5,199 research outputs found
Renormalization-group at criticality and complete analyticity of constrained models: a numerical study
We study the majority rule transformation applied to the Gibbs measure for
the 2--D Ising model at the critical point. The aim is to show that the
renormalized hamiltonian is well defined in the sense that the renormalized
measure is Gibbsian. We analyze the validity of Dobrushin-Shlosman Uniqueness
(DSU) finite-size condition for the "constrained models" corresponding to
different configurations of the "image" system. It is known that DSU implies,
in our 2--D case, complete analyticity from which, as it has been recently
shown by Haller and Kennedy, Gibbsianness follows. We introduce a Monte Carlo
algorithm to compute an upper bound to Vasserstein distance (appearing in DSU)
between finite volume Gibbs measures with different boundary conditions. We get
strong numerical evidence that indeed DSU condition is verified for a large
enough volume for all constrained models.Comment: 39 pages, teX file, 4 Postscript figures, 1 TeX figur
Can cooperation slow down emergency evacuations?
We study the motion of pedestrians through obscure corridors where the lack
of visibility hides the precise position of the exits. Using a lattice model,
we explore the effects of cooperation on the overall exit flux (evacuation
rate). More precisely, we study the effect of the buddying threshold (of
no--exclusion per site) on the dynamics of the crowd. In some cases, we note
that if the evacuees tend to cooperate and act altruistically, then their
collective action tends to favor the occurrence of disasters.Comment: arXiv admin note: text overlap with arXiv:1203.485
Finite size scaling in three-dimensional bootstrap percolation
We consider the problem of bootstrap percolation on a three dimensional
lattice and we study its finite size scaling behavior. Bootstrap percolation is
an example of Cellular Automata defined on the -dimensional lattice
in which each site can be empty or occupied by a single
particle; in the starting configuration each site is occupied with probability
, occupied sites remain occupied for ever, while empty sites are occupied by
a particle if at least among their nearest neighbor sites are
occupied. When is fixed, the most interesting case is the one :
this is a sort of threshold, in the sense that the critical probability
for the dynamics on the infinite lattice switches from zero to one
when this limit is crossed. Finite size effects in the three-dimensional case
are already known in the cases : in this paper we discuss the case
and we show that the finite size scaling function for this problem is
of the form . We prove a conjecture proposed by
A.C.D. van Enter.Comment: 18 pages, LaTeX file, no figur
Renormalization Group results for lattice surface models
We study the phase diagram of statistical systems of closed and open
interfaces built on a cubic lattice. Interacting closed interfaces can be
written as Ising models, while open surfaces as Z(2) gauge systems. When the
open surfaces reduce to closed interfaces with few defects, also the gauge
model can be written as an Ising spin model. We apply the lower bound
renormalization group (LBRG) transformation introduced by Kadanoff (Phys. Rev.
Lett. 34, 1005 (1975)) to study the Ising models describing closed and open
surfaces with few defects. In particular, we have studied the Ising-like
transition of self-avoiding surfaces between the random-isotropic phase and the
phase with broken global symmetry at varying values of the mean curvature. Our
results are compared with previous numerical work. The limits of the LBRG
transformation in describing regions of the phase diagram where not
ferromagnetic ground-states are relevant are also discussed.Comment: 24 pages, latex, 5 figures (available upon request to
[email protected]
Metastability for reversible probabilistic cellular automata with self--interaction
The problem of metastability for a stochastic dynamics with a parallel
updating rule is addressed in the Freidlin--Wentzel regime, namely, finite
volume, small magnetic field, and small temperature. The model is characterized
by the existence of many fixed points and cyclic pairs of the zero temperature
dynamics, in which the system can be trapped in its way to the stable phase.
%The characterization of the metastable behavior %of a system in the context of
parallel dynamics is a very difficult task, %since all the jumps in the
configuration space are allowed. Our strategy is based on recent powerful
approaches, not needing a complete description of the fixed points of the
dynamics, but relying on few model dependent results. We compute the exit time,
in the sense of logarithmic equivalence, and characterize the critical droplet
that is necessarily visited by the system during its excursion from the
metastable to the stable state. We need to supply two model dependent inputs:
(1) the communication energy, that is the minimal energy barrier that the
system must overcome to reach the stable state starting from the metastable
one; (2) a recurrence property stating that for any configuration different
from the metastable state there exists a path, starting from such a
configuration and reaching a lower energy state, such that its maximal energy
is lower than the communication energy
Stationary uphill currents in locally perturbed Zero Range Processes
Uphill currents are observed when mass diffuses in the direction of the
density gradient. We study this phenomenon in stationary conditions in the
framework of locally perturbed 1D Zero Range Processes (ZRP). We show that the
onset of currents flowing from the reservoir with smaller density to the one
with larger density can be caused by a local asymmetry in the hopping rates on
a single site at the center of the lattice. For fixed injection rates at the
boundaries, we prove that a suitable tuning of the asymmetry in the bulk may
induce uphill diffusion at arbitrarily large, finite volumes. We also deduce
heuristically the hydrodynamic behavior of the model and connect the local
asymmetry characterizing the ZRP dynamics to a matching condition relevant for
the macroscopic problem
Linear Boltzmann dynamics in a strip with large reflective obstacles: stationary state and residence time
The presence of obstacles modify the way in which particles diffuse. In
cells, for instance, it is observed that, due to the presence of macromolecules
playing the role of obstacles, the mean square displacement ofbiomolecules
scales as a power law with exponent smaller than one. On the other hand,
different situations in grain and pedestrian dynamics in which the presence of
an obstacle accelerate the dynamics are known. We focus on the time, called
residence time, needed by particles to cross a strip assuming that the dynamics
inside the strip follows the linear Boltzmann dynamics. We find that the
residence time is not monotonic with the sizeand the location of the obstacles,
since the obstacle can force those particles that eventually cross the strip to
spend a smaller time in the strip itself. We focus on the case of a rectangular
strip with two open sides and two reflective sides and we consider reflective
obstaclea into the strip
Does communication enhance pedestrians transport in the dark?
We study the motion of pedestrians through an obscure tunnel where the lack
of visibility hides the exits. Using a lattice model, we explore the effects of
communication on the effective transport properties of the crowd of
pedestrians. More precisely, we study the effect of two thresholds on the
structure of the effective nonlinear diffusion coefficient. One threshold
models pedestrians's communication efficiency in the dark, while the other one
describes the tunnel capacity. Essentially, we note that if the evacuees show a
maximum trust (leading to a fast communication), they tend to quickly find the
exit and hence the collective action tends to prevent the occurrence of
disasters
Metastability in the two-dimensional Ising model with free boundary conditions
We investigate metastability in the two dimensional Ising model in a square
with free boundary conditions at low temperatures. Starting with all spins down
in a small positive magnetic field, we show that the exit from this metastable
phase occurs via the nucleation of a critical droplet in one of the four
corners of the system. We compute the lifetime of the metastable phase
analytically in the limit , and via Monte Carlo simulations at
fixed values of and and find good agreement. This system models the
effects of boundary domains in magnetic storage systems exiting from a
metastable phase when a small external field is applied.Comment: 24 pages, TeX fil
Kink Localization under Asymmetric Double-Well Potential
We study diffuse phase interfaces under asymmetric double-well potential
energies with degenerate minima and demonstrate that the limiting sharp
profile, for small interface energy cost, on a finite space interval is in
general not symmetric and its position depends exclusively on the second
derivatives of the potential energy at the two minima (phases). We discuss an
application of the general result to porous media in the regime of solid-fluid
segregation under an applied pressure and describe the interface between a
fluid-rich and a fluid-poor phase. Asymmetric double-well potential energies
are also relevant in a very different field of physics as that of Brownian
motors. An intriguing analogy between our result and the direction of the dc
soliton current in asymmetric substrate driven Brownian motors is pointed out
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