3,085 research outputs found
Simple model with facilitated dynamics for granular compaction
A simple lattice model is used to study compaction in granular media. As in
real experiments, we consider a series of taps separated by large enough
waiting times. The relaxation of the density exhibits the characteristic
inverse logarithmic law. Moreover, we have been able to identify analytically
the relevant time scale, leading to a relaxation law independent of the
specific values of the parameters. Also, an expression for the asymptotic
density reached in the compaction process has been derived. The theoretical
predictions agree fairly well with the results from the Monte Carlo simulation.Comment: 15 pages, 4 figures, REVTeX file; no changes except for
single-spacing to save paper (previous version 22 pages
Activity phase transition for constrained dynamics
We consider two cases of kinetically constrained models, namely East and
FA-1f models. The object of interest of our work is the activity A(t) defined
as the total number of configuration changes in the interval [0,t] for the
dynamics on a finite domain. It has been shown in [GJLPDW1,GJLPDW2] that the
large deviations of the activity exhibit a non-equilibirum phase transition in
the thermodynamic limit and that reducing the activity is more likely than
increasing it due to a blocking mechanism induced by the constraints. In this
paper, we study the finite size effects around this first order phase
transition and analyze the phase coexistence between the active and inactive
dynamical phases in dimension 1. In higher dimensions, we show that the finite
size effects are also determined by the dimension and the choice of boundary
conditions.Comment: 38 pages, 3 figure
Kinetic Theory of Flux Line Hydrodynamics:LIQUID Phase with Disorder
We study the Langevin dynamics of flux lines of high--T superconductors
in the presence of random quenched pinning. The hydrodynamic theory for the
densities is derived by starting with the microscopic model for the flux-line
liquid. The dynamic functional is expressed as an expansion in the dynamic
order parameter and the corresponding response field. We treat the model within
the Gaussian approximation and calculate the dynamic structure function in the
presence of pinning disorder. The disorder leads to an additive static peak
proportional to the disorder strength. On length scales larger than the line
static transverse wandering length and at long times, we recover the
hydrodynamic results of simple frictional diffusion, with interactions
additively renormalizing the relaxational rate. On shorter length and time
scales line internal degrees of freedom significantly modify the dynamics by
generating wavevector-dependent corrections to the density relaxation rate.Comment: 61 pages and 6 figures available upon request, plain TEX using
Harvard macro
Singularities in ternary mixtures of k-core percolation
Heterogeneous k-core percolation is an extension of a percolation model which
has interesting applications to the resilience of networks under random damage.
In this model, the notion of node robustness is local, instead of global as in
uniform k-core percolation. One of the advantages of k-core percolation models
is the validity of an analytical mathematical framework for a large class of
network topologies. We study ternary mixtures of node types in random networks
and show the presence of a new type of critical phenomenon. This scenario may
have useful applications in the stability of large scale infrastructures and
the description of glass-forming systems.Comment: To appear in Complex Networks, Studies in Computational Intelligence,
Proceedings of CompleNet 201
What do we learn from the shape of the dynamical susceptibility of glass-formers?
We compute analytically and numerically the four-point correlation function
that characterizes non-trivial cooperative dynamics in glassy systems within
several models of glasses: elasto-plastic deformations, mode-coupling theory
(MCT), collectively rearranging regions (CRR), diffusing defects and
kinetically constrained models (KCM). Some features of the four-point
susceptibility chi_4(t) are expected to be universal. at short times we expect
an elastic regime characterized by a t or sqrt{t} growth. We find both in the
beta, and the early alpha regime that chi_4 sim t^mu, where mu is directly
related to the mechanism responsible for relaxation. This regime ends when a
maximum of chi_4 is reached at a time t=t^* of the order of the relaxation time
of the system. This maximum is followed by a fast decay to zero at large times.
The height of the maximum also follows a power-law, chi_4(t^*) sim t^{*lambda}.
The value of the exponents mu and lambda allows one to distinguish between
different mechanisms. For example, freely diffusing defects in d=3 lead to mu=2
and lambda=1, whereas the CRR scenario rather predicts either mu=1 or a
logarithmic behaviour depending on the nature of the nucleation events, and a
logarithmic behaviour of chi_4(t^*). MCT leads to mu=b and lambda =1/gamma,
where b and gamma are the standard MCT exponents. We compare our theoretical
results with numerical simulations on a Lennard-Jones and a soft-sphere system.
Within the limited time-scales accessible to numerical simulations, we find
that the exponent mu is rather small, mu < 1, with a value in reasonable
agreement with the MCT predictions.Comment: 26 pages, 6 figure
Interfaces of Modulated Phases
Numerically minimizing a continuous free-energy functional which yields
several modulated phases, we obtain the order-parameter profiles and
interfacial free energies of symmetric and non-symmetric tilt boundaries within
the lamellar phase, and of interfaces between coexisting lamellar, hexagonal,
and disordered phases. Our findings agree well with chevron, omega, and
T-junction tilt-boundary morphologies observed in diblock copolymers and
magnetic garnet films.Comment: 4 page
CHARACTERIZING FORAGING PATTERNS AMONG CATTLE AND BONDED AND NON-BONDED SMALL RUMINANTS USING SPATIAL POINT PROCESS TECHNIQUES
This paper uses the technique of spatial point processes to describe the spatial patterns of freeranging cattle and small ruminants. Two mixed-species livestock groups were monitored while foraging on 410 ha of brush-infested Southern New Mexico rangeland during July and August 1988. The groups consisted of crossbred Bos taurus and Bos indicus beef cattle with white-faced sheep (Ovis aries) and mohair goats (Capra hircus). The bonded group consisted of small ruminants that had their behaviours modified through socialization with cattle to form a ‘flerd’ in which small ruminants consistently remained near cattle. Small ruminants in the non-bonded group had not been socialized with cattle. A subset of animal location data measured during the morning and afternoon over five days for both the bonded and non-bonded groups was analyzed for spatial patterns. Only data for five morning periods (7:00-8:00 a.m.) are reported because morning and afternoon spatial patterns were similar. Observed nearest neighbor distances, mean number of small ruminant near an arbitrary cow, and point-to-animal distances were compared to Monte Carlo simulations of independently and uniformly distributed animal locations. Bonded and non-bonded groups were also compared. Results suggested bonded and non-bonded groups were similar in spatial patterns of intra-specific distances for both cattle and small ruminants. However, bonding changed the repulsive relationship observed between cattle and non-bonded small ruminants stocked together to one of inter-specific attraction. Bonded small ruminants remained close to and formed inter-specific clusters with cattle. In addition, the mean number of bonded small ruminants near an arbitrary cow was consistently higher than for non-bonded small ruminants. Finally, the spatial pattern of cattle across the paddock did not differ between bonded and non-bonded groups, while bonded small ruminants tended to disperse slightly more uniformly across the paddock than did non-bonded small ruminants. These findings indicate the usefulness of spatial point processes techniques to analyze such animal location data, substantiate on a larger scale conclusions of previous, replicated studies about the effect of bonding small ruminants to cattle, and suggest utilization of paddock landscapes may be positively influenced using flerds compared to flocks and herds
Dynamics of systems with isotropic competing interactions in an external field: a Langevin approach
We study the Langevin dynamics of a ferromagnetic Ginzburg-Landau Hamiltonian
with a competing long-range repulsive term in the presence of an external
magnetic field. The model is analytically solved within the self consistent
Hartree approximation for two different initial conditions: disordered or zero
field cooled (ZFC), and fully magnetized or field cooled (FC). To test the
predictions of the approximation we develop a suitable numerical scheme to
ensure the isotropic nature of the interactions. Both the analytical approach
and the numerical simulations of two-dimensional finite systems confirm a
simple aging scenario at zero temperature and zero field. At zero temperature a
critical field is found below which the initial conditions are relevant
for the long time dynamics of the system. For a logarithmic growth of
modulated domains is found in the numerical simulations but this behavior is
not captured by the analytical approach which predicts a growth law at
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