28 research outputs found
Bell's theorem as a signature of nonlocality: a classical counterexample
For a system composed of two particles Bell's theorem asserts that averages
of physical quantities determined from local variables must conform to a family
of inequalities. In this work we show that a classical model containing a local
probabilistic interaction in the measurement process can lead to a violation of
the Bell inequalities. We first introduce two-particle phase-space
distributions in classical mechanics constructed to be the analogs of quantum
mechanical angular momentum eigenstates. These distributions are then employed
in four schemes characterized by different types of detectors measuring the
angular momenta. When the model includes an interaction between the detector
and the measured particle leading to ensemble dependencies, the relevant Bell
inequalities are violated if total angular momentum is required to be
conserved. The violation is explained by identifying assumptions made in the
derivation of Bell's theorem that are not fulfilled by the model. These
assumptions will be argued to be too restrictive to see in the violation of the
Bell inequalities a faithful signature of nonlocality.Comment: Extended manuscript. Significant change
Individual rules for trail pattern formation in Argentine ants (Linepithema humile)
We studied the formation of trail patterns by Argentine ants exploring an
empty arena. Using a novel imaging and analysis technique we estimated
pheromone concentrations at all spatial positions in the experimental arena and
at different times. Then we derived the response function of individual ants to
pheromone concentrations by looking at correlations between concentrations and
changes in speed or direction of the ants. Ants were found to turn in response
to local pheromone concentrations, while their speed was largely unaffected by
these concentrations. Ants did not integrate pheromone concentrations over
time, with the concentration of pheromone in a 1 cm radius in front of the ant
determining the turning angle. The response to pheromone was found to follow a
Weber's Law, such that the difference between quantities of pheromone on the
two sides of the ant divided by their sum determines the magnitude of the
turning angle. This proportional response is in apparent contradiction with the
well-established non-linear choice function used in the literature to model the
results of binary bridge experiments in ant colonies (Deneubourg et al. 1990).
However, agent based simulations implementing the Weber's Law response function
led to the formation of trails and reproduced results reported in the
literature. We show analytically that a sigmoidal response, analogous to that
in the classical Deneubourg model for collective decision making, can be
derived from the individual Weber-type response to pheromone concentrations
that we have established in our experiments when directional noise around the
preferred direction of movement of the ants is assumed.Comment: final version, 9 figures, submitted to Plos Computational Biology
(accepted
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
Trail formation based on directed pheromone deposition
We propose an Individual-Based Model of ant-trail formation. The ants are
modeled as self-propelled particles which deposit directed pheromones and
interact with them through alignment interaction. The directed pheromones
intend to model pieces of trails, while the alignment interaction translates
the tendency for an ant to follow a trail when it meets it. Thanks to adequate
quantitative descriptors of the trail patterns, the existence of a phase
transition as the ant-pheromone interaction frequency is increased can be
evidenced. Finally, we propose both kinetic and fluid descriptions of this
model and analyze the capabilities of the fluid model to develop trail
patterns. We observe that the development of patterns by fluid models require
extra trail amplification mechanisms that are not needed at the
Individual-Based Model level
Optimal traffic organisation in ants under crowded conditions
Efficient transportation, a hot topic in nonlinear science, is essential for
modern societies and the survival of biological species. Biological evolution
has generated a rich variety of successful solutions, which have inspired
engineers to design optimized artificial systems. Foraging ants, for example,
form attractive trails that support the exploitation of initially unknown food
sources in almost the minimum possible time. However, can this strategy cope
with bottleneck situations, when interactions cause delays that reduce the
overall flow? Here, we present an experimental study of ants confronted with
two alternative routes. We find that pheromone-based attraction generates one
trail at low densities, whereas at a high level of crowding, another trail is
established before traffic volume is affected, which guarantees that an optimal
rate of food return is maintained. This bifurcation phenomenon is explained by
a nonlinear modelling approach. Surprisingly, the underlying mechanism is based
on inhibitory interactions. It implies capacity reserves, a limitation of the
density-induced speed reduction, and a sufficient pheromone concentration for
reliable trail perception. The balancing mechanism between cohesive and
dispersive forces appears to be generic in natural, urban and transportation
systems.Comment: For related work see http://www.helbing.or
From Cells to Societies: Models of Complex Coherent Action. Authorized translation from the English edition published by Springer-Verlag
From Cells to Societies: Models of Complex Coherent Action
This book shows how, by rather simple models, we can gain remarkable insights into the behavior of complex systems. It is devoted to the discussion of functional self-organization in large populations of interacting active elements. The possible forms of self-organization in such systems range from coherent collective motions in the physical coordinate space to the mutual synchronization of internal dynamics, the development of coherently operating groups, the rise of hierarchical structures, and the emergence of dynamical networks. Such processes play an important role in biological and social phenomena. The authors have chosen a series of models from physics, biochemistry, biology, sociology and economics, and will systematically discuss their general properties. The book addresses researchers and graduate students in a variety of disciplines, such as physics, chemistry, biology and the social sciences. Written for: Graduate and undergraduate student
Modélisation du comportement du suivi de la piste chez les fourmis
info:eu-repo/semantics/publishe
From Cells to Societies: Models of Complex Coherent Action
This book shows how, by rather simple models, we can gain remarkable insights into the behavior of complex systems. It is devoted to the discussion of functional self-organization in large populations of interacting active elements. The possible forms of self-organization in such systems range from coherent collective motions in the physical coordinate space to the mutual synchronization of internal dynamics, the development of coherently operating groups, the rise of hierarchical structures, and the emergence of dynamical networks. Such processes play an important role in biological and social phenomena. The authors have chosen a series of models from physics, biochemistry, biology, sociology and economics, and will systematically discuss their general properties. The book addresses researchers and graduate students in a variety of disciplines, such as physics, chemistry, biology and the social sciences. Written for: Graduate and undergraduate student
Frustration induced chaos in a system of coupled ODE's
SCOPUS: ar.jinfo:eu-repo/semantics/publishe