582 research outputs found
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
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
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
Validation and Calibration of Models for Reaction-Diffusion Systems
Space and time scales are not independent in diffusion. In fact, numerical
simulations show that different patterns are obtained when space and time steps
( and ) are varied independently. On the other hand,
anisotropy effects due to the symmetries of the discretization lattice prevent
the quantitative calibration of models. We introduce a new class of explicit
difference methods for numerical integration of diffusion and
reaction-diffusion equations, where the dependence on space and time scales
occurs naturally. Numerical solutions approach the exact solution of the
continuous diffusion equation for finite and , if the
parameter assumes a fixed constant value,
where is an odd positive integer parametrizing the alghorithm. The error
between the solutions of the discrete and the continuous equations goes to zero
as and the values of are dimension
independent. With these new integration methods, anisotropy effects resulting
from the finite differences are minimized, defining a standard for validation
and calibration of numerical solutions of diffusion and reaction-diffusion
equations. Comparison between numerical and analytical solutions of
reaction-diffusion equations give global discretization errors of the order of
in the sup norm. Circular patterns of travelling waves have a maximum
relative random deviation from the spherical symmetry of the order of 0.2%, and
the standard deviation of the fluctuations around the mean circular wave front
is of the order of .Comment: 33 pages, 8 figures, to appear in Int. J. Bifurcation and Chao
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
Renewable Energy Opportunities at Fort Sill, Oklahoma
This document provides an overview of renewable resource potential at Fort Sill, based primarily upon analysis of secondary data sources supplemented with limited on-site evaluations. This effort focuses on grid-connected generation of electricity from renewable energy sources and on ground source heat pumps for heating and cooling buildings. The effort was funded by the U.S. Army Installation Management Command (IMCOM) as follow-on to the 2005 Department of Defense (DoD) Renewables Assessment. The site visit to Fort Sill took place on June 10, 2010
Renewable Energy Opportunities at Fort Polk, Louisiana
This document provides an overview of renewable resource potential at Fort Polk, based primarily upon analysis of secondary data sources supplemented with limited on-site evaluations. This effort focuses on grid-connected generation of electricity from renewable energy sources and also on ground source heat pumps for heating and cooling buildings. The effort was funded by the U.S. Army Installation Management Command (IMCOM) as follow-on to the 2005 Department of Defense (DoD) Renewables Assessment. The site visit to Fort Polk took place on February 16, 2010
Extensions, expansions, Lie algebra cohomology and enlarged superspaces
After briefly reviewing the methods that allow us to derive consistently new
Lie (super)algebras from given ones, we consider enlarged superspaces and
superalgebras, their relevance and some possible applications.Comment: 9 pages. Invited talk delivered at the EU RTN Workshop, Copenhagen,
Sep. 15-19 and at the Argonne Workshop on Branes and Generalized Dynamics,
Oct. 20-24, 2003. Only change: wrong number of a reference correcte
Contractions and deformations of quasi-classical Lie algebras preserving a non-degenerate quadratic Casimir operator
By means of contractions of Lie algebras, we obtain new classes of
indecomposable quasi-classical Lie algebras that satisfy the Yang-Baxter
equations in its reformulation in terms of triple products. These algebras are
shown to arise naturally from non-compact real simple algebras with non-simple
complexification, where we impose that a non-degenerate quadratic Casimir
operator is preserved by the limiting process. We further consider the converse
problem, and obtain sufficient conditions on integrable cocycles of
quasi-classical Lie algebras in order to preserve non-degenerate quadratic
Casimir operators by the associated linear deformations.Comment: 12 pages. LATEX with revtex4; Proceedings of the XII International
Conference on Symmetry Methods in Physics, (Yerevan, 2006) eds. G.S. Pogosyan
et al
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