537 research outputs found
Absence of kinetic effects in reaction-diffusion processes in scale-free networks
We show that the chemical reactions of the model systems of A+A->0 and A+B->0
when performed on scale-free networks exhibit drastically different behavior as
compared to the same reactions in normal spaces. The exponents characterizing
the density evolution as a function of time are considerably higher than 1,
implying that both reactions occur at a much faster rate. This is due to the
fact that the discerning effects of the generation of a depletion zone (A+A)
and the segregation of the reactants (A+B) do not occur at all as in normal
spaces. Instead we observe the formation of clusters of A (A+A reaction) and of
mixed A and B (A+B reaction) around the hubs of the network. Only at the limit
of very sparse networks is the usual behavior recovered.Comment: 4 pages, 4 figures, to be published in Physical Review Letter
Characteristics of reaction-diffusion on scale-free networks
We examine some characteristic properties of reaction-diffusion processes of
the A+A->0 type on scale-free networks. Due to the inhomogeneity of the
structure of the substrate, as compared to usual lattices, we focus on the
characteristics of the nodes where the annihilations occur. We show that at
early times the majority of these events take place on low-connectivity nodes,
while as time advances the process moves towards the high-connectivity nodes,
the so-called hubs. This pattern remarkably accelerates the annihilation of the
particles, and it is in agreement with earlier predictions that the rates of
reaction-diffusion processes on scale-free networks are much faster than the
equivalent ones on lattice systems
From single steps to mass migration: the problem of scale in the movement ecology of the Serengeti wildebeest
A central question in ecology is how to link processes that occur over
different scales. The daily interactions of individual organisms ultimately
determine community dynamics, population fluctuations and the functioning
of entire ecosystems. Observations of these multiscale ecological
processes are constrained by various technological, biological or logistical
issues, and there are often vast discrepancies between the scale at which
observation is possible and the scale of the question of interest. Animal
movement is characterized by processes that act over multiple spatial and
temporal scales. Second-by-second decisions accumulate to produce
annual movement patterns. Individuals influence, and are influenced by,
collective movement decisions, which then govern the spatial distribution
of populations and the connectivity of meta-populations. While the
field of movement ecology is experiencing unprecedented growth in the
availability of movement data, there remain challenges in integrating
observations with questions of ecological interest. In this article, we present
the major challenges of addressing these issues within the context of the
Serengeti wildebeest migration, a keystone ecological phenomena that
crosses multiple scales of space, time and biological complexity.
This article is part of the theme issue ’Collective movement ecology’
Context-dependent interaction leads to emergent search behavior in social aggregates
Locating the source of an advected chemical signal is a common challenge
facing many living organisms. When the advecting medium is characterized by
either high Reynolds number or high Peclet number the task becomes highly
non-trivial due to the generation of heterogenous, dynamically changing
filamental concentrations which do not decrease monotonically with distance to
the source. Defining search strategies which are effective in these
environments has important implications for the understanding of animal
behavior and for the design of biologically inspired technology. Here we
present a strategy which is able to solve this task without the higher
intelligence required to assess spatial gradient direction, measure the
diffusive properties of the flow field or perform complex calculations. Instead
our method is based on the collective behavior of autonomous individuals
following simple social interaction rules which are modified according to the
local conditions they are experiencing. Through these context-dependent
interactions the group is able to locate the source of a chemical signal and in
doing so displays an awareness of the environment not present at the individual
level. Our model demonstrates the ability of decentralized information
processing systems to solve real world problems and also illustrates an
alternative pathway to the evolution of higher cognitive capacity via the
emergent, group level intelligence which can result from local interactions.Comment: 3 figure
Diffusion-Limited Coalescence with Finite Reaction Rates in One Dimension
We study the diffusion-limited process in one dimension, with
finite reaction rates. We develop an approximation scheme based on the method
of Inter-Particle Distribution Functions (IPDF), which was formerly used for
the exact solution of the same process with infinite reaction rate. The
approximation becomes exact in the very early time regime (or the
reaction-controlled limit) and in the long time (diffusion-controlled)
asymptotic limit. For the intermediate time regime, we obtain a simple
interpolative behavior between these two limits. We also study the coalescence
process (with finite reaction rates) with the back reaction , and in
the presence of particle input. In each of these cases the system reaches a
non-trivial steady state with a finite concentration of particles. Theoretical
predictions for the concentration time dependence and for the IPDF are compared
to computer simulations. P. A. C. S. Numbers: 82.20.Mj 02.50.+s 05.40.+j
05.70.LnComment: 13 pages (and 4 figures), plain TeX, SISSA-94-0
Fast-diffusion mean-field theory for k-body reactions in one dimension
We derive an improved mean-field approximation for k-body annihilation
reactions kA --> inert, for hard-core diffusing particles on a line,
annihilating in groups of k neighbors with probability 0 < q <= 1. The hopping
and annihilation processes are correlated to mimic chemical reactions. Our new
mean-field theory accounts for hard-core particle properties and has a larger
region of applicability than the standard chemical rate equation especially for
large k values. Criteria for validity of the mean-field theory and its use in
phenomenological data fits are derived. Numerical tests are reported for
k=3,4,5,6.Comment: 16 pages, TeX (plain
Two-Scale Annihilation
The kinetics of single-species annihilation, , is investigated in
which each particle has a fixed velocity which may be either with equal
probability, and a finite diffusivity. In one dimension, the interplay between
convection and diffusion leads to a decay of the density which is proportional
to . At long times, the reactants organize into domains of right- and
left-moving particles, with the typical distance between particles in a single
domain growing as , and the distance between domains growing as .
The probability that an arbitrary particle reacts with its
neighbor is found to decay as for same-velocity pairs and as
for pairs. These kinetic and spatial exponents and their
interrelations are obtained by scaling arguments. Our predictions are in
excellent agreement with numerical simulations.Comment: revtex, 5 pages, 5 figures, also available from
http://arnold.uchicago.edu/~eb
Particle Dynamics in a Mass-Conserving Coalescence Process
We consider a fully asymmetric one-dimensional model with mass-conserving
coalescence. Particles of unit mass enter at one edge of the chain and
coalescence while performing a biased random walk towards the other edge where
they exit. The conserved particle mass acts as a passive scalar in the reaction
process , and allows an exact mapping to a restricted ballistic
surface deposition model for which exact results exist. In particular, the
mass- mass correlation function is exactly known. These results complement
earlier exact results for the process without mass. We introduce a
comprehensive scaling theory for this process. The exact anaytical and
numerical results confirm its validity.Comment: 5 pages, 6 figure
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