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Transport Theory and Statistical Physics最新文献

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Diffusion Limit of a Small Mean Free Path of Radiative Transfer Equations with Absorbing Boundary Condition 具有吸收边界条件的辐射传递方程小平均自由程的扩散极限
Transport Theory and Statistical Physics Pub Date : 2012-12-01 DOI: 10.1080/00411450.2012.747540
B. Guo, Yongqian Han
{"title":"Diffusion Limit of a Small Mean Free Path of Radiative Transfer Equations with Absorbing Boundary Condition","authors":"B. Guo, Yongqian Han","doi":"10.1080/00411450.2012.747540","DOIUrl":"https://doi.org/10.1080/00411450.2012.747540","url":null,"abstract":"In this article, the nonlinear transfer equations with absorbing boundary condition, which describe the spatial transport of radiation in a material medium, are considered. We first establish the well-posedness of solutions for the radiative transfer equations based on the principle of contraction mapping and the comparison principle. Then we show that the radiative transfer equations have diffusion limits as the mean free path tends to zero if the specific intensity of radiation entering the system through the boundary of the domain is uniform with respect to the incoming direction. Our proof is based on asymptotic expansions. We show that the validity of these asymptotic expansions relies only on the smoothness of initial data and boundary functions, while two hypotheses, Fredholm alternative and centering condition, are removed.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"552 - 582"},"PeriodicalIF":0.0,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.747540","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909793","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: 2
Eigenvalues of the Anisotropic Transport Equation in a Slab 平板各向异性输运方程的特征值
Transport Theory and Statistical Physics Pub Date : 2012-10-01 DOI: 10.1080/00411450.2012.675217
E. Sauter, F. S. de Azevedo, M. Thompson, M. Vilhena
{"title":"Eigenvalues of the Anisotropic Transport Equation in a Slab","authors":"E. Sauter, F. S. de Azevedo, M. Thompson, M. Vilhena","doi":"10.1080/00411450.2012.675217","DOIUrl":"https://doi.org/10.1080/00411450.2012.675217","url":null,"abstract":"The critical eigenvalues of the transport equation play an important role in the description of the dynamics of transport problems both in nuclear physics as well as in radiative transport theory. This article treats the problem of calculating numerically the critical spectrum of the transport equation with semireflecting boundary conditions. The eigenvalue problem is solved using spectral methods and numerical results are presented. The scattering kernel is considered to be one of three types, namely, isotropic, linearly anisotropic, or Rayleigh scattering, even although more general kernels could be considered.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"448 - 472"},"PeriodicalIF":0.0,"publicationDate":"2012-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.675217","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909602","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: 4
Spatial Moments of Continuous Transport Problems Computed on Grids 网格上连续运输问题的空间矩计算
Transport Theory and Statistical Physics Pub Date : 2012-10-01 DOI: 10.1080/00411450.2012.671223
J. Densmore
{"title":"Spatial Moments of Continuous Transport Problems Computed on Grids","authors":"J. Densmore","doi":"10.1080/00411450.2012.671223","DOIUrl":"https://doi.org/10.1080/00411450.2012.671223","url":null,"abstract":"The method of moments is a well-known technique for determining exact expressions for spatial and angular moments of radiation distributions in infinite, homogeneous media. These moments can further be used to calculate other quantities of interest. We examine how the method of moments is altered when the underlying transport problem is spatially continuous but involves a grid and moments are computed on this grid instead of through integration over the entire domain. For the problem we consider, we employ both singular-eigenfunction and Fourier-transform approaches to show that when moments are evaluated in this manner (i) the flux-weighted average of x remains equal to the source-weighted average of x, but (ii) the flux-weighted average of (x−xa )2 is greater than the source-weighted average of (x−xa )2 by an additional error term, where x is the spatial variable and xa is an arbitrary point. We also demonstrate that the two resulting expressions for this error term are equivalent.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"389 - 405"},"PeriodicalIF":0.0,"publicationDate":"2012-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671223","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909940","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: 3
On Boundedness of Higher Velocity Moments for the Linear Boltzmann Equation with Diffuse Boundary Conditions 具有扩散边界条件的线性Boltzmann方程高速度矩的有界性
Transport Theory and Statistical Physics Pub Date : 2012-10-01 DOI: 10.1080/00411450.2012.671213
R. Pettersson
{"title":"On Boundedness of Higher Velocity Moments for the Linear Boltzmann Equation with Diffuse Boundary Conditions","authors":"R. Pettersson","doi":"10.1080/00411450.2012.671213","DOIUrl":"https://doi.org/10.1080/00411450.2012.671213","url":null,"abstract":"This article considers the time and space-dependent linear Boltzmann equation for elastic or inelastic (granular) collisions. First, in the angular cut-off case or with hard sphere collisions, mild L 1-solutions are constructed as limits of iterate functions. Then, in the case of hard potentials together with diffuse boundary conditions, global boundedness in time of higher velocity moments is proved, using our old collision velocity estimates together with a Jensen inequality.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"345 - 355"},"PeriodicalIF":0.0,"publicationDate":"2012-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671213","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909708","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
An Analytical Solution of the Time-Dependent Diffusion Equation in a Composite Slab 复合板中随时间扩散方程的解析解
Transport Theory and Statistical Physics Pub Date : 2012-10-01 DOI: 10.1080/00411450.2012.671217
V. Glivici-Cotruţă, B. Merk
{"title":"An Analytical Solution of the Time-Dependent Diffusion Equation in a Composite Slab","authors":"V. Glivici-Cotruţă, B. Merk","doi":"10.1080/00411450.2012.671217","DOIUrl":"https://doi.org/10.1080/00411450.2012.671217","url":null,"abstract":"The time-dependent, one-dimensional diffusion equation is solved for a finite slab of two layers. An external source is supplied to one of the layers. The differential equations are subject to the reflecting boundary conditions at the two outer boundary surfaces. The flux and the current density are continuous across the interface between two media. The exact analytical solution is expressed in terms of a Green’s function. The solution is developed by the application of the Laplace transformation.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"356 - 367"},"PeriodicalIF":0.0,"publicationDate":"2012-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671217","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909789","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: 5
Analytical Solutions for the Pencil-Beam Equation with Energy Loss and Straggling 具有能量损失和散列的铅笔束方程的解析解
Transport Theory and Statistical Physics Pub Date : 2012-10-01 DOI: 10.1080/00411450.2012.671207
Tobias Gebäck, M. Asadzadeh
{"title":"Analytical Solutions for the Pencil-Beam Equation with Energy Loss and Straggling","authors":"Tobias Gebäck, M. Asadzadeh","doi":"10.1080/00411450.2012.671207","DOIUrl":"https://doi.org/10.1080/00411450.2012.671207","url":null,"abstract":"In this article, we derive equations approximating the Boltzmann equation for charged particle transport under the continuous slowing down assumption. The objective is to obtain analytical expressions that approximate the solution to the Boltzmann equation. The analytical expressions found are based on the Fermi-Eyges solution, but include correction factors to account for energy loss and spread. Numerical tests are also performed to investigate the validity of the approximations.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"325 - 336"},"PeriodicalIF":0.0,"publicationDate":"2012-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671207","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58910014","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: 4
Kenneth Case and his Singular “Eigenfunctions” Kenneth Case及其奇异“特征函数”
Transport Theory and Statistical Physics Pub Date : 2012-10-01 DOI: 10.1080/00411450.2012.671225
P. Zweifel
{"title":"Kenneth Case and his Singular “Eigenfunctions”","authors":"P. Zweifel","doi":"10.1080/00411450.2012.671225","DOIUrl":"https://doi.org/10.1080/00411450.2012.671225","url":null,"abstract":"This talk was presented at the ICTT-22 meeting held in Portland, Oregon on September 12–16, 2011.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"406 - 417"},"PeriodicalIF":0.0,"publicationDate":"2012-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671225","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909965","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: 3
Henyey-Greenstein Model in the Shape Relaxation of Dilute Gas Mixtures 稀气体混合物形状松弛的Henyey-Greenstein模型
Transport Theory and Statistical Physics Pub Date : 2012-10-01 DOI: 10.1080/00411450.2012.671222
R. Sospedra‐Alfonso, B. Shizgal
{"title":"Henyey-Greenstein Model in the Shape Relaxation of Dilute Gas Mixtures","authors":"R. Sospedra‐Alfonso, B. Shizgal","doi":"10.1080/00411450.2012.671222","DOIUrl":"https://doi.org/10.1080/00411450.2012.671222","url":null,"abstract":"We study the relaxation of Li+ ions dilutely dispersed in He at equilibrium. We employ the Henyey-Greenstein phase function to model the angular dependence of the differential scattering cross section for Li+-He collisions. We solve the spatially homogeneous linear Boltzmann equation for this model cross section with the collision operator explicitly given in terms of the scattering kernel. With the Quadrature Discretization Method based on the speed polynomials, the Boltzmann equation is reduced to a set of ordinary differential equations. This numerical method provides a rapid convergence for the Li+ distribution function. We study the relaxation of the shape of the Li+ distribution function in terms of the Kullback-Leibler information relative to the steady state and local in time Maxwellians. A comparison of the relaxation times of these two functionals show that there is no formation of a local Maxwellian during the relaxation process. This was verified for several values of the g-parameter in the Henyey-Greenstein phase function model and the initial average energies investigated.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"368 - 388"},"PeriodicalIF":0.0,"publicationDate":"2012-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671222","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909928","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: 5
Diffusive Limits for a Quantum Transport Model with a Strong Field 强场下量子输运模型的扩散极限
Transport Theory and Statistical Physics Pub Date : 2012-10-01 DOI: 10.1080/00411450.2012.682618
L. Barletti, G. Frosali
{"title":"Diffusive Limits for a Quantum Transport Model with a Strong Field","authors":"L. Barletti, G. Frosali","doi":"10.1080/00411450.2012.682618","DOIUrl":"https://doi.org/10.1080/00411450.2012.682618","url":null,"abstract":"We derive semiclassical diffusive equations for the local electron densities in a semiconductor characterized by a two-band k·p Hamiltonian, under the action of a strong external field. By using a spinorial formalism, we consider the quantum kinetic (Wigner) system endowed with a Bhatnagar-Gross-Krook (BGK)-like interaction term. Diffusive equations are derived by the Chapman-Enskog method. The closure of such equations is obtained by using the quantum version of the minimum entropy principle. In practice, it is unfeasible to put in an explicit form the diffusive equations in the general case, even in the semiclassical limit. Then we investigate the case in which band parameters have little influence on the dynamics at the macroscopic scale.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"473 - 493"},"PeriodicalIF":0.0,"publicationDate":"2012-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.682618","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909657","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: 2
On SN-PN Equivalence 关于SN-PN等价
Transport Theory and Statistical Physics Pub Date : 2012-10-01 DOI: 10.1080/00411450.2012.672360
Richard Sanchez
{"title":"On SN-PN Equivalence","authors":"Richard Sanchez","doi":"10.1080/00411450.2012.672360","DOIUrl":"https://doi.org/10.1080/00411450.2012.672360","url":null,"abstract":"We consider the artificial conversion of the discrete–ordinates (SN) equations into a system of spherical harmonic (PN) equations. This is done by adding to the SN equations an artificial source that has two components. The first component transforms the SN scattering term into PN-like scattering, while the second modifies the SN streaming operator into a lower-order PN streaming operator. Denoting by and the spaces of solutions of the SN and PN equations, respectively, we define SN-PN equivalence via a constructive Proposition based on two linear morphisms, and , such that if ψ is the solution of the SN equations with source S+π*(S), then π K ψ is solution of the PN equations with source π K S. We proceed then to prove this Proposition by constructing the two components of the artificial source. We also prove that when the morphism π* is not unique, and propose a general form for the second component of the artificial source, which is shown to comprise all artificial sources previously proposed in the literature.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"418 - 447"},"PeriodicalIF":0.0,"publicationDate":"2012-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.672360","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58910040","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: 4
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