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mean field limit of a dynamical model of polymer systems

Science China Mathematics 2013年第12期56卷 2591-2598页

作者： E Weinan SHEN Hao School of Mathematical Sciences and BICMR Peking University Department of Mathematics and PACM Princeton UniversityPrinceton NJ 08544 USA Program in Applied and Computational Mathematics Princeton UniversityPrinceton NJ 08544 USA

This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string of points which are moving randomly as Brownian motions and under elastic forces. Every two points on the same string or on two different strings also interact under a pairwise potential V. The dynamics of the system is described by a system of N coupled stochastic partial differential equations （SPDEs）. We show that the mean field limit as N -＋ c~ of the system is a self-consistent McKean-Vlasov type equation, under suitable assumptions on the initial and boundary conditions and regularity of V. We also prove that both the SPDE system of the polymers and the mean field limit equation are well-posed.

关键词： polymers mean field limit stochastic PDEs McKean-Vlasov equation

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On the mean field limit of the Random Batch Method for interacting particle systems

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Science China Mathematics 2022年第1期65卷 169-202页

作者： Shi Jin Lei Li School of Mathematical Sciences Institute of Natural SciencesMOE-LSCShanghai Jiao Tong UniversityShanghai 200240China

The Random Batch Method proposed in our previous work(Jin et al.J Comput Phys,2020)is not only a numerical method for interacting particle systems and its mean-field limit,but also can be viewed as a model of the particle system in which particles interact,at discrete time,with randomly selected mini-batch of *** this paper,we investigate the mean-field limit of this model as the number of particles N→∞.Unlike the classical mean field limit for interacting particle systems where the law of large numbers plays the role and the chaos is propagated to later times,the mean field limit now does not rely on the law of large numbers and the chaos is imposed at every discrete *** this,we will not only justify this mean-field limit(discrete in time)but will also show that the limit,as the discrete time intervalτ→0,approaches to the solution of a nonlinear Fokker-Planck equation arising as the mean-field limit of the original interacting particle system in the Wasserstein distance.

关键词： Random Batch Method mean field limit chaos Wasserstein distance nonlinear Fokker-Planck equation

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Approximations for a Queueing Game Model with Join-the-Shortest-Queue Strategy

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Journal of the Operations Research Society of China 2023年第3期11卷 489-504页

作者： Qi-Hui Bu Li-Wei Liu Jia-Shan Tang Yi-Qiang Q.Zhao School of Science Nanjing University of Posts and TelecommunicationsNanjing210023JiangsuChina School of Science Nanjing University of Science and TechnologyNanjing210094JiangsuChina School of Mathematics and Statistics Carleton UniversityOttawaONK1S 5B6Canada

This paper investigates a partially observable queueing system with N nodes in which each node has a dedicated arrival *** is an extra arrival stream to balance the load of the system by routing its customers to the shortest *** addition,a reward-cost structure is considered to analyse customers'strategic *** equilibrium and socially optimal strategies are derived for the partially observable mean field limit ***,we show that the strategies obtained from the mean field model are good approximations to the model with finite N ***,numerical experiments are provided to compare the equilibrium and socially optimal behaviours,including joining probabilities and social benefits for different system parameters.

关键词： Game theory Queueing systems mean field limit Markov process

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A Differential Algebraic Method for the Solution of the Poisson Equation for Charged Particle Beams

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Communications in Computational Physics 2015年第1期17卷 47-78页

作者： B.Erdelyi E.Nissen S.Manikonda Department of Physics Northern Illinois UniversityDeKalbIL60115USA European Organization for Nuclear Research CH-1211 Geneva 23Switzerland Advanced Magnet Lab Palm BayFL32905USA

The design optimization and analysis of charged particle beam systems employing intense beams requires a robust and accurate Poisson *** paper presents a new type of Poisson solver which allows the effects of space charge to be elegantly included into the system *** is done by casting the charge distribution function into a series of basis functions,which are then integrated with an appropriate Green’s function to find a Taylor series of the potential at a given point within the desired distribution *** order to avoid singularities,a Duffy transformation is applied,which allows singularity-free integration and maximized convergence region when performed with the help of Differential Algebraic *** method is shown to perform well on the examples *** implementation choices and some of their limitations are also explored.

关键词： Charged particle beams mean field limit Poisson equation orthogonal polynomials differential algebra

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