56 research outputs found
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.Comment: submitted to Eur. Phys J. Special Topic
Interpreting the Wide Scattering of Synchronized Traffic Data by Time Gap Statistics
Based on the statistical evaluation of experimental single-vehicle data, we
propose a quantitative interpretation of the erratic scattering of flow-density
data in synchronized traffic flows. A correlation analysis suggests that the
dynamical flow-density data are well compatible with the so-called jam line
characterizing fully developed traffic jams, if one takes into account the
variation of their propagation speed due to the large variation of the netto
time gaps (the inhomogeneity of traffic flow). The form of the time gap
distribution depends not only on the density, but also on the measurement cross
section: The most probable netto time gap in congested traffic flow upstream of
a bottleneck is significantly increased compared to uncongested freeway
sections. Moreover, we identify different power-law scaling laws for the
relative variance of netto time gaps as a function of the sampling size. While
the exponent is -1 in free traffic corresponding to statistically independent
time gaps, the exponent is about -2/3 in congested traffic flow because of
correlations between queued vehicles.Comment: For related publications see http://www.helbing.or
Evolutionary dynamics of group formation
This is an open access article distributed under the terms of the Creative Commons Attribution License CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Group formation is a quite ubiquitous phenomenon across different animal species, whose individuals cluster together forming communities of diverse size. Previous investigations suggest that, in general, this phenomenon might have similar underlying reasons across the interested species, despite genetic and behavioral differences. For instance improving the individual safety (e.g. from predators), and increasing the probability to get food resources. Remarkably, the group size might strongly vary from species to species, e.g. shoals of fishes and herds of lions, and sometimes even within the same species, e.g. tribes and families in human societies. Here we build on previous theories stating that the dynamics of group formation may have evolutionary roots, and we explore this fascinating hypothesis from a purely theoretical perspective, with a model using the framework of Evolutionary Game Theory. In our model we hypothesize that homogeneity constitutes a fundamental ingredient in these dynamics. Accordingly, we study a population that tries to form homogeneous groups, i.e. composed of similar agents. The formation of a group can be interpreted as a strategy. Notably, agents can form a group (receiving a âgroup payoffâ), or can act individually (receiving an âindividual payoffâ). The phase diagram of the modeled population shows a sharp transition between the âgroup phaseâ and the âindividual phaseâ, characterized by a critical âindividual payoffâ. Our results then support the hypothesis that the phenomenon of group formation has evolutionary roots.Peer reviewedFinal Published versio
Congestion in a macroscopic model of self-driven particles modeling gregariousness
International audienceWe analyze a macroscopic model with a maximal density constraint which describes short range repulsion in biological systems. This system aims at modeling finite-size particles which cannot overlap and repel each other when they are too close. The parts of the fluid where the maximal density is reached behave like incompressible fluids while lower density regions are compressible. This paper investigates the transition between the compressible and incompressible regions. To capture this transition, we study a one-dimensional Riemann problem and introduce a perturbation problem which regularizes the compressible-incompressible transition. Specific difficulties related to the non-conservativity of the problem are discussed
Modeling Vortex Swarming In Daphnia
Based on experimental observations in \textit{Daphnia}, we introduce an
agent-based model for the motion of single and swarms of animals. Each agent is
described by a stochastic equation that also considers the conditions for
active biological motion. An environmental potential further reflects local
conditions for \textit{Daphnia}, such as attraction to light sources. This
model is sufficient to describe the observed cycling behavior of single
\textit{Daphnia}. To simulate vortex swarming of many \textit{Daphnia}, i.e.
the collective rotation of the swarm in one direction, we extend the model by
considering avoidance of collisions. Two different ansatzes to model such a
behavior are developed and compared. By means of computer simulations of a
multi-agent system we show that local avoidance - as a special form of
asymmetric repulsion between animals - leads to the emergence of a vortex
swarm. The transition from uncorrelated rotation of single agents to the vortex
swarming as a function of the swarm size is investigated. Eventually, some
evidence of avoidance behavior in \textit{Daphnia} is provided by comparing
experimental and simulation results for two animals.Comment: 24 pages including 11 multi-part figs. Major revisions compared to
version 1, new results on transition from uncorrelated rotation to vortex
swarming. Extended discussion. For related publications see
http://www.sg.ethz.ch/people/scfrank/Publication
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
Macroscopic limits and phase transition in a system of self-propelled particles
We investigate systems of self-propelled particles with alignment
interaction. Compared to previous work, the force acting on the particles is
not normalized and this modification gives rise to phase transitions from
disordered states at low density to aligned states at high densities. This
model is the space inhomogeneous extension of a previous work by Frouvelle and
Liu in which the existence and stability of the equilibrium states were
investigated. When the density is lower than a threshold value, the dynamics is
described by a non-linear diffusion equation. By contrast, when the density is
larger than this threshold value, the dynamics is described by a hydrodynamic
model for self-alignment interactions previously derived in Degond and Motsch.
However, the modified normalization of the force gives rise to different
convection speeds and the resulting model may lose its hyperbolicity in some
regions of the state space
Large scale dynamics of the Persistent Turning Walker model of fish behavior
International audienceThis paper considers a new model of individual displacement, based on fish motion, the so-called Persistent Turning Walker (PTW) model, which involves an Ornstein-Uhlenbeck process on the curvature of the particle trajectory. The goal is to show that its large time and space scale dynamics is of diffusive type, and to provide an analytic expression of the diffusion coefficient. Two methods are investigated. In the first one, we compute the large time asymptotics of the variance of the individual stochastic trajectories. The second method is based on a diffusion approximation of the kinetic formulation of these stochastic trajectories. The kinetic model is a Fokker-Planck type equation posed in an extended phase-space involving the curvature among the kinetic variables. We show that both methods lead to the same value of the diffusion constant. We present some numerical simulations to illustrate the theoretical results
Ecological Complex Systems
Main aim of this topical issue is to report recent advances in noisy
nonequilibrium processes useful to describe the dynamics of ecological systems
and to address the mechanisms of spatio-temporal pattern formation in ecology
both from the experimental and theoretical points of view. This is in order to
understand the dynamical behaviour of ecological complex systems through the
interplay between nonlinearity, noise, random and periodic environmental
interactions. Discovering the microscopic rules and the local interactions
which lead to the emergence of specific global patterns or global dynamical
behaviour and the noises role in the nonlinear dynamics is an important, key
aspect to understand and then to model ecological complex systems.Comment: 13 pages, Editorial of a topical issue on Ecological Complex System
to appear in EPJ B, Vol. 65 (2008
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