339 research outputs found
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
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
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
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
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
Geometric scaling as traveling waves
We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky-
Piscounov (KPP) equation to the problem of high energy evolution of the QCD
amplitudes. We explain how the traveling wave solutions of this equation are
related to geometric scaling, a phenomenon observed in deep-inelastic
scattering experiments. Geometric scaling is for the first time shown to result
from an exact solution of nonlinear QCD evolution equations. Using general
results on the KPP equation, we compute the velocity of the wave front, which
gives the full high energy dependence of the saturation scale.Comment: 4 pages, 1 figure. v2: references adde
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
Diffusive Capture Process on Complex Networks
We study the dynamical properties of a diffusing lamb captured by a diffusing
lion on the complex networks with various sizes of . We find that the life
time and the survival probability becomes finite on scale-free networks with degree exponent
. However, for has a long-living tail on
tree-structured scale-free networks and decays exponentially on looped
scale-free networks. It suggests that the second moment of degree distribution
kn(k)n(k)\sim k^{-\sigma}\gamma<3n(k)k\approx k_{max}n(k)n(k)\sim k^2P(k)N_{tot}, which
causes the dependent behavior of and $.Comment: 9 pages, 6 figure
Exact Results for Diffusion-Limited Reactions with Synchronous Dynamics
A new method is introduced allowing to solve exactly the reactions A+A->inert
and A+A->A on the 1D lattice with synchronous diffusional dynamics
(simultaneous hopping of all particles). Exact connections are found relating
densities and certain correlation properties of these two reactions at all
times. Asymptotic behavior at large times as well as scaling form describing
the regime of low initial density, are derived explicitly.Comment: 12 pages in plain Te
A supercritical series analysis for the generalized contact process with diffusion
We study a model that generalizes the CP with diffusion. An additional
transition is included in the model so that at a particular point of its phase
diagram a crossover from the directed percolation to the compact directed
percolation class will happen. We are particularly interested in the effect of
diffusion on the properties of the crossover between the universality classes.
To address this point, we develop a supercritical series expansion for the
ultimate survival probability and analyse this series using d-log Pad\'e and
partial differential approximants. We also obtain approximate solutions in the
one- and two-site dynamical mean-field approximations. We find evidences that,
at variance to what happens in mean-field approximations, the crossover
exponent remains close to even for quite high diffusion rates, and
therefore the critical line in the neighborhood of the multicritical point
apparently does not reproduce the mean-field result (which leads to )
as the diffusion rate grows without bound
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