6,663 research outputs found
Multiparticle trapping problem in the half-line
A variation of Rosenstock's trapping model in which independent random
walkers are all initially placed upon a site of a one-dimensional lattice in
the presence of a {\em one-sided} random distribution (with probability ) of
absorbing traps is investigated. The probability (survival probability)
that no random walker is trapped by time for is
calculated by using the extended Rosenstock approximation. This requires the
evaluation of the moments of the number of distinct sites visited in a
{\em given} direction up to time by independent random walkers. The
Rosenstock approximation improves when increases, working well in the range
, being the diffusion constant. The moments of the
time (lifetime) before any trapping event occurs are calculated asymptotically,
too. The agreement with numerical results is excellent.Comment: 11 pages (RevTex), 6 figures (eps). To be published in Physica
Francisco Salva's Electric Telegraph
This article takes a look at the life and accomplishments of Francisco Salva of Spain, including his work with an electric telegraph system. The author states that information herein is based on the original report and some practical demonstrations that Salva presented to the Barcelona Academy of Sciences in 1804
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
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.
Some exact results for the trapping of subdiffusive particles in one dimension
We study a generalization of the standard trapping problem of random walk
theory in which particles move subdiffusively on a one-dimensional lattice. We
consider the cases in which the lattice is filled with a one-sided and a
two-sided random distribution of static absorbing traps with concentration c.
The survival probability Phi(t) that the random walker is not trapped by time t
is obtained exactly in both versions of the problem through a fractional
diffusion approach. Comparison with simulation results is madeComment: 15 pages, 2 figure
Properties of the reaction front in a reaction-subdiffusion process
We study the reaction front for the process in which the reagents
move subdiffusively. We propose a fractional reaction-subdiffusion equation in
which both the motion and the reaction terms are affected by the subdiffusive
character of the process. Scaling solutions to these equations are presented
and compared with those of a direct numerical integration of the equations. We
find that for reactants whose mean square displacement varies sublinearly with
time as , the scaling behaviors of the reaction front can
be recovered from those of the corresponding diffusive problem with the
substitution Comment: Errata corrected, one reference update
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