Abstract : The objective of this special minisymposium is to bring together experts from multiple disciplines with complementary views and approaches to stochastic dynamics in the context of applications. The topics include but not limited to: Theoretical advances in stochastic dynamical systems and stochastic partial differential equations, connection with non-equilibrium statistical physics, non-Gaussian noise and nonlocal partial differential operators, dynamical indicators for phase transition and abrupt change, most probable transition pathways and early warning time, tools for predicting rare events or extreme events, machine learning tools for examining stochastic dynamics, multi-scale stochastic simulation algorithms, multiscale multiphase flow simulation and homogenization problems.
[04264] Three-dimensional numerical study on wrinkling of vesicles in elongation flow
Format : Talk at Waseda University
Author(s) :
Wang Xiao (Huazhong University of Science and Technology)
Abstract : We study the wrinkling dynamics of three-dimensional vesicles in time-dependent elongation flow by utilizing an immersed boundary method. The numerical results well match the predictions of perturbation analysis for a quasi-spherical vesicle. The parallel simulation can compute 512^3 Eulerian fluid grids and save the computation cost by at least an order of magnitude compared with the CPU algorithm. In addition, the parallel simulation can be directly extended to study other initial vesicles and external flows.
[04452] Energetic Variation associated with nonlinear Schrödinger equations with Anderson Hamiltonian
Format : Talk at Waseda University
Author(s) :
Qi Zhang (Yau Mathematical Sciences Center, Tsinghua University, China/Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, China)
Abstract : We study the variation problem associated with nonlinear Schrödinger equations with Anderson Hamiltonian in $2$-dimensional torus. Under the paracontrolled distribution framework from singular SPDEs theory, we obtain the existence of the ground state solution by considering the minimization problem of the corresponding energy functional with $L^2$ constraints. We also obtain the tail estimate on the distribution of the principal eigenvalue via the variational representation. This is joint work with Prof. Jinqiao Duan.
[04457] Macroscopic approximation for stochastic N-particle system with small mass
Format : Talk at Waseda University
Author(s) :
Wei Wang (Nanjing University)
Abstract : In this talk we present a small mass limit approximation on macroscopic scale for stochastic $N$-particle system.
On macroscopic scale we have a slow-fast system and then by coupling the system on microscopic scale, an averaging approach is applied to derive the small mass limit. We also present this method to several different systems.
[04557] Effective wave factorization for a stochastic Schrodinger equation
Format : Talk at Waseda University
Author(s) :
Ao Zhang (Central South University)
Abstract : We study the homogenization of a stochastic Schrodinger equation with a large periodic potential in solid state physics. Under a generic assumption on the spectral properties of the associated cell problem, we prove that the solution can be approximately factorized as the product of a fast oscillating cell eigenfunction and of a slowly varying solution of an effective equation. Our method is based on two-scale convergence and Bloch waves theory.
[04528] Approximation of nonlinear filtering for multiscale McKean-Vlasov stochastic differential equations
Format : Talk at Waseda University
Author(s) :
Huijie Qiao (Southeast University)
Wanlin Wei (Southeast University)
Abstract : The work concerns approximation of nonlinear filtering for multiscale McKean-Vlasov stochastic differential equations. First of all, by a Poisson equation we prove an average principle. Then we define nonlinear filtering of the origin multiscale equations and the average equation, and again by the Poisson equation show approximation between nonlinear filtering of the slow part for the origin multiscale equations and that of the average equation.
[04629] On the WKB approximation of confluent hypergeometric systems
Format : Talk at Waseda University
Author(s) :
Xiaomeng Xu
Abstract : This talk studies the WKB approximation of the linear meromorphic systems of Poncaré rank 1 via the isomonodromy approach. It gives a characterization of the WKB approximation via the periods on the underlying spectral curves. It also unveils a relation between the WKB approximation, the Cauchy interlacing inequality, cluster algebras and so on. It is based on a joint work with Anton Alekseev, Andrew Neitzke and Yan Zhou.
[04570] Global stability of stochastic functional differential equations
Format : Talk at Waseda University
Author(s) :
Xiang Lyu (Shanghai Normal University)
Abstract : This paper gives a criterion for the existence of a stationary solution for a class of semilinear stochastic functional differential equations with additive white noise and its global stability. To be more precise, we show that the infinite-dimensional stochastic flow possesses a unique globally attracting random equilibrium in the state space of continuous functions, which produces the globally stable stationary solution.
[04648] Averaging principle for slow-fast systems of stochastic PDEs with rough coefficients
Format : Online Talk on Zoom
Author(s) :
Yichun Zhu (University of Maryland, College Park)
Sandra Cerrai (University of Maryland, College Park)
Abstract : In this paper, we consider a class of slow-fast systems of stochastic partial differential
equations where the nonlinearity in the slow equation is not continuous and unbounded.
We first provide conditions that ensure the existence of a martingale solution. Then we
prove that the laws of the slow motions are tight, and any of their limiting points is a
martingale solution for a suitable averaged equation. Our results apply to systems of
stochastic reaction-diffusion equations where the reaction term in the slow equation is only
continuous and has polynomial growth.
[04756] Mean Asymptotic Behavior for Stochastic Kuramoto-Sivashinshy Equation in Bochner Spaces
Format : Online Talk on Zoom
Author(s) :
Xiaopeng Chen (Shantou University)
Abstract : In this talk we mainly present some asymptotic behavior of the Kuramoto-Sivashinshy equation with stochastic perturbation. We define the mean random dynamical systems for the stochastic Kuramoto-Sivashinshy equation in Bochner spaces. Then we consider the so-called weak pullback mean random attractor and invariant manifold for the stochastic Kuramoto-Sivashinshy equation with odd initial conditions.
[04325] The Poisson Equation and Application to Multi-Scale SDEs with State-Dependent Switching
Format : Online Talk on Zoom
Author(s) :
Xiaobin Sun (Jiangsu Normal University)
Abstract : In this talk, we discuss the Poisson equation associated with a Markov chain. By investigating the differentiability of the corresponding transition probability matrix with respect to parameters, we establish the regularity of the Poisson equation solution. As an application, we further study the averaging principle for a class of multi-scale stochastic differential equations with state-dependent switching, ultimately achieving an optimal strong convergence order of 1/2. This talk is based on a joint work with Yingchao Xie.
[04954] A stochastic fractional Schrodinger equation with multiplicative noise
Format : Talk at Waseda University
Author(s) :
Yan jie Zhang (Zhengzhou University)
Yanjie Zhang (Zhengzhou University )
Abstract : We establish the stochastic Strichartz estimate for the fractional Schr\"odinger equation with multiplicative noise. With the help of the deterministic Strichartz estimates, we prove the existence and uniqueness of a global solution to the stochastic fractional nonlinear Schr\"odinger equation
in $L_2(\mathbb{R}^n)$ and $H^{1}(\mathbb{R}^n)$, respectively. In addition, we also prove a general blow up result by deriving a localized virial estimate and the generalized Strauss inequality with $E[u_0]<0$.
[05083] The most probable dynamics of receptor-ligand binding on cell membrane
Format : Online Talk on Zoom
Author(s) :
Xi Chen (Xi'an University of Finance and Economics)
Abstract : We devise a method for predicting receptor-ligand binding behaviors, based on stochastic dynamical modelling. We consider the receptor and ligand perform different motions and are thus modeled by stochastic differential equations with Gaussian noise or non-Gaussian noise. We use neural networks based on Onsager-Machlup function to compute the probability of the receptor diffusing to the cell membrane. In this way, we conclude with some indication about where the ligand will most probably encounter the receptor.
