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Application of the Onsager-Machlup integral in solving dynamic equations in nonequilibrium systems
Doi, Masao1; Zhou, Jiajia1; Di, Yana2; Xu, Xianmin2
2019-06-10
Source PublicationPHYSICAL REVIEW E
ISSN2470-0045
Volume99Issue:6Pages:11
AbstractIn 1931, Onsager proposed a variational principle which has become the base of many kinetic equations for nonequilibrium systems. We have been showing that this principle is useful in obtaining approximate solutions for the kinetic equations, but our previous method has a weakness that it can be justified, strictly speaking, only for small incremental time. Here we propose an improved method which does not have this drawback. The improved method utilizes the integral proposed by Onsager and Machlup in 1953, and can tell us which of the approximate solutions is the best solution without knowing the exact solution. The improved method has an advantage that it allows us to determine the steady state in nonequilibrium system by a variational calculus. We demonstrate this using three examples, (a) simple diffusion problem, (b) capillary problem in a tube with corners, and (c) free boundary problem in liquid coating, for which the kinetic equations are written in second or fourth-order partial differential equations.
DOI10.1103/PhysRevE.99.063303
Language英语
Funding ProjectNational Natural Science Foundation of China (NSFC)[21504004] ; National Natural Science Foundation of China (NSFC)[21774004] ; Chinese Central Government in the Thousand Talents Program
WOS Research AreaPhysics
WOS SubjectPhysics, Fluids & Plasmas ; Physics, Mathematical
WOS IDWOS:000470876400012
PublisherAMER PHYSICAL SOC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35046
Collection计算数学与科学工程计算研究所
Corresponding AuthorDoi, Masao
Affiliation1.Beihang Univ, Ctr Soft Matter Phys & Its Applicat, 37 Xueyuan Rd, Beijing 100191, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Doi, Masao,Zhou, Jiajia,Di, Yana,et al. Application of the Onsager-Machlup integral in solving dynamic equations in nonequilibrium systems[J]. PHYSICAL REVIEW E,2019,99(6):11.
APA Doi, Masao,Zhou, Jiajia,Di, Yana,&Xu, Xianmin.(2019).Application of the Onsager-Machlup integral in solving dynamic equations in nonequilibrium systems.PHYSICAL REVIEW E,99(6),11.
MLA Doi, Masao,et al."Application of the Onsager-Machlup integral in solving dynamic equations in nonequilibrium systems".PHYSICAL REVIEW E 99.6(2019):11.
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