419 research outputs found
Ecosystems with mutually exclusive interactions self-organize to a state of high diversity
Ecological systems comprise an astonishing diversity of species that
cooperate or compete with each other forming complex mutual dependencies. The
minimum requirements to maintain a large species diversity on long time scales
are in general unknown. Using lichen communities as an example, we propose a
model for the evolution of mutually excluding organisms that compete for space.
We suggest that chain-like or cyclic invasions involving three or more species
open for creation of spatially separated sub-populations that subsequently can
lead to increased diversity. In contrast to its non-spatial counterpart, our
model predicts robust co-existence of a large number of species, in accordance
with observations on lichen growth. It is demonstrated that large species
diversity can be obtained on evolutionary timescales, provided that
interactions between species have spatial constraints. In particular, a phase
transition to a sustainable state of high diversity is identified.Comment: 4 pages, 4 figure
Non-Markovian Levy diffusion in nonhomogeneous media
We study the diffusion equation with a position-dependent, power-law
diffusion coefficient. The equation possesses the Riesz-Weyl fractional
operator and includes a memory kernel. It is solved in the diffusion limit of
small wave numbers. Two kernels are considered in detail: the exponential
kernel, for which the problem resolves itself to the telegrapher's equation,
and the power-law one. The resulting distributions have the form of the L\'evy
process for any kernel. The renormalized fractional moment is introduced to
compare different cases with respect to the diffusion properties of the system.Comment: 7 pages, 2 figure
Contact processes with long-range interactions
A class of non-local contact processes is introduced and studied using
mean-field approximation and numerical simulations. In these processes
particles are created at a rate which decays algebraically with the distance
from the nearest particle. It is found that the transition into the absorbing
state is continuous and is characterized by continuously varying critical
exponents. This model differs from the previously studied non-local directed
percolation model, where particles are created by unrestricted Levy flights. It
is motivated by recent studies of non-equilibrium wetting indicating that this
type of non-local processes play a role in the unbinding transition. Other
non-local processes which have been suggested to exist within the context of
wetting are considered as well.Comment: Accepted with minor revisions by Journal of Statistical Mechanics:
Theory and experiment
Contact process with long-range interactions: a study in the ensemble of constant particle number
We analyze the properties of the contact process with long-range interactions
by the use of a kinetic ensemble in which the total number of particles is
strictly conserved. In this ensemble, both annihilation and creation processes
are replaced by an unique process in which a particle of the system chosen at
random leaves its place and jumps to an active site. The present approach is
particularly useful for determining the transition point and the nature of the
transition, whether continuous or discontinuous, by evaluating the fractal
dimension of the cluster at the emergence of the phase transition. We also
present another criterion appropriate to identify the phase transition that
consists of studying the system in the supercritical regime, where the presence
of a "loop" characterizes the first-order transition. All results obtained by
the present approach are in full agreement with those obtained by using the
constant rate ensemble, supporting that, in the thermodynamic limit the results
from distinct ensembles are equivalent
Field theory of directed percolation with long-range spreading
It is well established that the phase transition between survival and
extinction in spreading models with short-range interactions is generically
associated with the directed percolation (DP) universality class. In many
realistic spreading processes, however, interactions are long ranged and well
described by L\'{e}vy-flights, i.e., by a probability distribution that decays
in dimensions with distance as . We employ the powerful
methods of renormalized field theory to study DP with such long range,
L\'{e}vy-flight spreading in some depth. Our results unambiguously corroborate
earlier findings that there are four renormalization group fixed points
corresponding to, respectively, short-range Gaussian, L\'{e}vy Gaussian,
short-range DP and L\'{e}vy DP, and that there are four lines in the plane which separate the stability regions of these fixed points. When the
stability line between short-range DP and L\'{e}vy DP is crossed, all critical
exponents change continuously. We calculate the exponents describing L\'{e}vy
DP to second order in -expansion, and we compare our analytical
results to the results of existing numerical simulations. Furthermore, we
calculate the leading logarithmic corrections for several dynamical
observables.Comment: 12 pages, 3 figure
Rare Events Statistics in Reaction--Diffusion Systems
We develop an efficient method to calculate probabilities of large deviations
from the typical behavior (rare events) in reaction--diffusion systems. The
method is based on a semiclassical treatment of underlying "quantum"
Hamiltonian, encoding the system's evolution. To this end we formulate
corresponding canonical dynamical system and investigate its phase portrait.
The method is presented for a number of pedagogical examples.Comment: 12 pages, 6 figure
Electrophysiological correlates of high-level perception during spatial navigation
We studied the electrophysiological basis of object recognition by recording scalp\ud
electroencephalograms while participants played a virtual-reality taxi driver game.\ud
Participants searched for passengers and stores during virtual navigation in simulated\ud
towns. We compared oscillatory brain activity in response to store views that were targets or\ud
nontargets (during store search) or neutral (during passenger search). Even though store\ud
category was solely defined by task context (rather than by sensory cues), frontal ...\ud
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Non-equilibrium Phase Transitions with Long-Range Interactions
This review article gives an overview of recent progress in the field of
non-equilibrium phase transitions into absorbing states with long-range
interactions. It focuses on two possible types of long-range interactions. The
first one is to replace nearest-neighbor couplings by unrestricted Levy flights
with a power-law distribution P(r) ~ r^(-d-sigma) controlled by an exponent
sigma. Similarly, the temporal evolution can be modified by introducing waiting
times Dt between subsequent moves which are distributed algebraically as P(Dt)~
(Dt)^(-1-kappa). It turns out that such systems with Levy-distributed
long-range interactions still exhibit a continuous phase transition with
critical exponents varying continuously with sigma and/or kappa in certain
ranges of the parameter space. In a field-theoretical framework such
algebraically distributed long-range interactions can be accounted for by
replacing the differential operators nabla^2 and d/dt with fractional
derivatives nabla^sigma and (d/dt)^kappa. As another possibility, one may
introduce algebraically decaying long-range interactions which cannot exceed
the actual distance to the nearest particle. Such interactions are motivated by
studies of non-equilibrium growth processes and may be interpreted as Levy
flights cut off at the actual distance to the nearest particle. In the
continuum limit such truncated Levy flights can be described to leading order
by terms involving fractional powers of the density field while the
differential operators remain short-ranged.Comment: LaTeX, 39 pages, 13 figures, minor revision
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