399 research outputs found
Influence of local carrying capacity restrictions on stochastic predator-prey models
We study a stochastic lattice predator-prey system by means of Monte Carlo
simulations that do not impose any restrictions on the number of particles per
site, and discuss the similarities and differences of our results with those
obtained for site-restricted model variants. In accord with the classic
Lotka-Volterra mean-field description, both species always coexist in two
dimensions. Yet competing activity fronts generate complex, correlated
spatio-temporal structures. As a consequence, finite systems display transient
erratic population oscillations with characteristic frequencies that are
renormalized by fluctuations. For large reaction rates, when the processes are
rendered more local, these oscillations are suppressed. In contrast with
site-restricted predator-prey model, we observe species coexistence also in one
dimension. In addition, we report results on the steady-state prey age
distribution.Comment: Latex, IOP style, 17 pages, 9 figures included, related movies
available at http://www.phys.vt.edu/~tauber/PredatorPrey/movies
Non-equilibrium relaxation and critical aging for driven Ising lattice gases
We employ Monte Carlo simulations to study the non-equilibrium relaxation of
driven Ising lattice gases in two dimensions. Whereas the temporal scaling of
the density auto-correlation function in the non-equilibrium steady state does
not allow a precise measurement of the critical exponents, these can be
accurately determined from the aging scaling of the two-time auto-correlations
and the order parameter evolution following a quench to the critical point. We
obtain excellent agreement with renormalization group predictions based on the
standard Langevin representation of driven Ising lattice gases.Comment: 5 pages, 4 figures included; to appear in Phys. Rev. Lett. (2012
Nonequilibrium critical dynamics of the relaxational models C and D
We investigate the critical dynamics of the -component relaxational models
C and D which incorporate the coupling of a nonconserved and conserved order
parameter S, respectively, to the conserved energy density rho, under
nonequilibrium conditions by means of the dynamical renormalization group.
Detailed balance violations can be implemented isotropically by allowing for
different effective temperatures for the heat baths coupling to the slow modes.
In the case of model D with conserved order parameter, the energy density
fluctuations can be integrated out. For model C with scalar order parameter, in
equilibrium governed by strong dynamic scaling (z_S = z_rho), we find no
genuine nonequilibrium fixed point. The nonequilibrium critical dynamics of
model C with n = 1 thus follows the behavior of other systems with nonconserved
order parameter wherein detailed balance becomes effectively restored at the
phase transition. For n >= 4, the energy density decouples from the order
parameter. However, for n = 2 and n = 3, in the weak dynamic scaling regime
(z_S <= z_rho) entire lines of genuine nonequilibrium model C fixed points
emerge to one-loop order, which are characterized by continuously varying
critical exponents. Similarly, the nonequilibrium model C with spatially
anisotropic noise and n < 4 allows for continuously varying exponents, yet with
strong dynamic scaling. Subjecting model D to anisotropic nonequilibrium
perturbations leads to genuinely different critical behavior with softening
only in subsectors of momentum space and correspondingly anisotropic scaling
exponents. Similar to the two-temperature model B the effective theory at
criticality can be cast into an equilibrium model D dynamics, albeit
incorporating long-range interactions of the uniaxial dipolar type.Comment: Revtex, 23 pages, 5 eps figures included (minor additions), to appear
in Phys. Rev.
Slow relaxation and aging kinetics for the driven lattice gas
We numerically investigate the long-time behavior of the density-density
auto-correlation function in driven lattice gases with particle exclusion and
periodic boundary conditions in one, two, and three dimensions using precise
Monte Carlo simulations. In the one-dimensional asymmetric exclusion process on
a ring with half the lattice sites occupied, we find that correlations induce
extremely slow relaxation to the asymptotic power law decay. We compare the
crossover functions obtained from our simulations with various analytic results
in the literature, and analyze the characteristic oscillations that occur in
finite systems away from half-filling. As expected, in three dimensions
correlations are weak and consequently the mean-field description is adequate.
We also investigate the relaxation towards the nonequilibrium steady state in
the two-time density-density auto-correlations, starting from strongly
correlated initial conditions. We obtain simple aging scaling behavior in one,
two, and three dimensions, with the expected power laws.Comment: 12 pages, 18 figures; to appear in Phys. Rev. E (2011
Critical behavior of the two dimensional 2A->3A, 4A->0 binary system
The phase transitions of the recently introduced 2A -> 3A, 4A -> 0
reaction-diffusion model (G.Odor, PRE 69 036112 (2004)) are explored in two
dimensions. This model exhibits site occupation restriction and explicit
diffusion of isolated particles. A reentrant phase diagram in the diffusion -
creation rate space is confirmed in agreement with cluster mean-field and
one-dimensional results. For strong diffusion a mean-field transition can be
observed at zero branching rate characterized by density decay
exponent. In contrast with this for weak diffusion the effective 2A ->3A->4A->0
reaction becomes relevant and the mean-field transition of the 2A -> 3A, 2A ->
0 model characterized by also appears for non-zero branching
rates.Comment: 5 pages, 5 figures included, small correction
Kinetics of phase-separation in the critical spherical model and local scale-invariance
The scaling forms of the space- and time-dependent two-time correlation and
response functions are calculated for the kinetic spherical model with a
conserved order-parameter and quenched to its critical point from a completely
disordered initial state. The stochastic Langevin equation can be split into a
noise part and into a deterministic part which has local scale-transformations
with a dynamical exponent z=4 as a dynamical symmetry. An exact reduction
formula allows to express any physical average in terms of averages calculable
from the deterministic part alone. The exact spherical model results are shown
to agree with these predictions of local scale-invariance. The results also
include kinetic growth with mass conservation as described by the
Mullins-Herring equation.Comment: Latex2e with IOP macros, 28 pp, 2 figures, final for
Localized Flux Lines and the Bose Glass
Columnar defects provide effective pinning centers for magnetic flux lines in
high-- superconductors. Utilizing a mapping of the statistical
mechanics of directed lines to the quantum mechanics of two--dimensional
bosons, one expects an entangled flux liquid phase at high temperatures,
separated by a second--order localization transition from a low--temperature
``Bose glass'' phase with infinite tilt modulus. Recent decoration experiments
have demonstrated that below the matching field the repulsive forces between
the vortices may be sufficiently large to produce strong spatial correlations
in the Bose glass. This is confirmed by numerical simulations, and a remarkably
wide soft ``Coulomb gap'' at the chemical potential is found in the
distribution of pinning energies. At low currents, the dominant transport
mechanism in the Bose glass phase proceeds via the formation of double kinks
between not necessarily adjacent columnar pins, similar to variable--range
hopping in disordered semiconductors. The strong correlation effects
originating in the long--range vortex interactions drastically reduce
variable--range hopping transport.Comment: 10 pages, latex ("lamuphys.sty" file included), 6 figures can be
obtained from the author ([email protected]); to appear in Proc. XIV
Sitges conference on "Complex Behaviour of Glassy Systems" (Springer--Verlag
Failure of Ceftriaxone in an Intravenous Drug User with Invasive Infection Due to Ralstonia pickettii
Abstract. : We report a case of septic arthritis due to Ralstonia pickettii in an intravenous drug user with unfavorable clinical course under antibiotic therapy with ceftriaxone despite in vitro susceptibility to the drug. The treatment failure may have been due to a discrepancy between in vitro and in vivo susceptibility of R. pickettii, or to resistance development mediated by a recently described inducible ß-lactamas
Stochastic population oscillations in spatial predator-prey models
It is well-established that including spatial structure and stochastic noise
in models for predator-prey interactions invalidates the classical
deterministic Lotka-Volterra picture of neutral population cycles. In contrast,
stochastic models yield long-lived, but ultimately decaying erratic population
oscillations, which can be understood through a resonant amplification
mechanism for density fluctuations. In Monte Carlo simulations of spatial
stochastic predator-prey systems, one observes striking complex spatio-temporal
structures. These spreading activity fronts induce persistent correlations
between predators and prey. In the presence of local particle density
restrictions (finite prey carrying capacity), there exists an extinction
threshold for the predator population. The accompanying continuous
non-equilibrium phase transition is governed by the directed-percolation
universality class. We employ field-theoretic methods based on the Doi-Peliti
representation of the master equation for stochastic particle interaction
models to (i) map the ensuing action in the vicinity of the absorbing state
phase transition to Reggeon field theory, and (ii) to quantitatively address
fluctuation-induced renormalizations of the population oscillation frequency,
damping, and diffusion coefficients in the species coexistence phase.Comment: 14 pages, 6 figures, submitted to J. Phys C: Conf. Ser. (2011
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