1,537 research outputs found
Spatial fluctuations of a surviving particle in the trapping reaction
We consider the trapping reaction, , where and particles
have a diffusive dynamics characterized by diffusion constants and .
The interaction with particles can be formally incorporated in an effective
dynamics for one particle as was recently shown by Bray {\it et al}. [Phys.
Rev. E {\bf 67}, 060102 (2003)]. We use this method to compute, in space
dimension , the asymptotic behaviour of the spatial fluctuation,
, for a surviving particle in the perturbative regime,
, for the case of an initially uniform distribution of
particles. We show that, for , with
. By contrast, the fluctuations of paths constrained to return to
their starting point at time grow with the larger exponent 1/3. Numerical
tests are consistent with these predictions.Comment: 10 pages, 5 figure
Reports Of Conferences, Institutes, And Seminars
This quarter\u27s column offers coverage of multiple sessions from the 2016 Electronic Resources & Libraries (ER&L) Conference, held April 3–6, 2016, in Austin, Texas. Topics in serials acquisitions dominate the column, including reports on altmetrics, cost per use, demand-driven acquisitions, and scholarly communications and the use of subscriptions agents; ERMS, access, and knowledgebases are also featured
Mechanism for the failure of the Edwards hypothesis in the SK spin glass
The dynamics of the SK model at T=0 starting from random spin configurations
is considered. The metastable states reached by such dynamics are atypical of
such states as a whole, in that the probability density of site energies,
, is small at . Since virtually all metastable states
have a much larger , this behavior demonstrates a qualitative failure of
the Edwards hypothesis. We look for its origins by modelling the changes in the
site energies during the dynamics as a Markov process. We show how the small
arises from features of the Markov process that have a clear physical
basis in the spin-glass, and hence explain the failure of the Edwards
hypothesis.Comment: 5 pages, new title, modified text, additional reference
Dyck Paths, Motzkin Paths and Traffic Jams
It has recently been observed that the normalization of a one-dimensional
out-of-equilibrium model, the Asymmetric Exclusion Process (ASEP) with random
sequential dynamics, is exactly equivalent to the partition function of a
two-dimensional lattice path model of one-transit walks, or equivalently Dyck
paths. This explains the applicability of the Lee-Yang theory of partition
function zeros to the ASEP normalization.
In this paper we consider the exact solution of the parallel-update ASEP, a
special case of the Nagel-Schreckenberg model for traffic flow, in which the
ASEP phase transitions can be intepreted as jamming transitions, and find that
Lee-Yang theory still applies. We show that the parallel-update ASEP
normalization can be expressed as one of several equivalent two-dimensional
lattice path problems involving weighted Dyck or Motzkin paths. We introduce
the notion of thermodynamic equivalence for such paths and show that the
robustness of the general form of the ASEP phase diagram under various update
dynamics is a consequence of this thermodynamic equivalence.Comment: Version accepted for publicatio
Relaxation time in a non-conserving driven-diffusive system with parallel dynamics
We introduce a two-state non-conserving driven-diffusive system in
one-dimension under a discrete-time updating scheme. We show that the
steady-state of the system can be obtained using a matrix product approach. On
the other hand, the steady-state of the system can be expressed in terms of a
linear superposition Bernoulli shock measures with random walk dynamics. The
dynamics of a shock position is studied in detail. The spectrum of the transfer
matrix and the relaxation times to the steady-state have also been studied in
the large-system-size limit.Comment: 10 page
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
Lee-Yang zeros and phase transitions in nonequilibrium steady states
We consider how the Lee-Yang description of phase transitions in terms of
partition function zeros applies to nonequilibrium systems. Here one does not
have a partition function, instead we consider the zeros of a steady-state
normalization factor in the complex plane of the transition rates. We obtain
the exact distribution of zeros in the thermodynamic limit for a specific
model, the boundary-driven asymmetric simple exclusion process. We show that
the distributions of zeros at the first and second order nonequilibrium phase
transitions of this model follow the patterns known in the Lee-Yang equilibrium
theory.Comment: 4 pages RevTeX4 with 4 figures; revised version to appear in Phys.
Rev. Let
New light curves and ephemeris for the close eclipsing binary V963 PER
We have obtained CCD photometry in 2010-11 of V963 Per (=GSC3355 0394), which
is a recently identified close binary star with unequal eclipse depths. The
seven new eclipse timings yield an improved ephemeris, but we caution that
secondary eclipse can be affected by variation of the light curve. This
variation seems to be on a monthly timescale at the few percent level.Comment: 6 pages, 3 figure
Survival probability of a diffusing particle in the presence of Poisson-distributed mobile traps
The problem of a diffusing particle moving among diffusing traps is analyzed
in general space dimension d. We consider the case where the traps are
initially randomly distributed in space, with uniform density rho, and derive
upper and lower bounds for the probability Q(t) (averaged over all particle and
trap trajectories) that the particle survives up to time t. We show that, for
1<=d<2, the bounds converge asymptotically to give where and D
is the diffusion constant of the traps, and that for d=2. For d>2 bounds can still be derived, but they no longer
converge for large t. For 1<=d<=2, these asymptotic form are independent of the
diffusion constant of the particle. The results are compared with simulation
results obtained using a new algorithm [V. Mehra and P. Grassberger, Phys. Rev.
E v65 050101 (2002)] which is described in detail. Deviations from the
predicted asymptotic forms are found to be large even for very small values of
Q(t), indicating slowly decaying corrections whose form is consistent with the
bounds. We also present results in d=1 for the case where the trap densities on
either side of the particle are different. For this case we can still obtain
exact bounds but they no longer converge.Comment: 13 pages, RevTeX4, 6 figures. Figures and references updated;
equations corrected; discussion clarifie
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