Brownian dynamics of a microswimmer

We report on dynamic properties of a simple model microswimmer composed of three spheres and propelling itself in a viscous fluid by spinning motion of the spheres under zero net torque constraint. At a fixed temperature and increasing the spinning frequency, the swimmer demonstrates a transition from dissipation-dominated to a pumping-dominated motion regime characterized by negative effective friction coefficient. In the limit of high frequencies, the diffusion of the swimmer can be described by a model of an active particle with constant velocity.Comment: Submitte

Crossover from Non-Equilibrium to Equilibrium Behavior in the Time-Dependent Kondo Model

We investigate the equilibration of a Kondo model that is initially prepared in a non-equilibrium state towards its equilibrium behavior. Such initial non-equilibrium states can e.g. be realized in quantum dot experiments with time-dependent gate voltages. We evaluate the non-equilibrium spin-spin correlation function at the Toulouse point of the Kondo model exactly and analyze the crossover between non-equilibrium and equilibrium behavior as the non-equilibrium initial state evolves as a function of the waiting time for the first spin measurement. Using the flow equation method we extend these results to the experimentally relevant limit of small Kondo couplings.Comment: 4 pages, 2 figures; revised version contains added references and improved layout for figure

Orientational hysteresis in swarms of active particles in external field

Structure and ordering in swarms of active particles have much in common with condensed matter systems like magnets or liquid crystals. A number of important characteristics of such materials can be obtained via dynamic tests such as hysteresis. In this work, we show that dynamic hysteresis can be observed also in swarms of active particles and possesses similar properties to the counterparts in magnetic materials. To study the swarm dynamics, we use computer simulations of the active Brownian particle model with dissipative interactions. The swarm is confined to a narrow linear channel and the one-dimensional polar order parameter is measured. In an oscillating external field, the order parameter demonstrates dynamic hysteresis with the shape of the loop and its area varying with the amplitude and frequency of the applied field, swarm density and the noise intensity. We measure the scaling exponents for the hysteresis loop area, which can be associated with the controllability of the swarm. Although the exponents are non-universal and depend on the system's parameters, their limiting values can be predicted using a generic model of dynamic hysteresis. We also discuss similarities and differences between the swarm ordering dynamics and two-dimensional magnets

Statistical properties of swarms of self-propelled particles with repulsions across the order-disorder transition

We study dynamic self-organisation and order-disorder transitions in a two-dimensional system of self-propelled particles. Our model is a variation of the Vicsek model, where particles align the motion to their neighbours but repel each other at short distances. We use computer simulations to measure the orientational order parameter for particle velocities as a function of intensity of internal noise or particle density. We show that in addition to the transition to an ordered state on increasing the particle density, as reported previously, there exists a transition into a disordered phase at the higher densities, which can be attributed to the destructive action of the repulsions. We demonstrate that the transition into the ordered phase is accompanied by the onset of algebraic behaviour of the two-point velocity correlation function and by a non-monotonous variation of the velocity relaxation time. The critical exponent for the decay of the velocity correlation function in the ordered phase depends on particle concentration at low densities but assumes a universal value in more dense systems.Comment: Submitted to EPJ

Tricritical points in a Vicsek model of self-propelled particles with bounded confidence

We study the orientational ordering in systems of self-propelled particles with selective interactions. To introduce the selectivity we augment the standard Vicsek model with a bounded-confidence collision rule: a given particle only aligns to neighbors who have directions quite similar to its own. Neighbors whose directions deviate more than a fixed restriction angle $\alpha$ are ignored. The collective dynamics of this systems is studied by agent-based simulations and kinetic mean field theory. We demonstrate that the reduction of the restriction angle leads to a critical noise amplitude decreasing monotonically with that angle, turning into a power law with exponent 3/2 for small angles. Moreover, for small system sizes we show that upon decreasing the restriction angle, the kind of the transition to polar collective motion changes from continuous to discontinuous. Thus, an apparent tricritical point is identified and calculated analytically. We also find that at very small interaction angles the polar ordered phase becomes unstable with respect to the apolar phase. We show that the mean-field kinetic theory permits stationary nematic states below a restriction angle of $0.681 \pi$. We calculate the critical noise, at which the disordered state bifurcates to a nematic state, and find that it is always smaller than the threshold noise for the transition from disorder to polar order. The disordered-nematic transition features two tricritical points: At low and high restriction angle the transition is discontinuous but continuous at intermediate $\alpha$. We generalize our results to systems that show fragmentation into more than two groups and obtain scaling laws for the transition lines and the corresponding tricritical points. A novel numerical method to evaluate the nonlinear Fredholm integral equation for the stationary distribution function is also presented.Comment: 20 pages, 18 figure

Electrostatic Interaction of Heterogeneously Charged Surfaces with Semipermeable Membranes

In this paper we study the electrostatic interaction of a heterogeneously charged wall with a neutral semipermeable membrane. The wall consists of periodic stripes, where the charge density varies in one direction. The membrane is in a contact with a bulk reservoir of an electrolyte solution and separated from the wall by a thin film of salt-free liquid. One type of ions (small counterions) permeates into the gap and gives rise to a distance-dependent membrane potential, which translates into a repulsive electrostatic disjoining pressure due to an overlap of counterion clouds in the gap. To quantify it we use two complementary approaches. First, we propose a mean-field theory based on a linearized Poisson-Boltzmann equation and Fourier analysis. These calculations allow us to estimate the effect of a heterogeneous charge pattern at the wall on the induced heterogeneous membrane potential, and the value of the disjoining pressure as a function of the gap. Second, we perform Langevin dynamics simulations of the same system with explicit ions. The results of the two approaches are in good agreement with each other at low surface charge and small gap, but differ due to nonlinearity at the higher charge. These results demonstrate that a heterogeneity of the wall charge can lead to a huge reduction in the electrostatic repulsion, which could dramatically facilitate a self-assembly in complex synthetic and biological systems.Comment: 14 pages, 6 figure

Electrophoresis of Janus Particles: a Molecular Dynamics simulation study

In this work, we use Molecular Dynamics and Lattice-Boltzmann simulations to study the properties of charged Janus particles in an electric field. We show that for relatively small net charge and thick electrostatic diffuse layer mobilities of Janus particles and uniformly charged colloids of the same net charge are identical. However, for higher charges and thinner diffuse layers Janus particles always show lower electrophoretic mobility. We also demonstrate that Janus particles align with the electric field and the angular deviation from the field's direction are related to their dipole moment. We show that the latter is affected by the thickness of the electrostatic diffuse layer and strongly correlates with the electrophoretic mobility.Comment: Accepted to JC

Colloidal electrophoresis: Scaling analysis, Green-Kubo relation, and numerical results

We consider electrophoresis of a single charged colloidal particle in a finite box with periodic boundary conditions, where added counterions and salt ions ensure charge neutrality. A systematic rescaling of the electrokinetic equations allows us to identify a minimum set of suitable dimensionless parameters, which, within this theoretical framework, determine the reduced electrophoretic mobility. It turns out that the salt-free case can, on the Mean Field level, be described in terms of just three parameters. A fourth parameter, which had previously been identified on the basis of straightforward dimensional analysis, can only be important beyond Mean Field. More complicated behavior is expected to arise when further ionic species are added. However, for a certain parameter regime, we can demonstrate that the salt-free case can be mapped onto a corresponding system containing additional salt. The Green-Kubo formula for the electrophoretic mobility is derived, and its usefulness demonstrated by simulation data. Finally, we report on finite-element solutions of the electrokinetic equations, using the commercial software package COMSOL.Comment: To appear in Journal of Physics: Condensed Matter - special issue on occasion of the CODEF 2008 conferenc