2,790 research outputs found

### Diffusion-Limited One-Species Reactions in the Bethe Lattice

We study the kinetics of diffusion-limited coalescence, A+A-->A, and
annihilation, A+A-->0, in the Bethe lattice of coordination number z.
Correlations build up over time so that the probability to find a particle next
to another varies from \rho^2 (\rho is the particle density), initially, when
the particles are uncorrelated, to [(z-2)/z]\rho^2, in the long-time asymptotic
limit. As a result, the particle density decays inversely proportional to time,
\rho ~ 1/kt, but at a rate k that slowly decreases to an asymptotic constant
value.Comment: To be published in JPCM, special issue on Kinetics of Chemical
Reaction

### Exact mean first-passage time on the T-graph

We consider a simple random walk on the T-fractal and we calculate the exact
mean time $\tau^g$ to first reach the central node $i_0$. The mean is performed
over the set of possible walks from a given origin and over the set of starting
points uniformly distributed throughout the sites of the graph, except $i_0$.
By means of analytic techniques based on decimation procedures, we find the
explicit expression for $\tau^g$ as a function of the generation $g$ and of the
volume $V$ of the underlying fractal. Our results agree with the asymptotic
ones already known for diffusion on the T-fractal and, more generally, they are
consistent with the standard laws describing diffusion on low-dimensional
structures.Comment: 6 page

### Wigner Surmise For Domain Systems

In random matrix theory, the spacing distribution functions $p^{(n)}(s)$ are
well fitted by the Wigner surmise and its generalizations. In this
approximation the spacing functions are completely described by the behavior of
the exact functions in the limits s->0 and s->infinity. Most non equilibrium
systems do not have analytical solutions for the spacing distribution and
correlation functions. Because of that, we explore the possibility to use the
Wigner surmise approximation in these systems. We found that this approximation
provides a first approach to the statistical behavior of complex systems, in
particular we use it to find an analytical approximation to the nearest
neighbor distribution of the annihilation random walk

### Diffusion-Limited Coalescence with Finite Reaction Rates in One Dimension

We study the diffusion-limited process $A+A\to A$ in one dimension, with
finite reaction rates. We develop an approximation scheme based on the method
of Inter-Particle Distribution Functions (IPDF), which was formerly used for
the exact solution of the same process with infinite reaction rate. The
approximation becomes exact in the very early time regime (or the
reaction-controlled limit) and in the long time (diffusion-controlled)
asymptotic limit. For the intermediate time regime, we obtain a simple
interpolative behavior between these two limits. We also study the coalescence
process (with finite reaction rates) with the back reaction $A\to A+A$, and in
the presence of particle input. In each of these cases the system reaches a
non-trivial steady state with a finite concentration of particles. Theoretical
predictions for the concentration time dependence and for the IPDF are compared
to computer simulations. P. A. C. S. Numbers: 82.20.Mj 02.50.+s 05.40.+j
05.70.LnComment: 13 pages (and 4 figures), plain TeX, SISSA-94-0

### A Method of Intervals for the Study of Diffusion-Limited Annihilation, A + A --> 0

We introduce a method of intervals for the analysis of diffusion-limited
annihilation, A+A -> 0, on the line. The method leads to manageable diffusion
equations whose interpretation is intuitively clear. As an example, we treat
the following cases: (a) annihilation in the infinite line and in infinite
(discrete) chains; (b) annihilation with input of single particles, adjacent
particle pairs, and particle pairs separated by a given distance; (c)
annihilation, A+A -> 0, along with the birth reaction A -> 3A, on finite rings,
with and without diffusion.Comment: RevTeX, 13 pages, 4 figures, 1 table. References Added, and some
other minor changes, to conform with final for

### Exact solution of the Nonconsensus Opinion Model on the line

The nonconcensus opinion model (NCO) introduced recently by Shao et al.,
[Phys. Rev. Lett.103, 018701 (2009)] is solved exactly on the line. Although,
as expected, the model exhibits no phase transition in one dimension, its study
is interesting because of the connection with invasion percolation with
trapping. The system evolves exponentially fast to the steady-state, rapidly
developing long-range correlations: The average cluster size in the steady
state scales as the square of the initial cluster size, of the (uncorrelated)
initial state. We also discuss briefly the NCO model on Bethe lattices, arguing
that its phase transition diagram is different than that of regular
percolation.Comment: New version corrects some spurious mistakes, conforms with version to
be published (PRE - Rapid Communication

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