831 research outputs found
Cardy's Formula for Certain Models of the Bond-Triangular Type
We introduce and study a family of 2D percolation systems which are based on
the bond percolation model of the triangular lattice. The system under study
has local correlations, however, bonds separated by a few lattice spacings act
independently of one another. By avoiding explicit use of microscopic paths, it
is first established that the model possesses the typical attributes which are
indicative of critical behavior in 2D percolation problems. Subsequently, the
so called Cardy-Carleson functions are demonstrated to satisfy, in the
continuum limit, Cardy's formula for crossing probabilities. This extends the
results of S. Smirnov to a non-trivial class of critical 2D percolation
systems.Comment: 49 pages, 7 figure
The spectral dimension of random trees
We present a simple yet rigorous approach to the determination of the
spectral dimension of random trees, based on the study of the massless limit of
the Gaussian model on such trees. As a byproduct, we obtain evidence in favor
of a new scaling hypothesis for the Gaussian model on generic bounded graphs
and in favor of a previously conjectured exact relation between spectral and
connectivity dimensions on more general tree-like structures.Comment: 14 pages, 2 eps figures, revtex4. Revised version: changes in section
I
Activated Random Walkers: Facts, Conjectures and Challenges
We study a particle system with hopping (random walk) dynamics on the integer
lattice . The particles can exist in two states, active or
inactive (sleeping); only the former can hop. The dynamics conserves the number
of particles; there is no limit on the number of particles at a given site.
Isolated active particles fall asleep at rate , and then remain
asleep until joined by another particle at the same site. The state in which
all particles are inactive is absorbing. Whether activity continues at long
times depends on the relation between the particle density and the
sleeping rate . We discuss the general case, and then, for the
one-dimensional totally asymmetric case, study the phase transition between an
active phase (for sufficiently large particle densities and/or small )
and an absorbing one. We also present arguments regarding the asymptotic mean
hopping velocity in the active phase, the rate of fixation in the absorbing
phase, and survival of the infinite system at criticality. Using mean-field
theory and Monte Carlo simulation, we locate the phase boundary. The phase
transition appears to be continuous in both the symmetric and asymmetric
versions of the process, but the critical behavior is very different. The
former case is characterized by simple integer or rational values for critical
exponents (, for example), and the phase diagram is in accord with
the prediction of mean-field theory. We present evidence that the symmetric
version belongs to the universality class of conserved stochastic sandpiles,
also known as conserved directed percolation. Simulations also reveal an
interesting transient phenomenon of damped oscillations in the activity
density
A Quality Improvement Initiative to Engage Older Adults in the Discharge Process Using the IDEAL Discharge Protocol
Robust nonparametric detection of objects in noisy images
We propose a novel statistical hypothesis testing method for detection of
objects in noisy images. The method uses results from percolation theory and
random graph theory. We present an algorithm that allows to detect objects of
unknown shapes in the presence of nonparametric noise of unknown level and of
unknown distribution. No boundary shape constraints are imposed on the object,
only a weak bulk condition for the object's interior is required. The algorithm
has linear complexity and exponential accuracy and is appropriate for real-time
systems. In this paper, we develop further the mathematical formalism of our
method and explore important connections to the mathematical theory of
percolation and statistical physics. We prove results on consistency and
algorithmic complexity of our testing procedure. In addition, we address not
only an asymptotic behavior of the method, but also a finite sample performance
of our test.Comment: This paper initially appeared in 2010 as EURANDOM Report 2010-049.
Link to the abstract at EURANDOM repository:
http://www.eurandom.tue.nl/reports/2010/049-abstract.pdf Link to the paper at
EURANDOM repository: http://www.eurandom.tue.nl/reports/2010/049-report.pd
Percolative shunting on electrified surface
The surface discharge of electrified dielectrics at high humidity is
considered. The percolative nature of charge transport in electrets is
established. Particular attention is given to the phenomena of adsorption and
nucleation of electrically conducting phase in the cause of percolation cluster
growth on electrified surface. The critical index of the correlation lenght for
percolation cluster is found, and its value is in good agreement with the known
theoretical estimations.Comment: 4 pages with 1 figure, revtex, published in Tech. Phys. Lett. 25
(1999) 877-879 with one additional figur
The statistical geometry of scale-free random trees
The properties of scale-free random trees are investigated using both
preconditioning on non-extinction and fixed size averages, in order to study
the thermodynamic limit. The scaling form of volume probability is found, the
connectivity dimensions are determined and compared with other exponents which
describe the growth. The (local) spectral dimension is also determined, through
the study of the massless limit of the Gaussian model on such trees.Comment: 21 pages, 2 figures, revtex4, minor changes (published version
Sequentializing Parameterized Programs
We exhibit assertion-preserving (reachability preserving) transformations
from parameterized concurrent shared-memory programs, under a k-round
scheduling of processes, to sequential programs. The salient feature of the
sequential program is that it tracks the local variables of only one thread at
any point, and uses only O(k) copies of shared variables (it does not use extra
counters, not even one counter to keep track of the number of threads).
Sequentialization is achieved using the concept of a linear interface that
captures the effect an unbounded block of processes have on the shared state in
a k-round schedule. Our transformation utilizes linear interfaces to
sequentialize the program, and to ensure the sequential program explores only
reachable states and preserves local invariants.Comment: In Proceedings FIT 2012, arXiv:1207.348
Statistics of reduced words in locally free and braid groups: Abstract studies and application to ballistic growth model
We study numerically and analytically the average length of reduced
(primitive) words in so-called locally free and braid groups. We consider the
situations when the letters in the initial words are drawn either without or
with correlations. In the latter case we show that the average length of the
reduced word can be increased or lowered depending on the type of correlation.
The ideas developed are used for analytical computation of the average number
of peaks of the surface appearing in some specific ballistic growth modelComment: 29 pages, LaTeX, 7 separated Postscript figures (available on
request), submitted to J. Phys. (A): Math. Ge
Square lattice site percolation at increasing ranges of neighbor interactions
We report site percolation thresholds for square lattice with neighbor
interactions at various increasing ranges. Using Monte Carlo techniques we
found that nearest neighbors (N), next nearest neighbors (N), next next
nearest neighbors (N) and fifth nearest neighbors (N) yield the same
. At odds, fourth nearest neighbors (N) give .
These results are given an explanation in terms of symmetry arguments. We then
consider combinations of various ranges of interactions with (N+N),
(N+N), (N+N+N) and (N+N). The calculated associated
thresholds are respectively . The
existing Galam--Mauger universal formula for percolation thresholds does not
reproduce the data showing dimension and coordination number are not sufficient
to build a universal law which extends to complex lattices.Comment: 4 pages, revtex
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