403 research outputs found
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.Comment: 11 pages, 2 figure
Active Brownian Particles. From Individual to Collective Stochastic Dynamics
We review theoretical models of individual motility as well as collective
dynamics and pattern formation of active particles. We focus on simple models
of active dynamics with a particular emphasis on nonlinear and stochastic
dynamics of such self-propelled entities in the framework of statistical
mechanics. Examples of such active units in complex physico-chemical and
biological systems are chemically powered nano-rods, localized patterns in
reaction-diffusion system, motile cells or macroscopic animals. Based on the
description of individual motion of point-like active particles by stochastic
differential equations, we discuss different velocity-dependent friction
functions, the impact of various types of fluctuations and calculate
characteristic observables such as stationary velocity distributions or
diffusion coefficients. Finally, we consider not only the free and confined
individual active dynamics but also different types of interaction between
active particles. The resulting collective dynamical behavior of large
assemblies and aggregates of active units is discussed and an overview over
some recent results on spatiotemporal pattern formation in such systems is
given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte
Canonical active Brownian motion
Active Brownian motion is the complex motion of active Brownian particles.
They are active in the sense that they can transform their internal energy into
energy of motion and thus create complex motion patterns. Theories of active
Brownian motion so far imposed couplings between the internal energy and the
kinetic energy of the system. We investigate how this idea can be naturally
taken further to include also couplings to the potential energy, which finally
leads to a general theory of canonical dissipative systems. Explicit analytical
and numerical studies are done for the motion of one particle in harmonic
external potentials. Apart from stationary solutions, we study non-equilibrium
dynamics and show the existence of various bifurcation phenomena.Comment: 11 pages, 6 figures, a few remarks and references adde
State Transitions and the Continuum Limit for a 2D Interacting, Self-Propelled Particle System
We study a class of swarming problems wherein particles evolve dynamically
via pairwise interaction potentials and a velocity selection mechanism. We find
that the swarming system undergoes various changes of state as a function of
the self-propulsion and interaction potential parameters. In this paper, we
utilize a procedure which, in a definitive way, connects a class of
individual-based models to their continuum formulations and determine criteria
for the validity of the latter. H-stability of the interaction potential plays
a fundamental role in determining both the validity of the continuum
approximation and the nature of the aggregation state transitions. We perform a
linear stability analysis of the continuum model and compare the results to the
simulations of the individual-based one
Thermal and Athermal Swarms of Self-Propelled Particles
Swarms of self-propelled particles exhibit complex behavior that can arise
from simple models, with large changes in swarm behavior resulting from small
changes in model parameters. We investigate the steady-state swarms formed by
self-propelled Morse particles in three dimensions using molecular dynamics
simulations optimized for GPUs. We find a variety of swarms of different
overall shape assemble spontaneously and that for certain Morse potential
parameters coexisting structures are observed. We report a rich "phase diagram"
of athermal swarm structures observed across a broad range of interaction
parameters. Unlike the structures formed in equilibrium self-assembly, we find
that the probability of forming a self-propelled swarm can be biased by the
choice of initial conditions. We investigate how thermal noise influences swarm
formation and demonstrate ways it can be exploited to reconfigure one swarm
into another. Our findings validate and extend previous observations of
self-propelled Morse swarms and highlight open questions for predictive
theories of nonequilibrium self-assembly.Comment: 21 pages, 7 figure
Nonequilibrium Brownian motion beyond the effective temperature
The condition of thermal equilibrium simplifies the theoretical treatment of
fluctuations as found in the celebrated Einstein's relation between mobility
and diffusivity for Brownian motion. Several recent theories relax the
hypothesis of thermal equilibrium resulting in at least two main scenarios.
With well separated timescales, as in aging glassy systems, equilibrium
Fluctuation-Dissipation Theorem applies at each scale with its own "effective"
temperature. With mixed timescales, as for example in active or granular fluids
or in turbulence, temperature is no more well-defined, the dynamical nature of
fluctuations fully emerges and a Generalized Fluctuation-Dissipation Theorem
(GFDT) applies. Here, we study experimentally the mixed timescale regime by
studying fluctuations and linear response in the Brownian motion of a rotating
intruder immersed in a vibro-fluidized granular medium. Increasing the packing
fraction, the system is moved from a dilute single-timescale regime toward a
denser multiple-timescale stage. Einstein's relation holds in the former and is
violated in the latter. The violation cannot be explained in terms of effective
temperatures, while the GFDT is able to impute it to the emergence of a strong
coupling between the intruder and the surrounding fluid. Direct experimental
measurements confirm the development of spatial correlations in the system when
the density is increased.Comment: 10 pages, 5 figure
Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles
A ring-kinetic theory for Vicsek-style models of self-propelled agents is
derived from the exact N-particle evolution equation in phase space. The theory
goes beyond mean-field and does not rely on Boltzmann's approximation of
molecular chaos. It can handle pre-collisional correlations and cluster
formation which both seem important to understand the phase transition to
collective motion. We propose a diagrammatic technique to perform a small
density expansion of the collision operator and derive the first two equations
of the BBGKY-hierarchy. An algorithm is presented that numerically solves the
evolution equation for the two-particle correlations on a lattice. Agent-based
simulations are performed and informative quantities such as orientational and
density correlation functions are compared with those obtained by ring-kinetic
theory. Excellent quantitative agreement between simulations and theory is
found at not too small noises and mean free paths. This shows that there is
parameter ranges in Vicsek-like models where the correlated closure of the
BBGKY-hierarchy gives correct and nontrivial results. We calculate the
dependence of the orientational correlations on distance in the disordered
phase and find that it seems to be consistent with a power law with exponent
around -1.8, followed by an exponential decay. General limitations of the
kinetic theory and its numerical solution are discussed
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