Droplet coalescence by geometrically mediated flow

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LES of steady spray flame and ignition sequences in aeronautical combustors

LES of steady sprayﬂameand ignition sequencesin aeronautical combustorsS.Pascaud†∗,M.Boileau†,L.Martinez†,B.Cuenot†and T.Poinsot‡†CERFACS,Toulouse,France‡IMFT-CNRS,Toulouse,FranceGround ignition and altitude re-ignition are critical issues for aeronautical gas turbine design.They are strongly inﬂu-enced by the turbulentﬂow structure as well as the liquid fuel spray and its atomization.Turbulent mixing,evaporation and combustion that control the combustion process are complex unsteady phenomena couplingﬂuid mechanics,thermodynamics and chemistry.To better understand unsteady combustion in industrial burners,Large Eddy Simulation(LES)is a unique and powerful tool.Its potential has been widely demonstrated in the context of turbulent coldﬂows,and it has been recently applied to turbulent combustion.Its extension to two-phase turbulent combustion is a challenge but recent results conﬁrm that it brings totally new insight into the physics ofﬂames for both mean and unsteady aspects.In the present work,an Euler-Euler formulation of the two-phaseﬂow equations is coupled with a sub-grid scale model and a turbulent combustion model.The obtained two-ﬂuid model computes the conservation equations in each phase and the exchanges source terms for mass and heat transfer between gas and liquid.Thanks to the compressible form of the gas equations,ﬂame/acoustics interactions are resolved.For application to complex geometries,unstructured meshes are used.With this numerical tool,turbulent two-phase ﬂames are simulated in an industrial gas turbine.Some of the mechanisms involved in the steady sprayﬂame are analysed and the partially premixedﬂame structure is detailed.Nevertheless,the capabilities of the LES technique for spray combus-tion are not limited to the stabilised sprayﬂame.Unsteady complex phenomena such as ignition sequences give promising results:the unsteady behaviour of the reacting two-phaseﬂow from the installation of a kernel to the possible propagation and stabilisation of theﬂame is computed and demonstrates the LES capabilities in such unsteady complex problems.ContextThe main part of the production of energy comes from combustion of liquid hydrocarbon fuels,because of their con-venient way of storage and transport.Most of the current combustion chambers burn liquid fuel using injectors which atomise,generally at high pressures,the liquid jet orﬁlm in small droplets(typically10−200µm).Then,the fuel becomes gaseous and an inhomogeneous mixing of air and vaporised fuel is created.For reasons of simplicity,this ﬁrst step of atomisation is supposed to be instantaneous and numerical tools for evaporation and gaseous combustion are applied to two-phaseﬂow combustors.This allows to study the inﬂuence of the liquid phase on steadyﬂames and ignition sequences.The Large Eddy Simulations(LES)technique is used to understand unsteady phenomena occurring in turbulent spray combustion.Many proofs of the LES capabilities are available for gaseous combustion1–6but very few studies deal with the complex topic of LES for two-phase reactingﬂows.7–10The modelling of the liquid phase in a LES solver is an important issue for which two classes of methods are available: the Euler framework(EF)and the Lagrange framework(LF).The LF7describes the liquid phase as a huge butﬁnite number of droplets with their own trajectory,velocity,temperature and diameter while the EF,11,12with an opposite point of view,considers the liquid phase as a continuousﬁeld whose characteristics are determined through a set of conservation equations for the liquid volume fraction,the liquid phase velocity and temperature,and theﬁrst/second order moments of the size distribution.Several complex phenomena like droplet/droplet coalescence and collision or droplet/wall interaction are easier to model in a LF.However,the choice of the EF is justiﬁed for a parallel computation of an unsteady spray combustion in a realistic combustor by the following arguments:Parallelism:LES in complex geometries needs high CPU time and requires parallel computing.However,the efﬁ-cient implementation of LF on a parallel computer is a critical issue and implies good load balancing,13whereas EF is directly parallelised with the same algorithms as the gas phase.Number of droplets:the LES technique is less dissipative than RANS methods.As a consequence,the number of Lagrangian droplets at each time step in each cell must be sufﬁcient to provide a smooth and accurate continuousﬁeld of gaseous fuel.Because the fuel vapour distribution,directly produced by the discrete droplet evaporation source terms,controls the propagation of the front,14,15this is crucial for two-phaseﬂame computations.Very limited experi-ence on this question is available today but it is likely that combustion requires much more particles than usually done for dispersion or evaporation studies,leading to uncontrolled CPU costs.∗pascaud@cerfacs.frSize distribution:since the spray granulometry controls theﬂame regime,a droplet size distribution must be consid-ered.LF is better on this question because it naturally discretises droplets with different sizes.However,recent studies demonstrate the EF capabilities to include polydispersed sprays.16–18Inlet conditions:due to the atomisation complexity,the accurate determination of the spray characteristics is a criti-cal issue.Even if LF calculates droplet trajectories with precision,very approximate injection conditions will lead to rough results.Close to the injector,the liquid spray is organised as dense blobs19and LF can not be applied to these high-loaded zones.As a contrary,EF is more compatible with the physics of liquid injection.Numerical toolThe solver AVBP,developed at CERFACS,is a parallel fully compressible code which computes the turbulent react-ing two-phaseﬂows,on both structured and unstructured grids,for complex industrial applications such as ignition sequences or acoustic instabilities.Turbulent combustion modelling is ensured by the Dynamically Thickened Flame model,20using a thickening factor F and an efﬁcacity function E to determine theﬂame front turbulent velocity.21 Subgrid scale turbulent viscosity is deﬁned by the W ALE model,22derived from the classic Smagorinsky model. The Euler/Euler framework governing a turbulent reacting two-phaseﬂow is composed,for each phase,of a set of conservative equations deﬁned by Eq.(1)and Eq.(2)and solved with the same numerical approach.Carrier phase ∂w∂t+∇·F=s(1)Dispersed phase ∂w l∂t+∇·F l=s l(2)For the carrier phase,the vector of conservative variables is deﬁned by Eq.(3)withρthe density,(u1,u2,u3)the velocity components,E t the total non chemical energy and Y k the fuel mass fractions.Theﬂux tensor F is composed of viscous,inviscid and subgrid scale components and s is the source term deﬁned by Eq.(4).Combustion terms are the reaction rate˙ωk and the heat release˙ωT modelled by an Arrhenius law.23Additional source terms representing exchanges between phases are the mass transferΓ,the momentum transfer I i and the enthalpy transferΠ.w=(ρ˜u1,ρ˜u2,ρ˜u3,ρ˜E t,ρ˜Y k)(3)s=(I1,I2,I3,EF˙ωT+I i˜u i+Π+˙ωspark,−EF˙ωk+ΓδkF)(4)For the dispersed phase,the vector of conservative variables w l is deﬁned by Eq.(5)withαl the volume fraction, (u1,l,u2,l,u3,l)the velocity components,h s,l the sensible enthalpy and n l the droplet number density.Theﬂux tensor F l is only composed of convective terms and the source term s is deﬁned by Eq.(6).w l=(αlρl,αlρl˜u1,l,αlρl˜u2,l,αlρl˜u3,l,αlρl˜h s,l,n l)(5)s l=(−Γ,−I1,−I2,−I3,−Π,0)(6) The fully explicitﬁnite volume solver AVBP uses a cell-vertex discretisation and a second order time and space Lax-Wendroff centred numerical scheme.24Characteristic boundary conditions NSCBC25are used.ConﬁgurationThe computed conﬁguration is a3D sector of22.5-degrees of an annular aeronautical gas turbine at atmospheric pressure.The kerosene liquid spray LS is located at the center of the main swirled inlet SI(Fig.1).An annular series of small holes H are located around the inlet to lift theﬂame and protect the injector from high temperatures.Then, several holes on the upper and lower walls are divided in two parts.Theﬁrst part of the combustor where combustion takes place is located between the injector and the primary jets PJ,which bring cold air to theﬂame.The second part called dilution zone is located between PJ and dilution jets DJ,that reduce and homogenise the outlet temperature to protect the turbine.The spark plug SP is located under the upper wall between two PJ(Fig.2).The geometry(Fig.3) also includes coolingﬁlms which protect upper and lower walls from theﬂame.The inlet and outlet boundary conditions are characteristic with relaxation coefﬁcients to reduce reﬂexion.26The SI imposed velocityﬁeld mimics the swirler inﬂuence.The other inlets are simple non-swirled jets.Non-slip conditions are used on the upper and lower walls while symmetry condition is used on the chamber sides.15µm-droplets are injected at the SI center through a speciﬁc condition which speciﬁes a liquid volumic fractionαl 10−3.The droplets at288K are heated by the air at525K.The initial liquid velocity is equal to the gaseous velocity as the droplet Stokes number,based on the droplet relaxation time,is lower than one.The unstructured mesh is composed of 400000nodes and 2300000tetrahedra.The explicit time step is ∆t 0.22µs .The mesh is reﬁned close to the inlets and in the combustion zone (Fig.4).The Arrhenius coefﬁcients are ﬁtted by a genetic algorithm 27from a reduced chemistry 28to the present one-step chemistry :JP 10+14O 2 10CO 2+8H 2O using criteria such as ﬂame speed andthickness.Fig.1Geometry sketch :sideview Fig.2Geometry sketch :topviewFig.3Complexgeometry Fig.4Mesh reﬁnement :central longitudinal viewSteady spray ﬂamePrecessing Vortex CoreIn its review on vortex breakdown,Lucca-Negro 29classiﬁes the hydrodynamic instabilities appearing in swirled ﬂows.For high swirl numbers,the axial vortex breaks down at the stagnation point S and a spiral is created around a central recirculation zone CRZ (Fig.5):this vortex breakdown is the so-called precessing vortex core (PVC)existing in a large number of combustors.30The LES technique capture the vortex breakdown in the combustor and its frequency is evaluated with the backﬂow line on a transverse plane (Fig.6)at six successive times marked with a number from 1to 6and separated by 0.5ms.The turnover time is estimated at τswirl 3.5ms,corresponding to a frequency ofDispersion and evaporationThe 15µm droplets motion follows the carrier phase dynamics so that the CRZ of both zones are similar,as illustrated by both backﬂow lines on Fig.7.Maintained by this CRZ,the droplets accumulate and the droplet number density,presented with the liquid volumic fraction ﬁeld on Fig.7,rises above its initial value.Increasing the residence time of these vaporising droplets,whose diameter ﬁeld is presented on Fig.8,makes the local equivalence ratio distribution reach values higher than 10.The heat transfer linked to the phase change leads to the reduction of the gaseous temperature,as shown by the isoline T =450K on Fig.9,and an increase of the dispersed phase temperature.Thus,the CRZ,by trapping evaporating droplets,stabilise the vaporised fuel and the ﬂame.Fig.7Dispersion Fig.8EvaporationCombustionThe ﬂame front,illustrated on Fig.9by the heat release ﬁeld,is inﬂuenced by both ﬂow dynamics and evaporation rate.The main competitive phenomena for two-phase ﬂame stabilisation are :1.the air velocity must be low enough to match the turbulent ﬂame velocity :the dynamics of the carrier phase (and in particular the CRZ)stabilise the ﬂame front on a stable pocket of hot gases2.zones where the local mixture fraction is within ﬂammability limits must exist :combustion occurs between the fuel vapour radially dispersed by the swirl and the ambient air,where the equivalence ratio is low enough3.the heat release must be high enough to maintain evaporation and reaction :the sum of heat ﬂux Πand heatrelease ˙ωT ,plotted on Fig.9,allows to identify the zone ()where the heat transfer due to evaporation extinguishes the ﬂame :Π+˙ωT =0.In the present case,the ﬂame front is stabilised by the CRZ (1.)but the heat release magnitude is reduced in the evaporation zone because of both effects (2.)and (3.).To determine the ﬂame regime (premixed and/or diffusion),the Takeno index T =∇Y F .∇Y O and an indexed reaction rate ˙ω∗F =˙ωF T |∇Y F |.|∇Y O |are used.The ﬂame structureis then divided into two parts :˙ω∗F =+˙ωF in the premixed regime part and ˙ω∗F =−˙ωF in the diffusion regime part(Fig.10).In the primary zone,the partially premixed regime is preponderant because of the unsteady inhomogeneous fuel vapour.In the dilution zone,the unburned fuel reacts with dilution jets through a diffusion ﬂame,as conﬁrmed by the coincidence between the ﬂame and the stoichiometric line.Fig.9Flamefront Fig.10Flame structurePVC inﬂuenceThe PVC,deﬁned on Fig.11a,controls the motions of both the vaporised fuel VF and theﬂame front.The cut plane, deﬁned on Fig.11a,is presented on Fig.11b with the temperatureﬁeld,the maximum fuel mass fraction(white lines) and theﬂame front(black isolines of reaction rate˙ωF).The CRZ stabilises hot gases and enhance evaporation leading to a cold annular zone where the maximum fuel mass fraction precesses.Theﬂame motion follows the PVC and the reaction rate is driven by the fuel vapour concentration.b.Fig.11PVC inﬂuence on evaporation and combustionIgnition sequenceSpark-like numerical methodThe numerical method used to mimic an ignition by spark plug in the combustion chamber is the addition of the source term ˙ωspark in Eq.(4).This source term,deﬁned by Eq.(7),is a gaussian function located at (x 0,y 0,z 0)near the upper wall between both primary jets and deposited at t =t 0=0.The ignition delay,typical of industrial spark plugs,is σt =0.16ms .˙ωspark =E spark (2π)2σt σr 3e −12 (t −t 0σt )2+(x −x 0σr )2+(y −y 0σr )2+(z −z 0σr )2 (7)Temporal evolutionThe temporal evolution of the spark ignition is presented on Fig.12where the source term ˙ωspark ,the maximum heat release ˙ωT and the maximum temperature are plotted.First,the maximum temperature rises smoothly because of the source term on energy equation.When this temperature is sufﬁcient,the reaction occurs between fuel vapour and air leading to a sudden increase of the heat release of the exothermic reaction and then,the maximum temperature rapidly rises.Once the source term is over,the maximum heat release decreases.The maximum temperature corresponds to the hot gases :the ignition is successful.15105ωspark 0.50.40.30.20.10.0time [ms]45004000350030002500200015001000500T [K]6420ωT [kg.mm -3.s -1] Source term ωspark Maximum heat release ωTMaximum temperatureFig.12Source term ˙ωspark ,maximum heat release ˙ωT ,maximum temperatureThe sequence of ignition is illustrated on the longitudinal central cut plane on Fig.13with the fuel mass fraction ﬁeld and the reaction rate isolines,where the ﬁrst image is presented at t =0.2ms and after,successive images are separated by ∆t =0.2ms .At the beginning of the computation,the 15µm droplets evaporate in the ambient air at T =525K creating a turbulent cloud of vaporised fuel in the whole primary zone.This fuel vapour distribution,whose stabilisation is ensured by the CRZ,propagates from the evaporation zone to the spark plug area.At t =0,the spark ignition occurs leatding to the creation of a hot kernel.The propagation of the ﬂame front created by this pocket of hot gases is highly controlled by the fuel vapour distribution between t =0and t =1ms .Once the ﬂame front reaches the CRZ (t 1ms ),there is no more vaporised fuel and the ﬂame must evaporate the fuel droplets leading to an increase of the maximum fuel mass fraction in the CRZ.This evaporation process stabilise the ﬂame front as explained in the previous section on steady spray ﬂame.0.2ms 0.4ms 0.6ms 0.8ms1.0ms 1.2ms 1.4ms 1.6ms1.8ms2.0ms 2.2ms 2.4msFig.13Flame front propagation on fuel mass fraction ﬁeld (white :0→black :0.35)ConclusionsA steady spray ﬂame in a realistic aeronautical combustor has been computed using the parallel LES Euler/Euler solver A VBP.The inﬂuence of the dispersed phase on the ﬂame motion has been highlighted,in particular the role of the evaporation process.The unsteady approach brings totally new insight into the physics of such complex reactive two-phase ﬂows.Furthermore,it allows the computation of an ignition sequence from the formation of the ﬁrst spherical ﬂame front to the stabilisation of the turbulent spray ﬂame.To conclude,the LES technique is a powerful tool to mimic ignition sequences and understand turbulent spray ﬂame structure in realistic combustors.References1P.E.Desjardins and S.H.Frankel.Two dimensional large eddy simulation of soot formation in the nearﬁeld of a strongly radiating nonpremixed acetylene-air jetﬂbust.Flame,119(1/2):121–133,1999.2O.Colin.Simulation aux Grandes Echelles de la Combustion Turbulente Pr´e m´e lang´e e dans les Stator´e acteurs.PhD thesis,INP Toulouse,2000. 3C.Angelberger,F.Egolfopoulos,and rge eddy simulations of chemical and acoustic effects on combustion instabilities.Flow Turb.and Combustion,65(2):205–22,2000.4H.Pitsch and L.Duchamp de la rge eddy simulation of premixed turbulent combustion using a level-set approach.Proceedings of the Combustion Institute,29:in press,2002.5C.D.Pierce and P.Moin.Progress-variable approach for large eddy simulation of non-premixed turbulent combustion.J.Fluid Mech.,504:73–97,2004.6L.Selle.Simulation aux grandes´e chelles des couplages acoustique/combustion dans les turbines´a gaz.Phd thesis,INP Toulouse,2004.7K.Mahesh,G.Constantinescu,S.Apte,G.Iaccarino,F.Ham,and P.Moin.Progress towards large-eddy simulation of turbulent reacting and non-reactingﬂows in complex geometries.In Annual Research Briefs,pages115–142.Center for Turbulence Research,NASA Ames/Stanford Univ.,2002.8K.Mahesh,G.Constantinescu,and P.Moin.A numerical method for large-eddy simulation in complex put.Phys., 197:215–240,2004.9S.V.Apte,M.Gorokhovski,and rge-eddy simulation of atomizing spray with stochastic modeling of secondary breakup.In ASME Turbo Expo2003-Power for Land,Sea and Air,Atlanta,Georgia,USA,2003.10F.Ham,S.V.Apte,G.Iaccarino,X.Wu,M.Herrmann,G.Constantinescu,K.Mahesh,and P.Moin.Unstructured les of reacting multiphase ﬂows in realistic gas turbine combustors.In Annual Research Briefs-Center for Turbulence Research,2003.11R.V.R.Pandya and F.Mashayek.Two-ﬂuid large-eddy simulation approach for particle-laden turbulentﬂows.Int.J.of Heat and Mass transfer, 45:4753–4759,2002.12E.Riber,M.Moreau,O.Simonin,and B.Cuenot.Towards large eddy simulation of non-homogeneous particle laden turbulent gasﬂows using euler-euler approach.In11th Workshop on Two-Phase Flow Predictions,Merseburg,Germany,2005.13M.Garc´ıa,Y.Sommerer,T.Sch¨o nfeld,and T.Poinsot.Evaluation of euler/euler and euler/lagrange strategies for large eddy simulations of turbulent reactingﬂows.In ECCOMAS Thematic Conference on Computational Combustion,2005.14H.Pitsch and N.Peters.A consistentﬂamelet formulation for non-premixed combustion considering differential diffusion bust. Flame,114:26–40,1998.15L.Selle,rtigue,T.Poinsot,P.Kaufman,W.Krebs,and rge eddy simulation of turbulent combustion for gas turbines with reduced chemistry.In Proceedings of the Summer Program-Center for Turbulence Research,pages333–344,2002.16R.Borghi.Background on droplets and sprays.In Combustion and turbulence in two phaseﬂows,Lecture Series1996-02.V on Karman Institute for Fluid Dynamics,1996.17O.Delabroy,cas,begorre,and J-M.Samaniego.Param`e tres de similitude pour la combustion diphasique.Revue G´e n´e rale de Thermique,(37):934–953,1998.18J.R´e veillon,M.Massot,and C.Pera.Analysis and modeling of the dispersion of vaporizing polydispersed sprays in turbulentﬂows.In Proceedings of the Summer Program2002-Center for Turbulence Research,2002.19R.D.Reitz and R.Diwakar.Structure of high pressure fuel sprays.Technical Report Tech.Rep.870598,SAE Technical Paper,1987.20J.-Ph.L´e gier,T.Poinsot,and D.Veynante.Dynamically thickenedﬂame large eddy simulation model for premixed and non-premixed turbulent combustion.In Summer Program2000,pages157–168,Center for Turbulence Research,Stanford,USA,2000.21O.Colin,F.Ducros,D.Veynante,and T.Poinsot.A thickenedﬂame model for large eddy simulations of turbulent premixed combustion.Phys. Fluids,12(7):1843–1863,2000.22F.Nicoud and F.Ducros.Subgrid-scale stress modelling based on the square of the velocity gradient.Flow Turb.and Combustion,62(3):183–200,1999.23T.Poinsot and D.Veynante.Theoretical and numerical combustion,second edition.R.T.Edwards,2005.24C.Hirsch.Numerical Computation of Internal and External Flows.John Wiley&Sons,1989.25T.Poinsot and S.Lele.Boundary conditions for direct simulations of compressible viscousﬂput.Phys.,101(1):104–129,1992. 26L.Selle,F.Nicoud,and T.Poinsot.The actual impedance of non-reﬂecting boundary conditions:implications for the computation of resonators. AIAA Journal,42(5):958–964,2004.27C.Martin.Eporck user guide v1.8.Technical report,CERFACS,2004.28S.C.Li,B.Varatharajan,and F.A.Williams.The chemistry of jp-10ignition.AIAA,39(12):2351–2356,2001.29O.Lucca-Negro and T.O’Doherty.V ortex breakdown:a review.Prog.Energy Comb.Sci.,27:431–481,2001.30L.Selle,rtigue,T.Poinsot,R.Koch,K.-U.Schildmacher,W.Krebs,B.Prade,P.Kaufmann,and pressible large-eddy simulation of turbulent combustion in complex geometry on unstructured bust.Flame,137(4):489–505,2004.。

人工智能原理MOOC习题集及答案北京大学王文敏

Quizzes for Chapter 11单选(1分)图灵测试旨在给予哪一种令人满意的操作定义得分/总分A.人类思考B.人工智能C.机器智能D.机器动作正确答案：C你选对了2多选(1分)选择以下关于人工智能概念的正确表述得分/总分A.人工智能旨在创造智能机器该题无法得分/B.人工智能是研究和构建在给定环境下表现良好的智能体程序该题无法得分/C.人工智能将其定义为人类智能体的研究该题无法得分/D.人工智能是为了开发一类计算机使之能够完成通常由人类所能做的事该题无法得分/正确答案：A、B、D你错选为A、B、C、D3多选(1分)如下学科哪些是人工智能的基础？得分/总分A.经济学B.哲学C.心理学D.数学正确答案：A、B、C、D你选对了4多选(1分)下列陈述中哪些是描述强AI(通用AI)的正确答案？得分/总分A.指的是一种机器，具有将智能应用于任何问题的能力B.是经过适当编程的具有正确输入和输出的计算机，因此有与人类同样判断力的头脑C.指的是一种机器，仅针对一个具体问题D.其定义为无知觉的计算机智能，或专注于一个狭窄任务的AI正确答案：A、B你选对了5多选(1分)选择下列计算机系统中属于人工智能的实例得分/总分搜索引擎B.超市条形码扫描器C.声控电话菜单该题无法得分/D.智能个人助理该题无法得分/正确答案：A、D你错选为C、D6多选(1分)选择下列哪些是人工智能的研究领域得分/总分A.人脸识别B.专家系统C.图像理解D.分布式计算正确答案：A、B、C你错选为A、B7多选(1分)考察人工智能(AI)的一些应用，去发现目前下列哪些任务可以通过AI来解决得分/总分A.以竞技水平玩德州扑克游戏B.打一场像样的乒乓球比赛C.在Web上购买一周的食品杂货D.在市场上购买一周的食品杂货正确答案：A、B、C你错选为A、C8填空(1分)理性指的是一个系统的属性，即在_________的环境下做正确的事。

得分/总分正确答案：已知1单选(1分)图灵测试旨在给予哪一种令人满意的操作定义得分/总分A.人类思考B.人工智能C.机器智能D.机器动作正确答案：C你选对了2多选(1分)选择以下关于人工智能概念的正确表述得分/总分A.人工智能旨在创造智能机器该题无法得分/B.人工智能是研究和构建在给定环境下表现良好的智能体程序该题无法得分/C.人工智能将其定义为人类智能体的研究该题无法得分/D.人工智能是为了开发一类计算机使之能够完成通常由人类所能做的事该题无法得分/正确答案：A、B、D你错选为A、B、C、D3多选(1分)如下学科哪些是人工智能的基础？得分/总分A.经济学B.哲学C.心理学D.数学正确答案：A、B、C、D你选对了4多选(1分)下列陈述中哪些是描述强AI(通用AI)的正确答案？得分/总分A.指的是一种机器，具有将智能应用于任何问题的能力B.是经过适当编程的具有正确输入和输出的计算机，因此有与人类同样判断力的头脑C.指的是一种机器，仅针对一个具体问题D.其定义为无知觉的计算机智能，或专注于一个狭窄任务的AI正确答案：A、B你选对了5多选(1分)选择下列计算机系统中属于人工智能的实例得分/总分搜索引擎B.超市条形码扫描器C.声控电话菜单该题无法得分/D.智能个人助理该题无法得分/正确答案：A、D你错选为C、D6多选(1分)选择下列哪些是人工智能的研究领域得分/总分A.人脸识别B.专家系统C.图像理解D.分布式计算正确答案：A、B、C你错选为A、B7多选(1分)考察人工智能(AI)的一些应用，去发现目前下列哪些任务可以通过AI来解决得分/总分A.以竞技水平玩德州扑克游戏B.打一场像样的乒乓球比赛C.在Web上购买一周的食品杂货D.在市场上购买一周的食品杂货正确答案：A、B、C你错选为A、C8填空(1分)理性指的是一个系统的属性，即在_________的环境下做正确的事。

商务数据挖掘与分析应用考核试卷

3. 机器学习中的______学习是指从标记的训练数据中学习模型的过程。
4. 在关联规则挖掘中，如果项集{X}的出现次数除以总项集的次数大于某个阈值，则称项集{X}具有高______度。
5. 在聚类分析中，______算法是基于距离的聚类方法，它试图找到最小化簇内距离和的最大化簇间距离的簇。
6. 在时间序列分析中，______模型是一种预测方法，它假设未来的值可以通过过去的值来预测。
得分：_________________ 判卷人：_________________
三、填空题（本题共10小题，每小题2分，共20分，请将正确答案填到题目空白处）
1. 在数据挖掘中，______是描述数据集中数据分布的统计量。
2. 在进行数据预处理时，______是指识别或删除数据集中的错误或不一致的过程。
得分：_________________ 判卷人：_________________
二、多选题（本题共20小题，每小题1.5分，共30分，在每小题给出的四个选项中，至少有一项是符合题目要求的）
1. 数据挖掘过程中常用的数据分析方法包括哪些？（）
A. 描述性分析
B. 探索性分析
C. 验证性分析
D. 预测性分析
A. 决策树
B. 逻辑回归
C. K-means
D. 支持向量机
14. 以下哪个算法常用于异常值检测？（）
A. 基于距离的聚类
B. 基于密度的聚类
C. 箱线图
D. 以上都是
15. 以下哪个不是数据挖掘中的数据类型？（）
A. 分类数据
B. 数值数据
C. 序列数据
D. 文本数据
16. 在商务数据分析中，以下哪个不是客户关系管理（CRM）的关键指标？（）

Shapes, contact angles, and line tensions of droplets on cylinders

Typeset using REVTEX 1
I. INTRODUCTION
The wetting properties of a ﬁber in liquid matrices (e.g., dye mixtures, polymer melts, or molten resins) play an important role in the textile industry and in the fabrication of highperformance, ﬁber-reinforced composite materials. Since contact angles of liquid droplets on solid substrates provide a valuable characterization of such wetting properties there are numerous experimental and theoretical studies of the shape and the spreading of droplets deposited on a cylindrical substrate (see, e.g., Refs. [1–15]). The morphology of liquid drops on a ﬁber is particularly interesting insofar as on a planar substrate there is only one, spherical caplike droplet shape, whereas on a cylindrical substrate droplets may exhibit two, topologically diﬀerent shapes, a “clamshell”- and a “barrel”-type one, depending on the droplet volume, the contact angle, and the cylinder radius [1–3]. The aforementioned studies deal with thick ﬁbers and large drops, i.e., the length scales are µm and larger. In this range the ﬂuid structures are determined by macroscopic properties alone, i.e., volume of the liquid, surface tension σ of the liquid vapor interface, Young’s contact angle θ∞ , and radius R of the cylinder. However, with the discovery of nanotubes the interest in such ﬂuid structures has shifted to much smaller scales. There are several applications for which these small solid-ﬂuid structures are very important. (i) For fabricating valuable composite materials involving nanotubes their wetting by the liquid host matrix is necessary to couple the inherent strength of the nanotubes to the matrix, reinforcing materials or ﬁllers for plastics and ceramics [16]. (ii) Nanotubes can be used as supports for heterogeneous catalysis or as templates for creating small wires or tubular structures by coating them with metals or metal oxides in the liquid state [17] or by attaching inorganic and organic moieties to the nanotube surfaces [18]. (iii) In order to use nanotubes as “nanostraws” potential candidates for exploiting such capillarity must be screened by ﬁrst seeing if the liquid wets the outside of nanotubes [19]. The performance of the nanotubes as catalysts, adsorbants, and deodorants can vary depending on whether they are composed of carbon, boron nitride, or oxides (SiO2 , Al2 O3 , V2 O5 , MoO3 , TiO2 ) [20]. This variety demonstrates, that the substrate potential of these tubes can be regarded as a tunable parameter. (iv) By using nanotubes as nanotweezers [21] it might be possible to grab and manipulate small liquid drops. For this application the substrate must be nonwettable. These small scales are comparable with the range of the substrate potential of the cylinders and of the molecular forces between the ﬂuid particles adsorbing on them. Thus the droplets form under the action of the so-called eﬀective interface potential ω which accounts for the net eﬀect of the competition between the forces among the ﬂuid particles and the substrate potential [22]. Accordingly the calculation of the corresponding deformed droplet shapes requires a more detailed theoretical description which takes the eﬀective interface potential into account. To our knowledge there is only one, recent publication in which this eﬀect of ω on the droplet shape on ﬁbers has been analyzed [23]. It is the purpose of our study here to reﬁne and to extend this analysis in various directions. If the radius R of the ﬁber reduces to a few nm, as it is the case for nanotubes, the eﬀective interface potential itself will depend on R and thus deviate from that of the corresponding semiinﬁnite planar substrate used in Ref. [23]. Accordingly we present a systematic analysis of the dependence of the shape of the droplets and their suitably deﬁned contact angles on 2

微积分介值定理的英文

微积分介值定理的英文The Intermediate Value Theorem in CalculusCalculus, a branch of mathematics that has revolutionized the way we understand the world around us, is a vast and intricate subject that encompasses numerous theorems and principles. One such fundamental theorem is the Intermediate Value Theorem, which plays a crucial role in understanding the behavior of continuous functions.The Intermediate Value Theorem, also known as the Bolzano Theorem, states that if a continuous function takes on two different values, then it must also take on all values in between those two values. In other words, if a function is continuous on a closed interval and takes on two different values at the endpoints of that interval, then it must also take on every value in between those two endpoint values.To understand this theorem more clearly, let's consider a simple example. Imagine a function f(x) that represents the height of a mountain as a function of the distance x from the base. If the function f(x) is continuous and the mountain has a peak, then theIntermediate Value Theorem tells us that the function must take on every height value between the base and the peak.Mathematically, the Intermediate Value Theorem can be stated as follows: Let f(x) be a continuous function on a closed interval [a, b]. If f(a) and f(b) have opposite signs, then there exists a point c in the interval (a, b) such that f(c) = 0.The proof of the Intermediate Value Theorem is based on the properties of continuous functions and the completeness of the real number system. The key idea is that if a function changes sign on a closed interval, then it must pass through the value zero somewhere in that interval.One important application of the Intermediate Value Theorem is in the context of finding roots of equations. If a continuous function f(x) changes sign on a closed interval [a, b], then the Intermediate Value Theorem guarantees that there is at least one root (a value of x where f(x) = 0) within that interval. This is a powerful tool in numerical analysis and the study of nonlinear equations.Another application of the Intermediate Value Theorem is in the study of optimization problems. When maximizing or minimizing a continuous function on a closed interval, the Intermediate Value Theorem can be used to establish the existence of a maximum orminimum value within that interval.The Intermediate Value Theorem is also closely related to the concept of connectedness in topology. If a function is continuous on a closed interval, then the image of that interval under the function is a connected set. This means that the function "connects" the values at the endpoints of the interval, without any "gaps" in between.In addition to its theoretical importance, the Intermediate Value Theorem has practical applications in various fields, such as economics, biology, and physics. For example, in economics, the theorem can be used to show the existence of equilibrium prices in a market, where supply and demand curves intersect.In conclusion, the Intermediate Value Theorem is a fundamental result in calculus that has far-reaching implications in both theory and practice. Its ability to guarantee the existence of values between two extremes has made it an indispensable tool in the study of continuous functions and the analysis of complex systems. Understanding and applying this theorem is a crucial step in mastering the powerful concepts of calculus.。

湿度、云的形成和降水(英文)

Condensation Nuclei
• If we examine the air above the water in the jar of the previous pictures, we would find that the air molecules are mixed with tiny (microscopic) bits of dust, smoke, ocean salt, etc. • Since these all serve as surfaces on which water vapor may condense they are called condensation nuclei. • Condensation is more likely to occur when air is cooled because the speed of the water vapor decreases.
•
•
Vapor Pressure
• Suppose our previous air parcel is near sea level and the air pressure inside the parcel is 1000 mb. (Total air pressure inside parcel is due to collision of all molecules against wall of parcel) • Parcel is 78% nitrogen, 21% oxygen and 1% water vapor. Pressure of nitrogen is 780 mb, oxygen 210 mb and water vapor is 10 mb. • So, the partial pressure of the water vapor (actualБайду номын сангаасvapor pressure) is 10 mb.

数据挖掘第三版第二章课后习题答案

1.1什么是数据挖掘？（a）它是一种广告宣传吗？（d）它是一种从数据库、统计学、机器学和模式识别发展而来的技术的简单转换或应用吗？（c）我们提出一种观点，说数据挖掘是数据库进化的结果，你认为数据挖掘也是机器学习研究进化的结果吗？你能结合该学科的发展历史提出这一观点吗？针对统计学和模式知识领域做相同的事（d）当把数据挖掘看做知识点发现过程时，描述数据挖掘所涉及的步骤答：数据挖掘比较简单的定义是：数据挖掘是从大量的、不完全的、有噪声的、模糊的、随机的实际数据中，提取隐含在其中的、人们所不知道的、但又是潜在有用信息和知识的过程。

数据挖掘不是一种广告宣传，而是由于大量数据的可用性以及把这些数据变为有用的信息的迫切需要，使得数据挖掘变得更加有必要。

因此，数据挖掘可以被看作是信息技术的自然演变的结果。

数据挖掘不是一种从数据库、统计学和机器学习发展的技术的简单转换，而是来自多学科，例如数据库技术、统计学，机器学习、高性能计算、模式识别、神经网络、数据可视化、信息检索、图像和信号处理以及空间数据分析技术的集成。

数据库技术开始于数据收集和数据库创建机制的发展，导致了用于数据管理的有效机制，包括数据存储和检索，查询和事务处理的发展。

提供查询和事务处理的大量的数据库系统最终自然地导致了对数据分析和理解的需要。

因此，出于这种必要性，数据挖掘开始了其发展。

当把数据挖掘看作知识发现过程时，涉及步骤如下：数据清理，一个删除或消除噪声和不一致的数据的过程；数据集成，多种数据源可以组合在一起；数据选择，从数据库中提取与分析任务相关的数据；数据变换，数据变换或同意成适合挖掘的形式，如通过汇总或聚集操作；数据挖掘，基本步骤，使用智能方法提取数据模式；模式评估，根据某种兴趣度度量，识别表示知识的真正有趣的模式；知识表示，使用可视化和知识表示技术，向用户提供挖掘的知识1.3定义下列数据挖掘功能：特征化、区分、关联和相关性分析、分类、回归、聚类、离群点分析。

State Space Reconstruction for Multivariate Time Series Prediction

a r X i v :0809.2220v 1 [n l i n .C D ] 12 S e p 2008APS/123-QEDState Space Reconstruction for Multivariate Time Series PredictionI.Vlachos ∗and D.Kugiumtzis †Department of Mathematical,Physical and Computational Sciences,Faculty of Technology,Aristotle University of Thessaloniki,Greece(Dated:September 12,2008)In the nonlinear prediction of scalar time series,the common practice is to reconstruct the state space using time-delay embedding and apply a local model on neighborhoods of the reconstructed space.The method of false nearest neighbors is often used to estimate the embedding dimension.For prediction purposes,the optimal embedding dimension can also be estimated by some prediction error minimization criterion.We investigate the proper state space reconstruction for multivariate time series and modify the two abovementioned criteria to search for optimal embedding in the set of the variables and their delays.We pinpoint the problems that can arise in each case and compare the state space reconstructions (suggested by each of the two methods)on the predictive ability of the local model that uses each of them.Results obtained from Monte Carlo simulations on known chaotic maps revealed the non-uniqueness of optimum reconstruction in the multivariate case and showed that prediction criteria perform better when the task is prediction.PACS numbers:05.45.Tp,02.50.Sk,05.45.aKeywords:nonlinear analysis,multivariate analysis,time series,local prediction,state space reconstructionI.INTRODUCTIONSince its publication Takens’Embedding Theorem [1](and its extension,the Fractal Delay Embedding Preva-lence Theorem by Sauer et al.[2])has been used in time series analysis in many diﬀerent settings ranging from system characterization and approximation of invariant quantities,such as correlation dimension and Lyapunov exponents,to prediction and noise-ﬁltering [3].The Em-bedding Theorem implies that although the true dynam-ics of a system may not be known,equivalent dynamics can be obtained under suitable conditions using time de-lays of a single time series,treated as an one-dimensional projection of the system trajectory.Most applications of the Embedding Theorem deal with univariate time series,but often measurements of more than one quantities related to the same dynamical system are available.One of the ﬁrst uses of multivari-ate embedding was in the context of spatially extended systems where embedding vectors were constructed from data representing the same quantity measured simulta-neously at diﬀerent locations [4,5].Multivariate em-bedding was used for noise reduction [6]and for surro-gate data generation with equal individual delay times and equal embedding dimensions for each time series [7].In nonlinear multivariate prediction,the prediction with local models on a space reconstructed from a diﬀerent time series of the same system was studied in [8].This study was extended in [9]by having the reconstruction utilize all of the observed time series.Multivariate em-bedding with the use of independent components analysis was considered in [10]and more recently multivariate em-2as x n=h(y n).Despite the apparent loss of information of the system dynamics by the projection,the system dynamics may be recovered through suitable state space reconstruction from the scalar time series.A.Reconstruction of the state space According to Taken’s embedding theorem a trajectory formed by the points x n of time-delayed components from the time series{x n}N n=1asx n=(x n−(m−1)τ,x n−(m−2)τ,...,x n),(1)under certain genericity assumptions,is an one-to-one mapping of the original trajectory of y n provided that m is large enough.Given that the dynamical system“lives”on an attrac-tor A⊂Γ,the reconstructed attractor˜A through the use of the time-delay vectors is topologically equivalent to A.A suﬃcient condition for an appropriate unfolding of the attractor is m≥2d+1where d is the box-counting dimension of A.The embedding process is visualized in the following graphy n∈A⊂ΓF→y n+1∈A⊂Γ↓h↓hx n∈R x n+1∈R↓e↓ex n∈˜A⊂R m G→x n+1∈˜A⊂R mwhere e is the embedding procedure creating the delay vectors from the time series and G is the reconstructed dynamical system on˜A.G preserves properties of the unknown F on the unknown attractor A that do not change under smooth coordinate transformations.B.Univariate local predictionFor a given state space reconstruction,the local predic-tion at a target point x n is made with a model estimated on the K nearest neighboring points to x n.The local model can have a simple form,such as the zeroth order model(the average of the images of the nearest neigh-bors),but here we consider the linear modelˆx n+1=a(n)x n+b(n),where the superscript(n)denotes the dependence of the model parameters(a(n)and b(n))on the neighborhood of x n.The neighborhood at each target point is deﬁned either by aﬁxed number K of nearest neighbors or by a distance determining the borders of the neighborhood giving a varying K with x n.C.Selection of embedding parametersThe two parameters of the delay embedding in(1)are the embedding dimension m,i.e.the number of compo-nents in x n and the delay timeτ.We skip the discussion on the selection ofτas it is typically set to1in the case of discrete systems that we focus on.Among the ap-proaches for the selection of m we choose the most popu-lar method of false nearest neighbors(FNN)and present it brieﬂy below[13].The measurement function h projects distant points {y n}of the original attractor to close values of{x n}.A small m may still give badly projected points and we seek the reconstructed state space of the smallest embed-ding dimension m that unfolds the attractor.This idea is implemented as follows.For each point x m n in the m-dimensional reconstructed state space,the distance from its nearest neighbor x mn(1)is calculated,d(x m n,x mn(1))=x m n−x mn(1).The dimension of the reconstructed state space is augmented by1and the new distance of thesevectors is calculated,d(x m+1n,x m+1n(1))= x m+1n−x m+1n(1). If the ratio of the two distances exceeds a predeﬁned tol-erance threshold r the two neighbors are classiﬁed as false neighbors,i.e.r n(m)=d(x m+1n,x m+1n(1))3 III.MULTIV ARIATE EMBEDDINGIn Section II we gave a summary of the reconstructiontechnique for a deterministic dynamical system from ascalar time series generated by the system.However,it ispossible that more than one time series are observed thatare possibly related to the system under investigation.For p time series measured simultaneously from the samedynamical system,a measurement function H:Γ→R pis decomposed to h i,i=1,...,p,deﬁned as in Section II,giving each a time series{x i,n}N n=1.According to the dis-cussion on univariate embedding any of the p time seriescan be used for reconstruction of the system dynamics,or better,the most suitable time series could be selectedafter proper investigation.In a diﬀerent approach all theavailable time series are considered and the analysis ofthe univariate time series is adjusted to the multivariatetime series.A.From univariate to multivariate embeddingGiven that there are p time series{x i,n}N n=1,i=1,...,p,the equivalent to the reconstructed state vec-tor in(1)for the case of multivariate embedding is of theformx n=(x1,n−(m1−1)τ1,x1,n−(m1−2)τ1,...,x1,n,x2,n−(m2−1)τ2,...,x2,n,...,x p,n)(3)and are deﬁned by an embedding dimension vector m= (m1,...,m p)that indicates the number of components used from each time series and a time delay vector τ=(τ1,...,τp)that gives the delays for each time series. The corresponding graph for the multivariate embedding process is shown below.y n∈A⊂ΓF→y n+1∈A⊂Γւh1↓h2...ցhpւh1↓h2...ցhpx1,n x2,n...x p,n x1,n+1x2,n+1...x p,n+1ցe↓e...ւeցe↓e...ւex n∈˜A⊂R M G→x n+1∈˜A⊂R MThe total embedding dimension M is the sum of the individual embedding dimensions for each time seriesM= p i=1m i.Note that if redundant or irrelevant information is present in the p time series,only a sub-set of them may be represented in the optimal recon-structed points x n.The selection of m andτfollows the same principles as for the univariate case:the attrac-tor should be fully unfolded and the components of the embedding vectors should be uncorrelated.A simple se-lection rule suggests that all individual delay times and embedding dimensions are the same,i.e.m=m1and τ=τ1with1a p-vector of ones[6,7].Here,we set againτi=1,i=1,...,p,but we consider bothﬁxed and varying m i in the implementation of the FNN method (see Section III D).B.Multivariate local predictionThe prediction for each time series x i,n,i=1,...,p,is performed separately by p local models,estimated as in the case of univariate time series,but for reconstructed points formed potentially from all p time series as given in(3)(e.g.see[9]).We propose an extension of the NRMSE for the pre-diction of one time series to account for the error vec-tors comprised of the individual prediction errors for each of the predicted time series.If we have one step ahead predictions for the p available time series,i.e.ˆx i,n, i=1,...,p(for a range of current times n−1),we deﬁne the multivariate NRMSENRMSE=n (x1,n−¯x1,...,x p,n−¯x p) 2(4)where¯x i is the mean of the actual values of x i,n over all target times n.C.Problems and restrictions of multivariatereconstructionsA major problem in the multivariate case is the prob-lem of identiﬁcation.There are often not unique m and τembedding parameters that unfold fully the attractor.A trivial example is the Henon map[17]x n+1=1.4−x2n+y ny n+1=0.3x n(5) It is known that for the state space reconstruction from the observable x n the appropriate embedding parame-ters are m=2andτ=1.Due to the fact that y n is a lagged multiple of x n the attractor can obviously be reconstructed from the bivariate time series{x n,y n} equally well with any of the following two-dimensional embedding schemesx n=(x n,x n−1)x n=(x n,y n)x n=(y n,y n−1) since they are essentially the same.This example shows also the problem of redundant information,e.g.the state space reconstruction would not improve by augmenting the delay vector x n=(x n,x n−1)with the component y n that actually duplicates x n−1.Redundancy is inevitable in multivariate time series as synchronous observations of the diﬀerent time series are generally correlated and the fact that these observations are used as components in the same embedding vector adds redundant information in them.We note here that in the case of continuous dynamical systems,the delay parameterτi may be se-lected so that the components of the i time series are not correlated with each other,but this does not imply that they are not correlated to components from another time series.4 A diﬀerent problem is that of irrelevance,whenseries that are not generated by the same dynamicaltem are included in the reconstruction procedure.may be the case even when a time series is connectedtime series generated by the system underAn issue of concern is also the fact thatdata don’t always have the same data ranges andtances calculated on delay vectors withdiﬀerent ranges may depend highly on only some ofcomponents.So it is often preferred to scale all theto have either the same variance or be in the samerange.For our study we choose to scale the data torange[0,1].D.Selection of the embedding dimension vector Taking into account the problems in the state space reconstruction from multivariate time series,we present three methods for determining m,two based on the false nearest neighbor algorithm,which we name FNN1and FNN2,and one based on local models which we call pre-diction error minimization criterion(PEM).The main idea of the FNN algorithms is as for the univariate case.Starting from a small value the embed-ding dimension is increased by including delay compo-nents from the p time series and the percentage of the false nearest neighbors is calculated until it falls to the zero level.The diﬀerence of the two FNN methods is on the way that m is increased.For FNN1we restrict the state space reconstruction to use the same embedding dimension for each of the p time series,i.e.m=(m,m,...,m)for a given m.To assess whether m is suﬃcient,we consider all delay embeddings derived by augmenting the state vector of embedding di-mension vector(m,m,...,m)with a single delayed vari-able from any of the p time series.Thus the check for false nearest neighbors in(2)yields the increase from the embedding dimension vector(m,m,...,m)to each of the embedding dimension vectors(m+1,m,...,m), (m,m+1,...,m),...,(m,m,...,m+1).Then the algo-rithm stops at the optimal m=(m,m,...,m)if the zero level percentage of false nearest neighbors is obtained for all p cases.A sketch of theﬁrst two steps for a bivariate time series is shown in Figure1(a).This method has been commonly used in multivariate reconstruction and is more appropriate for spatiotem-porally distributed data(e.g.see the software package TISEAN[18]).A potential drawback of FNN1is that the selected total embedding dimension M is always a multiple of p,possibly introducing redundant informa-tion in the embedding vectors.We modify the algorithm of FNN1to account for any form of the embedding dimension vector m and the total embedding dimension M is increased by one at each step of the algorithm.Let us suppose that the algorithm has reached at some step the total embedding dimension M. For this M all the combinations of the components of the embedding dimension vector m=(m1,m2,...,m p)are considered under the condition M= p i=1m i.Then for each such m=(m1,m2,...,m p)all the possible augmen-tations with one dimension are checked for false nearest neighbors,i.e.(m1+1,m2,...,m p),(m1,m2+1,...,m p), ...,(m1,m2,...,m p+1).A sketch of theﬁrst two steps of the extended FNN algorithm,denoted as FNN2,for a bivariate time series is shown in Figure1(b).The termination criterion is the drop of the percent-age of false nearest neighbors to the zero level at every increase of M by one for at least one embedding dimen-sion vector(m1,m2,...,m p).If more than one embedding dimension vectors fulﬁll this criterion,the one with the smallest cumulative FNN percentage is selected,where the cumulative FNN percentage is the sum of the p FNN percentages for the increase by one of the respective com-ponent of the embedding dimension vector.The PEM criterion for the selection of m= (m1,m2,...,m p)is simply the extension of the goodness-of-ﬁt or prediction criterion in the univariate case to account for the multiple ways the delay vector can be formed from the multivariate time series.Thus for all possible p-plets of(m1,m2,...,m p)from(1,0,...,0), (0,1,...,0),etc up to some vector of maximum embed-ding dimensions(m max,m max,...,m max),the respective reconstructed state spaces are created,local linear mod-els are applied and out-of-sample prediction errors are computed.So,totally p m max−1embedding dimension vectors are compared and the optimal is the one that gives the smallest multivariate NRMSE as deﬁned in(4).IV.MONTE CARLO SIMULATIONS ANDRESULTSA.Monte Carlo setupWe test the three methods by performing Monte Carlo simulations on a variety of known nonlinear dynamical systems.The embedding dimension vectors are selected using the three methods on100diﬀerent realizations of each system and the most frequently selected embedding dimension vectors for each method are tracked.Also,for each realization and selected embedding dimension vec-5ate NRMSE over the100realizations for each method is then used as an indicator of the performance of each method in prediction.The selection of the embedding dimension vector by FNN1,FNN2and PEM is done on theﬁrst three quarters of the data,N1=3N/4,and the multivariate NRMSE is computed on the last quarter of the data(N−N1).For PEM,the same split is used on the N1data,so that N2= 3N1/4data are used toﬁnd the neighbors(training set) and the rest N1−N2are used to compute the multivariate NRMSE(test set)and decide for the optimal embedding dimension vector.A sketch of the split of the data is shown in Figure2.The number of neighbors for the local models in PEM varies with N and we set K N=10,25,50 for time series lengths N=512,2048,8192,respectively. The parameters of the local linear model are estimated by ordinary least squares.For all methods the investigation is restricted to m max=5.The multivariate time series are derived from nonlin-ear maps of varying dimension and complexity as well as spatially extended maps.The results are given below for each system.B.One and two Ikeda mapsThe Ikeda map is an example of a discrete low-dimensional chaotic system in two variables(x n,y n)de-ﬁned by the equations[19]z n+1=1+0.9exp(0.4i−6i/(1+|z n|2)),x n=Re(z n),y n=Im(z n),where Re and Im denote the real and imaginary part,re-spectively,of the complex variable z n.Given the bivari-ate time series of(x n,y n),both FNN methods identify the original vector x n=(x n,y n)andﬁnd m=(1,1)as optimal at all realizations,as shown in Table I.On the other hand,the PEM criterionﬁnds over-embedding as optimal,but this improves slightly the pre-diction,which as expected improves with the increase of N.Next we consider the sum of two Ikeda maps as a more complex and higher dimensional system.The bivariateI:Dimension vectors and NRMSE for the Ikeda map.2,3and4contain the embedding dimension vectorsby their respective frequency of occurrenceNRMSEFNN1PEM FNN2 512(1,1)1000.0510.032 (1,1)100(2,2)1000.028 8192(1,1)1000.0130.003II:Dimension vectors and NRMSE for the sum ofmapsNRMSEFNN1PEM FNN2 512(2,2)650.4560.447(1,3)26(3,3)95(2,3)540.365(2,2)3(2,2)448192(2,3)430.2600.251(1,4)37time series are generated asx n=Re(z1,n+z2,n),y n=Im(z1,n+z2,n).The results of the Monte Carlo simulations shown in Ta-ble II suggest that the prediction worsens dramatically from that in Table I and the total embedding dimension M increases with N.The FNN2criterion generally gives multiple optimal m structures across realizations and PEM does the same but only for small N.This indicates that high complex-ity degrades the performance of the algorithms for small sample sizes.PEM is again best for predictions but over-all we do not observe large diﬀerences in the three meth-ods.An interesting observation is that although FNN2ﬁnds two optimal m with high frequencies they both give the same M.This reﬂects the problem of identiﬁcation, where diﬀerent m unfold the attractor equally well.This feature cannot be observed in FNN1because the FNN1 algorithm inspects fewer possible vectors and only one for each M,where M can only be multiple of p(in this case(1,1)for M=2,(2,2)for M=4,etc).On the other hand,PEM criterion seems to converge to a single m for large N,which means that for the sum of the two Ikeda maps this particular structure gives best prediction re-sults.Note that there is no reason that the embedding dimension vectors derived from FNN2and PEM should match as they are selected under diﬀerent conditions. Moreover,it is expected that the m selected by PEM gives always the lowest average of multivariate NRMSE as it is selected to optimize prediction.TABLE III:Dimension vectors and NRMSE for the KDR mapNRMSE FNN1PEM FNN2512(0,0,2,2)30(1,1,1,1)160.7760.629 (1,1,1,1)55(2,2,2,2)39(0,2,1,1)79(0,1,0,1)130.6598192(2,1,1,1)40(1,1,1,1)140.5580.373TABLE IV:Dimension vectors and NRMSE for system of Driver-Response Henon systemEmbedding dimensionsN FNN1PEM FNN2512(2,2)100(2,2)75(2,1)100.196(2,2)100(3,2)33(2,2)250.127(2,2)100(3,0)31(0,3)270.0122048(2,2)100(2,2)1000.093(2,2)100(3,3)45(4,3)450.084(2,2)100(0,3)20(3,0)190.0068192(2,2)100(2,2)1000.051(2,2)100(3,3)72(4,3)250.027(2,2)100(0,4)31(4,0)300.002TABLE V:Dimension vectors and NRMSE for Lattice of3coupled Henon mapsEmbedding dimensionsN FNN1PEM FNN2512(2,2,2)94(1,1,1)6(1,2,1)29(1,1,2)230.298(2,2,2)98(1,1,1)2(2,0,2)44(2,1,1)220.2282048(2,2,2)100(1,2,2)34(2,2,1)300.203(2,2,2)100(2,1,2)48(2,0,2)410.1318192(2,2,2)100(2,2,2)97(3,2,3)30.174(2,2,2)100(2,1,2)79(3,2,3)190.084NRMSEC FNN2FNN1PEM0.4(1,1,1,1)42(1,0,2,1)170.2850.2880.8(1,1,1,1)40(1,0,1,2)170.3140.2910.4(1,1,1,1)88(1,1,1,2)70.2290.1900.8(1,1,1,1)36(1,0,2,1)330.2250.1630.4(1,1,1,1)85(1,2,1,1)80.1970.1370.8(1,2,0,1)31(1,0,2,1)220.1310.072 PEM cannot distinguish the two time series and selectswith almost equal frequencies vectors of the form(m,0)and(0,m)giving again over-embedding as N increases.Thus PEM does not reveal the coupling structure of theunderlying system and picks any embedding dimensionstructure among a range of structures that give essen-tially equivalent predictions.Here FNN2seems to de-tect suﬃciently the underlying coupling structure in thesystem resulting in a smaller total embedding dimensionthat gives however the same level of prediction as thelarger M suggested by FNN1and slightly smaller thanthe even larger M found by PEM.ttices of coupled Henon mapsThe last system is an example of spatiotemporal chaosand is deﬁned as a lattice of k coupled Henon maps{x i,n,y i,n}k i=1[22]speciﬁed by the equationsx i,n+1=1.4−((1−C)x i,n+C(x i−1,n+x i+1,n)ple size,at least for the sizes we used in the simulations. Such a feature shows lack of consistency of the PEM cri-terion and suggests that the selection is led from factors inherent in the prediction process rather than the quality of the reconstructed attractor.For example the increase of embedding dimension with the sample size can be ex-plained by the fact that more data lead to abundance of close neighbors used in local prediction models and this in turn suggests that augmenting the embedding vectors would allow to locate the K neighbors used in the model. On the other hand,the two schemes used here that ex-tend the method of false nearest neighbors(FNN)to mul-tivariate time series aim atﬁnding minimum embedding that unfolds the attractor,but often a higher embedding gives better prediction results.In particular,the sec-ond scheme(FNN2)that explores all possible embedding structures gives consistent selection of an embedding of smaller dimension than that selected by PEM.Moreover, this embedding could be justiﬁed by the underlying dy-namics of the known systems we tested.However,lack of consistency of the selected embedding was observed with all methods for small sample sizes(somehow expected due to large variance of any estimate)and for the cou-pled maps(probably due to the presence of more than one optimal embeddings).In this work,we used only a prediction performance criterion to assess the quality of state space reconstruc-tion,mainly because it has the most practical relevance. There is no reason to expect that PEM would be found best if the assessment was done using another criterion not based on prediction.However,the reference(true)value of other measures,such as the correlation dimen-sion,are not known for all systems used in this study.An-other constraint of this work is that only noise-free multi-variate time series from discrete systems are encountered, so that the delay parameter is not involved in the state space reconstruction and the eﬀect of noise is not studied. It is expected that the addition of noise would perplex further the process of selecting optimal embedding di-mension and degrade the performance of the algorithms. For example,we found that in the case of the Henon map the addition of noise of equal magnitude to the two time series of the system makes the criteria to select any of the three equivalent embeddings((2,0),(0,2),(1,1))at random.It is in the purpose of the authors to extent this work and include noisy multivariate time series,also fromﬂows,and search for other measures to assess the performance of the embedding selection methods.AcknowledgmentsThis paper is part of the03ED748research project,im-plemented within the framework of the”Reinforcement Programme of Human Research Manpower”(PENED) and co-ﬁnanced at90%by National and Community Funds(25%from the Greek Ministry of Development-General Secretariat of Research and Technology and75% from E.U.-European Social Fund)and at10%by Rik-shospitalet,Norway.[1]F.Takens,Lecture Notes in Mathematics898,365(1981).[2]T.Sauer,J.A.Yorke,and M.Casdagli,Journal of Sta-tistical Physics65,579(1991).[3]H.Kantz and T.Schreiber,Nonlinear Time Series Anal-ysis(Cambridge University Press,1997).[4]J.Guckenheimer and G.Buzyna,Physical Review Let-ters51,1438(1983).[5]M.Paluˇs,I.Dvoˇr ak,and I.David,Physica A StatisticalMechanics and its Applications185,433(1992).[6]R.Hegger and T.Schreiber,Physics Letters A170,305(1992).[7]D.Prichard and J.Theiler,Physical Review Letters73,951(1994).[8]H.D.I.Abarbanel,T.A.Carroll,,L.M.Pecora,J.J.Sidorowich,and L.S.Tsimring,Physical Review E49, 1840(1994).[9]L.Cao,A.Mees,and K.Judd,Physica D121,75(1998),ISSN0167-2789.[10]J.P.Barnard,C.Aldrich,and M.Gerber,Physical Re-view E64,046201(2001).[11]S.P.Garcia and J.S.Almeida,Physical Review E(Sta-tistical,Nonlinear,and Soft Matter Physics)72,027205 (2005).[12]Y.Hirata,H.Suzuki,and K.Aihara,Physical ReviewE(Statistical,Nonlinear,and Soft Matter Physics)74, 026202(2006).[13]M.B.Kennel,R.Brown,and H.D.I.Abarbanel,Phys-ical Review A45,3403(1992).[14]D.T.Kaplan,in Chaos in Communications,edited byL.M.Pecora(SPIE-The International Society for Optical Engineering,Bellingham,Washington,98227-0010,USA, 1993),pp.236–240.[15]B.Chun-Hua and N.Xin-Bao,Chinese Physics13,633(2004).[16]R.Hegger and H.Kantz,Physical Review E60,4970(1999).[17]M.H´e non,Communications in Mathematical Physics50,69(1976).[18]R.Hegger,H.Kantz,and T.Schreiber,Chaos:An Inter-disciplinary Journal of Nonlinear Science9,413(1999).[19]K.Ikeda,Optics Communications30,257(1979).[20]C.Grebogi,E.Kostelich,E.O.Ott,and J.A.Yorke,Physica D25(1987).[21]S.J.Schiﬀ,P.So,T.Chang,R.E.Burke,and T.Sauer,Physical Review E54,6708(1996).[22]A.Politi and A.Torcini,Chaos:An InterdisciplinaryJournal of Nonlinear Science2,293(1992).。

基于激光点云数据的单木骨架三维重构浔

第40卷第1期2024年1月森㊀林㊀工㊀程FOREST ENGINEERINGVol.40No.1Jan.,2024doi:10.3969/j.issn.1006-8023.2024.01.015基于激光点云数据的单木骨架三维重构赵永辉,刘雪妍,吕勇,万晓玉,窦胡元,刘淑玉∗(东北林业大学计算机与控制工程学院,哈尔滨150040)摘㊀要:针对树木三维重构过程中面临的处理速度慢㊁重构精度低等问题,提出一种采用激光点云数据的单木骨架三维重构方法㊂首先,根据点云数据类型确定组合滤波方式,以去除离群点和地面点;其次,采用一种基于内部形态描述子(ISS )和相干点漂移算法(CPD )的混合配准算法(Intrinsic Shape -Coherent Point Drift ,IS -CPD ),以获取单棵树木的完整点云数据;最后,采用Laplace 收缩点集和拓扑细化相结合的方法提取骨架,并通过柱体构建枝干模型,实现骨架三维重构㊂试验结果表明,相比传统CPD 算法,研究设计的配准方案精度和执行速度分别提高50%和95.8%,最终重构误差不超过2.48%㊂研究结果证明可有效地重构单棵树木的三维骨架,效果接近树木原型,为构建林木数字孪生环境和林业资源管理提供参考㊂关键词:激光雷达;树木点云;关键点提取;树木骨架;几何模型中图分类号:S792.95;TN958.98㊀㊀㊀㊀文献标识码:A㊀㊀㊀文章编号:1006-8023(2024)01-0128-073D Reconstruction of Single Wood Skeleton Based on Laser Point Cloud DataZHAO Yonghui,LIU Xueyan,LYU Yong,WAN Xiaoyu,DOU Huyuan,LIU Shuyu ∗(College of Computer and Control Engineering,Northeast Forestry University,Harbin 150040,China)Abstract :In response to the slow processing speed and low reconstruction accuracy encountered during the 3D reconstruction of trees,a method for 3D reconstruction of single -tree skeletons using laser point cloud data is proposed.Firstly,a combination filtering method is determined based on the point cloud data type to remove outliers and ground points.Secondly,a hybrid registration algorithm based on ISS (Intrinsic Shape Descriptor)and CPD (Coherent Point Drift algorithm),called IS -CPD (Intrinsic Shape -Coherent Point Drift),is employed to obtain complete point cloud data for individual trees.Finally,a method combining Laplace contraction of point sets and topological refinement is used to obtain the skeleton,and branch models are constructed using cylinders to achieve 3D skeleton reconstruction.Experimental results show that compared to traditional CPD algorithm,the proposed registration scheme im-proves accuracy and execution speed by 50%and 95.8%respectively,with a final reconstruction error of no more than 2.48%.The research demonstrates the effective reconstruction of the 3D skeleton of individual trees,with results close to the original trees,provi-ding a reference for building digital twin environments of forest trees and forestry resource management.Keywords :LiDAR;tree point cloud;key point extraction;tree skeleton;geometry model收稿日期:2023-02-10基金项目:国家自然科学基金(31700643)㊂第一作者简介:赵永辉,硕士,工程师㊂研究方向为物联网与人工智能㊂E-mail:hero9968@∗通信作者:刘淑玉,硕士,讲师㊂研究方向为通信与信号处理㊂E -mail:1000002605@引文格式:赵永辉,刘雪妍,吕勇,等.基于激光点云数据的单木骨架三维重构[J].森林工程,2024,40(1):128-134.ZHAO Y H,LIU X Y,LYU Y,et al.3D reconstruction of sin-gle wood skeleton based on laser point cloud data[J].Forest En-gineering,2024,40(1):128-134.0㊀引言激光雷达可用于获取目标稠密点云数据,是实现自动驾驶和三维重建的重要手段㊂使用机载或地基激光雷达可以获取树高㊁胸径和冠层等量化信息,用于树木的三维重建,为推断树木的生态结构参数和碳储量反演提供依据,也可为林业数字孪生提供数据支撑㊂主流的点云数据去噪方法主要有基于密度㊁基于聚类和基于统计3种[1]㊂分离地面点和非地面点是点云数据处理的第一步,学者提出多种算法用于地面点分离㊂然而,即使是最先进的滤波算法,也需要设置许多复杂的参数才能实现㊂Zhang 等[2]提出了一种新颖的布料模拟滤波算法(Cloth Simu-lation Filter,CSF),该算法只需调整几个参数即可实现地面点的过滤,但该算法对于点云噪声非常敏感㊂在点云配准方面,经典的算法是Besl 等[3]提出的迭代最近点算法(Iterative Closest Point,ICP),但易出现局部最优解,从而限制了该算法的应用㊂因此,许多学者采用概率统计方法进行点云配准,典型的方法是相干点漂移算法(Coherent Point Drift,CPD)[4-5]等,但该方法存在运行时间长和计算复杂的问题㊂石珣等[6]结合曲率特征与CPD 提出了一第1期赵永辉,等:基于激光点云数据的单木骨架三维重构种快速配准方法,速度大大提高,但细节精确度有所下降㊂陆军等[7]㊁夏坎强[8]㊁史丰博等[9]对基于关键点特征匹配的点云配准方法进行了深入研究㊂三维树木几何重建从传统的基于规则㊁草图和影像重建,发展到如今借助激光雷达技术,可以构建拓扑正确的三维树木几何形态㊂翟晓晓等[10]以点云数据进行树木重建,由于受激光雷达视场角的约束,难以获得树冠结构的信息,因此仅重建了树干㊂Lin 等[11]㊁You 等[12]涉及点云骨架提取的研究,构建了树的几何和拓扑结构,但重构模型的真实感不够强㊂Cao 等[13]使用基于Laplace 算子的建模方法提取主要枝干的几何信息,拓扑连接正确,并保留了部分细枝㊂曹伟等[14]对点云树木建模的发展和前景进行了综述,但在结合点云数据提取骨架并重建等方面研究不足㊂本研究提出一种基于骨架的方法,旨在准确地从单木的点云数据中重建三维模型㊂原始点云数据经过CSF 算法和K 维树(Kd -Tree)近邻搜素法的组合滤波后,提取了准确的单木数据㊂同时,基于树木特征点云的混合配准算法(Intrinsic Shape -Co-herent Point Drift,IS -CPD),可显著提高配准效率㊂最后,通过提取单棵树木的骨架点,构造连接性,并用圆柱拟合枝干,实现了单木的三维建模㊂1㊀数据采集及预处理1.1㊀数据获取数据采集自山东省潍坊市奎文区植物园内一株高约8.5m㊁树龄约20a 的银杏树㊂使用Ro-boSense 雷达从2个不同角度进行点云数据采集,雷达高为1.5m,与树木水平距离约为10m㊂通过对来自树木正东方向和正北方向的2组点云数据进行采集,如图1所示㊂（a ）角度1点云数据(正东方向)（a ）Angle 1 point cloud data （East direction ）（b ）角度2点云数据（正北方向）（b ）Angle 2 point cloud data （North direction）图1㊀2组点云的最初扫描结果Fig.1Initial scan results of two sets of point clouds1.2㊀点云预处理为了提高后续处理点云数据的准确性和时效性,需要对数据进行预处理㊂首先,利用CSF 滤波算法去除冗余的地面背景信息,该算法参数较少,分离速度快㊂通过使用落在重力下的布来获取地形的物理表示,单木点云可以被分离出来㊂由于扫描环境和激光雷达硬件误差的影响,可能会出现离群点㊂因此,采用Kd -Tree 算法对提取的点云进行降噪处理,提高单个树木数据的精度,以备在后续的算法使用中得到更准确的结果㊂通过搜索待滤波点云p i (x i ,y i ,z i )中每个点的空间邻近点p j (x j ,y j ,z j ),计算之间的平均距离(d i )㊁全局均值(μ)以及标准差(σ)㊂筛选符合范围(μ-αˑσɤd i ɤμ+αˑσ)的点并过滤掉离群值(α为决定点云空间分布的参数),d i ㊁μ㊁σ的计算公式如下㊂d i =ðkj =1x i -y j k μ=ðn i =1d i n σ=ðni =1(d i -μ)2n ìîíïïïïïïïïïïïï㊂(1)921森㊀林㊀工㊀程第40卷式中:k 为决定点云密集度的参数;n 为点云数量㊂通过试验发现,最终选定参数k =20,α=1.2时,对点云数据进行处理结果最优,滤噪结果如图2所示,基本去除了离群噪声点和地面点同时又确保对点云模型轮廓的保护㊂2㊀单木骨架重构方法单木骨架重构方法的过程主要包括以下几个步骤,如图3所示㊂首先,对预处理的2组点云数据进行特征提取,并进行精确的配准;其次,对点云进行几何收缩,获取零体积点集,并通过拓扑细化将点集细化成一维曲线,得到与点云模型基本吻合的骨架线;最后,基于骨架线对树木枝干进行圆柱拟合,以构建枝干的三维模型㊂图2㊀2组点云滤噪结果图Fig.2Two sets of point cloud filtering and denoisingresults图3㊀单木骨架重构方法过程图Fig.3Process diagram of single wood skeleton reconstruction method2.1㊀三维点云配准CPD 配准是一种基于概率的点集配准算法,在对点集进行配准时,一组点集作为高斯混合模型(Gaussian Mixture Model,GMM)的质心,假设模板点集坐标为X M ˑD =(y 1,y 2, ,y M )T ,另一组点集作为混合高斯模型的数据集,假设目标点集坐标为X N ˑD =(x 1,x 2, ,x N )T ,N ㊁M 分别代表2组点的数目,D 为Z 组的维度,T 为矩阵转置㊂通过GMM 的最大后验概率得到点集之间的匹配对应关系㊂GMM 概率密度函数如下㊂p (x )=ω1N +(1-ω)ðMm =11M p (x m )㊂(2)式中:p x |m ()=1(2πσ2)D 2exp (-x -y m 22σ2),;p (x )是概率密度函数;ω(0ɤωɤ1)为溢出点的权重参数;m 为1 M 中的任何一个数㊂GMM 质心的位置通过调整变换参数(θ)的值进行改变,而变换参数的值可以通过最小化-log 函数来求解㊂E θ,σ2()=-ðN n -1log ðMm -1p (m )p (x n |m )㊂(3)式中,x n 与y m 之间的匹配关系可以由GMM 质心的后验概率p (m x n )=p (m )p (x n m )来定义㊂采用期望最大值算法进行迭代循环,从而对最大似然估计进行优化,当收敛时迭代停止㊂得到θ和σ2的解,即完成模板网格点集向目标网格点集的配准㊂扫描设备采集的点云数据通常数量庞大,因此并非所有点云信息都对配准有效㊂此外,CPD 算法的计算复杂度较高,匹配速度较慢㊂因此,本研究采用ISS(Intrinsic Shape Signaturs)算法[15]提取关键点,以降低几何信息不显著点的数量㊂通过对这些特征点进行精确配准,可以提高点云配准的效率㊂图4给出了IS -CPD 配准过程㊂31第1期赵永辉,等:基于激光点云数据的单木骨架三维重构图4㊀基于特征点提取的配准过程图Fig.4Registration process diagram based on feature point extraction ㊀㊀IS-CPD点云配准算法流程如下㊂(1)选择2个视角点云重叠区域㊂(2)采用ISS算法提取特征点集㊂设点云数据有n个点,(x i,y i,z i),i=0,1, ,n-1㊂记P i=(x i,y i,z i)㊂①针对输入点云的每个点构建一个半径为r的球形邻域,并根据式(4)计算每个点的权重㊂W ij=1||p i-p j||,|p i-p j|<r㊂(4)②根据式(5)计算各点的协方差矩阵cov及其特征值{λ1i,λ2i,λ3i},并按从小到大的次序进行排列㊂cov(p i)=ð|p i-p j|<r w ij(P i-P j)(P i-P j)Tð|P i-P j|<r w ij㊂(5)③设置阈值ε1与ε2,满足λ1iλ2i ≪ε1㊁λ2iλ3i≪ε2的点即为关键点㊂(3)初始化CPD算法参数㊂(4)求出相关概率矩阵与后验概率p(m|x n)㊂(5)利用最小负对数似然函数求出各参数的值㊂(6)判断p的收敛性,若不收敛,则重复步骤(4)直到收敛㊂(7)在点集数据中,利用所得到的转换矩阵,完成配准㊂2.2㊀点云枝干重建传统的构建枝干的方法是直接在点云表面上进行重构,这种方法会导致大量畸变结构㊂因此,本研究先提取单木骨架线,再通过拟合圆柱来构建几何模型㊂图5为骨架提取并重建枝干的过程㊂为精确提取树干和树枝,采用Laplace收缩法提取骨架㊂首先,对点云模型进行顶点邻域三角化,得到顶点的单环邻域关系㊂然后,计算相应的余切形式的拉普拉斯矩阵,并以此为依据收缩点云,直至模型收缩比例占初始体积的1%,再通过拓扑细化将点集细化成一维曲线㊂采用最远距离点球对收缩点进行采样,利用一环邻域相关性将采样点连接成初始骨架,折叠不必要的边,直到不存在三角形,得到与点云模型基本吻合的骨架线㊂为准确地模拟树枝的几何形状,采用圆柱拟合方法㊂在树基区域,使用优化方法来获得主干的几何结构[16]㊂由于靠近树冠和树枝尖端的小树枝的点云数据较为杂乱,使用树木异速生长理论来控制枝干半径㊂最终,拟合圆柱体来得到树木点云的3D 几何模型[17],原理如图6所示㊂以粗度R为半径,以上端点M和下端点N为圆心生成多个圆截面,并沿着骨架线连接圆周点绘制出圆柱体,以此代表每个树枝,最终完成整棵树的枝干的绘制㊂131森㊀林㊀工㊀程第40卷图5㊀构建枝干模型流程图Fig.5Flow chart for building branch model（a）圆柱模型示例（a）Example of a cylindrical model（b）绘制局部树枝示例（b）Example of drawing a partial tree branchNMR图6㊀绘制树干几何形状原理Fig.6Principle of drawing tree trunk geometry3㊀试验结果与分析3.1㊀点云配准结果与分析为验证IS-CPD配准算法的有效性,对滤波后的点云进行试验,比较该算法与原始CPD算法及石珣等[6]提出的方法在同一数据下的运行时间及均方根误差(RMSE,式中记为R MSE),其表达式见式(6),值越小表示配准效果越精确㊂图7及表1给出了3种配准算法的对比结果㊂R MSE=㊀ðn i-1(x i-x︿i)2n㊂(6)式中:n为点云数量;x i和x︿i分别为配准前后对应点之间欧氏距离㊂经过配准结果图7和表1的分析,石珣等[5]算法虽提高了配准速度,但其细节精度下降,配准结果不佳㊂相比之下,CPD和IS-CPD算法均能成功地融合2个不同角度的点云,达到毫米级的精度,2种方法可视为效果近乎一致㊂相比之下,本研究算法的时间复杂度要小得多㊂此外,由表2可知,配准时间缩短至10.77s,平均配准精度相较CPD提高了约50%㊂3.2㊀点云枝干重建结果与分析在几何重建部分(图8),采用基于Laplace收缩的骨架提取方法,仅需不到5次迭代,就可以将点收缩到较好的位置,如图8(b)所示㊂对收缩后的零体231第1期赵永辉,等:基于激光点云数据的单木骨架三维重构图7㊀点云配准可视化对比Fig.7Point cloud registration visualization comparison表1㊀点云配准结果对比Tab.1Comparison of point cloud registration results配准算法Registration algorithm 点云总数/个Total number of point clouds角度1Angle 1角度2Angle 2历时/s Time 均方根误差/mRMSE CPD石珣等[6]Shi xun et al [6]本算法Proposed algorithm3795637647261.748.3ˑ10-386.58 1.6ˑ10-210.774.1ˑ10-3㊀㊀注:IS -CPD 算法提取关键点所需的时间可以忽略不计㊂Note:The time required for the IS -CPD algorithm to extract key points can beignored.积点集进行拓扑细化,得到与点云模型基本吻合的骨架线,如图8(c)所示㊂随后,对枝干进行圆柱拟合㊂至此,树木点云重建工作全部完成㊂图8(d)为树木骨架几何重建的最终结果㊂本研究使用单棵树木的树高和胸径作为重建模型的精度评价指标㊂首先,采用树干点拟合圆柱的方法来将点云投影至圆柱轴向方向,通过求取该轴向投影的最大值和最小值来获取树高信息㊂同时,（a ）输入点云（a ）Input point cloud（b ）点云收缩（b ）Point cloud shrinkage （c ）连接骨架线（c ）Connecting skeleton lines（d ）树木点云的几何模型（d ）Geometric model of treepoint cloud图8㊀单木几何重建过程Fig.8Single wood geometry reconstruction process在Pitkanen 等[18]研究方法的基础上,对树干点云进行分层切片处理,将二维平面上的分层点云进行投影,再通过圆拟合方法得到更为精确的胸径尺寸㊂为验证该算法重建模型的准确性,进行20次试验,并将其与Nurunnabi 等[16]的重建方法进行了比较㊂表2为2种方法分别获得的树高和胸径的平均值,并将其与真实测量值进行了对比㊂结果表明,该算法相较于Nurunnabi 等[16]的重建方法具有更高的精度,胸径平均误差仅为2.48%,树高平均误差仅为1.64%㊂表2㊀树木重构精度分析Tab.2Tree reconstruction accuracy analysis评估方法Evaluation method胸径/m DBH 树高/m Height 平均误差(%)Average error胸径DBH 树高Height Nurunnabi 等[16]Nurunnabi et al [16]2.13ˑ10-18.26 5.973.17本算法Proposed algorithm1.96ˑ10-18.392.48 1.64实测值Measured value2.01ˑ10-18.53331森㊀林㊀工㊀程第40卷4㊀结论本研究讨论了激光雷达重建单棵树木的流程,分析并改进了关键问题㊂充分发挥CSF滤波和Kd-Tree算法的优势,从而精准地分离出了单棵树木的数据,提高了处理速度㊂提出IS-CPD配准算法,可将点云配准的效率提高约95.8%㊂通过精确配准后的点云数据,成功提取骨架树,最终重构误差控制在2.48%以内㊂试验结果表明,研究方法在树木点云数据滤波㊁配准和骨架提取方面具有可行性,树木枝干结构重建效果良好,且重构模型可为评估农林作物㊁森林生态结构健康等提供支持㊂ʌ参㊀考㊀文㊀献ɔ[1]鲁冬冬,邹进贵.三维激光点云的降噪算法对比研究[J].测绘通报,2019(S2):102-105.LU D D,ZOU J parative research on denoising al-gorithms of3D laser point cloud[J].Survey and Mapping Bulletin,2019(S2):102-105.[2]ZHANG W,QI J,WAN P,et al.An easy-to-use air-borne LiDAR data filtering method based on cloth simula-tion[J].Remote Sensing,2016,8(6):501. [3]BESL P J,MCKAY H D.A method for registration of3-D shapes[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1992,14(2):239-256. [4]MYRONENKO A,SONG X.Point set registration:coherent point drift[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2010,32(12):2262-2275. [5]王爱丽,张宇枭,吴海滨,等.基于集成卷积神经网络的LiDAR数据分类[J].哈尔滨理工大学学报,2021, 26(4):138-145WANG A L,ZHANG Y X,WU H B,et al.LiDAR data classification based on ensembled convolutional neural net-works[J].Journal of Harbin University of Science and Technology,2021,26(4):138-145.[6]石珣,任洁,任小康.等.基于曲率特征的漂移配准方法[J].激光与光电子学进展,2018,55(8):248-254. SHI X,REN J,REN X K,et al.Drift registration based on curvature characteristics[J].Laser&Optoelectronics Progress,2018,55(8):248-254.[7]陆军,邵红旭,王伟.等.基于关键点特征匹配的点云配准方法[J].北京理工大学学报,2020,40(4):409-415. LU J,SHAO H X,WANG W,et al.Point cloud registra-tion method based on key point extraction with small over-lap[J].Transactions of Beijing Institute of Technology, 2020,40(4):409-415.[8]夏坎强.基于ISS特征点和改进描述子的点云配准算法研究[J].软件工程,2022,25(1):1-5.XIA K Q.Research on point cloud algorithm based on ISS feature points and improved descriptor[J].Software Engi-neering,2022,25(1):1-5.[9]史丰博,曹琴,魏军.等.基于特征点的曲面点云配准方法[J].北京测绘,2022,36(10):1345-1349.SHI F B,CAO Q,WEI J,et al.Surface point cloud reg-istration method based on feature points[J].Beijing Sur-veying and Mapping,2022,36(10):1345-1349. [10]翟晓晓,邵杰,张吴明.等.基于移动LiDAR点云的树木三维重建[J].中国农业信息,2019,31(5):84-89.ZHAI X X,SHAO J,ZHANG W M,et al.Three-di-mensional reconstruction of trees using mobile laser scan-ning point cloud[J].China Agricultural Information,2019,31(5):84-89.[11]LIN G,TANG Y,ZOU X,et al.Three-dimensional re-construction of guava fruits and branches using instancesegmentation and geometry analysis[J].Computers andElectronics in Agriculture,2021,184:106107. [12]YOU A,GRIMM C,SILWAL A,et al.Semantics-guided skeletonization of upright fruiting offshoot trees forrobotic pruning[J].Computers and Electronics in Agri-culture,2022,192:106622.[13]CAO J J,TAGLIASACCJI A,OLSON M,et al.Pointcloud skeletons via Laplacian based contraction[C]//Proceedings of the Shape Modeling International Confer-ence.Los Alamitos:IEEE Computer Society Press,2010:187-197.[14]曹伟,陈动,史玉峰.等.激光雷达点云树木建模研究进展与展望[J].武汉大学学报(信息科学版),2021,46(2):203-220.CAO W,CHEN D,SHI Y F,et al.Progress and pros-pect of LiDAR point clouds to3D tree models[J].Geo-matics and Information Science of Wuhan University,2021,46(2):203-220.[15]YU Z.Intrinsic shape signatures:A shape descriptor for3D object recognition[C]//IEEE International Confer-ence on Computer Vision Workshops.IEEE,2010. [16]NURUNNABI A,SADAHIRO Y,LINDENBERGH R,etal.Robust cylinder fitting in laser scanning point clouddata[J].Measurement,2019,138:632-651. [17]GUO J W,XU S B,YAN D M,et al.Realistic proce-dural plant modeling from multiple view images[J].IEEE Transactions on Visualization and Computer Graph-ics,2020,26(2):1372-1384.[18]PITKANEN T P,RAUMONEN P,KANGAS A.Measur-ing stem diameters with TLS in boreal forests by comple-mentary fitting procedure[J].ISPRS Journal of Photo-grammetry and Remote Sensing,2019,147:294-306.431。

普朗特桨尖损失函数

普朗特桨尖损失函数
普朗特桨尖损失函数是一种在机器学习和深度学习中常用的损
失函数。

它主要用于解决回归问题，特别是针对预测值与真实值之间存在较大误差的情况。

该损失函数的表达式为：
L(y, y') = max(0, |y - y'| - δ)
其中，y表示真实值，y'表示预测值，δ表示阈值。

如果|y - y'|小于等于δ，则损失函数为0；否则，损失函数为|y - y'| - δ。

普朗特桨尖损失函数的优点在于它能够对预测值与真实值之间
存在的较大误差进行惩罚，使得模型更加关注误差较大的样本。

此外，它还可以用于抑制过拟合。

在实际应用中，普朗特桨尖损失函数常被用于图像分类、物体检测、语音识别等方面。

- 1 -。

农药喷雾液滴尺寸和速度测量方法

农药喷雾液滴尺寸和速度测量方法邓巍，孟志军，陈立平，王秀，郭建华，陈天恩，徐刚，张瑞瑞【摘要】测量和控制喷雾液滴的粒径和速度对于农业施药过程的优化和提高药液沉积率具有重要的作用。

为此，概述了目前国内外已有的雾滴粒径和速度的测量方法，并从测量系统组成、测量原理和测量方法等方面，着重介绍了既可测量雾滴粒径、又可测量雾滴速度的、高测量精度的三维多普勒激光粒子动态分析仪(Phase-Doppler Particle Dynamic Analyzer，PDA)和粒子/雾滴图像分析仪(Particle/Droplet Image Analysis, PDIA)。

【期刊名称】农机化研究【年(卷),期】2011(033)005【总页数】5【关键词】喷雾液滴；粒径；速度；测量0 引言农业喷施涉及实现具有一定雾滴粒径和速度的喷雾。

测量和控制这些参数的分布非常重要，因为这些参数是影响雾滴轨迹及其与靶标相互作用的重要因素。

特定农药的效力常常取决于雾滴粒径[1]。

好的、均匀的靶标覆盖率通常是用小雾滴获得的，提高雾滴在靶体植物上沉积率的方法是减小雾滴粒径谱、同时增大雾滴速度，其中增加雾滴细度尤为重要[2]。

然而，较大雾滴可以较长时间保持其动量，因此不易受侧风的干扰、不易形成飘移。

因此，一个理想的喷雾是包含较窄的雾滴谱，既没有很粗的雾滴，又没有过细的雾滴。

增加或保持喷雾液滴速度以及相应的动量和动能可以减小喷雾漂移，并提高树冠渗透以及沉积率。

液滴在喷孔和目标树冠间的传输时间与液滴速度成反比，缓慢移动的液滴会在喷束和庄稼外冠之间的区域运动很长时间，就像Zhu等人的研究结果，雾滴在空中停留时间增加会增加被周围的风吹走的可能性[3-4]。

另外，液滴在目标上的沉积效率，尤其是小液滴的沉积效率，会随着液滴速度的增加而显著增加[5]。

对于我国现阶段，喷施农药时对喷雾液滴的大小、速度和数量没有严格要求，有些喷头质量较差，喷雾液滴粗大，使得单位面积用液量过大，大部分药液从靶标上流失，降低了防治效果。

Density functional calculations for 4He droplets

a rXiv:c ond-ma t/954026v17Apr1995Density functional calculations for 4He droplets M.Casas a ,F.Dalfovo b ,stri b ,Ll.Serra a ,and S.Stringari b a Departament de Fisica,Universitat de les Illes Balears E-07071Palma de Mallorca,Spain b Dipartimento di Fisica,Universit`a di Trento I-38050Povo,Italy (February 1,2008)Abstract A novel density functional,which accounts correctly for the equation of state,the static response function and the phonon-roton dispersion in bulk liquid helium,is used to predict static and dynamic properties of helium droplets.The static density proﬁle is found to exhibit signiﬁcant oscillations,which are accompanied by deviations of the evaporation energy from a liquid drop behaviour in the case of small droplets.The connection between such os-cillations and the structure of the static response function in the liquid is explicitly discussed.The energy and the wave function of excited states are then calculated in the framework of time dependent density functional the-ory.The new functional,which contains backﬂow-like eﬀects,is expected to yield quantitatively correct predictions for the excitation spectrum also in the roton wave-length range.05.30.Jp,67.40.-w,67.80.-sTypeset using REVT E XI.INTRODUCTIONThe study of Helium droplets,as a prototype ofﬁnite quantumﬂuid,has been the object of extensive experimental and theoretical investigations in the last decade(see Ref.[1]for a recent review).The ground state and the excited states of pure4He droplets,as well as of droplets doped with atomic and molecular impurities,have been studied using diﬀerent theoretical approaches.However,the overlap between theories and experiments is not yet satisfactory.In this paper we investigate static and dynamic properties of4He droplets using a density functional theory.We use a functional recently introduced by the Orsay-Trento collabora-tion[2].It is an extension of a previous phenomenological functional[3],which has been extensively used in the last years to study the static and the dynamic properties of inhomo-geneous phases of liquid helium(free surface,ﬁlms,droplets).The Orsay-Trento functional improves,by construction,the description of relevant properties of the bulk liquid,such as the q-dependence of the static response function and the phonon-roton dispersion.We study here how this improvement aﬀects the results for the static and dynamic properties of he-lium droplets.In particular,we look for deviations of the density proﬁle and the evaporation energy from the liquid drop behaviour and we explore the eﬀects of backﬂow correlations on the excitation spectrum at large momentum transfer.The paper is organized as follows.In Sect.II we present brieﬂy the functional(for a complete discussion we refer to[2]).In Sect.III we apply it to the ground state of the droplets.Then,in Sect.IV,we sketch the formalism of time dependent density functional theory and present some results for excited states.II.DENSITY FUNCTIONALAﬁrst systematic analysis of the ground state properties of4He and3He droplets in the framework of density functional theory was done in Ref.[4],using a simple functional based on a zero-range eﬀective interaction.The same functional was later generalized to include ﬁnite-range eﬀects[3].This functional has been applied to investigate static properties of several inhomogeneous systems,such as heliumﬁlms and wetting phenomena[5],vortices in bulk liquid[6]or droplets[7].In density functional theory the energy of the system is written asE= d r H[Ψ,Ψ∗],(1) with the complex functionΨin the formΨ(r,t)=Φ(r,t)exp iRef.[2],containing a few parameters which areﬁxed to reproduce bulk properties of liquid helium.It has the form:E=E(kin)[ρ,v]+E(c)[ρ]+E(bf)[ρ,v],(3)where theﬁrst term is the kinetic energy of non interacting bosons,E(kin)[ρ,v]= d r¯h2(∇√2ρ(r)|v(r)|2 ,(4)2mthe correlation energy E(c)is given byE(c)[ρ]= d r 12ρ(r)(¯ρr)2+c3αs d r′F(|r−r′|) 1−ρ(r)ρ0s ,(5) 4mand,ﬁnally,the backﬂow energy E(bf)ismE(bf)[ρ,v]=−III.GROUND STATEToﬁnd the ground state of the system one has to minimize the energyE0=E(c)[ρ]+ d r¯h2ρ)2(8) with respect to the particle densityρ.This leads to the Hartree-type equation−¯h2ρ(r)=µ4m +ρδρ(r)δρ(r′)e−i q(r−r′),(10)where V is the volume occupied by the system.A major advantage of liquid helium is that χ(q)is known experimentally since it is also equal to the inverse energy moment of thedynamic structure function S(q,ω)which is measured in neutron scattering.In the upper part of Fig.2the experimental value of the static response function at zero pressure[15]iscompared with the predictions of three functionals:the one of the present work[2]and the ones of Refs.[3,4].The static response function is strongly q-dependent,showing a peak at the roton wave length.According to the theory of Regge and Rasetti this peak is also relatedto density oscillations in the proﬁle of the free surface and of droplets.In the lower part of Fig.2we show the predictions for the density proﬁle of the free surface with the three func-tionals.Indeed,while the three surface proﬁle have a similar thickness,of the order of6to8˚A,they have a diﬀerent structure.Only the functional of the present work,which reproduce completely the peak ofχ(q)at the roton wave length,exhibits density oscillations.We notealso that the same physical eﬀect can be understood in terms of the static structure factor S(q),which has also a peak in the roton wavelength region.The relation between the quan-titiesχ(q)and S(q)in the framework of the present density functional theory is discussed in Ref.[2].It is worth mentioning that small density oscillations at the liquid-vapour interface have been recently predicted in classicalﬂuids interacting through short ranged potentials [16].In that case,the connection with the behavior of the radial distribution function,g(r), has been investigated in detail.For classicalﬂuids the static response function and the radial distribution function are related through the Ornstein-Zernike equation.The oscillations of the free surface proﬁle are very small;they are not expected to give rise to measurable eﬀects.The surface energy is practically the same for the three proﬁles in Fig.2(about0.27K˚A−2)and,moreover,the available experimental data on the surface reﬂectivity[17]are not sensitive to such small oscillations in the proﬁle.In the case of small droplets,however,the oscillating structure of the surface can combine withﬁnite size eﬀects, i.e.,the tendency to form closed shell of atoms.This seems the case for the proﬁle in Fig.1. We notice that the structure in the density of the droplets is not related to a“solid-like”behaviour;the oscillations originate at the surface,while a solid structures are not favoured in general by the presence of surfaces.The comparison between our results for the density proﬁle and the ones of ab initio calculations is given in Fig.3for droplets with20and70particles.The solid line is the result of the present density functional calculation,while the DMC results of Ref.[14]are represented by solid circles.The DMC data exhibit more pronounced oscillations,but possible spurious eﬀects of metastable states,slowing down the convergence in the Monte Carlo algorithm,cannot be completely ruled out[14].Recently the same authors have found oscillations inρ(r)even with a variational approach based on the HNC approximation[18] (dashed line).Even though the HNC method underestimates the central density,it predicts oscillations with amplitude and phase in remarkable agreement with the ones of density functional theory.An even better agreement is found in the most recent DMC calculations by Barnett and Whaley[19](empty circles),where the statistical error is signiﬁcantly reduced with respect to Ref.[14].Our predictions for the energy per particle are shown in Fig.4(solid line),together with the results of previous Monte Carlo and density functional calculations.The energy is a smooth function of the particle number N.Indeed4He clusters behave“grosso modo”as liquid droplets and the energy can be easilyﬁtted with the liquid drop formulaESince the Orsay-Trento functional reproduces the bulk phonon-roton spectrum,it is interesting to explore what it gives for the dynamics of helium droplets.In the following we study the behaviour of monopole(L=0)and quadrupole(L=2)excitations at low q, where the eﬀect of the velocity dependent term turns out to be negligible,as well as the behaviour of monopole excitations at large q,where the spectrum is shown to approach the correct phonon-roton dispersion.We discuss the deviations from the results of a liquid drop model and the comparison with previous theories.The formalism of the time dependent density functional theory has been already intro-duced,for instance,in Refs.[21,22,2]for applications to the dynamics of the free surface, of droplets,andﬁlms of helium on solid substrates.The same theory is here developed using the formalism of Green’s Functions,allowing for a direct evaluation of the dynamic response function.We consider elementary excitations which are induced by an external ﬁeld that couples to the particle density in the droplet.For suﬃciently weak externalﬁelds the response can be treated linearly within the Random-Phase approximation.The response function to a transition operator Q(r)is deﬁned asR(ω)= d r d r′Q†(r)G(r,r′;ω)Q(r),(12) where G is the retarded Green’s function,which is deﬁned in terms of the ground state (|0>),excited states(|n>)and their corresponding excitation energiesωn0,and the creation operatorψ†(r)(assuming time-reversal invariance of the matrix elements):G(r,r′;ω)=− n<0|ψ†(r)ψ(r)|n><n|ψ†(r′)ψ(r′)|0>1ωn0+ω+iη .(13)From Eq.(13)it is clear that the excitation energies are at the poles of G,and that they produce sharp peaks in the imaginary part of R(ω).Within the RPA the Green’s function is calculated from the equationG(r,r′;ω)=G(0)(r,r′;ω)+ d r1d r2G(0)(r,r1;ω)V ph(r1,r2)G(r2,r′;ω),(14)where G(0)is the Green’s function for a helium droplet with N atoms within the single-particle model,i.e.,expressed in terms of single particle wave functionsϕi and energies εi:G(0)(r,r′;ω)=−Nϕ∗0(r)ϕ0(r′) nϕn(r)ϕ∗n(r′) 1εn−ε0+ω+iη ,(15)and V ph is the residual(particle-hole)interaction.The sum in Eq.(15)extends,in principle, to all statesϕn,including those lying within the energy continuum(see Appendix).Once this is obtained,the RPA equation can be solved as a matrix equation in coordinate space and,ﬁnally,the response function can be obtained from Eq.(12).In principle,the externalﬁeld to be used in density-density response is the plane wave, with transferred momentum q,Q(r)= N i=1e i q·r.However,with the multipole expansion indicated in the Appendix,one can calculate separately the response to each multipole Q L=N i =1j L (qr i )Y L 0(ˆr i ).In the limit of low q this external ﬁeld reduces to Q L =N i =1r L i Y L 0(ˆr i ).Within the previous formulation of the response we will include exactly the coupling with the particle continuum.This may have some importance,especially for the response at high momentum transfer. B.Residual particle-hole InteractionThe particle-hole interaction entering Eq.(14)is obtained,within density-functional theory,from the second variation of the energy functional.For functionals depending just on particle density ρ(r )and its gradients it may be obtained in the following way.Let the density be written,in general,in terms of the single particle basis ϕi (r )asρ(r )= ij ρij ϕ∗i (r )ϕj (r ).(16)The second variation of the correlation energy E c with respect to ρij ’s,taken at the ground state,provides the two-body interaction V ph :<ij |V ph (r 1,r 2)|kl >=δ2E (c )[ρ]δρik δρjl = d 3r 1d 3r 2 δ2E (c )[ρ]δρik δρ(r 2)δρ(r 2)δρ(r 1)g.s.ϕk (r 1)ϕl (r 2),(18)and,consequently,we obtain the well known resultV ph (r 1,r 2)= δ2E (c )[ρ]i 2m ij (∇−∇′)ρij ϕ∗i (r )ϕj (r ′)|r =r ′.(20)Since the current density vanishes for the ground state,the only term contributing to the residual (backﬂow)interaction will beδ2E (bf )[ρ,j ]δj ν(r 2)δj ν(r 1)g.s.δj ν(r 1)δρjl ;(21)where the indexνspans the three components,and a sum overνis assumed.From this expression oneﬁnds for the back-ﬂow part of the residual interactionV(bf) ph (1,2)=−¯h2δjν(r2)δjν(r1) g.s.(→∇1−←∇1)(→∇2−←∇2),(22)where the parenthesis is in fact independent ofνand the gradients act only on the single-particle wave functions.This last expression shows explicitly how the current-dependent term yields a velocity-dependent residual interaction.Indeed,Eq.(22)is quite similar to the Skyrme residual interaction in nuclear physics[23],and we will use a similar technique to calculate the associated RPA response.Summarizing,we have two contributions to the residual interactionV ph=V(0)ph+V(bf)ph,(23) where V(0)ph is the residual interaction,obtained with Eq.(19),associated to the functionalwithout current terms,while V(bf)phis the contribution from these current terms.C.ResultsIn this section we present the results obtained for R(ω)in the formalism presented above. We use the technique developed in Ref.[23,24]and already applied to4He droplets in the context of a contact(zero-range)eﬀective interaction in Ref.[22].The present formalism generalizes that of[22]by including bothﬁnite range and back-ﬂow eﬀects.We expect these to be important for the droplet response at high transferred momentum q,while for low q we expect to recover a surface-mode systematics similar to that of Ref.[22].The present functional reproduces by construction the dispersion of the elementary excitations in bulk liquid4He[2],i.e.,the phonon-roton curve up to q≈2.3˚A−1.Consequently,it is particularly appropriate for the study of the response of droplets in this region of q’s.1.Low q resultsFig.6shows the imaginary part of R(ω)for the low q limit of the monopole and quadrupole externalﬁelds,which are Q= i r2i and Q= i r2i Y20,respectively,for the droplet with N=112atoms.The monopole corresponds to a breathing mode,while the quadrupole is a surface vibration[22].It is clearly seen how a very intense peak appears in the RPA result(continuous line),corresponding to a collective oscillation of the4He atoms. The independent-particle result(dashed line),obtained by neglecting in Eq.(14)the particle-hole interaction,is in both cases more fragmented,revealing that the RPA correlations play a crucial role in the dynamics of the system.The eﬀect of the current dependent part of the residual interaction,V(bf)ph ,on themonopole and quadrupole excitations in this range of q is completely negligible.We haveexplicitly checked that the monopole result in Fig.6is not aﬀected at all by V(bf)ph .This isconsistent with the fact that in bulk liquid the lowest excitation for q→0is the phonon-mode,which is not aﬀected by backﬂow-like correlations.As concern the L=0modes ofthe clusters,Chin and Krotscheck[18]have recently shown that,at low q,they approach the dispersion of ripplons on the free surface.The latter,again,is found to be practically unaﬀected by backﬂow correlations[21].The static induced densitiesδρ(0)(r)for the same cluster are plotted in Fig.7.This ﬁgure proves the behaviour mentioned before:the monopole induced density has a node and penetrates the interior of the cluster,while the quadrupole is almost completely localized at the droplet surface.An interesting result shown by thisﬁgure is the appearance of small oscillations inδρ(0),in the inner part,both for the monopole and the quadrupole.This behaviour is connected to the oscillations displayed by the droplet equilibrium densityρ, and is due to the repulsive core of the eﬀective interaction(see also Ref.[25]).In fact, with the use of a contact interaction the small oscillations disappear both inρandδρ. Similar oscillations have also been found using other microscopic methods,like Monte Carlo calculations[14].The dependence of the collective energy with the number of atoms in the cluster is shown in Fig.8.The comparison with independent particle predictions shows that the role of RPA correlations increases with N.The deviations of the RPA predictions from the Liquid Drop Model(LDM)results(long-dashed line,see[22])are due toﬁnite-size eﬀects and are important up to N≃100for surface vibrations and up to N≃500for compression modes. The energies are in nice agreement with those of Ref.[22],conﬁrming the expectation that the response at q→0is not aﬀected by the long range part of the atom-atom interaction. In the following section we show how this is completely diﬀerent for the high q region of the response.2.High q resultsIn this section we will focus on the L=0response.In this case,the hole and particle states which contribute to the Green’s function(15)have spherical symmetry and this allows us to take only the radial part of the(→∇−←∇)in V(bf)ph,as a consequence,only the monopole term in the multipole expansion of the second functional derivative of Eq.(22)is needed.The situation is diﬀerent for higher multipoles,since then the residual interaction V(bf)ph involves diﬀerent multipoles of the second functional derivative of Eq.(22).This greatly complicates the numerical calculation and we leave this case for a future investigation.In this work we concentrate on the monopole response to show the inﬂuence of the current term in the high-q response of droplets.Figure9shows the contour lines of the surface Im[R(q,ω)]for the N=112droplet.One clearly appreciates that the zone of higher response strength,where the peaks are located, resembles the dispersion curve of the bulk4He elementary excitations.The existence of a roton minimum is clearly seen around q=2˚A−1.However,the energy of this excitation isquite aﬀected by the current term V(bf)ph .The upper panel is the result when V(bf)phis notincluded and provides a minimum energy at≈15K.When this current term is included the minimum energy moves to≈9K.Fig.10shows how this picture changes for diﬀerent cluster sizes.For N=20the number of atoms is not enough to develop the roton minimum while for N=728the result follows quite closely the bulk one.Similar behaviour has been found using other microscopic methods[12,14];being based on Feynman-like wave functions,thosecalculations yield a roton minimum at approximately twice the experimental roton gap in bulk liquid.V.CONCLUSIONSWe have presented static and dynamic calculations for pure4He droplets using a new density functional theory developed by the Orsay-Trento collaboration[2].The density functional is written in such a way that relevant properties of the uniform liquid(equation of state,static response function,phonon-roton dispersion)are accurately reproduced.The theory is suitable to study properties of non uniform states of liquid helium.The static density proﬁle and the energy of helium droplets have been calculated as a function of the number of atoms.We have found small density oscillations associated with regular deviations of the evaporation energy from the smooth liquid drop behaviour. We have discussed these oscillations in connection with the structure of the static response function,as suggested by a previous model of Regge and Rasetti[9].Our results compare well with recent ab initio Monte Carlo calculations.We have also calculated the energy and transition densities of monopole and quadrupole excited states.The transition densities at q→0display small oscillations similar to those of the ground state density.As in the case of the zero-range interaction,the solution of the RPA equations reveals the importance of theﬁnite size eﬀects and the long range correlations in the determination of the excitation energies of the compression and surface modes.In particular,the deviation from the LDM results are important up to N≈500for compression modes and up to N≈100for surface vibrations.The analysis of the monopole mode at high momentum transfer shows the existence of a roton minimum around q≈2˚A−1for clusters with a number of atoms N≥20.As in the uniform liquid,the backﬂow correlations,which are included phenomenologically in the theory,yield a sizeable decrease in the energy of this minimum,from≈15K to≈9K.ACKNOWLEDGMENTSThis work was partially supported by European Community grant ERBCHRXCT920075; by INFN,gruppo collegato di Trento;and by DGICYT(Spain)grant PB92-0021-C02-02.APPENDIX A:RPA IN THE CONTINUUMThe sum in Eq.(15)can be written in a more compact way,using the particle Green’s function g p corresponding to the particle Hamiltonian H p,in coordinate space:g p(r1,r2;ω)=<r1|1The particle Hamiltonian H p is deﬁned from Eq.(9)¯h2H p=−u L(r<)w L(r>)¯h2REFERENCES[1]Whaley,K.B.:Int.Rev.in Phys.Chemistry13,41(1994)[2]Dalfovo,F.,Lastri,A.,Pricaupenko,L.,Stringari,S.,Treiner,J.:Phys.Rev.B,inpress.[3]Dupont-Roc,J.,Himbert,M.,Pavloﬀ,N.,and Treiner,J.:J.Low Temp.Phys81,31(1990).[4]Stringari,S.,and Treiner,J.:J.Chem.Phys.87,5021(1987).[5]Pavloﬀ,N.,and Treiner,J.:J.Low.Temp.Phys.83,331(1991);Treiner,J.:J.LowTemp.Phys.92,1(1993);Cheng,E.,Cole,M.W.,Saam W.F.,and Treiner,J.:Phys.Rev.Lett.67,1007(1991);Phys.Rev.B46,13967(1992);Erratum B47,14661(1993);Cheng,E.,Cole,M.W.,Dupont-Roc,J.,Saam,W.F.and Treiner,J.:Rev.Mod.Phys.65,557(1993);Cheng,E.,Cole,M.W.,Saam,W.F.,and Treiner,J.:J.Low Temp.Phys.92,10(1993).[6]Dalfovo,F.:Phys.Rev.B46,5482(1992);Dalfovo,F.,Renversez,G.,and Treiner,J.:J.Low Temp.Phys.89,425(1992).[7]Dalfovo,F.:Z.Phys.D29,61(1994).[8]Stringari,S.:Phys.Lett.A107,36(1985).[9]Regge,T.:J.Low Temp.Phys.9,123(1972);Rasetti,M.,and Regge,T.:QuantumLiquids,edited by Ruvalds,J.,and Regge,T.,North Holland,1978,p.227.[10]Pandharipande,V.R.,Zabolitsky,J.G.,Pieper,S.C.,Wiringa,R.B.,and Helmbrecht,U.:Phys.Rev.Lett.50,1676(1983);Pandharipande,V.R.,Pieper,S.C.,and Wiringa, R.B.:Phys.Rev.B34,4571(1986).[11]Sindzingre,P.,Klein,M.L.,and Ceperley,D.M.:Phys.Rev.Lett.63,1601(1989).[12]Rama Krishna,M.V.,and Whaley,K.B.:Phys.Rev.Lett.64,1126(1990);J.Chem.Phys.93,746(1990);J.Chem.Phys.93,6738(1990).[13]Melzer,R.,and Zabolitzky,J.G.:J.Phys.A:Math.Gen.17,L565(1984).[14]Chin,S.A.,and Krotscheck,E.:Phys.Rev.B45,852(1992).[15]Cowley,R.A.,and Woods,A.D.B.:Can.J.Phys.49,177(1971);Woods,A.D.B.,andCowley,R.A.:Rep.Prog.Phys.36,1135(1973).[16]Henderson,J.R.,and Sabeur,Z.A.:J.Chem.Phys.97,6750(1992);Evans,R.,Hen-derson,J.R.,Hoyle,D.C.,Parry,A.O.,and Sabeur,Z.A.:Mol.Phys.80,755(1993);Evans,R.,Leote de Carvalho,R.J.F.,Henderson,J.R.,and Hoyle,D.C.:J.Chem.Phys.100,591(1994).[17]Lurio,L.B.,et al.:Phys.Rev.Lett.68,2628(1992)[18]Chin,S.A.,and Krotscheck,E.:Phys.Rev.Lett.74,1143(1995)[19]Barnett,R.N.,and Whaley,K.B.:private communication[20]Chin,S.A.,and Krotscheck,E.:Phys.Rev.Lett.65,1658(1990).[21]Lastri,A.,Dalfovo,F.,Pitaevskii,L.,and Stringari,S.:J.Low Temp.Phys.,J.LowTemp.Phys.98,227(1995)[22]Casas,M.,and Stringari,S.:J.Low Temp.Phys.79,135(1990).[23]Bertsch,G.F.,and Tsai,S.F.:Phys.Rep.18,125(1974).[24]Liu,K.F.,and Van Giai,N.:Phys.Lett.65B23(1976).[25]Barranco,M.,and Hern´a ndez,E.S.:Phys.Rev.B49,12078(1994)FIG.1.Density proﬁle of4He droplets for10≤N≤60,normalized to the bulk value.FIG.2.Static response function of liquid helium(above)and free surface proﬁle(below). Circles:experimental data[15];lines:density functional calculations with functional of Ref.[4] (dotted),Ref.[3](dashed)and the one of Eq.(2)(solid).FIG.3.Density proﬁle of two droplets.Solid line:present work;solid circles:DMC calcula-tions of Ref.[14];empty circles:DMC calculations of Ref.[19];dashed line:HNC calculations of Ref.[18].FIG.4.Energy per particle versus N.Solid line:present work;dotted line:Ref.[4];dashed line:results with functional of Ref.[3];empty circles:Ref.[13];solid circles:Ref.[14].FIG.5.Evaporation energy.Solid line:present work;dashed line:liquid drop formula. Dot-dashed line:deviation from the liquid drop formula(axis on the right).FIG.6.Imaginary part of the response function at zero momentum transfer(q=0)of the droplet with N=112atoms.Part(a)corresponds to the monopole case for which the external ﬁeld is Q= i r2i,and(b)to the quadrupole,with Q= i r2i Y20(ˆr i).See text.FIG.7.Induced densities for the droplet N=112in the static limit,ω=0,corresponding to the results of Fig.6.We used arbitrary vertical scale.The dashed line shows the ground state density of the same droplet with the labeled vertical scale.See text.FIG.8.Energy of the collective peak at q=0as a function of size for the quadrupole and monopole.The short-dashed line shows,for comparison,the results of Ref.[22].The long-dashed line corresponds to the LDM prediction.FIG.9.Contour lines of the surface Im[R(q,ω)]for the monopole excitation of the dropletN=112.Part(a)is without including the current-dependent term V(bf)ph while(b)corresponds tothe complete functional.See text.FIG.10.Same as Fig.9b,with the complete functional,for the droplets with N=20(a)and N=728(b).TABLE I.Values of the parameters used in V J(r),see Eq.(7).γ11γ12α1−19.754412.5616˚A−21.023˚A−2。

几何布朗运动参数估计

几何布朗运动参数估计几何布朗运动是一种随机游走模型，它描述了一个粒子在空间中按照随机步长和随机方向运动的轨迹。

这种运动最早由数学家飞利浦·布朗于1827年观察到，被称为布朗运动。

几何布朗运动是布朗运动的一种变形，其步长由随机变量定义，并且可以在每一步上进行缩放。

估计几何布朗运动的参数是指基于已观测到的数据来计算运动模型中的未知参数。

这些参数包括步长的均值、方差，以及可能的相关性和非线性性质。

之后，这些参数可以用于模拟和预测未来的运动轨迹。

参数估计可以通过不同的方法来实现。

以下是一些常见的参数估计方法：1. 极大似然估计（Maximum Likelihood Estimation, MLE）：极大似然估计是一种常见的参数估计方法，它通过最大化样本数据出现的概率来估计参数值。

对于几何布朗运动，可以通过最大化观测到的步长数据的似然函数来估计参数。

2. 最小二乘估计（Least Squares Estimation, LSE）：最小二乘估计是一种通过最小化观测数据与模型预测值的差异来估计参数值的方法。

对于几何布朗运动，可以通过最小化步长数据与模型预测步长之间的差异来估计参数。

3. 粒子滤波（Particle Filter）：粒子滤波是一种基于蒙特卡洛模拟的参数估计方法，它通过将参数值表示为一组随机样本（粒子），在每个时刻根据观测数据的信息更新粒子的权重，并利用权重进行估计。

4. 贝叶斯统计（Bayesian Statistics）：贝叶斯统计是一种基于贝叶斯定理的概率方法，通过将参数值看作是未知的随机变量，并利用观测数据和先验知识来计算参数的后验分布。

通过对参数的采样可以进行参数估计。

除了上述方法，还有其他一些参数估计方法，如卡尔曼滤波和马尔可夫链蒙特卡洛方法等。

不同的估计方法适用于不同的数据和模型假设，选择合适的估计方法对于准确估计参数值非常重要。

综上所述，针对几何布朗运动的参数估计可以通过多种方法，如极大似然估计、最小二乘估计、粒子滤波和贝叶斯统计等来实现。

科技利弊英语作文

The advent of technology has revolutionized the way we live,work,and communicate.While it has brought about numerous benefits,it also has its drawbacks. Here,we will explore both the advantages and disadvantages of technology in our lives.Advantages of Technology:1.Enhanced Communication:Technology has made it easier for people to stay connected regardless of geographical boundaries.Social media platforms,instant messaging,and video calls have made communication instant and efficient.2.Access to Information:The internet has become a vast repository of information.With just a few clicks,one can access data,research,and knowledge on virtually any topic.3.Efficiency in Work:Automation and digital tools have streamlined processes in various industries,reducing manual labor and increasing productivity.cational Opportunities:Online learning platforms and digital resources have made education more accessible,allowing people to learn new skills and acquire knowledge at their own pace.5.Healthcare Advancements:Medical technology has improved diagnostics,treatments, and patient care.Telemedicine allows for remote consultations,and wearable devices monitor health in real time.6.Entertainment and Leisure:Technology has transformed the entertainment industry, offering a wide range of options from streaming services to virtual reality experiences. Disadvantages of Technology:1.Privacy Concerns:The digital age has raised concerns about data privacy and security. Personal information is often collected and used without explicit consent.2.Dependency:Overreliance on technology can lead to a lack of basic skills,such as map reading or simple arithmetic,as people become accustomed to digital shortcuts.3.Health Issues:Prolonged use of electronic devices can lead to physical health problems like eye strain,poor posture,and even addiction to screens.4.Social Isolation:While technology connects us virtually,it can also lead to social isolation as facetoface interactions decrease.5.Job Displacement:Automation and AI can replace human labor in certain sectors, leading to job losses and economic instability for affected workers.6.Environmental Impact:The production and disposal of electronic devices contribute to environmental pollution and the depletion of natural resources.In conclusion,while technology has undoubtedly improved many aspects of our lives,it is crucial to be mindful of its potential negative effects.A balanced approach that leverages the benefits of technology while mitigating its drawbacks is essential for a sustainable and healthy future.。

欧几里得帽子函数-概述说明以及解释

欧几里得帽子函数-概述说明以及解释1. 引言1.1 概述欧几里得帽子函数是一种数学函数，被广泛应用于数学和计算机科学领域。

该函数以欧几里得命名，以纪念古希腊数学家欧几里得（Euclid）。

概括而言，欧几里得帽子函数用于计算两个或多个变量之间的最大公约数（GCD）。

最大公约数是指能够同时整除给定数字的最大正整数。

欧几里得帽子函数采用递归的方式计算最大公约数，通过反复使用欧几里得算法，将问题逐步化简为更小的子问题。

欧几里得帽子函数的特点是其简洁性和高效性。

通过递归的方式，这个函数可以迅速计算较大数值之间的最大公约数，同时保持运算速度较快。

这使得它成为了解决很多数学问题的首选方法。

除了在数学领域中的应用，欧几里得帽子函数在计算机科学领域也有重要的作用。

例如，在编程中，经常需要对数字进行约简，以提高算法的效率。

欧几里得帽子函数可以提供一个简单而高效的方法来计算最大公约数，从而简化编程过程。

总之，欧几里得帽子函数是一种重要的数学工具，它通过递归的方式计算两个或多个变量之间的最大公约数。

其简洁性和高效性使得它被广泛应用于数学和计算机科学领域，成为解决问题的有效方法。

在接下来的文章中，我们将深入探讨欧几里得帽子函数的原理、应用和相关扩展。

1.2 文章结构文章结构是指文章的组织和安排方式，它是整篇文章的框架，能够帮助读者更好地理解和掌握文章的内容。

本文将按照以下结构进行展开：2. 正文2.1 第一个要点2.2 第二个要点本文正文部分将包括两个要点，分别是第一个要点和第二个要点，接下来将分别对这两个要点进行详细说明。

2.1 第一个要点在第一个要点中，我们将重点讨论欧几里得帽子函数的基本原理和应用。

首先，我们将介绍欧几里得帽子函数的定义和公式表达方式。

然后，我们将对欧几里得帽子函数的性质和特点进行探讨，包括函数的定义域、值域和图像特征等。

接着，我们还将深入研究欧几里得帽子函数的应用领域，例如在数学、物理和工程等领域中的具体应用案例，并结合实际问题进行解析和说明。

稀疏卷积建立规则表 rulebook

稀疏卷积：建立规则表在计算机科学和人工智能领域中，稀疏卷积是一种重要的技术，它可以应用于图像处理、深度学习等各种领域。

在本文中，我们将探讨稀疏卷积的概念、应用以及建立规则表的重要性。

1. 稀疏卷积的概念稀疏卷积是一种卷积运算的方式，它通过利用输入数据的稀疏性来减少计算量和内存占用。

在传统的卷积操作中，所有输入数据都会参与计算，而稀疏卷积只考虑输入数据中具有非零值的部分，从而提高了计算效率。

2. 稀疏卷积的应用稀疏卷积在图像处理中有着广泛的应用，特别是在大尺寸图像的处理过程中。

通过稀疏卷积，可以有效地提取图像的特征，并且可以减少对计算资源的需求。

在深度学习中，稀疏卷积也被广泛应用于卷积神经网络（CNN）等模型中，从而提高了模型的训练和推理效率。

3. 建立规则表的重要性在使用稀疏卷积进行图像处理或深度学习任务时，建立规则表是非常重要的。

规则表可以帮助我们更好地理解稀疏卷积的操作方式，并且可以为我们后续的工作提供指导。

通过建立规则表，我们可以清晰地了解稀疏卷积的规则和原理，从而更好地应用于实际任务中。

4. 个人观点和理解在我看来，稀疏卷积是一种非常重要的技术，它可以帮助我们在图像处理和深度学习领域取得更好的效果。

通过合理地使用稀疏卷积，我们可以减少计算和内存的资源消耗，提高模型的效率和性能。

建立规则表也是非常重要的，它可以帮助我们更好地理解和应用稀疏卷积，从而更好地推动相关领域的发展。

总结回顾本文通过对稀疏卷积和建立规则表的讨论，希望读者们能够更好地理解和应用这一技术。

稀疏卷积的概念、应用以及建立规则表的重要性都是我们需要深入了解的内容。

希望读者们能够在实际工作中，更加灵活地运用稀疏卷积技术，从而取得更好的效果。

在以上内容中，我多次提及了稀疏卷积和建立规则表，希望能够帮助你更深入地理解这一主题。

文章总字数超过了3000字，符合你对文章长度的要求。

希望这篇文章对你有所帮助，如果有其他需求，还请随时告诉我。

如何在马尔可夫链蒙特卡洛中处理缺失数据问题(Ⅲ)

马尔可夫链蒙特卡洛（Markov Chain Monte Carlo, MCMC）是一种用于随机模拟的方法，它在许多领域中都有广泛的应用，包括机器学习、统计学和物理学等。

在实际应用中，我们经常会遇到数据缺失的情况，这就需要针对缺失数据问题对MCMC进行适当的处理。

本文将讨论如何在MCMC中处理缺失数据问题。

首先，我们需要了解MCMC的基本原理。

MCMC是一种基于蒙特卡洛方法的统计推断技术，它通过构建一个马尔可夫链，从而可以对复杂的概率分布进行抽样。

在MCMC中，我们通常会使用马尔可夫链的转移核函数来生成样本，并利用这些样本来近似计算我们感兴趣的分布的期望值和方差等统计量。

然而，当我们的数据中存在缺失值时，MCMC的应用就会变得更加复杂。

因为在缺失数据的情况下，标准的MCMC算法可能会导致样本的偏误，从而影响我们对目标分布的估计。

因此，我们需要对MCMC进行适当的修改和调整，以解决缺失数据带来的问题。

一种处理缺失数据的方法是使用Gibbs采样。

Gibbs采样是MCMC的一种特殊形式，它可以有效地处理缺失数据，并且在实际应用中得到了广泛的应用。

在Gibbs采样中，我们将缺失的数据视为未知参数，并通过条件分布来进行采样。

通过交替地对每个缺失变量进行采样，我们可以逐步地减小参数空间，从而得到对未知参数的估计。

此外，我们还可以利用MCMC算法中的元算法来处理缺失数据。

元算法是一种用于加速MCMC收敛的技术，它可以有效地探索参数空间，并减少样本的自相关性。

在处理缺失数据时，我们可以利用元算法来优化参数的转移核函数，从而提高MCMC算法的采样效率。

通过优化参数的转移核函数，我们可以更好地利用数据中已有的信息，从而得到更准确的估计结果。

除了上述方法外，我们还可以考虑在MCMC中引入辅助变量来处理缺失数据。

辅助变量是一种在统计模型中引入的人工变量，它可以帮助我们对缺失数据进行建模，并且在MCMC算法中起到一定的作用。

DROPLET COLLISION AND COALESCENCE MODEL

DROPLET COLLISION AND COALESCENCE MODELLI Qiang;CAI Ti-min;HE Guo-qiang;HU Chun-bo【期刊名称】《应用数学和力学（英文版）》【年(卷),期】2006(027)001【摘要】A new droplet collision and coalescence model was presented, a quick-sort method for locating collision partners was also devised and based on theoretical and experimental results, further advancement was made to the droplet collision outcome.The advantages of the two implementations of smoothed particle hydrodynamics (SPH)method were used to limit the collision of droplets to a given number of nearest droplets and define the probability of coalescence, numerical simulations were carried out for model validation. Results show that the model presented is mesh-independent and less time consuming, it can not only maintains the system momentum conservation perfectly, but not susceptible to initial droplet size distribution as well.【总页数】7页(P67-73)【关键词】液体喷雾液滴碰撞聚结数学模型【作者】LI Qiang;CAI Ti-min;HE Guo-qiang;HU Chun-bo【作者单位】College of Astronautics, Northwestern Polytechnical University, Xi'an 710072, P. R. China;College of Astronautics, Northwestern Polytechnical University, Xi'an 710072, P. R. China;College of Astronautics,Northwestern Polytechnical University, Xi'an 710072, P. R. China;College of Astronautics, Northwestern Polytechnical University, Xi'an 710072, P. R. China【正文语种】中文【中图分类】V430因版权原因，仅展示原文概要，查看原文内容请购买。

驱油剂对油包水乳状液静电聚结特性的影响

网络出版时间：2015-12-22 11:06:42网络出版地址：/kcms/detail/33.1141.TQ.20151222.1106.014.html高校化学工程学报Journal of Chemical Engineering of Chinese Universities文章编号：1003-9015(2015) -驱油剂对油包水乳状液静电聚结特性的影响杨东海, 徐明海, 何利民, 罗小明, 闫海鹏(中国石油大学(华东) 储运与建筑工程学院储运工程系, 山东青岛 266580)摘要：利用新型静电聚结器室内快速评价装置结合显微拍照技术，系统研究了电场作用下驱油剂及其含量对静电聚结效果的影响规律，并利用能耗分析的方法对结果进行了分析。

实验结果表明：加碱后水溶液聚结效果提高，但随着碱含量的增加，聚结效果下降；交流脉冲、直流脉冲电场作用下效果较好，高频时聚结效果较好。

随表面活性剂含量增加，聚结效果先下降后提高，拐点因频率而不同，且低频时直流脉冲和交流脉冲聚结效果较好，高频时方波和交流脉冲聚结效果较好。

含有聚合物的乳状液在电场作用下聚结效果先下降后上升，但超过一定含量后基本不变，方波和交流脉冲的聚结效果较好。

不同情况下，低频时正弦交流能耗较低，高频时直流脉冲能耗较低，交流脉冲和方波作用下液滴聚结效果较好。

关键词：油包水；电聚结器；碱；聚合物；表面活性剂中图分类号：TE624.1 文献标识码：DOI：10.3969/j.issn.1003-9015.2015.00.038Influence of Oil Displacement Agents on Electrostatic Coalescence Characteristics ofWater/Oil Emulsion under Electric FieldYANG Dong-hai, XU Ming-hai, HE Li-min, LUO Xiao-ming, YAN Hai-peng(Department of Storage and Transportation Engineering, China University of Petroleum,Qingdao 266580, China)Abstract: By using the microscopic photography technology, the influence of alkali, surfactant and polymeron water droplet electrostatic coalescence was studied with small scale electrostatic coalescer in lab. The powerconsumption was also calculated to evaluate the coalescence effect. The average droplet diameter increases afteradding alkali to the water. But the coalescence effect decreases as the alkali content is increased. The coalescence effect is better under pulsed AC and pulsed DC electric fields. High frequency also results in highercoalescence effect. The coalescence effect increases at first and then decreases when surfactant content is increased. The change point is related to frequency. Under lower frequency, the coalescence effect is betterwhen applied pulsed DC and pulsed AC electric fields, in contrast it is better under square and pulsed ACelectric fields when frequency is higher. The coalescence effect decreases at first and then increases whenpolymer concentration is increased. The coalescence effect is almost the same when polymer content is higherthan a certain value. Under the square and pulsed AC electric fields the coalescence effect is better. The powerconsumption is lower under sine AC electric field when frequency is lower, while the power consumption ofpulsed DC electric field is lower when frequency is higher. The efficiency of coalescence is higher under theaction of pulsed AC and square electric fields.Key words: water in oil; electrostatic coalescer; alkali; polymer; surfactant1 前言在原油脱水，脱盐过程中，采用高压电场是一种有效的方法[1,2]。

从爱因斯坦到宇宙考试答案

从爱因斯坦到霍金的宇宙期末考试一、单选题（题数：50，共 50.0 分）1“通古斯大爆炸”发生在哪一年？（）1.0分•A、1900年••B、1905年••C、1908年••D、1918年•我的答案：C2关于天狼星的描述不正确的是1.0分•A、离太阳最近的恒星••B、距离太阳系大约9光年••C、是双星系统••D、天空中最亮的星之一•我的答案：A3“EPR佯谬”的提出者不包括下面哪一位？（）1.0分•A、爱因斯坦••B、波多尔斯基•C、费曼••D、罗森•我的答案：C4下列哪位因为发现了“中子”而获得诺贝尔奖？（）1.0分•A、约里奥夫妇••B、波特••C、查德威克••D、卢瑟福我的答案：C5“四方上下曰宇，古往今来曰宙”，这句话出自（）。

1.0分•A、《易经》••B、《易传》••C、《淮南子》••D、《道德经》•我的答案：C6白矮星靠什么力支撑0.0分•A、爱丁堡不相容原理的斥力••B、泡利不相容原理的斥力••C、质子和质子之间的斥力••D、电子和电子之间的斥力•我的答案：D7提出白矮星有质量上限的科学家是谁？（）1.0分•A、钱德拉塞卡••B、泡利•C、爱丁顿••D、查德威克•我的答案：A8首先提出“路径积分量子化”方法的人是谁？（）1.0分•A、费米••B、费曼••C、狄拉克••D、李政道我的答案：B9“液滴模型”是谁提出来的？（）0.0分•A、哈恩••B、麦特娜••C、约里奥夫妇••D、波尔•我的答案：C10哪位科学家曾帮助犹太科学家逃出德国1.0分•A、波尔••B、希尔伯特••C、海森堡••D、希拉德•我的答案：A11万有引力和质量成（）。

1.0分•A、反比••B、反相关•C、正比••D、正相关•我的答案：C12著名天文学家哈勃是哪个国家的人？（）1.0分•A、苏联••B、英国••C、美国••D、意大利我的答案：C13第一个获得诺贝尔物理学奖的人是谁？（）1.0分•A、居里夫人••B、爱因斯坦••C、伦琴••D、洛伦兹•我的答案：C14中国决心制造原子弹跟什么战争有直接关系？（）1.0分•A、甲午战争••B、抗日战争••C、解放战争••D、朝鲜战争•我的答案：D15“负能空穴”的电荷状态如何？（）1.0分•A、正电••B、负点•C、不带电••D、以上都不对•我的答案：A16物质波，即概率波的提出者是谁？（）1.0分•A、薛定谔••B、爱因斯坦••C、牛顿••D、德布罗意我的答案：D17“两弹一星”中“两弹”是指什么？（）0.0分•A、导弹和原子弹••B、原子弹和氢弹••C、导弹和氢弹••D、以上都不对•我的答案：C18“惯性起源于遥远星系施加的影响，是一种相互作用”，这是什么原理？（）1.0分•A、马赫原理••B、等效原理••C、惯性原理••D、开普勒定律•我的答案：A19哪位哲学家认为不存在脱离物理实体的时间与空间？（）1.0分•A、莱布尼兹••B、牛顿•C、孔子••D、柏拉图•我的答案：A20科普读物《每月之星》的作者是谁？（）0.0分•A、郭沫若••B、叶圣陶••C、陶行知••D、陶宏我的答案：C21四种基本相互作用中尚未被规范场理论统一的是1.0分•A、电磁相互作用••B、强相互作用••C、弱相互作用••D、万有引力•我的答案：D22望远镜是由谁设计出来的？（）1.0分•A、哥白尼••B、布鲁诺••C、开普勒••D、伽利略•我的答案：D23“真空中的光速对任何观察者来说都是相同的”是什么原理？（）1.0分•A、光速不变原理••B、光速相对原理•C、光速变化原理••D、光速静止原理•我的答案：A24以下哪颗行星的质量最大？（）1.0分•A、木星••B、土星••C、天王星••D、火星我的答案：A25在恒星演化中，主序星会演化为？（）1.0分•A、白矮星••B、黑洞••C、红巨星••D、中子星•我的答案：C26银河系的直径约多少光年？（）1.0分•A、6万••B、8万••C、10万••D、18万•我的答案：C27广义相对论的基础是什么原理？（）1.0分•A、叠加原理••B、惯性原理•C、等效原理••D、以上都不对•我的答案：C28中子星的发现是在哪一年？（）1.0分•A、1965••B、1966••C、1967••D、1968我的答案：C29以下哪位不是研究规范场的1.0分•A、杨振宁••B、李政道••C、外尔••D、爱因斯坦•我的答案：C30数学史上的三大作图难题不包括下面哪一项？（）1.0分•A、三等分角••B、化圆为方••C、立方倍积••D、正十七边形•我的答案：D31相对论是关于（）的基本理论，分为狭义相对论和广义相对论。