Adsorption of Line Segments on a Square Lattice

We study the deposition of line segments on a two-dimensional square lattice. The estimates for the coverage at jamming obtained by Monte-Carlo simulations and by $7^{th}$-order time-series expansion are successfully compared. The non-trivial limit of adsorption of infinitely long segments is studied, and the lattice coverage is consistently obtained using these two approaches.Comment: 19 pages in Latex+5 postscript files sent upon request ; PTB93_

Theory of the NO+CO surface reaction model

We derive a pair approximation (PA) for the NO+CO model with instantaneous reactions. For both the triangular and square lattices, the PA, derived here using a simpler approach, yields a phase diagram with an active state for CO-fractions y in the interval y_1 < y < y_2, with a continuous (discontinuous) phase transition to a poisoned state at y_1 (y_2). This is in qualitative agreement with simulation for the triangular lattice, where our theory gives a rather accurate prediction for y_2. To obtain the correct phase diagram for the square lattice, i.e., no active state, we reformulate the PA using sublattices. The (formerly) active regime is then replaced by a poisoned state with broken symmetry (unequal sub- lattice coverages), as observed recently by Kortluke et al. [Chem. Phys. Lett. 275, 85 (1997)]. In contrast with their approach, in which the active state persists, although reduced in extent, we report here the first qualitatively correct theory of the NO+CO model on the square lattice. Surface diffusion of nitrogen can lead to an active state in this case. In one dimension, the PA predicts that diffusion is required for the existence of an active state.Comment: 15 pages, 9 figure

Tricritical directed percolation

We consider a modification of the contact process incorporating higher-order reaction terms. The original contact process exhibits a non-equilibrium phase transition belonging to the universality class of directed percolation. The incorporated higher-order reaction terms lead to a non-trivial phase diagram. In particular, a line of continuous phase transitions is separated by a tricritical point from a line of discontinuous phase transitions. The corresponding tricritical scaling behavior is analyzed in detail, i.e., we determine the critical exponents, various universal scaling functions as well as universal amplitude combinations

Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated

Knowledge verification in expert systems combining declarative and procedural representations

We present an algorithm to verify the consistency and completeness of an object-oriented structured knowledge base of an expert system which combines procedures with a declarative representation using if-then rules. The algorithm has three stages. The first stage of the algorithm converts the procedures into rules which are added to the existing rules to produce the equivalent rule set. The second stage of the algorithm partitions the equivalent rule set into decision subtables by regrouping rules with similar conditions in their if part or similar actions in their then part. In the third stage, each subtable is checked for consistency by looking for redundant rules and potentially or strictly conflicting rules. Completeness is verified by looking for unreferenced attribute values and missing rules. The algorithm is designed to automatically check any modification to the knowledge base as the system is being developed or updated. We demonstrate the algorithm on examples from process control