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After summarizing basic features of self-organization such as entropy export, feedbacks and nonlinear dynamics, we discuss several examples in biology. The main part of the paper is devoted to a model of active Brownian motion that allows a…
In this work we studied the diffusive behavior of active brownian particles under lateral parabolic confinement. The results showed that we go from subdiffusion to ballistic motion as we vary the angular noise strength and confinement…
We analyse large deviations of the dynamical activity in one-dimensional systems of diffusing hard particles. Using an optimal-control representation of the large-deviation problem, we analyse effective interaction forces which can be added…
Using Brownian vibrators, we conducted a study on the structures and dynamics of quasi-2d granular materials with packing fractions ($\phi$) ranging from 0.111 to 0.832. Our observations revealed a remarkable large-scale collective motion…
We present a class of stochastic processes in which the large deviation functions of time-integrated observables exhibit singularities that relate to dynamical phase transitions of trajectories. These illustrative examples include Brownian…
These lecture notes are designed to provide a brief introduction into the phenomenology of active matter and to present some of the analytical tools used to rationalize the emergent behavior of active systems. Such systems are made of…
We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and…
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…
Rare transitions between long-lived metastable states underlie a great variety of physical, chemical and biological processes. Our quantitative understanding of reactive mechanisms has been driven forward by the insights of transition state…
Phase separation in a low-density gas-like phase and a high-density liquid-like one is a common trait of biological and synthetic self-propelling particles' systems. The competition between motility and stochastic forces is assumed to fix…
Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states, and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies,…
Self-propelled active matter can exhibit vastly different behavior than systems with purely Brownian motion. In Eur. Phys. J. E 40, 23 (2017), Zeitz, Wolf, and Stark compared an active matter particle with a Brownian particle moving in a…
We examine the collective states of run-and-tumble active matter disks driven over a periodic obstacle array. When the drive is applied along a symmetry direction of the array, we find a clog-free uniform liquid state for low activity,…
Active Brownian particles (ABPs) are termed out to be a successful way of modeling the moving microorganism on the substrate. In recent studies, it is shown that such organisms can sense the characteristics of the substrate. Motivated by…
We revisit the elementary problem of moving a particle in a harmonic trap in finite time with minimal work cost, and extend it to the case of an active particle. By comparing the Gaussian case of an Active Ornstein-Uhlenbeck particle and…
We explore the dynamics of active elements performing persistent random motion with fluctuating active speed and in the presence of translational noise in a $d$-dimensional harmonic trap, modeling active speed generation through an…
It is well known that path probabilities of Brownian motion correspond to the equilibrium configurational probabilities of flexible Gaussian polymers, while those of active Brownian motion correspond to in-extensible semiflexible polymers.…
Ensemble data assimilation is a problem in determining the most likely phase space trajectory of a model of an observed dynamical sys- tem as it receives inputs from measurements passing information to the model. Using methods developed in…
We study motion of tagged particles in a harmonic chain of active particles. We consider three models of active particle dynamics - run and tumble particle, active Ornstein-Uhlenbeck particle and active Brownian particle. We investigate the…
Using simulations, we examine the average velocity as a function of applied drift force for active matter particles moving through a random obstacle array. We find that for low drift force, there is an initial flow regime where the mobility…