551 research outputs found
Two site self consistent method for front propagation in reaction-diffusion system
We study front propagation in the reaction diffusion process
on one dimensional lattice with hard core interaction
between the particles. We propose a two site self consistent method (TSSCM) to
make analytic estimates for the front velocity and are in excellent agreement
with the simulation results for all parameter regimes. We expect that the
simplicity of the method will allow one to use this technique for estimating
the front velocity in other reaction diffusion processes as well.Comment: 6 figure
Universality and tree structure of high energy QCD
Using non-trivial mathematical properties of a class of nonlinear evolution
equations, we obtain the universal terms in the asymptotic expansion in
rapidity of the saturation scale and of the unintegrated gluon density from the
Balitsky-Kovchegov equation. These terms are independent of the initial
conditions and of the details of the equation. The last subasymptotic terms are
new results and complete the list of all possible universal contributions.
Universality is interpreted in a general qualitative picture of high energy
scattering, in which a scattering process corresponds to a tree structure
probed by a given source.Comment: 4 pages, 3 figure
Exact asymptotics of the freezing transition of a logarithmically correlated random energy model
We consider a logarithmically correlated random energy model, namely a model
for directed polymers on a Cayley tree, which was introduced by Derrida and
Spohn. We prove asymptotic properties of a generating function of the partition
function of the model by studying a discrete time analogy of the KPP-equation -
thus translating Bramson's work on the KPP-equation into a discrete time case.
We also discuss connections to extreme value statistics of a branching random
walk and a rescaled multiplicative cascade measure beyond the critical point
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
Condensation phase transitions of symmetric conserved-mass aggregation model on complex networks
We investigate condensation phase transitions of symmetric conserved-mass
aggregation (SCA) model on random networks (RNs) and scale-free networks (SFNs)
with degree distribution . In SCA model, masses diffuse
with unite rate, and unit mass chips off from mass with rate . The
dynamics conserves total mass density . In the steady state, on RNs and
SFNs with for , we numerically show that SCA
model undergoes the same type condensation transitions as those on regular
lattices. However the critical line depends on network
structures. On SFNs with , the fluid phase of exponential mass
distribution completely disappears and no phase transitions occurs. Instead,
the condensation with exponentially decaying background mass distribution
always takes place for any non-zero density. For the existence of the condensed
phase for at the zero density limit, we investigate one
lamb-lion problem on RNs and SFNs. We numerically show that a lamb survives
indefinitely with finite survival probability on RNs and SFNs with ,
and dies out exponentially on SFNs with . The finite life time
of a lamb on SFNs with ensures the existence of the
condensation at the zero density limit on SFNs with at which
direct numerical simulations are practically impossible. At ,
we numerically confirm that complete condensation takes place for any on RNs. Together with the recent study on SFNs, the complete condensation
always occurs on both RNs and SFNs in zero range process with constant hopping
rate.Comment: 6 pages, 6 figure
Model of Cluster Growth and Phase Separation: Exact Results in One Dimension
We present exact results for a lattice model of cluster growth in 1D. The
growth mechanism involves interface hopping and pairwise annihilation
supplemented by spontaneous creation of the stable-phase, +1, regions by
overturning the unstable-phase, -1, spins with probability p. For cluster
coarsening at phase coexistence, p=0, the conventional structure-factor scaling
applies. In this limit our model falls in the class of diffusion-limited
reactions A+A->inert. The +1 cluster size grows diffusively, ~t**(1/2), and the
two-point correlation function obeys scaling. However, for p>0, i.e., for the
dynamics of formation of stable phase from unstable phase, we find that
structure-factor scaling breaks down; the length scale associated with the size
of the growing +1 clusters reflects only the short-distance properties of the
two-point correlations.Comment: 12 page
Coherent State path-integral simulation of many particle systems
The coherent state path integral formulation of certain many particle systems
allows for their non perturbative study by the techniques of lattice field
theory. In this paper we exploit this strategy by simulating the explicit
example of the diffusion controlled reaction . Our results are
consistent with some renormalization group-based predictions thus clarifying
the continuum limit of the action of the problem.Comment: 20 pages, 4 figures. Minor corrections. Acknowledgement and reference
correcte
A phenomenological theory giving the full statistics of the position of fluctuating pulled fronts
We propose a phenomenological description for the effect of a weak noise on
the position of a front described by the Fisher-Kolmogorov-Petrovsky-Piscounov
equation or any other travelling wave equation in the same class. Our scenario
is based on four hypotheses on the relevant mechanism for the diffusion of the
front. Our parameter-free analytical predictions for the velocity of the front,
its diffusion constant and higher cumulants of its position agree with
numerical simulations.Comment: 10 pages, 3 figure
Shift in the velocity of a front due to a cut-off
We consider the effect of a small cut-off epsilon on the velocity of a
traveling wave in one dimension. Simulations done over more than ten orders of
magnitude as well as a simple theoretical argument indicate that the effect of
the cut-off epsilon is to select a single velocity which converges when epsilon
tends to 0 to the one predicted by the marginal stability argument. For small
epsilon, the shift in velocity has the form K(log epsilon)^(-2) and our
prediction for the constant K agrees very well with the results of our
simulations. A very similar logarithmic shift appears in more complicated
situations, in particular in finite size effects of some microscopic stochastic
systems. Our theoretical approach can also be extended to give a simple way of
deriving the shift in position due to initial conditions in the
Fisher-Kolmogorov or similar equations.Comment: 12 pages, 3 figure
Exact Solutions of Anisotropic Diffusion-Limited Reactions with Coagulation and Annihilation
We report exact results for one-dimensional reaction-diffusion models A+A ->
inert, A+A -> A, and A+B -> inert, where in the latter case like particles
coagulate on encounters and move as clusters. Our study emphasized anisotropy
of hopping rates; no changes in universal properties were found, due to
anisotropy, in all three reactions. The method of solution employed mapping
onto a model of coagulating positive integer charges. The dynamical rules were
synchronous, cellular-automaton type. All the asymptotic large-time results for
particle densities were consistent, in the framework of universality, with
other model results with different dynamical rules, when available in the
literature.Comment: 28 pages in plain TeX + 2 PostScript figure
- …