71 research outputs found
Spatial Organization in the Reaction A + B --> inert for Particles with a Drift
We describe the spatial structure of particles in the (one dimensional)
two-species annihilation reaction A + B --> 0, where both species have a
uniform drift in the same direction and like species have a hard core
exclusion. For the case of equal initial concentration, at long times, there
are three relevant length scales: the typical distance between similar
(neighboring) particles, the typical distance between dissimilar (neighboring)
particles, and the typical size of a cluster of one type of particles. These
length scales are found to be generically different than that found for
particles without a drift.Comment: 10 pp of gzipped uuencoded postscrip
Scaling Model of Annihilation-Diffusion Kinetics for Charged Particles with Long-Range Interactions
We propose the general scaling model for the diffusio n-annihilation reaction
with long-range power-law i
nteractions. The presented scaling arguments lead to the finding of three
different regimes, dep ending on the space dimensionality d and the long-range
force power e xponent n. The obtained kinetic phase diagram agrees well with
existing simulation data and approximate theoretical results.Comment: RevTEX, 7 pages, no figures, accepted to Physical Review
Two-Species Annihilation with Drift: A Model with Continuous Concentration-Decay Exponents
We propose a model for diffusion-limited annihilation of two species, or , where the motion of the particles is subject to a drift. For equal
initial concentrations of the two species, the density follows a power-law
decay for large times. However, the decay exponent varies continuously as a
function of the probability of which particle, the hopping one or the target,
survives in the reaction. These results suggest that diffusion-limited
reactions subject to drift do not fall into a limited number of universality
classes.Comment: 10 pages, tex, 3 figures, also available upon reques
Classification of phase transitions and ensemble inequivalence, in systems with long range interactions
Systems with long range interactions in general are not additive, which can
lead to an inequivalence of the microcanonical and canonical ensembles. The
microcanonical ensemble may show richer behavior than the canonical one,
including negative specific heats and other non-common behaviors. We propose a
classification of microcanonical phase transitions, of their link to canonical
ones, and of the possible situations of ensemble inequivalence. We discuss
previously observed phase transitions and inequivalence in self-gravitating,
two-dimensional fluid dynamics and non-neutral plasmas. We note a number of
generic situations that have not yet been observed in such systems.Comment: 42 pages, 11 figures. Accepted in Journal of Statistical Physics.
Final versio
Self-similarity and power-like tails in nonconservative kinetic models
In this paper, we discuss the large--time behavior of solution of a simple
kinetic model of Boltzmann--Maxwell type, such that the temperature is time
decreasing and/or time increasing. We show that, under the combined effects of
the nonlinearity and of the time--monotonicity of the temperature, the kinetic
model has non trivial quasi-stationary states with power law tails. In order to
do this we consider a suitable asymptotic limit of the model yielding a
Fokker-Planck equation for the distribution. The same idea is applied to
investigate the large-time behavior of an elementary kinetic model of economy
involving both exchanges between agents and increasing and/or decreasing of the
mean wealth. In this last case, the large-time behavior of the solution shows a
Pareto power law tail. Numerical results confirm the previous analysis
Anisotropic Diffusion-Limited Reactions with Coagulation and Annihilation
One-dimensional reaction-diffusion models A+A -> 0, A+A -> A, and $A+B -> 0,
where in the latter case like particles coagulate on encounters and move as
clusters, are solved exactly with anisotropic hopping rates and assuming
synchronous dynamics. Asymptotic large-time results for particle densities are
derived and discussed in the framework of universality.Comment: 13 pages in plain Te
Multispecies reaction-diffusion systems
Multispecies reaction-diffusion systems, for which the time evolution
equation of correlation functions become a closed set, are considered. A formal
solution for the average densities is found. Some special interactions and the
exact time dependence of the average densities in these cases are also studied.
For the general case, the large time behaviour of the average densities has
also been obtained.Comment: LaTeX file, 15 pages, to appear in Phys. Rev.
Coarsening of Sand Ripples in Mass Transfer Models with Extinction
Coarsening of sand ripples is studied in a one-dimensional stochastic model,
where neighboring ripples exchange mass with algebraic rates, , and ripples of zero mass are removed from the system. For ripples vanish through rare fluctuations and the average ripples mass grows
as \avem(t) \sim -\gamma^{-1} \ln (t). Temporal correlations decay as
or depending on the symmetry of the mass transfer, and
asymptotically the system is characterized by a product measure. The stationary
ripple mass distribution is obtained exactly. For ripple evolution
is linearly unstable, and the noise in the dynamics is irrelevant. For the problem is solved on the mean field level, but the mean-field theory
does not adequately describe the full behavior of the coarsening. In
particular, it fails to account for the numerically observed universality with
respect to the initial ripple size distribution. The results are not restricted
to sand ripple evolution since the model can be mapped to zero range processes,
urn models, exclusion processes, and cluster-cluster aggregation.Comment: 10 pages, 8 figures, RevTeX4, submitted to Phys. Rev.
Local multiresolution order in community detection
Community detection algorithms attempt to find the best clusters of nodes in
an arbitrary complex network. Multi-scale ("multiresolution") community
detection extends the problem to identify the best network scale(s) for these
clusters. The latter task is generally accomplished by analyzing community
stability simultaneously for all clusters in the network. In the current work,
we extend this general approach to define local multiresolution methods, which
enable the extraction of well-defined local communities even if the global
community structure is vaguely defined in an average sense. Toward this end, we
propose measures analogous to variation of information and normalized mutual
information that are used to quantitatively identify the best resolution(s) at
the community level based on correlations between clusters in
independently-solved systems. We demonstrate our method on two constructed
networks as well as a real network and draw inferences about local community
strength. Our approach is independent of the applied community detection
algorithm save for the inherent requirement that the method be able to identify
communities across different network scales, with appropriate changes to
account for how different resolutions are evaluated or defined in a particular
community detection method. It should, in principle, easily adapt to
alternative community comparison measures.Comment: 19 pages, 11 figure
On a kinetic model for a simple market economy
In this paper, we consider a simple kinetic model of economy involving both
exchanges between agents and speculative trading. We show that the kinetic
model admits non trivial quasi-stationary states with power law tails of Pareto
type. In order to do this we consider a suitable asymptotic limit of the model
yielding a Fokker-Planck equation for the distribution of wealth among
individuals. For this equation the stationary state can be easily derived and
shows a Pareto power law tail. Numerical results confirm the previous analysis
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