Related papers: Brownian Dynamics of Globules
We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust,…
We consider the problem of strong existence and uniqueness of a Brownian motion forced to stay in the quadrant by an electrostatic repulsion from the sides that works obliquely. The results are reminiscent of the study of a Brownian motion…
Herein we develop a dynamical foundation for fractional Brownian Motion. A clear relation is established between the asymptotic behaviour of the correlation function and diffusion in a dynamical system. Then, assuming that scaling is…
We consider a family of hard core objects moving as independent Brownian motions confined to a vessel by reflection. These are subject to gravitational forces modeled by drifts. The stationary distribution for the process has many…
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…
We describe a novel method of tracking the rotational motion of clusters of colloidal particles. Our method utilizes rigid body transfor- mations to determine the rotations of a cluster and extends conventional proven particle tracking…
Many stochastic processes in the physical and biological sciences can be modelled as Brownian dynamics with multiplicative noise. However, numerical integrators for these processes can lose accuracy or even fail to converge when the…
Brownian motion of a particle with an arbitrary shape is investigated theoretically. Analytical expressions for the time-dependent cross-correlations of the Brownian translational and rotational displacements are derived from the…
In this note we consider generalized diffusion equations in which the diffusivity coefficient is not necessarily constant in time, but instead it solves a nonlinear fractional differential equation involving fractional Riemann-Liouville…
Anomalous-diffusion, the departure of the spreading dynamics of diffusing particles from the traditional law of Brownian-motion, is a signature feature of a large number of complex soft-matter and biological systems. Anomalous-diffusion…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
We study solutions of a class of one-dimensional continuous reflected backward stochastic Volterra integral equations driven by Brownian motion, where the reflection keeps the solution above a given stochastic process (lower obstacle). We…
We deal with complex spatial diffusion equations with time-fractional derivative and study their stochastic solutions. In particular, we complexify the integral operator solution to the heat-type equation where the time derivative is…
We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of…
We show that solutions of free stochastic differential equations with regular drifts and diffusion coefficients, when considered backwards in time, still satisfy free SDEs for an explicit free Brownian motion and drift. We also study the…
We generalize the Green-Kubo approach, previously applied to bulk systems of spherically symmetric active particles [J. Chem. Phys. 145, 161101 (2016)], to include spatially inhomogeneous activity. The method is applied to predict the…
We construct obliquely reflected Brownian motions in all bounded simply connected planar domains, including non-smooth domains, with general reflection vector fields on the boundary. Conformal mappings and excursion theory are our main…
In this article, we consider non-smooth time-dependent domains and single-valued, smoothly varying directions of reflection at the boundary. In this setting, we first prove existence and uniqueness of strong solutions to stochastic…
One century after Einstein's work, Brownian Motion still remains both a fundamental open issue and a continous source of inspiration for many areas of natural sciences. We first present a discussion about stochastic and deterministic…
We obtain a stochastic differential equation (SDE) satisfied by the first $n$ coordinates of a Brownian motion on the unit sphere in $\mathbb{R}^{n+\ell}$. The SDE has non-Lipschitz coefficients but we are able to provide an analysis of…