相关论文: Stochastic limit approximation for rapidly decayin…
In this paper, we aim to study the diffusion approximation for multi-scale McKean-Vlasov stochastic differential equations. More precisely, we prove the weak convergence of slow process $X^\varepsilon$ in $C([0,T];\mathbb{R}^n)$ towards the…
Lyman limit and damped Lyman-alpha absorption systems probe the distribution of collapsed, cold gas at high redshift. Numerical simulations that incorporate gravity and gas dynamics can predict the abundance of such absorbers in…
A stochastic system under the influence of a stochastic environment is correlated with both present and future states of the environment. Such a system can be seen as implicitly implementing a predictive model of future environmental…
This paper is concerned with tuning friction and temperature in Langevin dynamics for fast sampling from the canonical ensemble. We show that near-optimal acceleration is achieved by choosing friction so that the local quadratic…
In this paper we address the convergence of stochastic approximation when the functions to be minimized are not convex and nonsmooth. We show that the "mean-limit" approach to the convergence which leads, for smooth problems, to the ODE…
The starting point for this work is a static macroscopic model for a high-contrast layered material in single-slip finite crystal plasticity, identified in [Christowiak & Kreisbeck, Calc. Var. PDE (2017)] as a homogenization limit via…
This work establishes the weak convergence of Euler-Maruyama's approximation for stochastic differential equations (SDEs) with singular drifts under the integrability condition in lieu of the widely used growth condition. This method is…
We use the stochastic limit method to study long time quantum dynamics of a test particle interacting with a dilute Bose gas. The case of arbitrary form-factors and an arbitrary, not necessarily equilibrium, quasifree low density state of…
Dissipative particle dynamics is a widely used mesoscale technique for the simulation of hydrodynamics (as well as immersed particles) utilizing coarse-grained molecular dynamics. While the method is capable of describing any fluid, the…
We investigate microscopically the tunneling dynamics in spontaneous fission of atomic nuclei. To this end, we employ a schematic solvable model with a pairing-plus-quadrupole interaction. The spontaneous decay of a system is simulated by…
Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. We revisit a…
Gaining insights from realistic dynamical models of biochemical systems can be challenging given their large number of state variables. Model reduction techniques can mitigate this by decreasing complexity by mapping the model onto a…
We demonstrate how to derive the exponential decrease of amplitude and an excellent approximation of the energy decay of a weakly damped harmonic oscillator without solving the associated equation of motion and without insight into the…
In energy management, it is common that strategic investment decisions (storage capacity, production units) are made at a slow time scale, whereas operational decisions (storage, production) are made at a fast time scale: for such problems,…
We study quantum dissipative dynamics of entanglement in the spin-boson model, described by the generalized master equation. We consider the two opposite limits of pure-dephasing and relaxation models, measuring the degree of entanglement…
The time evolution of the thermally activated decay rates is considered. This evolution is of particular importance for the recent nanoscale experiments discussed in the literature, where the potential barrier is relatively low (or the…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
This paper develops a two-stage stochastic model to investigate evolution of random fields on the unit sphere $\bS^2$ in $\R^3$. The model is defined by a time-fractional stochastic diffusion equation on $\bS^2$ governed by a diffusion…
We explore the near adiabatic dynamics in a non-Hermitian quantum many-body system by investigating a finite-time ramp of the imaginary vector potential in the interacting Hatano-Nelson model. The excess energy, the Loschmidt echo, and the…
Stochastic optimization naturally appear in many application areas, including machine learning. Our goal is to go further in the analysis of the Stochastic Average Gradient Accelerated (SAGA) algorithm. To achieve this, we introduce a new…