Related papers: Programmable Persistent Random Walks in Active Bro…
Continuous-time random walks offer powerful coarse-grained descriptions of transport processes. We here microscopically derive such a model for a Brownian particle diffusing in a deep periodic potential. We determine both the waiting-time…
We study systems of interacting Brownian particles in one dimension constructed as the diffusion scaling limits of Fisher's vicious walk models. We define two types of nonintersecting Brownian motions, in which we impose no condition (resp.…
We consider an active Brownian particle moving in a disordered two-dimensional energy or motility landscape. The averaged mean-square-displacement (MSD) of the particle is calculated analytically within a systematic short-time expansion. As…
We consider a previously devised model describing Levy random walks (Phys. Rev E 79, 011110; 80, 031148, (2009)). It is demonstrated numerically that the given model describes Levy random walks with superdiffusive, ballistic, as well as…
We consider one-dimensional systems comprising either active run-and-tumble particles (RTPs) or passive Brownian random walkers. These particles are either noninteracting or have hardcore exclusions. We study the dynamics of a single tracer…
A drop bouncing on a vertically-vibrated surface may self-propel forward by standing waves and travels along a fluid interface. This system called walking drop forms a non-quantum wave-particle association at the macroscopic scale. The…
Elastic confinements are an important component of many biological systems and dictate the transport properties of suspended particles under flow. In this chapter, we review the Brownian motion of a particle moving in the vicinity of a…
Particles kicked by external forces to produce mobility distinct from thermal diffusion are an iconic feature of the active matter problem. Here, we map this onto a minimal model for experiment and theory covering the wide time and length…
Swimmers and self-propelled particles are physical models for the collective behaviour and motility of a wide variety of living systems, such as bacteria colonies, bird flocks and fish schools. Such artificial active materials are amenable…
A colloidal suspension of active Brownian particles (ABPs) driven by controllable forces into directed or persistent motions can serve as a model for understanding the biological systems. Experiments and numerical simulations are…
Complex systems display anomalous diffusion, whose signature is a space/time scaling $x\sim t^\delta$ with $\delta \ne 1/2$ in the Probability Density Function (PDF). Anomalous diffusion can emerge jointly with both Gaussian, e.g.,…
We present a generalized energy-depot model in which the conversion rate of the internal energy into motion can be dependent on the position and the velocity of a particle. When the conversion rate is a general function of the velocity, the…
In this thesis, branching Brownian motion (BBM) is a random particle system where the particles diffuse on the real line according to Brownian motions and branch at constant rate into a random number of particles with expectation greater…
As a rough model for the collective motions of cells and organisms we develop here the statistical mechanics of swarms of self-propelled particles. Our approach is closely related to the recently developed theory of active Brownian motion…
Self-propelled particles possessing permanent magnetic dipole moments occur naturally in magnetotactic bacteria and in man-made systems like active colloids or micro-robots. Yet, the interplay between self-propulsion and anisotropic…
We investigate a two-dimensional system of active particles confined to a narrow annular domain. Despite the absence of explicit interactions among the velocities or the active forces of different particles, the system displays a transition…
Numerical algorithms are proposed for simulating the Brownian dynamics of charged particles in an external magnetic field, taking into account the Brownian motion of charged particles, damping effect and the effect of magnetic field…
Scaled Brownian motion (SBM) is widely used to model anomalous diffusion of passive tracers in complex and biological systems. It is a highly non-stationary process governed by the Langevin equation for Brownian motion, however, with a…
Collective rotations are common in active matter, enhancing cohesion, transport, and mixing. They are typically attributed to chiral non-reciprocal dynamics due to intrinsic particle chirality, torque-generating interactions among units, or…
Mixtures of active and passive particles are ubiquitous at the microscale. Many essential microbial processes involve interactions with dead or immotile cells or passive crowders. When passive objects are immersed in active baths, their…