposition (CVD)9-11or“normal”CVD.12-15Because of cost,grain size,etchability,and their wide use and acceptance by the semiconductor industry,Ni and Cu have received the most attention as a graphene substrate material.Several groups have already demonstrated the growth of graphene and few-layer graphene(FLG)on polycrystalline Ni12-14while large area graphene has been grown on Cu15substrates by CVD. It has been proposed that CVD growth of graphene on Ni is due to a C segregation12or precipitation13process and that a fast cooling rate in conjunction with thinfilms are needed to suppress the formation of multiple graphene layers.12,14 But to date the graphenefilms grown on Ni foils or on Ni thinfilms have not yielded uniform graphene layers,that is, they have a wide variation in thickness over the metal surface from a monolayer to many layers.Recently,in a different publication,we have shown that Cu is an excellent candidate for making large-area graphenefilms with uniform thickness due to the low solubility of C in Cu.15In that publication it was suggested that the graphene growth is somehow surface mediated and self-limiting.In this work,we used isotopic labeling of the carbon precursor to study the mechanism and kinetics of CVD growth of graphene on Ni and Cu substrates.We took advantage of the separation of the12C and13C Raman modes to observe the spatial distribution of graphene domains.The frequencies of Raman modes are given by eq1with the assumption that the12C or13C atoms are randomly mixed and the bond force constants are equal16*To whom correspondence should be addressed.E-mail:(R.S.R.)r.ruoff@;(L.C.)colombo@.†The University of Texas at Austin.‡Texas Instruments Incorporated.ω)ω12 m12n12m12+n13m13(1)200912where ω12is the Raman mode frequency of 12C graphene/graphite,n 12and n 13are the atomic fractions,and m 12and m 13are the atomic masses of 12C and 13C,respectively.We used thin Ni film (∼700nm,deposited by sputtering on SiO 2/Si wafer)rather than on Ni foil to minimize the saturation time and the amount of carbon in the Ni film since the solubility of C in Ni is high,about ∼0.9at.%at 900°C.For Cu,we used foils having a thickness of 25µm since the carbon solubility is negligible.The experimental proce-dure for graphene growth is similar to that reported previ-ously 15with a deposition temperature of 900°C for Ni and 1000°C for Cu.However,in this work both normal methane and 13CH 4(99.95%pure)were introduced to the growth chamber in a specific sequence.The duration of exposure of methane is defined as j t i as,where j )12or 13denotes 12CH 4or 13CH 4,and i denotes the step in the sequence (e.g.,13t 1means the first gas introduced was 13CH 4with the duration of exposure being t 1).Figure 1shows schematically the possible distributions of 12C and 13C in graphene films based on different assumed growth mechanisms when 12CH 4or 13CH 4are introduced sequentially.We want to emphasize that “segregation”and “precipitation”should be distinguished as different concepts,which have been well explained by Shelton et al.,17that is,segregation refers to compositional heterogeneity in thermal equilibrium under conditions which correspond to a “one-phase”field,while precipitation refers to inhomogeneities that arise as a result of equilibrium “phase separation”.Blakely and coauthors have performed extensive studies on the formation of carbon films by cooling Ni foils saturated with C at high temperatures and found that a monolayer graphite grows first by C segregation,followed by more C precipitation thus forming graphite.17-20This previous work can be extended to explain CVD growth of FLG films on Ni film as well,as will be demonstrated in the following section.Figure 1a shows the case of carbon segregation from the bulk to the metal surface followed by precipitation growth.In the case of metals like Ni where the carbonsolubility is high,carbon diffuses into the metal first before segregating and precipitating to the surface.As a result,sequential dosing of 12CH 4and 13CH 4is expected to yield a uniform C-metal solution,and the segregated and/or pre-cipitated graphene will consist of randomly mixed isotopes (Figure 1a).In contrast,if carbon does not diffuse into the metal,graphene grown with the sequential dosing of 12CH 4and 13CH 4grows by surface adsorption and the isotope distribution in the local graphene regions will reflect the dosing sequence employed (Figure 1b).Figure 2shows the results of graphene growth on Ni film.We evaluated several sets of feeding time sequences of C isotopes on Ni films,but no distinguishable separation of isotopes was found.Figure 2a shows an optical micrograph of a graphene film grown on a Ni film (13t 1,3,5,7)12t 2,4,6,8)1min)and transferred onto a SiO 2/Si wafer by poly (methyl methacrylate)(PMMA)similar to the reported method.15,21The variation of color contrast indicates the film is not uniform in thickness and consists of one to tens of graphene layers.Figure 2b further shows the map of the G band and Figure 2c shows a typical Raman spectrum from this FLG film,which is located at ∼1553cm -1,corresponding to the composition of 45%-13C/55%-12C according to eq 1.The uniformity of the G-band and the uniform shift according to eq 1demonstrates the uniformity of the 12C and 13C distribution across the metal surface supporting the idea that the growth mechanism is as that described in Figure 1a.Figure 3shows the results of graphene grown on Cu foils (13t 1,3,5,7)12t 2,4,6,8)1min).Figure 3a shows an optical micrograph of the resulting graphene film transferred onto a SiO 2/Si substrate using PMMA as the carrier material for transfer as previously reported.15,21The surface of the transferred graphene is relatively uniform with the exception of wrinkles that are believed to be formed during cool-down.The wrinkles are a result of the different coefficient of thermal expansion between graphene/graphite and the un-derlying metal substrate.22,23Figure 1.Schematic diagrams of the possible distribution of C isotopes in graphene films based on different growth mechanisms for sequential input of C isotopes.(a)Graphene with randomly mixed isotopes such as might occur from surface segregation and/or precipitation.(b)Graphene with separated isotopes such as might occur by surfaceadsorption.Figure 2.Optical micrograph and distribution of C isotopes in a FLG film grown on Ni.(a)An optical micrograph of a FLG film transferred onto a SiO 2/Si wafer.(b)The corresponding Raman map of location of the G bands and (c)a typical Raman spectrum from this film,showing the film consists of randomly mixed isotopes (with an overall composition of ∼45%13C and ∼55%12C).Scale bars are 5µm.The Raman spectra,Figure 3b,show the presence of graphene with regions having close to pure 12C from natural methane (∼99%12CH 4),regions of isotopically pure 13C,and regions where both 12C and 13C are present.An analysis of both the color contrast of the optical micrograph,24and the Raman spectra 13,25-27show that the carbon layer is a monolayer of graphite,that is,graphene.When the Raman laser beam was focused at the junction of 12C and 13C graphene regions,the characteristic bands for both 12C and 13C graphene appeared in the spectrum.The intensity of each band depends on the area occupied by each isotopically labeled region under the laser spot and the sum of the intensity of two bands (e.g.,G 13+G 12)was found to be essentially equal to that of the intensity from either the pure 13C or 12C regions of the graphene film.Figures 3d -i shows the Raman G and D band maps of the graphene film shown in Figure 3a for both 12C and 13C.Figure 3d is a map of the overall G band intensity (G 13+G 12)of the area shown in Figure 3a.The uniform intensity distribution demonstrates that the thickness is uniform except for the wrinkles (bright lines).Figure 3e,f shows the mapsof the G-band of 13C and of 12C,respectively,which show the time evolution of graphene growth.The bright solid centers in the G 13map in Figure 3e correspond to 13C-graphene grown during 13t 1;the low intensity,dark rings correspond to 12C-graphene grown during 12t 2,which are seen as bright rings in the G 12map in Figure 2f;the bright area between the dark rings in Figure 3e corresponds to 13C-graphene grown during 13t 3.Figure 3c shows a line scan (marked with dashed lines across Figures 2d -f)where the 12C-graphene and 13C-graphene domains are clearly seen with the blue line representing the G 13(i.e.,13C-graphene)domains and the pink line representing the G 12(i.e.,12C-graphene)domains.The green line,which is the most uniform across the film,is the overall G band intensity (G 13+G 12)with the peak corresponding to the wrinkle in the film.It is interesting to note that we flowed eight cycles of alternating 12CH 4and 13CH 4but the resulting graphene grew only during the first three dosings.The fourth and subsequent doses played no role because the surface was already saturated with graphene.These data show that single layer graphene on Cu grows in less than 3min under the conditions weused,Figure 3.Micro-Raman characterization of the isotope-labeled graphene grown on Cu foil and transferred onto a SiO 2/Si wafer.(a)An optical micrograph of the identical region analyzed with micro-Raman spectroscopy.(b)Raman spectra from 12C-graphene (green),13C-graphene (blue),and the junction of 12C-and 13C-graphene (red),respectively,marked with the corresponded colored circles in (a)and (e).(c)Line scan of the dashed lines in (d -f).Integrated intensity Raman maps of (d)G 13+12(1500-1620cm -1),(e)G 13(1500-1560cm -1),(f)G 12(1560-1620cm -1),(g)D 13+12(1275-1375cm -1),(h)D 13(1275-1325cm -1),and (i)D 12(1325-1375cm -1)of the area shown in (a).Scale bars are 5µm.growth occurs in two-dimensions and thus is a consequence of a surface-adsorption process,and that growth is self-limiting since there is no catalyst to promote decomposition and growth after thefirst layer of carbon(graphene)is deposited.Thefilms grown on Cu show a nonuniform presence of the Raman D-band.The D maps in Figure3g-i provide additional information.Other than the high intensity of the D band from the wrinkles,some bright spots and lines are also seen corresponding to defective centers and boundaries between graphene domains,respectively.We define a domain as the area of graphene grown from one nucleus.The domain size will depend on the specific growth conditions and for the conditions used in this work the diameter of the domain is about10µm.The interdomain defects can occur where the graphene domains join,for example in the current case, after13t3,defects are observed as indicated by the blue arrows in Figure3g.The nature of the defects could be the formation of pentagonal and/or heptagonal arrangements of carbon atoms that form mis-oriented graphene domains resultingfrom the Cu surface roughness,as was found for Ir.28In contrast,the low defect boundaries(indicated by the white arrows in Figure3g)may indicate a“good”registration between two domains.A detailed understanding of such defects is suggested for future work.Careful observation of the optical micrograph(Figure3a)and the Raman maps (Figures3d-i)shows that there is no overlap of the graphene layers where the domains join,suggesting that there is crystallographic registration to the Cu substrate.If there were overlap,a high contrast or bright line would be present in the micrograph and the G-band Raman maps.This sequential distribution of13C and12C clearly shows that graphene growth on Cu is based on the surface adsorption mechanism. As we reported previously,15there can also be a small fraction of few-layerflakes stacked on the graphenefilm.For the samples discussed here,Raman imaging showed that these flakes also consist of separated13C and12C rings,indicating that they grow by surface adsorption,but not by segregation/ precipitation(Figure4).Theseflakes show the same or smaller number of isotopic sequential rings as thefirst layer graphene, indicating thatflake growth stops once the Cu surface is fully covered with graphene.Termination offlake growth due to the full coverage of Cu surface with graphene suggests that the carbon source forflake growth is from the catalytic decomposition of methane by the active Cu surface.Further work is necessary to understand the exact origin of theflake defects.We also studied the graphene growth rate from the growing front of either12CH4or13CH4.For the case of thefirst graphene layer,the edge growth rate for thefirst minute is3-6µm/min and for the second minute it is1-2µm/min.The growth rate is found to be dependent on the Cu grain orientation as was previously observed by scanning electron microscopy imaging of an interrupted growth runs.15The domain advancement rate that decrease with time could be associated with a decrease in the number of catalytic sites as the domainsfill the Cu surface area.This will require further investigation and the subject of a future publication.In contrast,the growth rate of the second and third layers is slower(<160and<40nm/min,respectively), and the multilayerflakes thus occupy a very small area(<5%) of the wholefilm.The slower growth rate of higher order layers may be attributed to a much lower concentration of Cu catalyst available to promote the decomposition of methane in these regions.The two mechanisms of graphene growth on Ni and Cu can be understood from the C-metal binary phase diagram.The binary phase diagrams of C-Ni and C-Cu are similar in that C has a limited solubility in the metal without the presence of a metal-carbide line compound.The only significant difference is that the solubility of C in Cu is much lower than that in Ni. Since only a small amount of carbon can be dissolved in Cu, the source for graphene formation is mainly from the CH4that is catalytically decomposed on the Cu surface with minimal carbon diffusion into the Cu.As mentioned previously,once the surface is fully covered with graphene growth terminates because of the absence of a catalyst to decompose CH4.In contrast,Ni can dissolve more carbon atoms and hence it is difficult to get uniform graphenefilms due to precipitation of extra C during the cool-down.The C precipitation process is a nonequilibrium process,which should be suppressed if one aims to achieve monolayer graphene growth,for example,by using a controlled thin Nifilm and/or high cooling rate.12-14However, because of microstructural defects,predominantly grain boundaries,it is very difficult to fully eliminate the effect of precipitation for metals with high carbon solubility.Hence, metals with low C solubility such as Cu offer a possible path to large-area growth of graphene.Discrete regions of isotopically labeled graphene such as presented here for growth on Cu may also yield novel devices and transport physics in future studies.Acknowledgment.We would like to thank the Nanoelec-tronic Research Initiative(NRI-SWAN;no.2006-NE-1464), the DARPA CERA Center,and The University of Texas at Austin forsupport.Figure4.Raman imaging spectroscopy of few-layer(FL)regions.(a)Optical micrograph.(b-d)Raman maps of overall G,G13,and G12,respectively,corresponding to the region in(a).The FL regions can be easily located from the optical micrograph due to their high contrast(a)and also from their high intensity in the overall G map (b).The layer and growth sequences are schematically shown in (e),where red,orange,yellow show13C grown in thefirst minute, blue,purple,teal show12C grown in the second minute,and maroon, lime show13C grown in the third minute.Scale bar is2µm.References(1)Geim,A.K.;Novoselov,K.S.Nat.Mater.2007,6(3),183–191.(2)Greber,T.[Online early access.]DOI:arXiv:0904.1520v1,2009.(3)Dikin,D.A.;Stankovich,S.;Zimney,E.J.;Piner,R.D.;Dommett,G.H.B.;Evmenenko,G.;Nguyen,S.T.;Ruoff,R.S.Nature2007,448(7152),457–460.(4)Gilje,S.;Han,S.;Wang,M.;Wang,K.L.;Kaner,R.B.Nano Lett.2007,7(11),3394–3398.(5)Stankovich,S.;Dikin,D.A.;Dommett,G.H.B.;Kohlhaas,K.M.;Zimney,E.J.;Stach,E.A.;Piner,R.D.;Nguyen,S.T.;Ruoff,R.S.Nature2006,442(7100),282–286.(6)Park,S.;Ruoff,R.S.Nat.Nanotechnol2009,4,217–224.(7)Berger,C.;Song,Z.;Li,X.;Wu,X.;Brown,N.;Naud,C.;Mayou,D.;Li,T.;Hass,J.;Marchenkov,a.A.N.;Conrad,E.H.;First,P.N.;de Heer,W.A.Science2006,312,1991–1996.(8)Emtsev,K.V.;Bostwick,A.;Horn,K.;Jobst,J.;Kellogg,G.L.;Ley,L.;McChesney,J.L.;Ohta,T.;Reshanov,S.A.;Rohrl,J.;Rotenberg,E.;Schmid,A.K.;Waldmann,D.;Weber,H.B.;Seyller,T.Nat.Mater.2009,8(3),203–207.(9)Marchini,S.;Gunther,S.;Wintterlin,J.Phys.Re V.B2007,76(7),075429.(10)Loginova,E.;Bartelt,N.C.;Feibelman,P.J.;McCarty,K.F.New J.Phys.2008,10,093026.(11)Sutter,P.W.;Flege,J.-I.;Sutter,E.A.Nat.Mater.2008,7,406–411.(12)Yu,Q.;Lian,J.;Siriponglert,S.;Li,H.;Chen,Y.P.;Pei,S.-S.Appl.Phys.Lett.2008,93,113103.(13)Reina, A.;Jia,X.;Ho,J.;Nezich, D.;Son,H.;Bulovic,V.;Dresselhaus,M.S.;Kong,J.Nano Lett.2009,9,30–35.(14)Kim,K.S.;Zhao,Y.;Jang,H.;Lee,S.Y.;Kim,J.M.;Kim,K.S.;Ahn,J.-H.;Kim,P.;Choi,J.-Y.;Hong,B.H.Nature2009,457,706–710.(15)Li,X.S.;Cai,W.W.;An,J.H.;Kim,S.;Nah,J.;Yang,D.X.;Piner,R.D.;Velamakanni,A.;Jung,I.;Tutuc,E.;Banerjee,S.K.;Colombo, L.;Ruoff,R.S.Science2009,324,1312.(16)Fan,S.;Liu,L.;Liu,M.Nanetechnology2003,14,1118–1123.(17)Shelton,J.C.;Patil,H.R.;Blakely,J.M.Surf.Sci.1974,43,493–520.(18)Isett,L.C.;Blakely,J.M.Surf.Sci.1976,58(2),397–414.(19)Eizenberg,M.;Blakely,J.M.Surf.Sci.1979,82(1),228–236.(20)Eizenberg,M.;Blakely,J.M.J.Chem.Phys.1979,71(8),3467–3477.(21)Reina,A.;Son,H.;Jiao,L.;Fan,B.;Dresselhaus,M.S.;Liu,Z.F.;Kong,J.J.Phys.Chem.C2008,112,17741–17744.(22)Cai,W.W.;Piner,R.D.;Stadermann,F.J.;Park,S.;Shaibat,M.A.;Ishii,Y.;Yang,D.X.;Velamakanni,A.;An,S.J.;Stoller,M.;An, J.H.;Chen,D.M.;Ruoff,R.S.Science2008,321(5897),1815–1817.(23)Obraztsov,A.N.;Obraztsova,E.A.;Tyurnina,A.V.;Zolotukhin,A.A.Carbon2007,45,2017–2021.(24)Ni,Z.H.;Wang,H.M.;Kasim,J.;Fan,H.M.;Yu,T.;Wu,Y.H.;Feng,Y.P.;Shen,Z.X.Nano Lett.2007,7(9),2758–2763. 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