3,990 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
The equivalent nonlinearity for a nonlinear system with dither
AbstractGiven a single loop nonlinear control system. The problem of constructing a dither signal in order to obtain a desired equivalent nonlinearity is considered. It is assumed that the nonlinearity may be described by a kth order polynomial. For this case it is shown that in general k different levels for the dither signal are necessary
Exactly solvable models through the empty interval method, for more-than-two-site interactions
Single-species reaction-diffusion systems on a one-dimensional lattice are
considered, in them more than two neighboring sites interact. Constraints on
the interaction rates are obtained, that guarantee the closedness of the time
evolution equation for 's, the probability that consecutive sites
are empty at time . The general method of solving the time evolution
equation is discussed. As an example, a system with next-nearest-neighbor
interaction is studied.Comment: 19 pages, LaTeX2
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
Wigner Surmise For Domain Systems
In random matrix theory, the spacing distribution functions 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
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