230 research outputs found
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
Symmetry and species segregation in diffusion-limited pair annihilation
We consider a system of q diffusing particle species A_1,A_2,...,A_q that are
all equivalent under a symmetry operation. Pairs of particles may annihilate
according to A_i + A_j -> 0 with reaction rates k_{ij} that respect the
symmetry, and without self-annihilation (k_{ii} = 0). In spatial dimensions d >
2 mean-field theory predicts that the total particle density decays as n(t) ~
1/t, provided the system remains spatially uniform. We determine the conditions
on the matrix k under which there exists a critical segregation dimension
d_{seg} below which this uniformity condition is violated; the symmetry between
the species is then locally broken. We argue that in those cases the density
decay slows down to n(t) ~ t^{-d/d_{seg}} for 2 < d < d_{seg}. We show that
when d_{seg} exists, its value can be expressed in terms of the ratio of the
smallest to the largest eigenvalue of k. The existence of a conservation law
(as in the special two-species annihilation A + B -> 0), although sufficient
for segregation, is shown not to be a necessary condition for this phenomenon
to occur. We work out specific examples and present Monte Carlo simulations
compatible with our analytical results.Comment: latex, 19 pages, 3 eps figures include
An antipeptide antibody that specifically inhibits insulin receptor autophosphorylation and protein kinase activity.
Directed Ising type dynamic preroughening transition in one dimensional interfaces
We present a realization of directed Ising (DI) type dynamic absorbing state
phase transitions in the context of one-dimensional interfaces, such as the
relaxation of a step on a vicinal surface. Under the restriction that particle
deposition and evaporation can only take place near existing kinks, the
interface relaxes into one of three steady states: rough, perfectly ordered
flat (OF) without kinks, or disordered flat (DOF) with randomly placed kinks
but in perfect up-down alternating order. A DI type dynamic preroughening
transition takes place between the OF and DOF phases. At this critical point
the asymptotic time evolution is controlled not only by the DI exponents but
also by the initial condition. Information about the correlations in the
initial state persists and changes the critical exponents.Comment: 12 pages, 10 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
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
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
How the geometry makes the criticality in two - component spreading phenomena?
We study numerically a two-component A-B spreading model (SMK model) for
concave and convex radial growth of 2d-geometries. The seed is chosen to be an
occupied circle line, and growth spreads inside the circle (concave geometry)
or outside the circle (convex geometry). On the basis of generalised
diffusion-annihilation equation for domain evolution, we derive the mean field
relations describing quite well the results of numerical investigations. We
conclude that the intrinsic universality of the SMK does not depend on the
geometry and the dependence of criticality versus the curvature observed in
numerical experiments is only an apparent effect. We discuss the dependence of
the apparent critical exponent upon the spreading geometry and
initial conditions.Comment: Uses iopart.cls, 11 pages with 8 postscript figures embedde
Renormalization Group Study of the A+B->0 Diffusion-Limited Reaction
The diffusion-limited reaction, with equal initial densities
, is studied by means of a field-theoretic renormalization
group formulation of the problem. For dimension an effective theory is
derived, from which the density and correlation functions can be calculated. We
find the density decays in time as a,b \sim C\sqrt{\D}(Dt)^{-d/4} for , with \D = n_0-C^\prime n_0^{d/2} + \dots, where is a universal
constant, and is non-universal. The calculation is extended to the
case of unequal diffusion constants , resulting in a new
amplitude but the same exponent. For a controlled calculation is not
possible, but a heuristic argument is presented that the results above give at
least the leading term in an expansion. Finally, we address
reaction zones formed in the steady-state by opposing currents of and
particles, and derive scaling properties.Comment: 17 pages, REVTeX, 13 compressed figures, included with epsf. Eq.
(6.12) corrected, and a moderate rewriting of the introduction. Accepted for
publication in J. Stat. Phy
Reentrant phase diagram of branching annihilating random walks with one and two offsprings
We investigate the phase diagram of branching annihilating random walks with
one and two offsprings in one dimension. A walker can hop to a nearest neighbor
site or branch with one or two offsprings with relative ratio. Two walkers
annihilate immediately when they meet. In general, this model exhibits a
continuous phase transition from an active state into the absorbing state
(vacuum) at a finite hopping probability. We map out the phase diagram by Monte
Carlo simulations which shows a reentrant phase transition from vacuum to an
active state and finally into vacuum again as the relative rate of the
two-offspring branching process increases. This reentrant property apparently
contradicts the conventional wisdom that increasing the number of offsprings
will tend to make the system more active. We show that the reentrant property
is due to the static reflection symmetry of two-offspring branching processes
and the conventional wisdom is recovered when the dynamic reflection symmetry
is introduced instead of the static one.Comment: 14 pages, Revtex, 4 figures (one PS figure file upon request)
(submitted to Phy. Rev. E
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