279 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
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
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
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.
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
Ocular Prosthesis: Indications to Management
Caring for patients with a prosthetic eye can be a challenge to clinicians. Regardless of the circumstances leading to eye removal, inspection of the underlying tissue should be part of a comprehensive eye exam. Maintaining the overall health of the anophthalmic socket is critical in patient comfort and optimal prosthetic fit. Discussions will focus on anophthalmic procedures and preparation of the socket for prosthetic fitting. Care and management of the prosthesis and the anophthalmic socket, including associated ocular tissue disorders will be emphasized. the article will enhance the clinician’s comfort level managing patients wearing ocular prosthesis
The concurrence of cortical surface area expansion and white matter myelination in human brain development
The human brain undergoes dramatic structural changes during childhood that co-occur with behavioral development. These age-related changes are documented for the brain’s gray matter and white matter. However, their interrelation is largely unknown. In this study, we investigated age-related effects in cortical thickness (CT) and in cortical surface area (SA) as parts of the gray matter volume as well as age effects in T1 relaxation times in the white matter. Data from N = 170 children between the ages of 3 and 7 years contributed to the sample. We found a high spatial overlap of age-related correlations between SA and T1 relaxation times of the corresponding white matter connections, but no such relation between SA and CT. These results indicate that during childhood the developmental expansion of the cortical surface goes hand-in-hand with age-related increase of white matter fiber connections terminating in the cortical surface
Statistical properties of fractures in damaged materials
We introduce a model for the dynamics of mud cracking in the limit of of
extremely thin layers. In this model the growth of fracture proceeds by
selecting the part of the material with the smallest (quenched) breaking
threshold. In addition, weakening affects the area of the sample neighbour to
the crack. Due to the simplicity of the model, it is possible to derive some
analytical results. In particular, we find that the total time to break down
the sample grows with the dimension L of the lattice as L^2 even though the
percolating cluster has a non trivial fractal dimension. Furthermore, we obtain
a formula for the mean weakening with time of the whole sample.Comment: 5 pages, 4 figures, to be published in Europhysics Letter
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