Related papers: A First-Passage Kinetic Monte Carlo Method for Rea…
The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the…
A free boundary diffusive logistic model finds application in many different fields from biological invasion to wildfire propagation. However, many of these processes show a random nature and contain uncertainties in the parameters. In this…
In the first part of this paper we study approximations of trajectories of Piecewise Deter-ministic Processes (PDP) when the flow is not explicit by the thinning method. We also establish a strong error estimate for PDPs as well as a weak…
In this paper, we first present the general propagation multiple-relaxation-time lattice Boltzmann (GPMRT-LB) model and obtain the corresponding macroscopic finite-difference (GPMFD) scheme on conservative moments. Then based on the Maxwell…
This article reviews the basic computational techniques for carrying out multi-scale simulations using statistical methods, with the focus on simulations of epitaxial growth. First, the statistical-physics background behind Monte Carlo…
A continuous-time formulation of the Diffusion Monte Carlo method for lattice models is presented. In its simplest version, without the explicit use of trial wavefunctions for importance sampling, the method is an excellent tool for…
At the scale of the individual cell, protein production is a stochastic process with multiple time scales, combining quick and slow random steps with discontinuous and smooth variation. Hybrid stochastic processes, in particular…
In this paper we consider parameter estimation for discretely observed diffusion processes. In particular, we focus on data that are observed at low frequency and methodology that can estimate parameters with uncertainty quantification.…
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…
Multi-color Stochastic Rotation Dynamics (SRDmc) has been introduced by Inoue et al. as a particle based simulation method to study the flow of emulsion droplets in non-wetting microchannels. In this work, we extend the multi-color method…
While Diffusion Monte Carlo (DMC) is in principle an exact stochastic method for \textit{ab initio} electronic structure calculations, in practice the fermionic sign problem necessitates the use of the fixed-node approximation and trial…
One of the most significant drawbacks of the all-electron ab initio diffusion Monte Carlo (DMC) is that its computational cost drastically increases with the atomic number ($Z$), which typically scales with $Z^{\sim 6}$. In this study, we…
Diffusion models generate high-quality images but require dozens of forward passes. We introduce Distribution Matching Distillation (DMD), a procedure to transform a diffusion model into a one-step image generator with minimal impact on…
Diffusion Monte Carlo (DMC) is one of the most accurate techniques available for calculating the electronic properties of molecules and materials, yet it often remains a challenge to economically compute forces using this technique. As a…
We investigate a numerical behaviour of robust deterministic optimal control problem subject to a convection diffusion equation containing uncertain inputs. Stochastic Galerkin approach, turning the original optimization problem containing…
We propose a novel Markov chain Monte-Carlo (MCMC) method for reverse engineering the topological structure of stochastic reaction networks, a notoriously challenging problem that is relevant in many modern areas of research, like…
We expand upon the recent semi-stochastic adaptation to full configuration interaction quantum Monte Carlo (FCIQMC). We present an alternate method for generating the deterministic space without a priori knowledge of the wave function and…
Two-component submonolayer growth on triangular lattice is qualitatively studied by kinetic Monte Carlo techniques. The hopping barrier governing surface diffusion of the atoms is estimated with an improved formula and using realistic pair…
Pattern formation in reaction-diffusion systems is of great importance in surface micro-patterning [Grzybowski et al. Soft Matter. 1, 114 (2005)], self-organization of cellular micro-organisms [Schulz et al. Annu. Rev. Microbiol. 55, 105…
By considering a lattice model of extended phase space, and using techniques of noncommutative differential geometry, we are led to: (a) the conception of vector fields as generators of motion and transition probability distributions on the…