56 research outputs found
Number of distinct sites visited by N random walkers on a Euclidean lattice
The evaluation of the average number S_N(t) of distinct sites visited up to
time t by N independent random walkers all starting from the same origin on an
Euclidean lattice is addressed. We find that, for the nontrivial time regime
and for large N, S_N(t) \approx \hat S_N(t) (1-\Delta), where \hat S_N(t) is
the volume of a hypersphere of radius (4Dt \ln N)^{1/2},
\Delta={1/2}\sum_{n=1}^\infty \ln^{-n} N \sum_{m=0}^n s_m^{(n)} \ln^{m} \ln N,
d is the dimension of the lattice, and the coefficients s_m^{(n)} depend on the
dimension and time. The first three terms of these series are calculated
explicitly and the resulting expressions are compared with other approximations
and with simulation results for dimensions 1, 2, and 3. Some implications of
these results on the geometry of the set of visited sites are discussed.Comment: 15 pages (RevTex), 4 figures (eps); to appear in Phys. Rev.
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
Water-like anomalies for core-softened models of fluids: One dimension
We use a one-dimensional (1d) core-softened potential to develop a physical
picture for some of the anomalies present in liquid water. The core-softened
potential mimics the effect of hydrogen bonding. The interest in the 1d system
stems from the facts that closed-form results are possible and that the
qualitative behavior in 1d is reproduced in the liquid phase for higher
dimensions. We discuss the relation between the shape of the potential and the
density anomaly, and we study the entropy anomaly resulting from the density
anomaly. We find that certain forms of the two-step square well potential lead
to the existence at T=0 of a low-density phase favored at low pressures and of
a high-density phase favored at high pressures, and to the appearance of a
point at a positive pressure, which is the analog of the T=0 ``critical
point'' in the Ising model. The existence of point leads to anomalous
behavior of the isothermal compressibility and the isobaric specific heat
.Comment: 22 pages, 7 figure
Manufacturing flow line systems: a review of models and analytical results
The most important models and results of the manufacturing flow line literature are described. These include the major classes of models (asynchronous, synchronous, and continuous); the major features (blocking, processing times, failures and repairs); the major properties (conservation of flow, flow rate-idle time, reversibility, and others); and the relationships among different models. Exact and approximate methods for obtaining quantitative measures of performance are also reviewed. The exact methods are appropriate for small systems. The approximate methods, which are the only means available for large systems, are generally based on decomposition, and make use of the exact methods for small systems. Extensions are briefly discussed. Directions for future research are suggested.National Science Foundation (U.S.) (Grant DDM-8914277
Clusters of galaxies: setting the stage
Clusters of galaxies are self-gravitating systems of mass ~10^14-10^15 Msun.
They consist of dark matter (~80 %), hot diffuse intracluster plasma (< 20 %)
and a small fraction of stars, dust, and cold gas, mostly locked in galaxies.
In most clusters, scaling relations between their properties testify that the
cluster components are in approximate dynamical equilibrium within the cluster
gravitational potential well. However, spatially inhomogeneous thermal and
non-thermal emission of the intracluster medium (ICM), observed in some
clusters in the X-ray and radio bands, and the kinematic and morphological
segregation of galaxies are a signature of non-gravitational processes, ongoing
cluster merging and interactions. In the current bottom-up scenario for the
formation of cosmic structure, clusters are the most massive nodes of the
filamentary large-scale structure of the cosmic web and form by anisotropic and
episodic accretion of mass. In this model of the universe dominated by cold
dark matter, at the present time most baryons are expected to be in a diffuse
component rather than in stars and galaxies; moreover, ~50 % of this diffuse
component has temperature ~0.01-1 keV and permeates the filamentary
distribution of the dark matter. The temperature of this Warm-Hot Intergalactic
Medium (WHIM) increases with the local density and its search in the outer
regions of clusters and lower density regions has been the quest of much recent
observational effort. Over the last thirty years, an impressive coherent
picture of the formation and evolution of cosmic structures has emerged from
the intense interplay between observations, theory and numerical experiments.
Future efforts will continue to test whether this picture keeps being valid,
needs corrections or suffers dramatic failures in its predictive power.Comment: 20 pages, 8 figures, accepted for publication in Space Science
Reviews, special issue "Clusters of galaxies: beyond the thermal view",
Editor J.S. Kaastra, Chapter 2; work done by an international team at the
International Space Science Institute (ISSI), Bern, organised by J.S.
Kaastra, A.M. Bykov, S. Schindler & J.A.M. Bleeke
FLUID-TO-PARTICLE CONVECTIVE HEAT TRANSFER COEFFICIENT AS EVALUATED IN an ASEPTIC PROCESSING HOLDING TUBE SIMULATOR
Anti-Windup Command Filtered Adaptive Backstepping Autopilot Design for a Tail-Controlled Air-Defense Missile
Isolation of syncytial microvillous membrane vesicles from human term placenta and their application in drug-nutrient interaction studies
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