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We develop a theory of fluctuations for Brownian systems with weak long-range interactions. For these systems, there exists a critical point separating a homogeneous phase from an inhomogeneous phase. Starting from the stochastic…
We study interacting systems of linear Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. Our main objective has been to study the long range behavior of the…
We use the Fokker-Planck equation and its moment equations to study the collective behavior of interacting particles in unsteady one-dimensional flows. Particles interact according to a long-range attractive and a short-range repulsive…
Brownian motion is modelled by a harmonic oscillator (Brownian particle) interacting with a continuous set of uncoupled harmonic oscillators. The interaction is linear in the coordinates and the momenta. The model has an analytical solution…
We study the role of fluctuations in particle systems modeled by Dean-Kawasaki-type equations, which describe the evolution of particle densities in systems with Brownian motion. By comparing microscopic simulations, stochastic partial…
We provide a comprehensive analysis of the positional dynamics and average thermodynamics of an overdamped Brownian particle subject to both, harmonic confinement and annealed disorder due to a temporarily fluctuating trap stiffness. We…
Nonintersecting motion of Brownian particles in one dimension is studied. The system is constructed as the diffusion scaling limit of Fisher's vicious random walk. N particles start from the origin at time t=0 and then undergo mutually…
A thermal analogue of the classical brachistochrone problem, which minimizes the connection time between two equilibrium states of harmonically confined Brownian particles, has recently been solved theoretically. Here we report its…
In the coarse grained Brownian Dynamics simulation method the many solvent molecules are replaced by random thermal kicks and an effective friction acting on the particles of interest. For Brownian Dynamics the friction has to be so strong…
Collective motions emerging from the interaction of autonomous mobile individuals play a key role in many phenomena, from the growth of bacterial colonies to the coordination of robotic swarms. For these collective behaviours to take hold,…
Active matter systems - such as a collection of active colloidal particles - operate far from equilibrium with complex inter-particle interactions that govern their collective dynamics. Predicting the collective dynamics of such systems may…
Depletion interactions between colloidal particles dispersed in a fluid medium are effective interactions induced by the presence of other types of colloid. They are not instantaneous but build up in time. We show by means Brownian dynamics…
Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing…
The same system can exhibit a completely different dynamical behavior when it evolves in equilibrium conditions or when it is driven out-of-equilibrium by, e.g., connecting some of its components to heat baths kept at different…
We investigate motility-induced phase separation of active Brownian particles, which are modeled as purely repulsive spheres that move due to a constant swim force with freely diffusing orientation. We develop on the basis of power…
In this paper, we introduce a new stochastic process of $N$ interacting particles on the line that evolve via Dyson Brownian motion (DBM) with Dyson's index $\beta > 0$ and undergo simultaneous resetting to their initial positions at a…
This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential…
This study analyses the dynamical consequences of heterogeneous temporal delays within a quorum sensing-inspired (QS-inspired) system, specifically addressing the differential response kinetics of two sub-populations to signalling…
The structural and dynamical properties of suspensions of self-propelled Brownian particles of spherical shape are investigated in three spatial dimensions. Our simulations reveal a phase separation into a dilute and a dense phase, above a…
We investigate the emergent interactions between two active Brownian particles coupled by an attractive harmonic potential and in contact with a thermal reservoir. By analyzing the stationary distribution of their separation, we demonstrate…