Transport Theory and Statistical Physics最新文献_第8页

On a Class of Mean Field Solutions of the Monge Problem for Perfect and Self-Interacting Systems 完备自相互作用系统Monge问题的一类平均场解

Transport Theory and Statistical Physics Pub Date : 2010-03-31 DOI: 10.1080/00411450.2010.542711

P. Choquard

{"title":"On a Class of Mean Field Solutions of the Monge Problem for Perfect and Self-Interacting Systems","authors":"P. Choquard","doi":"10.1080/00411450.2010.542711","DOIUrl":"https://doi.org/10.1080/00411450.2010.542711","url":null,"abstract":"The Monge problem (Monge 1781; Taton 1951), as reformulated by Kantorovich (2006a, 2006b) is that of the transportation at a minimum “cost” of a given mass distribution from an initial to a final position during a given time interval. It is an optimal transport problem (Villani, 2003, sects. 1, 2). Following the fluid mechanical solution provided by Benamou and Brenier (2000) for quadratic cost functions (Villani, 2003, sects. 5.4, 8.1), Lagrangian formulations are needed to solve this boundary value problem in time and to determine the Actions as time integral of Lagrangians that are measures of the “cost” of the transportations (Benamou and Brenier, 2000, prop. 1.1). Given canonical Hamilltonians of perfect and self-interacting systems expressed in function of mass densities and velocity potentials, four versions of explicit constructions of Lagrangians, with their corresponding generalized coordinates, are proposed: elimination of the velocity potentials as a function of the densities and their time derivatives by inversion of the continuity equations; elimination of the gradient of the velocity potentials from the continuity equations thanks to the introduction of vector fields such that their divergences give the mass densities; generalization in nD of Gelfand mass coordinate (1963) by the introduction of n-dimensional vector fields such that the determinant of their Jacobian matrices give the mass densities; and, last, introduction of the Lagrangian coordinates that describe the characteristics of the different models and are parametrized by the former auxiliary vector fields. Using this version, weak solutions of several models of Coulombian and Newtonian systems known in Plasma Physics and in Cosmology, with spherically symmetric boundary densities, are given as illustrations.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"39 1","pages":"313 - 359"},"PeriodicalIF":0.0,"publicationDate":"2010-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2010.542711","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58908676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Numerical Simulations of the Fourier-Transformed Vlasov-Maxwell System in Higher Dimensions—Theory and Applications 高维傅里叶变换Vlasov-Maxwell系统的数值模拟——理论与应用

Transport Theory and Statistical Physics Pub Date : 2010-03-31 DOI: 10.1080/00411450.2011.563711

B. Eliasson

{"title":"Numerical Simulations of the Fourier-Transformed Vlasov-Maxwell System in Higher Dimensions—Theory and Applications","authors":"B. Eliasson","doi":"10.1080/00411450.2011.563711","DOIUrl":"https://doi.org/10.1080/00411450.2011.563711","url":null,"abstract":"We present a review of recent developments of simulations of the Vlasov-Maxwell system of equations using a Fourier transform method in velocity space. In this method, the distribution functions for electrons and ions are Fourier transformed in velocity space, and the resulting set of equations are solved numerically. In the original Vlasov equation, phase mixing may lead to an oscillatory behavior and sharp gradients of the distribution function in velocity space, which is problematic in simulations where it can lead to unphysical electric fields and instabilities and to the recurrence effect where parts of the initial condition recur in the simulation. The particle distribution function is in general smoother in the Fourier-transformed velocity space, which is desirable for the numerical approximations. By designing outflow boundary conditions in the Fourier-transformed velocity space, the highest oscillating terms are allowed to propagate out through the boundary and are removed from the calculations, thereby strongly reducing the numerical recurrence effect. The outflow boundary conditions in higher dimensions including electromagnetic effects are discussed. The Fourier transform method is also suitable to solve the Fourier-transformed Wigner equation, which is the quantum mechanical analogue of the Vlasov equation for classical particles.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"39 1","pages":"387 - 465"},"PeriodicalIF":0.0,"publicationDate":"2010-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2011.563711","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58908737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 30

Out-of-Equilibrium Phase Transitions and Time-Asymptotic One-Particle Dynamics in the Vlasov Limit of The Hamiltonian Mean Field Model 哈密顿平均场模型Vlasov极限下的非平衡相变和时间渐近单粒子动力学

Transport Theory and Statistical Physics Pub Date : 2010-03-31 DOI: 10.1080/00411450.2011.563707

M. Firpo

{"title":"Out-of-Equilibrium Phase Transitions and Time-Asymptotic One-Particle Dynamics in the Vlasov Limit of The Hamiltonian Mean Field Model","authors":"M. Firpo","doi":"10.1080/00411450.2011.563707","DOIUrl":"https://doi.org/10.1080/00411450.2011.563707","url":null,"abstract":"When starting from specific initial conditions, the ferromagnetic-like XY Hamiltonian mean field (HMF) model evolves toward quasistationary states, with lifetimes diverging with the number N of degrees of freedom that violate equilibrium statistical mechanics predictions. Phase transitions have been reported between low-energy magnetized quasistationary states and large energy unexpected, antiferromagnetic-like ones with low, but nonvanishing, magnetization. This issue is addressed here in the Vlasov N→∞ limit. It is argued that the time asymptotic states emerging in the Vlasov limit can be related to simple generic time asymptotic forms for the force field. The proposed picture unveils the nature of the out-of-equilibrium phase transitions reported for the ferromagnetic HMF in the second order regime: This is a bifurcation point connecting an effective integrable Vlasov one-particle time-asymptotic dynamic to a partly ergodic one, which means an abrupt open-up of the Vlasov one-particle phase space. This is proposed as a mechanism for second-order phase transitions compatible with nonvanishing time-asymptotic values of the order parameter in mean-field long-range systems.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"39 1","pages":"370 - 386"},"PeriodicalIF":0.0,"publicationDate":"2010-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2011.563707","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58908727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Theoretical Aspects of the Simplified Pn Equations 简化Pn方程的理论方面

Transport Theory and Statistical Physics Pub Date : 2010-03-01 DOI: 10.1080/00411450.2010.535088

R. McClarren

引用次数: 78

Fifty Years of the Simplified Pn Method 简化Pn法的五十年

Transport Theory and Statistical Physics Pub Date : 2010-03-01 DOI: 10.1080/00411450.2010.531879

R. McClarren

{"title":"Fifty Years of the Simplified Pn Method","authors":"R. McClarren","doi":"10.1080/00411450.2010.531879","DOIUrl":"https://doi.org/10.1080/00411450.2010.531879","url":null,"abstract":"In 1968, Ely Gelbard quipped in reference to the spherical harmonics (Pn) method, “Now we live in a period when whole fields of technology are born, mature, and, sometimes, die in a decade. In times when physics changes so quickly a 40-year-old method must be regarded as very old indeed,” (Gelbard, 1968). In this special issue we celebrate a very old method conceived by Gelbard as a simplification of the spherical harmonics method: the simplified Pn or SPn method. In a September 1960 review of nuclear reactor technology at the Bettis Atomic Power Laboratory (Gelbard, 1960), Gelbard presented a simplification to the full spherical harmonics method that greatly reduced the number of unknowns, and also provided an analysis of when the method was equivalent to the full Pn equations. A new method was born and researchers have been applying and studying it for the past 50 years. I was motivated to organize this special issue in 2009 while trying to extend the equivalence of the SPn and Pn equations to more general cases. In reading the literature I realized that the next year was the 50th anniversary of SPn. Like many in the field of transport I was initially intrigued by the simplicity of SPn, later amazed that in many cases SPn is equivalent to the more complicated Pn equations, and finally disappointed that in some problems it can give worse answers than diffusion.1 To encapsulate all of these feelings and to highlight the successes in using SPn, I decided that a special issue commemorating SPn was in order. I hope that this issue both takes a snapshot of the current uses and understanding of","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"39 1","pages":"71 - 72"},"PeriodicalIF":0.0,"publicationDate":"2010-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2010.531879","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58908985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Moment Analysis of Angular APproximation Methods for Time-Dependent Radiation Transport 时变辐射输运角近似方法的矩分析

Transport Theory and Statistical Physics Pub Date : 2010-03-01 DOI: 10.1080/00411450.2010.533742

J. Densmore, R. McClarren

{"title":"Moment Analysis of Angular APproximation Methods for Time-Dependent Radiation Transport","authors":"J. Densmore, R. McClarren","doi":"10.1080/00411450.2010.533742","DOIUrl":"https://doi.org/10.1080/00411450.2010.533742","url":null,"abstract":"We extend moment analysis, a technique developed for investigating the accuracy of discrete-ordinates spatial discretization schemes, to time-dependent radiation transport and apply it to several angular approximation methods. Specifically, we examine the diffusion approximation, the P 1/3 approximation, and three time-dependent generalizations of the simplified PNapproximation: the SP 2 , SP 3 , and SSP 3 approximations. We show that all of the these methods preserve the correct flux-weighted average of x but not the correct flux-weighted average of (x-xa)2, where x is the spatial variable and xais an arbitrary point. We also demonstrate that, for general cross sections and large elapsed time, the error in the flux-weighted average of (x-xa)2 is smallest in magnitude for the SP 2 and approximations. In addition, we present a simple improvement to the SP 2 approximation that allows this method to produce the correct flux-weighted average of (x-xa)2. We present numerical results that test this analysis. From these results, we find that the angular approximation methods with the most accurate solutions also have the most accurate values for the flux-weighted average of (x-xa)2. In particular, the SP 2 and SP 3 approximations are two of the most accurate methods at large elapsed times, while the improved SP 2 approximation is one of the most accurate methods at all times. We also observe, however, that an accurate value for the flux-weighted average of (x-xa)2 is not always accompanied by an accurate solution. Consequently, we conclude that an accurate flux-weighted average of (x-xa)2 is a necessary rather than sufficient condition for an overall accurate angular approximation method.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"39 1","pages":"192 - 233"},"PeriodicalIF":0.0,"publicationDate":"2010-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2010.533742","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 6

On the Relation Between Spherical Harmonics and Simplified Spherical Harmonics Methods 论球面谐波与简化球面谐波方法的关系

Transport Theory and Statistical Physics Pub Date : 2010-03-01 DOI: 10.1080/00411450.2010.531877

G. Coppa, V. Giusti, B. Montagnini, P. Ravetto

引用次数: 13

Asymptotic Diffusion and Simplified PN Approximations for Diffusive and Deep Penetration Problems. Part 1: Theory 扩散和深穿透问题的渐近扩散和简化PN逼近。第一部分:理论

Transport Theory and Statistical Physics Pub Date : 2010-03-01 DOI: 10.1080/00411450.2010.531878

E. Larsen

引用次数: 12

Optimal Control of Glass Cooling Using Simplified PN Theory 基于简化PN理论的玻璃冷却最优控制

Transport Theory and Statistical Physics Pub Date : 2010-03-01 DOI: 10.1080/00411450.2010.533740

M. Frank, A. Klar, R. Pinnau

引用次数: 31

Application of h-, p-, and hp -Mesh Adaptation Techniques to the SP 3 Equations h-、p-和hp -网格自适应技术在sp3方程中的应用

Transport Theory and Statistical Physics Pub Date : 2010-03-01 DOI: 10.1080/00411450.2010.533743

J. Ragusa

引用次数: 9