188 research outputs found
Uphill Motion of Active Brownian Particles in Piecewise Linear Potentials
We consider Brownian particles with the ability to take up energy from the
environment, to store it in an internal depot, and to convert internal energy
into kinetic energy of motion. Provided a supercritical supply of energy, these
particles are able to move in a ``high velocity'' or active mode, which allows
them to move also against the gradient of an external potential. We investigate
the critical energetic conditions of this self-driven motion for the case of a
linear potential and a ratchet potential. In the latter case, we are able to
find two different critical conversion rates for the internal energy, which
describe the onset of a directed net current into the two different directions.
The results of computer simulations are confirmed by analytical expressions for
the critical parameters and the average velocity of the net current. Further,
we investigate the influence of the asymmetry of the ratchet potential on the
net current and estimate a critical value for the asymmetry in order to obtain
a positive or negative net current.Comment: accepted for publication in European Journal of Physics B (1999), for
related work see http://summa.physik.hu-berlin.de/~frank/active.htm
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.Comment: 10 pages, 12 figure
Self-Organization, Active Brownian Dynamics, and Biological Applications
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 stochastic description of the active motion of biological entities
based on energy consumption and conversion. This model is applied to the
dynamics of swarms with external and interaction potentials. By means of
analytical results, we can distiguish between translational, rotational and
amoebic modes of swarm motion. We further investigate swarms of active Brownian
particles interacting via chemical fields and demonstrate the application of
this model to phenomena such as biological aggregation and trail formation in
insects.Comment: 22 pages, 9 multipart figures (minor changes after vers.1), For
related papers see http://www.ais.fraunhofer.de/~frank/papers.htm
Directed motion of Brownian particles with internal energy depot
A model of Brownian particles with the ability to take up energy from the
environment, to store it in an internal depot, and to convert internal energy
into kinetic energy of motion, is discussed. The general dynamics outlined in
Sect. 2 is investigated for the deterministic and stochastic particle's motion
in a non-fluctuating ratchet potential. First, we discuss the attractor
structure of the ratchet system by means of computer simulations. Dependent on
the energy supply, we find either periodic bound attractors corresponding to
localized oscillations, or one/two unbound attractors corresponding to directed
movement in the ratchet potential. Considering an ensemble of particles, we
show that in the deterministic case two currents into different directions can
occur, which however depend on a supercritical supply of energy. Considering
stochastic influences, we find the current only in one direction. We further
investigate how the current reversal depends on the strength of the stochastic
force and the asymmetry of the potential. We find both a critical value of the
noise intensity for the onset of the current and an optimal value where the net
current reaches a maximum. Eventually, the dynamics of our model is compared
with other ratchet models previously suggested.Comment: 24 pages, 11 Figs., For related work see
http://summa.physik.hu-berlin.de/~frank/active.htm
Statistical Mechanics of Canonical-Dissipative Systems and Applications to Swarm Dynamics
We develop the theory of canonical-dissipative systems, based on the
assumption that both the conservative and the dissipative elements of the
dynamics are determined by invariants of motion. In this case, known solutions
for conservative systems can be used for an extension of the dynamics, which
also includes elements such as the take-up/dissipation of energy. This way, a
rather complex dynamics can be mapped to an analytically tractable model, while
still covering important features of non-equilibrium systems. In our paper,
this approach is used to derive a rather general swarm model that considers (a)
the energetic conditions of swarming, i.e. for active motion, (b) interactions
between the particles based on global couplings. We derive analytical
expressions for the non-equilibrium velocity distribution and the mean squared
displacement of the swarm. Further, we investigate the influence of different
global couplings on the overall behavior of the swarm by means of
particle-based computer simulations and compare them with the analytical
estimations.Comment: 14 pages incl. 13 figures. v2: misprints in Eq. (40) corrected, ref.
updated. For related work see also:
http://summa.physik.hu-berlin.de/~frank/active.htm
Phase transitions in social impact models of opinion formation
We study phase transitions in models of opinion formation which are based on
the social impact theory. Two different models are discussed: (i) a
cellular--automata based model of a finite group with a strong leader where
persons can change their opinions but not their spatial positions, and (ii) a
model with persons treated as active Brownian particles interacting via a
communication field. In the first model, two stable phases are possible: a
cluster around the leader, and a state of social unification. The transition
into the second state occurs for a large leader strength and/or for a high
level of social noise. In the second model, we find three stable phases, which
correspond either to a ``paramagnetic'' phase (for high noise and strong
diffusion), a ``ferromagnetic'' phase (for small nose and weak diffusion), or a
phase with spatially separated ``domains'' (for intermediate conditions).Comment: 15 pages, 4 figures, submitted for publication in Physica
Monte Carlo Procedure for Protein Design
A new method for sequence optimization in protein models is presented. The
approach, which has inherited its basic philosophy from recent work by Deutsch
and Kurosky [Phys. Rev. Lett. 76, 323 (1996)] by maximizing conditional
probabilities rather than minimizing energy functions, is based upon a novel
and very efficient multisequence Monte Carlo scheme. By construction, the
method ensures that the designed sequences represent good folders
thermodynamically. A bootstrap procedure for the sequence space search is
devised making very large chains feasible. The algorithm is successfully
explored on the two-dimensional HP model with chain lengths N=16, 18 and 32.Comment: 7 pages LaTeX, 4 Postscript figures; minor change
Coordination of Decisions in a Spatial Agent Model
For a binary choice problem, the spatial coordination of decisions in an
agent community is investigated both analytically and by means of stochastic
computer simulations. The individual decisions are based on different local
information generated by the agents with a finite lifetime and disseminated in
the system with a finite velocity. We derive critical parameters for the
emergence of minorities and majorities of agents making opposite decisions and
investigate their spatial organization. We find that dependent on two essential
parameters describing the local impact and the spatial dissemination of
information, either a definite stable minority/majority relation
(single-attractor regime) or a broad range of possible values (multi-attractor
regime) occurs. In the latter case, the outcome of the decision process becomes
rather diverse and hard to predict, both with respect to the share of the
majority and their spatial distribution. We further investigate how a
dissemination of information on different time scales affects the outcome of
the decision process. We find that a more ``efficient'' information exchange
within a subpopulation provides a suitable way to stabilize their majority
status and to reduce ``diversity'' and uncertainty in the decision process.Comment: submitted for publication in Physica A (31 pages incl. 17 multi-part
figures
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