Related papers: Lenses in Skew Brownian Flow
It is well-known that a stochastic differential equation (sde) on a Euclidean space driven by a (possibly infinite-dimensional) Brownian motion with Lipschitz coefficients generates a stochastic flow of homeomorphisms. If the Lipschitz…
We consider the system of sticky-reflected Brownian particles on the real line proposed in [arXiv:1711.03011]. The model is a modification of the Howitt-Warren flow but now the diffusion rate of particles is inversely proportional to the…
In many physical situations involving diverse length scales, waves or rays representing them travel through media characterized by spatially smooth, random, modest refactive index variations. "Primary" diffraction (by individual…
A non-linear differential equation arising from a stochastic process known as branching Brownian motion is considered. We find an explicit solution and show the uniqueness of the solution under some boundedness conditions using…
Motivated by the probabilistic representation for solutions of the Navier-Stokes equations, we introduce a novel class of stochastic differential equations that depend on the entire flow of its time marginals. We establish the existence and…
We introduce a technique to merge two biased Brownian motions into a single regular process. The outcome follows a stochastic differential equation with a constant diffusion coefficient and a non-linear drift. The emerging stochastic…
Given a one-dimensional stochastic differential equation, one can associate to this equation a stochastic flow on $[0,+\infty )$, which has an absorbing barrier at zero. Then one can define its dual stochastic flow. In \cite{AW}, Akahori…
A recent first-principles approach to the non-linear rheology of dense colloidal suspensions is evaluated and compared to simulation results of sheared systems close to their glass transitions. The predicted scenario of a universal…
We consider the problem of leakage or effusion of an ensemble of independent stochastic processes from a region where they are initially randomly distributed. The case of Brownian motion, initially confined to the left half line with…
We study a system of reflected Brownian motions on the positive half-line in which each particle has a drift toward the origin determined by the local times at the origin of all the particles. If this local time drift is too strong, such…
We study the linear response of interacting active Brownian particles in an external potential to simple shear flow. Using a path integral approach, we derive the linear response of any state observable to initiating shear in terms of…
Geometrical optics provides an instructive insight into Brownian motion, ``pushed" into a large-deviations regime by imposed constraints. Here we extend geometrical optics of Brownian motion by accounting for diffusion inhomogeneity in…
A discrete model of traffic on a multilane road is considered. The traffic is presented as particles movement with a deterministic component and a stochastic one. Formulas for the traffic characteristics have been found. The model can…
In this article, we introduce the notion of stochastic symmetry of a differential equation. It consists in a stochastic flow that acts over a solution of a differential equation and produces another solution of the same equation. In the…
We construct a two-dimensional diffusion process with rank-dependent local drift and dispersion coefficients, and with a full range of patterns of behavior upon collision that range from totally frictionless interaction, to elastic…
Branched flow can be observed when a laser beam is coupled into a soap film. This research theoretically explored the phenomenon through analogy between light wave and particles in form of Hamilton-Jacobian equation, further discussed the…
The purpose of this note is to give an example of stochastic flows of kernels, which naturally interpolates between the Arratia coalescing flow associated with systems of coalescing independent Brownian particles on the circle and the…
For a system of Brownian particles interacting via a soft exponential potential we investigate the interaction between equilibrium crystallization and spatially varying shear flow. For thermodynamic state points within the liquid part of…
In this paper, we consider two skew Brownian motions, driven by the same Brownian motion, with different starting points and different skewness coefficients. We show that we can describe the evolution of the distance between the two…
The nonlinear rheological properties of dense suspensions are discussed within simplified models, suggested by a recent first principles approach to the model of Brownian particles in a constant-velocity-gradient solvent flow. Shear…