Alsophis rufiventris

Number of Pages: 4Integrative BiologyGeological Science

Duality transformations for general abelian systems

We describe the general structure of duality transformations for a very broad set of abelian statistical and field theoretic systems. This includes theories with many different types of fields and a large variety of kinds of interactions including, but not limited to nearest neighbor, next nearest neighbor, multi-spin interactions, etc. We find that the dual form of a theory does not depend directly on the dimensionality of the theory, but rather on the number of fields and number of different kinds of interactions. The dual forms we find have a generalized gauge symmetry and possess the usual property of having a temperature (or coupling constant) which is inverted from that of the original theory. Our results reduce to the well-known results in those particular cases that have heretofore been studied. Our procedure also suggests variations capable of generating other forms of the dual theory which may be useful in various specific cases.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24071/1/0000323.pd

Phase Structure of Resource Allocation Games

We consider a class of games that are generalizations of the minority game, in that the demand and supply of the resource are specified independently. This allows us to study systems in which agents compete under different demand loads. Among other features, we find the existence of a robust phase change with a coexistence region as the demand load is varied, separating regions with nearly balanced supply and demand from regions of scarce or abundant resources. The coexistence region exists when the amount of information used by the agents to make their choices is greater than a critical value, which is related to the point at which there is a phase transition in the standardd minority game.Comment: 11 pages 4 figures. Submitted to Physics Letter A, Feb. 2002W

Dynamics of infinite-range ballistic aggregation

The authors calculate the width of the growing interface of ballistic aggregation in the limit in which the range of the sticking interaction between the particles becomes infinite. They derive a scaling form for the width, and they compute the short- and long-time exponents finding nu =3/4 and alpha =1/2. Furthermore, they find that the crossover exponent defining the argument of the scaling function is gamma =1/2. They compare these exact results with computer simulations, finding excellent agreement. They also discuss the relation of these results to those of ordinary finite-range ballistic aggregation. Finally, they present a simple expression for the density of all ballistic aggregation clusters, regardless of the range of the interaction, which agrees with known results and interpolates between the infinite- and finite-range cases.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/48814/2/jav20i18p6391.pd

Growth oscillations

The authors describe an up till now unrecognised phenomenon in kinetic growth models which leads to observable oscillations in such quantities as the density and velocity of growth. These oscillations, which can occur on length scales of many lattice spacings, arise because of an induced incommensuration in the growth mechanism. To illustrate the phenomenon, they present results for a particularly simple model, but the phenomenon is expected to be quite general and appear in a wide range of growth processes. The essential ingredients for the existence of the oscillations are that the growth take place at a reasonably well defined interface and that the growth process be discrete (e.g. that the cluster grows by the addition of discrete particles of finite size). The growth process is related to a functional stochastic iterative map so that the growth oscillations play the role of limit cycles. They suggest that the fixed point of this map is related to critical fractal kinetic growth.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/48806/2/jav19i16pL973.pd