817 research outputs found
A Simplification of Combinatorial Link Floer Homology
We define a new combinatorial complex computing the hat version of link Floer
homology over Z/2Z, which turns out to be significantly smaller than the
Manolescu-Ozsvath-Sarkar one.Comment: 20 pages with figures, final version printed in JKTR, v.3 of
Oberwolfach Proceeding
Search for universality in one-dimensional ballistic annihilation kinetics
We study the kinetics of ballistic annihilation for a one-dimensional ideal
gas with continuous velocity distribution. A dynamical scaling theory for the
long time behavior of the system is derived. Its validity is supported by
extensive numerical simulations for several velocity distributions. This leads
us to the conjecture that all the continuous velocity distributions \phi(v)
which are symmetric, regular and such that \phi(0) does not vanish, are
attracted in the long time regime towards the same Gaussian distribution and
thus belong to the same universality class. Moreover, it is found that the
particle density decays as n(t)~t^{-\alpha}, with \alpha=0.785 +/- 0.005.Comment: 8 pages, needs multicol, epsf and revtex. 8 postscript figures
included. Submitted to Phys. Rev. E. Also avaiable at
http://mykonos.unige.ch/~rey/publi.html#Secon
Kinetics of ballistic annihilation and branching
We consider a one-dimensional model consisting of an assembly of two-velocity
particles moving freely between collisions. When two particles meet, they
instantaneously annihilate each other and disappear from the system. Moreover
each moving particle can spontaneously generate an offspring having the same
velocity as its mother with probability 1-q. This model is solved analytically
in mean-field approximation and studied by numerical simulations. It is found
that for q=1/2 the system exhibits a dynamical phase transition. For q<1/2, the
slow dynamics of the system is governed by the coarsening of clusters of
particles having the same velocities, while for q>1/2 the system relaxes
rapidly towards its stationary state characterized by a distribution of small
cluster sizes.Comment: 10 pages, 11 figures, uses multicol, epic, eepic and eepicemu. Also
avaiable at http://mykonos.unige.ch/~rey/pubt.htm
Probabilistic ballistic annihilation with continuous velocity distributions
We investigate the problem of ballistically controlled reactions where
particles either annihilate upon collision with probability , or undergo an
elastic shock with probability . Restricting to homogeneous systems, we
provide in the scaling regime that emerges in the long time limit, analytical
expressions for the exponents describing the time decay of the density and the
root-mean-square velocity, as continuous functions of the probability and
of a parameter related to the dissipation of energy. We work at the level of
molecular chaos (non-linear Boltzmann equation), and using a systematic Sonine
polynomials expansion of the velocity distribution, we obtain in arbitrary
dimension the first non-Gaussian correction and the corresponding expressions
for the decay exponents. We implement Monte-Carlo simulations in two
dimensions, that are in excellent agreement with our analytical predictions.
For , numerical simulations lead to conjecture that unlike for pure
annihilation (), the velocity distribution becomes universal, i.e. does
not depend on the initial conditions.Comment: 10 pages, 9 eps figures include
Liesegang patterns : Studies on the width law
The so-called "width law" for Liesegang patterns, which states that the
positions x_n and widths w_n of bands verify the relation x_n \sim w_n^{\alpha}
for some \alpha>0, is investigated both experimentally and theoretically. We
provide experimental data exhibiting good evidence for values of \alpha close
to 1. The value \alpha=1 is supported by theoretical arguments based on a
generic model of reaction-diffusion.Comment: 7 pages, RevTeX, two columns, 5 figure
Motion of influential players can support cooperation in Prisoner's Dilemma
We study a spatial Prisoner's dilemma game with two types (A and B) of players located on a square lattice. Players following either cooperator or defector strategies play Prisoner's Dilemma games with their 24 nearest neighbors. The players are allowed to adopt one of their neighbor's strategy with a probability dependent on the payoff difference and type of the given neighbor. Players A and B have different efficiency in the transfer of their own strategies; therefore the strategy adoption probability is reduced by a multiplicative factor (w < 1) from the players of type B. We report that the motion of the influential payers (type A) can improve remarkably the maintenance of cooperation even for their low densitie
Formation of Liesegang patterns: Simulations using a kinetic Ising model
A kinetic Ising model description of Liesegang phenomena is studied using
Monte Carlo simulations. The model takes into account thermal fluctuations,
contains noise in the chemical reactions, and its control parameters are
experimentally accessible. We find that noisy, irregular precipitation takes
place in dimension d=2 while, depending on the values of the control
parameters, either irregular patterns or precipitation bands satisfying the
regular spacing law emerge in d=3.Comment: 7 pages, 8 ps figures, RevTe
Derivation of the Matalon-Packter law for Liesegang patterns
Theoretical models of the Liesegang phenomena are studied and simple
expressions for the spacing coefficients characterizing the patterns are
derived. The emphasis is on displaying the explicit dependences on the
concentrations of the inner- and the outer-electrolytes. Competing theories
(ion-product supersaturation, nucleation and droplet growth, induced sol-
coagulation) are treated with the aim of finding the distinguishing features of
the theories. The predictions are compared with experiments and the results
suggest that the induced sol-coagulation theory is the best candidate for
describing the experimental observations embodied in the Matalon-Packter law.Comment: 9 pages, 7 figures, RevTe
On the universality of a class of annihilation-coagulation models
A class of -dimensional reaction-diffusion models interpolating
continuously between the diffusion-coagulation and the diffusion-annihilation
models is introduced. Exact relations among the observables of different models
are established. For the one-dimensional case, it is shown how correlations in
the initial state can lead to non-universal amplitudes for time-dependent
particles density.Comment: 18 pages with no figures. Latex file using REVTE
A field theoretic approach to master equations and a variational method beyond the Poisson ansatz
We develop a variational scheme in a field theoretic approach to a stochastic
process. While various stochastic processes can be expressed using master
equations, in general it is difficult to solve the master equations exactly,
and it is also hard to solve the master equations numerically because of the
curse of dimensionality. The field theoretic approach has been used in order to
study such complicated master equations, and the variational scheme achieves
tremendous reduction in the dimensionality of master equations. For the
variational method, only the Poisson ansatz has been used, in which one
restricts the variational function to a Poisson distribution. Hence, one has
dealt with only restricted fluctuation effects. We develop the variational
method further, which enables us to treat an arbitrary variational function. It
is shown that the variational scheme developed gives a quantitatively good
approximation for master equations which describe a stochastic gene regulatory
network.Comment: 13 pages, 2 figure
- …