Related papers: Propagator for a driven Brownian particle in step …
In this paper, we introduce a mathematical model to describe the nanoparticles transport carried by a two-phase flow in a porous medium including gravity, capillary forces and Brownian diffusion. Nonlinear iterative IMPES scheme is used to…
The proper time formalism for a particle propagator in an external electromagnetic field is combined with the path-dependent formulation of the gauge theory to simplify the quasiclassical propagator. The latter is achieved due to a specific…
We consider the stochastic target problem of finding the collection of initial laws of a mean-field stochastic differential equation such that we can control its evolution to ensure that it reaches a prescribed set of terminal probability…
We consider a family of branching-selection particle systems in which particles branch at time dependent rate $r$ and are killed with a probability which is dependent on their rank via some function $\psi$. We show that, under fairly…
Brownian dynamics play a key role in understanding the diffusive transport of micro particles in a bounded environment. In geometries containing confining walls, physical laws determine the behavior of the random trajectories at the…
Recent experimental studies have demonstrated that cellular motion can be directed by topographical gradients, such as those resulting from spatial variations in the features of a micropatterned substrate. This phenomenon, known as…
In order to optimize the directed motion of an inertial Brownian motor, we identify the operating conditions that both maximize the motor current and minimize its dispersion. Extensive numerical simulation of an inertial rocked ratchet…
This chapter aims at emphasizing the crucial role of partial reactivity of a catalytic surface or a target molecule in diffusion-controlled reactions. We discuss various microscopic mechanisms that lead to imperfect reactions, the Robin…
We describe a simple numerical simulation, suitable for an undergraduate project (or graduate problem set), of the Brownian motion of a particle in a Hooke-law potential well. Understanding this physical situation is a practical necessity…
We propose a simulation method for Brownian dynamics of hard rods in one dimension for arbitrary continuous external force fields. It is an event-driven procedure based on the fragmentation and mergers of clusters formed by particles in…
While it is very common to model diffusion as a random walk by assuming memorylessness of the trajectory and diffusive step lengths, these assumptions can lead to significant errors. This paper describes the extent to which a physical…
A propagator for the one dimensional time-dependent Schr\"odinger equation with an asymmetric rectangular potential is obtained using the multiple-scattering theory approach. It allows for the consideration of the reflection and…
We show that, under certain smoothness conditions, a Brownian martingale at a fixed time can be represented as an exponential of its value at a later time. The time-dependent generator of this exponential operator is equal to one half times…
We introduce a Predictor-Corrector type method suitable for performing many-particle Brownian Dynamics simulations. Since the method goes over to the Gear's method for Molecular Dynamics simulation in the limit of vanishing friction, we…
We study pathwise approximation of scalar stochastic differential equations at a single point. We provide the exact rate of convergence of the minimal errors that can be achieved by arbitrary numerical methods that are based (in a…
A propagator-based approach is investigated for Monte-Carlo (MC) modeling of neutral particles transport in fusion boundary plasmas. The propagator is essentially a Green function for the neutral kinetic equation, which depends on the…
We introduce the idea of {\it collisional models} for Brownian particles, in which a particle is sequentially placed in contact with distinct thermal environments and external forces. Thermodynamic properties are exactly obtained,…
The emergent dynamics in phase-separated mixtures of isometric active and passive Brownian particles is studied numerically in two dimensions. A novel steady-state of well-defined traveling fronts is observed, where the interface between…
The Brownian dynamics of a single microorganism coupled by chemotaxis to a diffusing concentration field which is secreted by the microorganism itself is studied by computer simulations in spatial dimensions $d=1,2,3$. Both cases of a…
The Active Brownian Particle (ABP) model exemplifies a wide class of active matter particles. In this work, we demonstrate how this model can be cast into a field theory in both two and three dimensions. Our aim is manifold: we wish both to…