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

Expanding Lie (super)algebras through abelian semigroups

We propose an outgrowth of the expansion method introduced by de Azcarraga et al. [Nucl. Phys. B 662 (2003) 185]. The basic idea consists in considering the direct product between an abelian semigroup S and a Lie algebra g. General conditions under which relevant subalgebras can systematically be extracted from S \times g are given. We show how, for a particular choice of semigroup S, the known cases of expanded algebras can be reobtained, while new ones arise from different choices. Concrete examples, including the M algebra and a D'Auria-Fre-like Superalgebra, are considered. Finally, we find explicit, non-trace invariant tensors for these S-expanded algebras, which are essential ingredients in, e.g., the formulation of Supergravity theories in arbitrary space-time dimensions.Comment: 42 pages, 8 figures. v2: Improved figures, updated notation and terminolog

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 $n\leq 8$, and obtain the non-solvable contractions of the latter class of algebras.Comment: 21 pages. 2 Tables, 2 figure