655 research outputs found
The effect of asymmetric disorder on the diffusion in arbitrary networks
Considering diffusion in the presence of asymmetric disorder, an exact
relationship between the strength of weak disorder and the electric resistance
of the corresponding resistor network is revealed, which is valid in arbitrary
networks. This implies that the dynamics are stable against weak asymmetric
disorder if the resistance exponent of the network is negative. In the
case of , numerical analyses of the mean first-passage time on
various fractal lattices show that the logarithmic scaling of with the
distance , , is a general rule, characterized by a new
dynamical exponent of the underlying lattice.Comment: 5 pages, 4 figure
Effective target arrangement in a deterministic scale-free graph
We study the random walk problem on a deterministic scale-free network, in
the presence of a set of static, identical targets; due to the strong
inhomogeneity of the underlying structure the mean first-passage time (MFPT),
meant as a measure of transport efficiency, is expected to depend sensitively
on the position of targets. We consider several spatial arrangements for
targets and we calculate, mainly rigorously, the related MFPT, where the
average is taken over all possible starting points and over all possible paths.
For all the cases studied, the MFPT asymptotically scales like N^{theta}, being
N the volume of the substrate and theta ranging from (1 - log 2/log3), for
central target(s), to 1, for a single peripheral target.Comment: 8 pages, 5 figure
Solution of an infection model near threshold
We study the Susceptible-Infected-Recovered model of epidemics in the
vicinity of the threshold infectivity. We derive the distribution of total
outbreak size in the limit of large population size . This is accomplished
by mapping the problem to the first passage time of a random walker subject to
a drift that increases linearly with time. We recover the scaling results of
Ben-Naim and Krapivsky that the effective maximal size of the outbreak scales
as , with the average scaling as , with an explicit form for
the scaling function
Citation Statistics from 110 Years of Physical Review
Publicly available data reveal long-term systematic features about citation
statistics and how papers are referenced. The data also tell fascinating
citation histories of individual articles.Comment: This is esssentially identical to the article that appeared in the
June 2005 issue of Physics Toda
Freezing and Slow Evolution in a Constrained Opinion Dynamics Model
We study opinion formation in a population that consists of leftists,
centrists, and rightist. In an interaction between neighboring agents, a
centrist and a leftist can become both centrists or leftists (and similarly for
a centrist and a rightist). In contrast, leftists and rightists do not affect
each other. The initial density of centrists rho_0 controls the evolution. With
probability rho_0 the system reaches a centrist consensus, while with
probability 1-rho_0 a frozen population of leftists and rightists results. In
one dimension, we determine this frozen state and the opinion dynamics by
mapping the system onto a spin-1 Ising model with zero-temperature Glauber
kinetics. In the frozen state, the length distribution of single-opinion
domains has an algebraic small-size tail x^{-2(1-psi)} and the average domain
size grows as L^{2*psi}, where L is the system length. The approach to this
frozen state is governed by a t^{-psi} long-time tail with psi-->2*rho_0/pi as
rho_0-->0.Comment: 4 pages, 6 figures, 2-column revtex4 format, for submission to J.
Phys. A. Revision contains lots of stylistic changes and 1 new result; the
main conclusions are the sam
Hopping Conduction and Bacteria: Transport in Disordered Reaction-Diffusion Systems
We report some basic results regarding transport in disordered
reaction-diffusion systems with birth (A->2A), death (A->0), and binary
competition (2A->A) processes. We consider a model in which the growth process
is only allowed to take place in certain areas--"oases"--while the rest of
space--the "desert"--is hostile to growth. In the limit of low oasis density,
transport is mediated through rare "hopping" events, necessitating the
inclusion of discreteness effects in the model. By first considering transport
between two oases, we are able to derive an approximate expression for the
average time taken for a population to traverse a disordered medium.Comment: 4 pages, 2 figure
Effect of antiferromagnetic exchange interactions on the Glauber dynamics of one-dimensional Ising models
We study the effect of antiferromagnetic interactions on the single spin-flip
Glauber dynamics of two different one-dimensional (1D) Ising models with spin
. The first model is an Ising chain with antiferromagnetic exchange
interaction limited to nearest neighbors and subject to an oscillating magnetic
field. The system of master equations describing the time evolution of
sublattice magnetizations can easily be solved within a linear field
approximation and a long time limit. Resonant behavior of the magnetization as
a function of temperature (stochastic resonance) is found, at low frequency,
only when spins on opposite sublattices are uncompensated owing to different
gyromagnetic factors (i.e., in the presence of a ferrimagnetic short range
order). The second model is the axial next-nearest neighbor Ising (ANNNI)
chain, where an antiferromagnetic exchange between next-nearest neighbors (nnn)
is assumed to compete with a nearest-neighbor (nn) exchange interaction of
either sign. The long time response of the model to a weak, oscillating
magnetic field is investigated in the framework of a decoupling approximation
for three-spin correlation functions, which is required to close the system of
master equations. The calculation, within such an approximate theoretical
scheme, of the dynamic critical exponent z, defined as (where \tau is the longest relaxation time and \xi is the
correlation length of the chain), suggests that the T=0 single spin-flip
Glauber dynamics of the ANNNI chain is in a different universality class than
that of the unfrustrated Ising chain.Comment: 5 figures. Phys. Rev. B (accepted July 12, 2007
Exact calculations of first-passage quantities on recursive networks
We present general methods to exactly calculate mean-first passage quantities
on self-similar networks defined recursively. In particular, we calculate the
mean first-passage time and the splitting probabilities associated to a source
and one or several targets; averaged quantities over a given set of sources
(e.g., same-connectivity nodes) are also derived. The exact estimate of such
quantities highlights the dependency of first-passage processes with respect to
the source-target distance, which has recently revealed to be a key parameter
to characterize transport in complex media. We explicitly perform calculations
for different classes of recursive networks (finitely ramified fractals,
scale-free (trans)fractals, non-fractals, mixtures between fractals and
non-fractals, non-decimable hierarchical graphs) of arbitrary size. Our
approach unifies and significantly extends the available results in the field.Comment: 16 pages, 10 figure
Quantum random walk : effect of quenching
We study the effect of quenching on a discrete quantum random walk by
removing a detector placed at a position abruptly at time from its
path. The results show that this may lead to an enhancement of the occurrence
probability at provided the time of removal where
scales as . The ratio of the occurrence probabilities
for a quenched walker () and free walker () shows that it
scales as at large values of independent of . On the other
hand if is fixed this ratio varies as for small . The
results are compared to the classical case. We also calculate the correlations
as functions of both time and position.Comment: 5 pages, 6 figures, accepted version in PR
Perturbation theory for the one-dimensional trapping reaction
We consider the survival probability of a particle in the presence of a
finite number of diffusing traps in one dimension. Since the general solution
for this quantity is not known when the number of traps is greater than two, we
devise a perturbation series expansion in the diffusion constant of the
particle. We calculate the persistence exponent associated with the particle's
survival probability to second order and find that it is characterised by the
asymmetry in the number of traps initially positioned on each side of the
particle.Comment: 18 pages, no figures. Uses IOP Latex clas
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