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pro vyhledávání: '"Liu Jian-Guo"'
Linear response theory is a fundamental framework studying the macroscopic response of a physical system to an external perturbation. This paper focuses on the rigorous mathematical justification of linear response theory for Langevin dynamics. We gi
Externí odkaz:
http://arxiv.org/abs/2408.13600
In this paper, we propose a drift-diffusion process on the probability simplex to study stochastic fluctuations in probability spaces. We construct a counting process for linear detailed balanced chemical reactions with finite species such that its t
Externí odkaz:
http://arxiv.org/abs/2408.08505
The Random Batch Method (RBM) proposed in [Jin et al. J Comput Phys, 2020] is an efficient algorithm for simulating interacting particle systems. In this paper, we investigate the Random Batch Method with replacement (RBM-r), which is the same as the
Externí odkaz:
http://arxiv.org/abs/2407.19315
Autor:
Qi, Di, Liu, Jian-Guo
We present a new strategy for filtering high-dimensional multiscale systems characterized by high-order non-Gaussian statistics using observations from leading-order moments. A closed stochastic-statistical modeling framework suitable for systematic
Externí odkaz:
http://arxiv.org/abs/2407.04881
In this paper, we consider a Hele-Shaw model that describes tumor growth subject to nutrient supply. This model was recently studied in \cite{feng2022tumor} via asymptotic analysis. Our contributions are twofold: Firstly, we provide a rigorous deriva
Externí odkaz:
http://arxiv.org/abs/2404.16353
In this paper, we investigate the tumor instability by employing both analytical and numerical techniques to validate previous results and extend the analytical findings presented in a prior study by Feng et al 2023. Building upon the insights derive
Externí odkaz:
http://arxiv.org/abs/2401.04954
Autor:
Degond, Pierre, Liu, Jian-Guo
We investigate a kinetic model for interacting particles whose masses are integer multiples of an elementary mass. These particles undergo binary collisions which preserve momentum and energy but during which some number of elementary masses can be e
Externí odkaz:
http://arxiv.org/abs/2401.04562
We consider the completely positive discretizations of fractional ordinary differential equations (FODEs) on nonuniform meshes. Making use of the resolvents for nonuniform meshes, we first establish comparison principles for the discretizations. Then
Externí odkaz:
http://arxiv.org/abs/2401.02050
Among various rare events, the effective computation of transition paths connecting metastable states in a stochastic model is an important problem. This paper proposes a stochastic optimal control formulation for transition path problems in an infin
Externí odkaz:
http://arxiv.org/abs/2311.07795
Autor:
Qi, Di, Liu, Jian-Guo
We propose a high-order stochastic-statistical moment closure model for efficient ensemble prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. The statistical moment equations are
Externí odkaz:
http://arxiv.org/abs/2306.10026