94 research outputs found
Topological Effects caused by the Fractal Substrate on the Nonequilibrium Critical Behavior of the Ising Magnet
The nonequilibrium critical dynamics of the Ising magnet on a fractal
substrate, namely the Sierpinski carpet with Hausdorff dimension =1.7925,
has been studied within the short-time regime by means of Monte Carlo
simulations. The evolution of the physical observables was followed at
criticality, after both annealing ordered spin configurations (ground state)
and quenching disordered initial configurations (high temperature state), for
three segmentation steps of the fractal. The topological effects become evident
from the emergence of a logarithmic periodic oscillation superimposed to a
power law in the decay of the magnetization and its logarithmic derivative and
also from the dependence of the critical exponents on the segmentation step.
These oscillations are discussed in the framework of the discrete scale
invariance of the substrate and carefully characterized in order to determine
the critical temperature of the second-order phase transition and the critical
exponents corresponding to the short-time regime. The exponent of the
initial increase in the magnetization was also obtained and the results suggest
that it would be almost independent of the fractal dimension of the susbstrate,
provided that is close enough to d=2.Comment: 9 figures, 3 tables, 10 page
Black Holes, Space-Filling Chains and Random Walks
Many approaches to a semiclassical description of gravity lead to an integer
black hole entropy. In four dimensions this implies that the Schwarzschild
radius obeys a formula which describes the distance covered by a Brownian
random walk. For the higher-dimensional Schwarzschild-Tangherlini black hole,
its radius relates similarly to a fractional Brownian walk. We propose a
possible microscopic explanation for these random walk structures based on
microscopic chains which fill the interior of the black hole.Comment: 18 pages, 4 figures, 2 tables; v2 and v3: minor changes and refs.
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A mean-field kinetic lattice gas model of electrochemical cells
We develop Electrochemical Mean-Field Kinetic Equations (EMFKE) to simulate
electrochemical cells. We start from a microscopic lattice-gas model with
charged particles, and build mean-field kinetic equations following the lines
of earlier work for neutral particles. We include the Poisson equation to
account for the influence of the electric field on ion migration, and
oxido-reduction processes on the electrode surfaces to allow for growth and
dissolution. We confirm the viability of our approach by simulating (i) the
electrochemical equilibrium at flat electrodes, which displays the correct
charged double-layer, (ii) the growth kinetics of one-dimensional
electrochemical cells during growth and dissolution, and (iii) electrochemical
dendrites in two dimensions.Comment: 14 pages twocolumn, 17 figure
The role of cell-cell adhesion in wound healing
We present a stochastic model which describes fronts of cells invading a
wound. In the model cells can move, proliferate, and experience cell-cell
adhesion. We find several qualitatively different regimes of front motion and
analyze the transitions between them. Above a critical value of adhesion and
for small proliferation large isolated clusters are formed ahead of the front.
This is mapped onto the well-known ferromagnetic phase transition in the Ising
model. For large adhesion, and larger proliferation the clusters become
connected (at some fixed time). For adhesion below the critical value the
results are similar to our previous work which neglected adhesion. The results
are compared with experiments, and possible directions of future work are
proposed.Comment: to appear in Journal of Statistical Physic
Kinetics in one-dimensional lattice gas and Ising models from time-dependent density functional theory
Time-dependent density functional theory, proposed recently in the context of
atomic diffusion and non-equilibrium processes in solids, is tested against
Monte Carlo simulation. In order to assess the basic approximation of that
theory, the representation of non-equilibrium states by a local equilibrium
distribution function, we focus on one-dimensional lattice models, where all
equilibrium properties can be worked exactly from the known free energy as a
functional of the density. This functional determines the thermodynamic driving
forces away from equilibrium. In our studies of the interfacial kinetics of
atomic hopping and spin relaxation, we find excellent agreement with
simulations, suggesting that the method is useful also for treating more
complex problems.Comment: 8 pages, 5 figures, submitted to Phys. Rev.
Viscous stabilization of 2D drainage displacements with trapping
We investigate the stabilization mechanisms due to viscous forces in the
invasion front during drainage displacement in two-dimensional porous media
using a network simulator. We find that in horizontal displacement the
capillary pressure difference between two different points along the front
varies almost linearly as function of height separation in the direction of the
displacement. The numerical result supports arguments taking into account the
loopless displacement pattern where nonwetting fluid flow in separate strands
(paths). As a consequence, we show that existing theories developed for viscous
stabilization, are not compatible with drainage when loopless strands dominate
the displacement process.Comment: The manuscript has been substantially revised. Accepted in Phys. Rev.
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A New Exponent Characterizing the Effect of Evaporation on Imbibition Experiments
We report imbibition experiments investigating the effect of evaporation on
the interface roughness and mean interface height. We observe a new exponent
characterizing the scaling of the saturated surface width. Further, we argue
that evaporation can be usefully modeled by introducing a gradient in the
strength of the disorder, in analogy with the gradient percolation model of
Sapoval {\it et~al.}. By incorporating this gradient we predict a new critical
exponent and a novel scaling relation for the interface width. Both the
exponent value and the form of the scaling agree with the experimental results.Comment: 12 pages, REVTeX 3.0, figures on request (accepted for PRL
Structural Properties of Self-Attracting Walks
Self-attracting walks (SATW) with attractive interaction u > 0 display a
swelling-collapse transition at a critical u_{\mathrm{c}} for dimensions d >=
2, analogous to the \Theta transition of polymers. We are interested in the
structure of the clusters generated by SATW below u_{\mathrm{c}} (swollen
walk), above u_{\mathrm{c}} (collapsed walk), and at u_{\mathrm{c}}, which can
be characterized by the fractal dimensions of the clusters d_{\mathrm{f}} and
their interface d_{\mathrm{I}}. Using scaling arguments and Monte Carlo
simulations, we find that for u<u_{\mathrm{c}}, the structures are in the
universality class of clusters generated by simple random walks. For
u>u_{\mathrm{c}}, the clusters are compact, i.e. d_{\mathrm{f}}=d and
d_{\mathrm{I}}=d-1. At u_{\mathrm{c}}, the SATW is in a new universality class.
The clusters are compact in both d=2 and d=3, but their interface is fractal:
d_{\mathrm{I}}=1.50\pm0.01 and 2.73\pm0.03 in d=2 and d=3, respectively. In
d=1, where the walk is collapsed for all u and no swelling-collapse transition
exists, we derive analytical expressions for the average number of visited
sites and the mean time to visit S sites.Comment: 15 pages, 8 postscript figures, submitted to Phys. Rev.
The scale dependence and structure of convergence fields preceding the initiation of deep convection
Links between convergence and convection are poor in global models, and poor representation of convection is the source of many model biases in the tropics. State-of-the-art convection-permitting simulations allow us to analyze realistic convection statistically. The analysis of fractal dimension is used to show that in convection-permitting simulations (grid spacings 1.5, 4, and 12 km) of the West African monsoon, 50% of deep convective initiations occur in the near vicinity of low-level boundary layer convergence lines that are orientated along the mean wind. In these simulations, more than 80% of the initiations occur within large-scale (300 × 300 km) convergence, with some 20% in large-scale divergence, and almost all cases occur within local scale (60 × 60 km) convergence. The behavior alters in a simulation with a convection scheme and a grid spacing of 12 km; initiation is less frequent over convergence lines, and there is less dependency on high-magnitude low-level local convergence. Key Points Fifty percent of storms initiate along convergence lines Most initiations occur in large and local scale convergence Parameterized convection exhibits a weaker dependence on strong convergence ©2014. American Geophysical Union. All Rights Reserved
Dynamic correlations in an ordered c(22) lattice gas
We obtain the dynamic correlation function of two-dimensional lattice gas
with nearest-neighbor repulsion in ordered c(22) phase
(antiferromagnetic ordering) under the condition of low concentration of
structural defects. It is shown that displacements of defects of the ordered
state are responsible for the particle number fluctuations in the probe area.
The corresponding set of kinetic equations is derived and solved in linear
approximation on the defect concentration. Three types of strongly correlated
complex jumps are considered and their contribution to fluctuations is
analysed. These are jumps of excess particles, vacancies and flip-flop jumps.
The kinetic approach is more general than the one based on diffusion-like
equations used in our previous papers. Thus, it becomes possible to adequately
describe correlations of fluctuations at small times, where our previous theory
fails to give correct results. Our new analytical results for fluctuations of
particle number in the probe area agree well with those obtained by Monte Carlo
simulations.Comment: 10 pages, 7 figure
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