Related papers: Brownian Motion after Einstein: Some new applicati…
We consider the degenerate Einsteins Brownian motion model when the time interval of the moving particles before the collisions, is reciprocal to the number of particles per unit volume u(x,t), at the point of observation x at time t. The…
Starting with a Brownian motion, we define and study a novel diffusion process by combining stickiness and oscillation properties. The associated stochastic differential equation, resolvent and semigroup are provided. Also the trivariate…
A fully quantum treatment of Einstein's Brownian motion is given, showing in particular the role played by the two original requirements of translational invariance and connection between dynamics of the Brownian particle and atomic nature…
Brownian motions in the infinite-dimensional group of all unitary operators are studied under strong continuity assumption rather than norm continuity. Every such motion can be described in terms of a countable collection of independent…
On the occasion of the 100th anniversary of the beginning of the revolutionary contributions to physics by Einstein, I am happy to respond to a problem posed by him in 1905. He said: In this paper it will be shown that according to the…
We investigate the motility of a growing population of cells in a idealized setting: we consider a system of hard disks in which new particles are added according to prescribed growth kinetics, thereby dynamically changing the number…
A new extension of the sub-fractional Brownian motion, and thus of the Brownian motion, is introduced. It is a linear combination of a finite number of sub-fractional Brownian motions, that we have chosen to call the mixed sub-fractional…
In this article we explore the phenomena of nonequilibrium stochastic process starting from the phenomenological Brownian motion. The essential points are described in terms of Einstein's theory of Brownian motion and then the theory…
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…
Optical tweezers are tools made of light that enable contactless pushing, trapping, and manipulation of objects ranging from atoms to space light sails. Since the pioneering work by Arthur Ashkin in the 1970s, optical tweezers have evolved…
As the title suggests, we will describe (and justify through the presentation of some of the relevant mathematics) prediction methodologies for sensor measurements. This exposition will mainly be concerned with the mathematics related to…
Sticky Brownian motion is the simplest example of a diffusion process that can spend finite time both in the interior of a domain and on its boundary. It arises in various applications such as in biology, materials science, and finance.…
The problem of Brownian motion in a periodic potential, under the influence of external forcing, which is either random or periodic in time, is studied in this paper. Multiscale techniques are used to derive general formulae for the steady…
We study the motion of a solid particle immersed in a Newtonian fluid and confined between two parallel elastic membranes possessing shear and bending rigidity. The hydrodynamic mobility depends on the frequency of the particle motion due…
The paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and…
We present a method to design driving protocols that achieve fast thermal equilibration of a system of interest using techniques inspired by machine learning training algorithms. For example, consider a Brownian particle manipulated by…
Brownian motion (BM) is pivotal in natural science for the stochastic motion of microscopic droplets. In this study, we investigate BM driven by thermal composition noise at sub-micro scales, where inter-molecular diffusion and surface…
Circular Dyson Brownian motion describes the Brownian dynamics of particles on a circle (periodic boundary conditions), interacting through a logarithmic, long-range two-body potential. Within the log-gas picture of random matrix theory, it…
In this work we introduce and study fractional measure theoretic elliptic operators on the torus and a new stochastic process named W-Brownian motion. We establish some regularity and spectral results related to the operators cited above,…
Over a century ago, Einstein formulated a precise mathematical model for describing Brownian motion. While this model adequately explains the diffusion of micron-sized particles in fluids, its limitations become apparent when applied to…