Related papers: Mixed analytical-stochastic simulation method for …
We develop a computational approach to locate the source of a steady-state gradient of diffusing particles from the fluxes through narrow windows distributed either on the boundary of a three dimensional half-space or on a sphere. This…
Recovering the position of a source from the fluxes of diffusing particles through small receptors allows a biological cell to determine its relative position, spatial localization and guide it to a final target. However, how a source can…
Brownian simulations can be used to generate statistics relevant for studying molecular interactions or trafficking. However, the concurrent simulation of many Brownian trajectories at can become computationally intractable. Replacing…
When a flux of Brownian particles is injected in a narrow window located on the surface of a bounded domain, these particles diffuse and can eventually escape through a cluster of narrow windows. At steady-state, we compute asymptotically…
We investigate the Brownian diffusion of particles in one spatial dimension and in the presence of finite regions within which particles can either evaporate or be reset to a given location. For open boundary conditions, we highlight the…
We develop a formally exact technique for obtaining steady-state distributions of non-interacting active Brownian particles in a variety of systems. Our technique draws on results from the theory of two-way diffusion equations to solve the…
We investigate a diffusive motion of a system of interacting Brownian particles in quasi-one-dimensional micropores. In particular, we consider a semi-infinite 1D geometry with a partially absorbing boundary and the hard-core inter-particle…
In the context of PDE-constrained optimization theory, source identification problems traditionally entail particles emerging from an unknown source distribution inside a domain, moving according to a prescribed stochastic process,…
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…
How can cells embedded into a gradient concentration triangulate the position of the source and migrate toward their final destination? The source triangulation requires to recover the three dimensional coordinates of the source from the…
The motion of weakly inertial Brownian particles, transported by steady two-dimensional fluid flows, is investigated by means of asymptotic methods. We focus on the phenomenon of noise-induced separatrix crossing, which can force particles…
Stochastically gated interfaces play an important role in a variety of cellular diffusion processes. Examples include intracellular transport via stochastically gated ion channels and pores in the plasma membrane of a cell, intercellular…
We study the dynamics of overdamped Brownian particles diffusing in conservative force fields and undergoing stochastic resetting to a given location with a generic space-dependent rate of resetting. We present a systematic approach…
This work proposes a method for the two-dimensional simulation of Brownian particles in a fluid with restrictions. The method is based on simple numerical rules between two matrices. One of the matrix represent the identification of all…
The stochastic motion of particles in living cells is often spatially inhomogeneous with a higher effective diffusivity in a region close to the cell boundary due to active transport along actin filaments. As a first step to understand the…
There is considerable current interest in the emergence of statistical correlations within a population of otherwise non-interacting Brownian particles subject to a common fluctuating environment or drive. Examples include global stochastic…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
For optimizing a non-convex function in finite dimension, a method is to add Brownian noise to a gradient descent, allowing for transitions between basins of attractions of different minimizers. To adapt this for optimization over a space…
Our object is to formulate and analyze a physically plausible and mathematically sound model to better understand the phenomenon of clumping in colloid dispersions. Our model is stochastic but rigorously derived from a deterministic setup…
In this paper we discuss the analysis of a cross-diffusion PDE system for a mixture of hard spheres, which was derived by Bruna and Chapman from a stochastic system of interacting Brownian particles using the method of matched asymptotic…