60 research outputs found
Multifractality in a broad class of disordered systems
We study multifractality in a broad class of disordered systems which
includes, e.g., the diluted x-y model. Using renormalized field theory we
analyze the scaling behavior of cumulant averaged dynamical variables (in case
of the x-y model the angles specifying the directions of the spins) at the
percolation threshold. Each of the cumulants has its own independent critical
exponent, i.e., there are infinitely many critical exponents involved in the
problem. Working out the connection to the random resistor network, we
determine these multifractal exponents to two-loop order. Depending on the
specifics of the Hamiltonian of each individual model, the amplitudes of the
higher cumulants can vanish and in this case, effectively, only some of the
multifractal exponents are required.Comment: 4 pages, 1 figur
Fractal to Nonfractal Phase Transition in the Dielectric Breakdown Model
A fast method is presented for simulating the dielectric-breakdown model
using iterated conformal mappings. Numerical results for the dimension and for
corrections to scaling are in good agreement with the recent RG prediction of
an upper critical , at which a transition occurs between branching
fractal clusters and one-dimensional nonfractal clusters.Comment: 5 pages, 7 figures; corrections to scaling include
Master Operators Govern Multifractality in Percolation
Using renormalization group methods we study multifractality in percolation
at the instance of noisy random resistor networks. We introduce the concept of
master operators. The multifractal moments of the current distribution (which
are proportional to the noise cumulants of the
resistance between two sites x and located on the same cluster) are
related to such master operators. The scaling behavior of the multifractal
moments is governed exclusively by the master operators, even though a myriad
of servant operators is involved in the renormalization procedure. We calculate
the family of multifractal exponents for the scaling behavior of the
noise cumulants, ,
where is the correlation length exponent for percolation, to two-loop
order.Comment: 6 page
Effective RFID-based object tracking for manufacturing
International audienceAbstract Automated Identification and in particular, Radio Frequency Identification (RFID) promises to assist with the automation of mass customised production processes by simplifying the retrieval, tracking and usage of highly specialised components. RFID has long been used to gather a history or trace of object movements, but its use as an integral part of the automated control process is yet to be fully exploited. Such (automated) use places stringent demands on the quality of the sensor data collected and the method used to interpret that data. In particular, this paper focuses on the issue of correctly identifying, tracking and dealing with aggregated objects in customised production with the use of RFID. In particular, this work presents approaches for making best use of RFID data in this context. The presented approach is evaluated in the context of a laboratory manufacturing system that produces customised gift boxes
Transition from Knudsen to molecular diffusion in activity of absorbing irregular interfaces
We investigate through molecular dynamics the transition from Knudsen to
molecular diffusion transport towards 2d absorbing interfaces with irregular
geometry. Our results indicate that the length of the active zone decreases
continuously with density from the Knudsen to the molecular diffusion regime.
In the limit where molecular diffusion dominates, we find that this length
approaches a constant value of the order of the system size, in agreement with
theoretical predictions for Laplacian transport in irregular geometries.
Finally, we show that all these features can be qualitatively described in
terms of a simple random-walk model of the diffusion process.Comment: 4 pages, 4 figure
Exact solution of diffusion limited aggregation in a narrow cylindrical geometry
The diffusion limited aggregation model (DLA) and the more general dielectric
breakdown model (DBM) are solved exactly in a two dimensional cylindrical
geometry with periodic boundary conditions of width 2. Our approach follows the
exact evolution of the growing interface, using the evolution matrix E, which
is a temporal transfer matrix. The eigenvector of this matrix with an
eigenvalue of one represents the system's steady state. This yields an estimate
of the fractal dimension for DLA, which is in good agreement with simulations.
The same technique is used to calculate the fractal dimension for various
values of eta in the more general DBM model. Our exact results are very close
to the approximate results found by the fixed scale transformation approach.Comment: 18 pages RevTex, 6 eps figure
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.
Noisy random resistor networks: renormalized field theory for the multifractal moments of the current distribution
We study the multifractal moments of the current distribution in randomly
diluted resistor networks near the percolation treshold. When an external
current is applied between to terminals and of the network, the
th multifractal moment scales as , where is the correlation length exponent of
the isotropic percolation universality class. By applying our concept of master
operators [Europhys. Lett. {\bf 51}, 539 (2000)] we calculate the family of
multifractal exponents for to two-loop order. We find
that our result is in good agreement with numerical data for three dimensions.Comment: 30 pages, 6 figure
Breast cancer evaluation by fluorescent dot detection using combined mathematical morphology and multifractal techniques
Computer aided system for segmentation and visualization of microcalcifications in digital mammograms.
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