arXiv subjects

Udo Erdmann

Publications and source records attributed to Udo Erdmann.

7 recordsLinked to original sources

arXiv2010

Collective motion of active Brownian particles in one dimension

We analyze a model of active Brownian particles with non-linear friction and velocity coupling in one spatial dimension. The model exhibits two modes of motion observed in biological swarms: A disordered phase with vanishing mean velocity and an ordered phase with finite mean velocity. Starting from the microscopic Langevin equations, we derive mean-field equations of the collective dynamics. We identify the fixed points of the mean-field equations corresponding to the two modes and analyze their stability with respect to the model parameters. Finally, we compare our analytical findings with numerical simulations of the microscopic model.

cond-mat.stat-mech↗

arXiv2005

On the attractors of two-dimensional Rayleigh oscillators including noise

We study sustained oscillations in two-dimensional oscillator systems driven by Rayleigh-type negative friction. In particular we investigate the influence of mismatch of the two frequencies. Further we study the influence of external noise and nonlinearity of the conservative forces. Our consideration is restricted to the case that the driving is rather weak and that the forces show only weak deviations from radial symmetry. For this case we provide results for the attractors and the bifurcations of the system. We show that for rational relations of the frequencies the system develops several rotational excitations with right/left symmetry, corresponding to limit cycles in the four-dimensional phase space. The corresponding noisy distributions have the form of hoops or tires in the four-dimensional space. For irrational frequency relations, as well as for increasing strength of driving or noise the periodic excitations are replaced by chaotic oscillations.

nlin.AO↗

arXiv2004

Noise-Induced Transition from Translational to Rotational Motion of Swarms

We consider a model of active Brownian agents interacting via a harmonic attractive potential in a two-dimensional system in the presence of noise. By numerical simulations, we show that this model possesses a noise-induced transition characterized by the breakdown of translational motion and the onset of swarm rotation as the noise intensity is increased. Statistical properties of swarm dynamics in the weak noise limit are further analytically investigated.

physics.bio-ph↗

arXiv2004

Advantages of Hopping on a Zig-zag Course

We investigate self-moving particles which prefer to hop with a certain turning angle equally distributed to the right or left. We assume this turning angle distribution to be given by a double Gaussian distribution. Based on the model of Active Brownian particles and we calculate the diffusion coefficient in dependence on the mean and the dispersion of the turning angles. It is shown that bounded distribution of food in patches will be optimally consumed by the objects if they hop preferably with a given angle and not straight forwardly.

q-bio.PE↗

arXiv2004

Active Brownian Particle and Random Walk Theories of the Motions of Zooplankton: Application to Experiments with Swarms of Daphnia

Active Brownian Particles are self-propelled particles that move in a dissipative medium subject to random forces, or noise . Additionally, they can be confined by an external field and/or they can interact with one another. The external field may actually be an attractive marker, for example a light field (as in the experiment) or an energy potential or a chemical gradient (as in the theory). The potential energy can also be the result of interparticle attractive and/or repulsive forces summed over all particles (a mean field potential). Four, qualitatively different motions of the particles are possible: at small particle density their motions are approximately independent of one another subject only to the external field and the noise, which results in moving randomly through or performing rotational motions about a central point in space. At increasing densities interactions play an important role and individuals form a swarm performing several types of self-organized collective motion. We apply this model for the description of zooplankton Daphnia swarms. In the case of the zooplankton Daphnia (and probably many other aquatic animals that form similar motions as well) this vortex is hydrodynamical but motivated by the self-propelled motion of the individuals. Similar vortex-type motions have been observed for other creatures ranging in size from bacteria to flocks of birds and schools of fish. However, our experiment with Daphnia is unique in that all four motions can be observed in controlled laboratory conditions with the same animal. Moreover, the theory, presented in both continuous differential equation and random walk forms, offers a quantitative, physically based explanation of the four motions.

q-bio.PE↗

arXiv2003

Nonequilibrium statistical mechanics of swarms of driven particles

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 and the theory of canonical-dissipative systems. Free motion and motion of a swarms confined in an external field is studied. Briefly the case of particles confined on a ring and interacting by repulsive forces is studied. In more detail we investigate self-confinement by Morse-type attracting forces. We begin with pairs N = 2; the attractors and distribution functions are discussed, then the case N > 2 is discussed. Simulations for several dynamical modes of swarms of active Brownian particles interacting by Morse forces are presented. In particular we study rotations, drift, fluctuations of shape and cluster formation.

cond-mat.stat-mech↗

arXiv1999

Brownian Particles far from Equilibrium

We study a model of Brownian particles which are pumped with energy by means of a non-linear friction function, for which different types are discussed. A suitable expression for a non-linear, velocity-dependent friction function is derived by considering an internal energy depot of the Brownian particles. In this case, the friction function describes the pumping of energy in the range of small velocities, while in the range of large velocities the known limit of dissipative friction is reached. In order to investigate the influence of additional energy supply, we discuss the velocity distribution function for different cases. Analytical solutions of the corresponding Fokker-Planck equation in 2d are presented and compared with computer simulations. Different to the case of passive Brownian motion, we find several new features of the dynamics, such as the formation of limit cycles in the four-dimensional phase-space, a large mean squared displacement which increases quadratically with the energy supply, or non-equilibrium velocity distributions with crater-like form. Further, we point to some generalizations and possible applications of the model.

cond-mat.stat-mech↗