1,188 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
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
Monte Carlo study of the growth of striped domains
We analyze the dynamical scaling behavior in a two-dimensional spin model
with competing interactions after a quench to a striped phase. We measure the
growth exponents studying the scaling of the interfaces and the scaling of the
shrinking time of a ball of one phase plunged into the sea of another phase.
Our results confirm the predictions found in previous papers. The correlation
functions measured in the direction parallel and transversal to the stripes are
different as suggested by the existence of different interface energies between
the ground states of the model. Our simulations show anisotropic features for
the correlations both in the case of single-spin-flip and spin-exchange
dynamics.Comment: 15 pages, ReVTe
A combinatorial proof of tree decay of semi-invariants
We consider finite range Gibbs fields and provide a purely combinatorial
proof of the exponential tree decay of semi--invariants, supposing that the
logarithm of the partition function can be expressed as a sum of suitable local
functions of the boundary conditions. This hypothesis holds for completely
analytical Gibbs fields; in this context the tree decay of semi--invariants has
been proven via analyticity arguments. However the combinatorial proof given
here can be applied also to the more complicated case of disordered systems in
the so called Griffiths' phase when analyticity arguments fail
A model for enhanced and selective transport through biological membranes with alternating pores
We investigate the outflux of ions through the channels in a cell membrane.
The channels undergo an open/close cycle according to a periodic schedule. Our
study is based both on theoretical considerations relying on homogenization
theory, and on Monte Carlo numerical simulations. We examine the onset of a
limiting boundary behavior characterized by a constant ratio between the
outflux and the local density, in the thermodynamics limit. The focus here is
on the issue of selectivity, that is on the different behavior of the ion
currents through the channel in the cases of the selected and non-selected
species.Comment: arXiv admin note: text overlap with arXiv:1307.418
Renormalization Group in the uniqueness region: weak Gibbsianity and convergence
We analyze the block averaging transformation applied to lattice gas models
with short range interaction in the uniqueness region below the critical
temperature. We prove weak Gibbsianity of the renormalized measure and
convergence of the renormalized potential in a weak sense. Since we are
arbitrarily close to the coexistence region we have a diverging characteristic
length of the system: the correlation length or the critical length for
metastability, or both. Thus, to perturbatively treat the problem we have to
use a scale-adapted expansion. Moreover, such a model below the critical
temperature resembles a disordered system in presence of Griffiths'
singularity. Then the cluster expansion that we use must be graded with its
minimal scale length diverging when the coexistence line is approached
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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