1,218 research outputs found
Pair correlation function of short-ranged square-well fluids
We have performed extensive Monte Carlo simulations in the canonical (NVT)
ensemble of the pair correlation function for square-well fluids with well
widths ranging from 0.1 to 1.0, in units of the diameter
of the particles. For each one of these widths, several densities and
temperatures in the ranges and
, where is the
critical temperature, have been considered. The simulation data are used to
examine the performance of two analytical theories in predicting the structure
of these fluids: the perturbation theory proposed by Tang and Lu [Y. Tang and
B. C.-Y. Lu, J. Chem. Phys. {\bf 100}, 3079, 6665 (1994)] and the
non-perturbative model proposed by two of us [S. B. Yuste and A. Santos, J.
Chem. Phys. {\bf 101}, 2355 (1994)]. It is observed that both theories
complement each other, as the latter theory works well for short ranges and/or
moderate densities, while the former theory does for long ranges and high
densities.Comment: 10 pages, 10 figure
Survival probability and order statistics of diffusion on disordered media
We investigate the first passage time t_{j,N} to a given chemical or
Euclidean distance of the first j of a set of N>>1 independent random walkers
all initially placed on a site of a disordered medium. To solve this
order-statistics problem we assume that, for short times, the survival
probability (the probability that a single random walker is not absorbed by a
hyperspherical surface during some time interval) decays for disordered media
in the same way as for Euclidean and some class of deterministic fractal
lattices. This conjecture is checked by simulation on the incipient percolation
aggregate embedded in two dimensions. Arbitrary moments of t_{j,N} are
expressed in terms of an asymptotic series in powers of 1/ln N which is
formally identical to those found for Euclidean and (some class of)
deterministic fractal lattices. The agreement of the asymptotic expressions
with simulation results for the two-dimensional percolation aggregate is good
when the boundary is defined in terms of the chemical distance. The agreement
worsens slightly when the Euclidean distance is used.Comment: 8 pages including 9 figure
Order statistics for d-dimensional diffusion processes
We present results for the ordered sequence of first passage times of arrival
of N random walkers at a boundary in Euclidean spaces of d dimensions
Order statistics of the trapping problem
When a large number N of independent diffusing particles are placed upon a
site of a d-dimensional Euclidean lattice randomly occupied by a concentration
c of traps, what is the m-th moment of the time t_{j,N} elapsed
until the first j are trapped? An exact answer is given in terms of the
probability Phi_M(t) that no particle of an initial set of M=N, N-1,..., N-j
particles is trapped by time t. The Rosenstock approximation is used to
evaluate Phi_M(t), and it is found that for a large range of trap
concentracions the m-th moment of t_{j,N} goes as x^{-m} and its variance as
x^{-2}, x being ln^{2/d} (1-c) ln N. A rigorous asymptotic expression (dominant
and two corrective terms) is given for for the one-dimensional
lattice.Comment: 11 pages, 7 figures, to be published in Phys. Rev.
A model for the atomic-scale structure of a dense, nonequilibrium fluid: the homogeneous cooling state of granular fluids
It is shown that the equilibrium Generalized Mean Spherical Model of fluid
structure may be extended to nonequilibrium states with equation of state
information used in equilibrium replaced by an exact condition on the two-body
distribution function. The model is applied to the homogeneous cooling state of
granular fluids and upon comparison to molecular dynamics simulations is found
to provide an accurate picture of the pair distribution function.Comment: 29 pages, 11 figures Revision corrects formatting of the figure
Spatial fluctuations of a surviving particle in the trapping reaction
We consider the trapping reaction, , where and particles
have a diffusive dynamics characterized by diffusion constants and .
The interaction with particles can be formally incorporated in an effective
dynamics for one particle as was recently shown by Bray {\it et al}. [Phys.
Rev. E {\bf 67}, 060102 (2003)]. We use this method to compute, in space
dimension , the asymptotic behaviour of the spatial fluctuation,
, for a surviving particle in the perturbative regime,
, for the case of an initially uniform distribution of
particles. We show that, for , with
. By contrast, the fluctuations of paths constrained to return to
their starting point at time grow with the larger exponent 1/3. Numerical
tests are consistent with these predictions.Comment: 10 pages, 5 figure
Dendritic Spine Shape Analysis: A Clustering Perspective
Functional properties of neurons are strongly coupled with their morphology.
Changes in neuronal activity alter morphological characteristics of dendritic
spines. First step towards understanding the structure-function relationship is
to group spines into main spine classes reported in the literature. Shape
analysis of dendritic spines can help neuroscientists understand the underlying
relationships. Due to unavailability of reliable automated tools, this analysis
is currently performed manually which is a time-intensive and subjective task.
Several studies on spine shape classification have been reported in the
literature, however, there is an on-going debate on whether distinct spine
shape classes exist or whether spines should be modeled through a continuum of
shape variations. Another challenge is the subjectivity and bias that is
introduced due to the supervised nature of classification approaches. In this
paper, we aim to address these issues by presenting a clustering perspective.
In this context, clustering may serve both confirmation of known patterns and
discovery of new ones. We perform cluster analysis on two-photon microscopic
images of spines using morphological, shape, and appearance based features and
gain insights into the spine shape analysis problem. We use histogram of
oriented gradients (HOG), disjunctive normal shape models (DNSM), morphological
features, and intensity profile based features for cluster analysis. We use
x-means to perform cluster analysis that selects the number of clusters
automatically using the Bayesian information criterion (BIC). For all features,
this analysis produces 4 clusters and we observe the formation of at least one
cluster consisting of spines which are difficult to be assigned to a known
class. This observation supports the argument of intermediate shape types.Comment: Accepted for BioImageComputing workshop at ECCV 201
Average shape of fluctuations for subdiffusive walks
We study the average shape of fluctuations for subdiffusive processes, i.e.,
processes with uncorrelated increments but where the waiting time distribution
has a broad power-law tail. This shape is obtained analytically by means of a
fractional diffusion approach. We find that, in contrast with processes where
the waiting time between increments has finite variance, the fluctuation shape
is no longer a semicircle: it tends to adopt a table-like form as the
subdiffusive character of the process increases. The theoretical predictions
are compared with numerical simulation results.Comment: 4 pages, 6 figures. Accepted for publication Phys. Rev. E (Replaced
for the latest version, in press.) Section II rewritte
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