890 research outputs found
A New Class of Cellular Automata for Reaction-Diffusion Systems
We introduce a new class of cellular automata to model reaction-diffusion
systems in a quantitatively correct way. The construction of the CA from the
reaction-diffusion equation relies on a moving average procedure to implement
diffusion, and a probabilistic table-lookup for the reactive part. The
applicability of the new CA is demonstrated using the Ginzburg-Landau equation.Comment: 4 pages, RevTeX 3.0 , 3 Figures 214972 bytes tar, compressed,
uuencode
Cellular automaton model of precipitation/dissolution coupled with solute transport
Precipitation/dissolution reactions coupled with solute transport are
modelled as a cellular automaton in which solute molecules perform a random
walk on a regular lattice and react according to a local probabilistic rule.
Stationary solid particles dissolve with a certain probability and, provided
solid is already present or the solution is saturated, solute particles have a
probability to precipitate. In our simulation of the dissolution of a solid
block inside uniformly flowing water we obtain solid precipitation downstream
from the original solid edge, in contrast to the standard reaction-transport
equations. The observed effect is the result of fluctuations in solute density
and diminishes when we average over a larger ensemble. The additional
precipitation of solid is accompanied by a substantial reduction in the
relatively small solute concentration. The model is appropriate for the study
of the r\^ole of intrinsic fluctuations in the presence of reaction thresholds
and can be employed to investigate porosity changes associated with the
carbonation of cement.Comment: LaTeX file, 13 pages. To appear in Journal of Statistical Physics
(Proceedings of Lattice Gas'94, June 1994, Princeton). Figures available from
author. Requests may be submitted by E-mail ([email protected]) or ordinary
mail (Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
Construction of an isotropic cellular automaton for a reaction-diffusion equation by means of a random walk
We propose a new method to construct an isotropic cellular automaton
corresponding to a reaction-diffusion equation. The method consists of
replacing the diffusion term and the reaction term of the reaction-diffusion
equation with a random walk of microscopic particles and a discrete vector
field which defines the time evolution of the particles. The cellular automaton
thus obtained can retain isotropy and therefore reproduces the patterns found
in the numerical solutions of the reaction-diffusion equation. As a specific
example, we apply the method to the Belousov-Zhabotinsky reaction in excitable
media
Non-solvable contractions of semisimple Lie algebras in low dimension
The problem of non-solvable contractions of Lie algebras is analyzed. By
means of a stability theorem, the problem is shown to be deeply related to the
embeddings among semisimple Lie algebras and the resulting branching rules for
representations. With this procedure, we determine all deformations of
indecomposable Lie algebras having a nontrivial Levi decomposition onto
semisimple Lie algebras of dimension , and obtain the non-solvable
contractions of the latter class of algebras.Comment: 21 pages. 2 Tables, 2 figure
Quasi-classical Lie algebras and their contractions
After classifying indecomposable quasi-classical Lie algebras in low
dimension, and showing the existence of non-reductive stable quasi-classical
Lie algebras, we focus on the problem of obtaining sufficient conditions for a
quasi-classical Lie algebras to be the contraction of another quasi-classical
algebra. It is illustrated how this allows to recover the Yang-Mills equations
of a contraction by a limiting process, and how the contractions of an algebra
may generate a parameterized families of Lagrangians for pairwise
non-isomorphic Lie algebras.Comment: 17 pages, 2 Table
Lowest dimensional example on non-universality of generalized In\"on\"u-Wigner contractions
We prove that there exists just one pair of complex four-dimensional Lie
algebras such that a well-defined contraction among them is not equivalent to a
generalized IW-contraction (or to a one-parametric subgroup degeneration in
conventional algebraic terms). Over the field of real numbers, this pair of
algebras is split into two pairs with the same contracted algebra. The example
we constructed demonstrates that even in the dimension four generalized
IW-contractions are not sufficient for realizing all possible contractions, and
this is the lowest dimension in which generalized IW-contractions are not
universal. Moreover, this is also the first example of nonexistence of
generalized IW-contraction for the case when the contracted algebra is not
characteristically nilpotent and, therefore, admits nontrivial diagonal
derivations. The lower bound (equal to three) of nonnegative integer parameter
exponents which are sufficient to realize all generalized IW-contractions of
four-dimensional Lie algebras is also found.Comment: 15 pages, extended versio
Generalization of the Gell-Mann formula for sl(5, R) and su(5) algebras
The so called Gell-Mann formula expresses the Lie algebra elements in terms
of the corresponding Inonu-Wigner contracted ones. In the case of sl(n, R) and
su(n) algebras contracted w.r.t. so(n) subalgebras, the Gell-Mann formula is
generally not valid, and applies only in the cases of some algebra
representations. A generalization of the Gell-Mann formula for sl(5,R) and
su(5) algebras, that is valid for all representations, is obtained in a group
manifold framework of the SO(5) and/or Spin(5) group
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