Related papers: Exact simulation of Brownian diffusions with drift…
We introduce methods for large scale Brownian Dynamics (BD) simulation of many rigid particles of arbitrary shape suspended in a fluctuating fluid. Our method adds Brownian motion to the rigid multiblob method at a cost comparable to the…
We obtain exact asymptotic results for the disorder averaged persistence of a Brownian particle moving in a biased Sinai landscape. We employ a new method that maps the problem of computing the persistence to the problem of finding the…
Brownian motion has served as a pilot of studies in diffusion and other transport phenomena for over a century. The foundation of Brownian motion, laid by Einstein, has generally been accepted to be far from being complete since the late…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
Fractional Brownian motion is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically fractional Brownian motion confined to a finite…
This note concerns distributions of Skew Brownian motion with dry friction and its occupation time. These distributions were obtained in [2] by using the Laplace transform and joint characteristic functions. We provide an alternative…
We have studied the temporal evolution of a quantum system subjected to strong dissipation at ultra-low temperatures where the system-bath interaction represents the leading energy scale. In this regime, theory predicts the time evolution…
A new and very general technique for simulating solid-fluid suspensions has been described in a previous paper (Part I); the most important feature of the new method is that the computational cost scales with the number of particles. In…
We study various combinations of active diffusion with branching, as an extension of standard reaction-diffusion processes. We concentrate on the selection of the asymptotic wavefront speed for thermal run-and-tumble and for thermal active…
In this paper, we study reflecting Brownian motion with Poissonian resetting. After providing a probabilistic description of the phenomenon using jump diffusions and semigroups, we analyze the time-reversed process starting from the…
Semimartingale reflecting Brownian motions (SRBMs) are diffusion processes with state space the d-dimensional nonnegative orthant, in the interior of which the processes evolve according to a Brownian motion, and that reflect against the…
This short note is motivated by a recently discovered connection between a drift-diffusion process in $n$-dimensional Euclidean space with a divergence-free drift sampled from a stationary and isotropic Gaussian ensemble of critical scaling…
Activity significantly enhances the escape rate of a Brownian particle over a potential barrier. Whereas constant activity has been extensively studied in the past, little is known about the effect of time-dependent activity on the escape…
Motivated by the phenomenon of transport barriers in fusion plasma devices, we write a mathematical model of heat dispersion in a turbulent fluid with a transport barrier, properly idealized; in a scaling limit of the turbulence model with…
We establish diffusion and fractional Brownian motion approximations for motions in a Markovian Gaussian random field with a nonzero mean.
Brownian dynamics is a popular fine-grained method for simulating systems of interacting particles, such as chemical reactions. Though the method is simple to simulate, it is generally assumed that the dynamics is impossible to solve…
We systematically develop general tools to apply Fukushima's absolute continuity condition. These tools comprise methods to obtain a Hunt process on a locally compact separable metric state space whose transition function has a density…
We propose a method for estimating first passage time densities of one-dimensional diffusions via Monte Carlo simulation. Our approach involves a representation of the first passage time density as expectation of a functional of the…
We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit…
We construct a class of one-dimensional diffusion processes on the particles of branching Brownian motion that are symmetric with respect to the limits of random martingale measures. These measures are associated with the extended extremal…