272 research outputs found
Theory of Boundary Effects in Invasion Percolation
We study the boundary effects in invasion percolation with and without
trapping. We find that the presence of boundaries introduces a new set of
surface critical exponents, as in the case of standard percolation. Numerical
simulations show a fractal dimension, for the region of the percolating cluster
near the boundary, remarkably different from the bulk one. We find a
logarithmic cross-over from surface to bulk fractal properties, as one would
expect from the finite-size theory of critical systems. The distribution of the
quenched variables on the growing interface near the boundary self-organises
into an asymptotic shape characterized by a discontinuity at a value ,
which coincides with the bulk critical threshold. The exponent of
the boundary avalanche distribution for IP without trapping is
; this value is very near to the bulk one. Then we
conclude that only the geometrical properties (fractal dimension) of the model
are affected by the presence of a boundary, while other statistical and
dynamical properties are unchanged. Furthermore, we are able to present a
theoretical computation of the relevant critical exponents near the boundary.
This analysis combines two recently introduced theoretical tools, the Fixed
Scale Transformation (FST) and the Run Time Statistics (RTS), which are
particularly suited for the study of irreversible self-organised growth models
with quenched disorder. Our theoretical results are in rather good agreement
with numerical data.Comment: 11 pages, 13 figures, revte
Grain reserves and food security in the Middle East and North Africa.
Aggregate stocks of major grains declined to minimal feasible levels in 2007–2008, due to high global income growth and biofuel mandates. Given these minimal stocks, prices were very sensitive to shocks, such as the Australian drought, and biofuel demand boosts due to the oil price spike. The effects of these shocks were magnified by a sequence of trade restrictions by key exporters to protect vulnerable consumers. Beginning in the 'thin' global rice market in the fall of 2007, these turned market anxiety into panic. Recognizing the unreliability of imports, vulnerable countries, including some in the Middle East and North Africa (MENA), are now considering investing in strategic reserves, pursuing self sufficiency and acquiring foreign land to ensure grain supplies for domestic consumption. The associated expense and negative incentive effects on national reserves may be acceptable if they have quantitative targets related to the needs of the most vulnerable, for distribution only in emergencies. In many MENA countries, heavy subsidies on grain consumption for both rich and poor reduce the stabilizing response of consumption to price, and increase reserves needed to ensure food security. Accumulation of stocks is a more efficient strategy than pursuit of self-sufficiency in most MENA countries, as they have no comparative advantage in expanding agriculture, given restricted water supplies. Acquisition of foreign lands leaves food supplies exposed to sovereign risk and other supply chain problems beyond importers' control. MENA countries could cooperate and so smooth much of the risk posed by fluctuations in their own harvests
Generalized Dielectric Breakdown Model
We propose a generalized version of the Dielectric Breakdown Model (DBM) for
generic breakdown processes. It interpolates between the standard DBM and its
analog with quenched disorder, as a temperature like parameter is varied. The
physics of other well known fractal growth phenomena as Invasion Percolation
and the Eden model are also recovered for some particular parameter values. The
competition between different growing mechanisms leads to new non-trivial
effects and allows us to better describe real growth phenomena.
Detailed numerical and theoretical analysis are performed to study the
interplay between the elementary mechanisms. In particular, we observe a
continuously changing fractal dimension as temperature is varied, and report an
evidence of a novel phase transition at zero temperature in absence of an
external driving field; the temperature acts as a relevant parameter for the
``self-organized'' invasion percolation fixed point. This permits us to obtain
new insight into the connections between self-organization and standard phase
transitions.Comment: Submitted to PR
Laplacian Fractal Growth in Media with Quenched Disorder
We analyze the combined effect of a Laplacian field and quenched disorder for
the generation of fractal structures with a study, both numerical and
theoretical, of the quenched dielectric breakdown model (QDBM). The growth
dynamics is shown to evolve from the avalanches of invasion percolation (IP) to
the smooth growth of Laplacian fractals, i. e. diffusion limited aggregation
(DLA) and the dielectric breakdown model (DBM). The fractal dimension is
strongly reduced with respect to both DBM and IP, due to the combined effect of
memory and field screening. This implies a specific relation between the
fractal dimension of the breakdown structures (dielectric or mechanical) and
the microscopic properties of disordered materials.Comment: 11 pages Latex (revtex), 3 postscript figures included. Submitted to
PR
Dynamics of Fractures in Quenched Disordered Media
We introduce a model for fractures in quenched disordered media. This model
has a deterministic extremal dynamics, driven by the energy function of a
network of springs (Born Hamiltonian). The breakdown is the result of the
cooperation between the external field and the quenched disorder. This model
can be considered as describing the low temperature limit for crack propagation
in solids. To describe the memory effects in this dynamics, and then to study
the resistance properties of the system we realized some numerical simulations
of the model. The model exhibits interesting geometric and dynamical
properties, with a strong reduction of the fractal dimension of the clusters
and of their backbone, with respect to the case in which thermal fluctuations
dominate. This result can be explained by a recently introduced theoretical
tool as a screening enhancement due to memory effects induced by the quenched
disorder.Comment: 7 pages, 9 Postscript figures, uses revtex psfig.sty, to be published
on Phys. Rev.
Theory of Self-organized Criticality for Problems with Extremal Dynamics
We introduce a general theoretical scheme for a class of phenomena
characterized by an extremal dynamics and quenched disorder. The approach is
based on a transformation of the quenched dynamics into a stochastic one with
cognitive memory and on other concepts which permit a mathematical
characterization of the self-organized nature of the avalanche type dynamics.
In addition it is possible to compute the relevant critical exponents directly
from the microscopic model. A specific application to Invasion Percolation is
presented but the approach can be easily extended to various other problems.Comment: 11 pages Latex (revtex), 3 postscript figures included. Submitted to
Europhys. Let
A perturbative approach to the Bak-Sneppen Model
We study the Bak-Sneppen model in the probabilistic framework of the Run Time
Statistics (RTS). This model has attracted a large interest for its simplicity
being a prototype for the whole class of models showing Self-Organized
Criticality. The dynamics is characterized by a self-organization of almost all
the species fitnesses above a non-trivial threshold value, and by a lack of
spatial and temporal characteristic scales. This results in {\em avalanches} of
activity power law distributed. In this letter we use the RTS approach to
compute the value of , the value of the avalanche exponent and the
asymptotic distribution of minimal fitnesses.Comment: 4 pages, 3 figures, to be published on Physical Review Letter
Phase separation in systems with absorbing states
We study the problem of phase separation in systems with a positive definite
order parameter, and in particular, in systems with absorbing states. Owing to
the presence of a single minimum in the free energy driving the relaxation
kinetics, there are some basic properties differing from standard phase
separation. We study analytically and numerically this class of systems; in
particular we determine the phase diagram, the growth laws in one and two
dimensions and the presence of scale invariance. Some applications are also
discussed.Comment: Submitted to Europhysics Let
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