Related papers: A First-Passage Kinetic Monte Carlo Method for Rea…
Stochasticity plays important roles in reaction systems. Vector fields of probability flux and velocity characterize time-varying and steady-state properties of these systems, including high probability paths, barriers, checkpoints among…
We propose improved versions of the standard diffusion Monte Carlo (DMC) and the lattice regularized diffusion Monte Carlo (LRDMC) algorithms. For the DMC method, we refine a scheme recently devised to treat non-local pseudopotential in a…
The theoretical description of non-renewal stochastic systems is a challenge. Analytical results are often not available or can only be obtained under strong conditions, limiting their applicability. Also, numerical results have mostly been…
We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of multi-dimensional non-linear stochastic differential equations, which relies upon discrete-time observations of the state. The…
In plasma edge simulations, kinetic Monte Carlo (MC) is often used to simulate neutral particles and estimate source terms. For large-sized reactors, like ITER and DEMO, high particle collision rates lead to a substantial computational cost…
This work describes a new 1D hybrid approach for modeling atmospheric pressure discharges featuring complex chemistry. In this approach electrons are described fully kinetically using Particle-In-Cell/Monte-Carlo (PIC/MCC) scheme, whereas…
Many physical systems are described by probability distributions that evolve in both time and space. Modeling these systems is often challenging to due large state space and analytically intractable or computationally expensive dynamics. To…
KMCLib is a general framework for lattice kinetic Monte Carlo (KMC) simulations. The program can handle simulations of the diffusion and reaction of millions of particles in one, two, or three dimensions, and is designed to be easily…
We consider the problem of using diffusion models to generate fast, smooth, and temporally consistent robot motions. Although diffusion models have demonstrated superior performance in robot learning due to their task scalability and…
This paper presents an algorithm for Monte Carlo fixed-lag smoothing in state-space models defined by a diffusion process observed through noisy discrete-time measurements. Based on a particles approximation of the filtering and smoothing…
We present a novel way of performing kinetic Monte Carlo simulations which does not require an {\it a priori} list of diffusion processes and their associated energetics and reaction rates. Rather, at any time during the simulation,…
We propose a new Markov Chain Monte Carlo (MCMC) method for constrained target distributions. Our method first maps the $D$-dimensional constrained domain of parameters to the unit ball ${\bf B}_0^D(1)$. Then, it augments the resulting…
Monte Carlo methods are state-of-the-art when it comes to dosimetric computations in radiotherapy. However, the execution time of these methods suffers in high-collisional regimes. We address this problem by introducing a kinetic-diffusion…
The Fokker-Planck equation is a partial differential equation that describes the evolution of a probability distribution over time. It is used to model a wide range of physical and biological phenomena, such as diffusion, chemical…
Path sampling allows the study of rare events like chemical reactions, nucleation and protein folding via a Monte Carlo (MC) exploration in path space. Instead of configuration points, this method samples short molecular dynamics (MD)…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
Motivated by single-molecule experiments on synaptic membrane protein domains, we use a stochastic lattice model to study protein reaction and diffusion processes in crowded membranes. We find that the stochastic reaction-diffusion dynamics…
Partial differential equations (p.d.e) equipped of spatial derivatives of fractional order capture anomalous transport behaviors observed in diverse fields of Science. A number of numerical methods approximate their solutions in dimension…
We present a general method to produce well-conditioned continuum reaction-drift-diffusion equations directly from master equations on a discrete, periodic state space. We assume the underlying data to be kinetic Monte Carlo models (i.e.,…
We present two Diffusion Monte Carlo (DMC) algorithms for systems of ultracold quantum gases featuring synthetic spin-orbit interactions. The first one is a discrete spin generalization of the T- moves spin-orbit DMC, which provides an…