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We simulate, using nonperturbative methods, the real-time dynamics of small bubbles of "false vacuum" in a quantum spin chain near criticality, where the low-energy physics is described by a relativistic (1+1)-dimensional quantum field…
To determine the effect of nonradiative excitation energy transfer on the fluorescence of a rigid multicomponent solution, a new analytical method was developed by treating this transfer as a time-resolved Markov chain (TRMC). In the TRMC…
We are interested in the analysis of very large continuous-time Markov chains (CTMCs) with many distinct rates. Such models arise naturally in the context of reliability analysis, e.g., of computer network performability analysis, of power…
In this paper we apply the Diffusion approximation procedure to a discrete time Adaptive Markov Chain Monte Carlo (AMCMC) method when the target distribution is standard Normal. We show that the limiting distribution of the diffusion admits…
Physical notions of stochastic resonance for potential diffusions in periodically changing double-well potentials such as the spectral power amplification have proved to be defective. They are not robust for the passage to their effective…
The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method,…
Sticky Brownian motions, as time-changed semimartingale reflecting Brownian motions, have various applications in many fields, including queuing theory and mathematical finance. In this paper, we are concerned about the stationary…
We show that for the simulation of crack propagation in quasi-brittle, two-dimensional solids, very good results can be obtained with an embedded strong discontinuity quadrilateral finite element that has incompatible modes. Even more…
In this work we study the spreading dynamics of tiny liquid droplets on solid surfaces in the case where the ends of the molecules feel different interactions with respect to the surface. We consider a simple model of dimers and short…
We consider a rate control problem for an $N$-particle weakly interacting finite state Markov process. The process models the state evolution of a large collection of particles and allows for multiple particles to change state…
This study uses a combination of stochastic optimization, statistical mechanical theory, and molecular simulation to test the extent to which the long-time dynamics of a single tracer particle can be enhanced by rationally modifying its…
In this paper, we develop a mathematical framework for modeling the time-variant stochastic channels of diffusive mobile MC systems. In particular, we consider a diffusive mobile MC system consisting of a pair of transmitter and receiver…
Estimating the transition dynamics of controlled Markov chains is crucial in fields such as time series analysis, reinforcement learning, and system exploration. Traditional non-parametric density estimation methods often assume independent…
Applications of stochastic models often involve the evaluation of steady-state performance, which requires solving a set of balance equations. In most cases of interest, the number of equations is infinite or even uncountable. As a result,…
Fastest arrival events, where the first among many diffusing particles reaches a target, are central in triggering signal initiation in molecular stochastic systems. Classical approaches to simulate such events rely on full trajectory…
We presented a methodology to approximate the entropy production for Brownian motion in a tilted periodic potential. The approximation stems from the well known thermodynamic uncertainty relation. By applying a virial-like expansion, we…
We present a novel hybrid computational method to simulate accurately dendritic solidification in the low undercooling limit where the dendrite tip radius is one or more orders of magnitude smaller than the characteristic spatial scale of…
Simple modifications for higher-order Godunov-type difference schemes are presented which allow for accurate advection of multi-fluid flows in hydrodynamic simulations. The constraint that the sum of all mass fractions has to be equal to…
Adaptive and interacting Markov Chains Monte Carlo (MCMC) algorithms are a novel class of non-Markovian algorithms aimed at improving the simulation efficiency for complicated target distributions. In this paper, we study a general…
In this paper, we develop and analyze a stochastic algorithm for solving space-time fractional diffusion models, which are widely used to describe anomalous diffusion dynamics. These models pose substantial numerical challenges due to the…