Interface motion in a two-dimensional Ising model with a field

We determine by Monte Carlo simulations the width of an interface between the stable phase and the metastable phase in a two-dimensional Ising model with a magnetic field, in the case of nonconversed order parameter (Glauber dynamics). At zero temperature, the width increases ast with–1/3, as predicted by earlier theories. As temperature increases, the value of the effective exponent that we measure decreases toward the value 1/4, which is the value in the absence of magnetic field.     

Fluctuation-dominated kinetics in the a+b→0 reaction between immobile particles

We consider the accumulation of immobile particles landing on a one-dimensional lattice and annihilating via the A + B 0 bimolecular reaction. Here we focus on short-range interactions with cutoff. We investigate through computer simulations both the kinetics of the particles' accumulation and also their spatial distribution. The relation between the exponents describing the growth of the particles' concentration and the correlation length of their distribution shows that the kinetics of accumulation is fluctuation-dominated.This work is dedicated to Prof. George H. Weiss.     

Modelling of the pressure-velocity correlation in turbulence diffusion

Most current computations of trubulent flows with second-moment closure adopt the diffusion models which neglect the effect of pressure-velocity correlation. In the present paper the importance of this correlation effect is elucidated the neglect of this effect accounts for some major defects in the wide application of the second-moment closures. Through the relation between and , established by Lumley, we propose here a new turbulence diffusion model which takes into consideration the pressure effect. Applications of this new model in the computation of shearless turbulence mixing layer and plane and round-jet flows show that the spreading rate of these flows can be satisfactorily captured.     

Multicolor particle systems with large threshold and range

In this paper we consider the Greenberg-Hastings and cyclic color models. These models exhibit (at least) three different types of behavior. Depending on the number of colors and the size of two parameters called the threshold and range, the Greenberg-Hastings model either dies out, or has equilibria that consist of debris or fire fronts. The phase diagram for the cyclic color models is more complicated. The main result of this paper, Theorem 1, proves that the debris phase exists for both systems.     

Random infinite-volume Gibbs states for the Curie-Weiss random field Ising model

An approach to the definition of infinite-volume Gibbs states for the (quenched) random-field Ising model is considered in the case of a Curie-Weiss ferromagnet. It turns out that these states are random quasi-free measures. They are random convex linear combinations of the free product-measures shifted by the corresponding effective mean fields. The conditional self-averaging property of the magnetization related to this randomness is also discussed.This paper is dedicated to Robert A. Minlos on the occasion of his 60th birthday.     

Monte carlo calculations of the conformal charge

The conformal charge is an important quantity which characterizes the nature of the two-dimensional phase transition. We report a first attempt to use a new numerical method to calculate the conformal charge. In this paper, we apply our method to the 2-dimensional, ⁴, continuous-spin Ising model. By varying the parameters in the Hamiltonian, one can change continuously from the known Gaussian limit to the Ising limit. It is well known that the critical points for these two systems are not in the same universality class. We study this behavior for the Gaussian model, the single-well ⁴ model, the border model, and the double-well ⁴ model for a large lattice. Our results, while giving a good general picture, are not so far sufficient to differentiate whether the non-Gaussian cases studied belong to the Ising model universality class or not. Further studies of other lattice sizes should serve to improve greatly our conclusions.     

Rigorous bounds on the storage capacity of the dilute Hopfield model

We study a neural network model consisting ofN neurons where a dendritic connection between each pair of neurons exists with probabilityp and is absent with probability 1-p. For the Hopfield Hamiltonian on such a network, we prove that ifp c[(lnN)/N]^1/2, the model can store at leastm= _cpN patterns, where _c 0.027 ifc 3 and decreases proportional to 1/(–lnc) forc small. This generalizes the results of Newman for the standard Hopfield model.     

Analyticity of the density of states in the anderson model on the Bethe lattice

Let H=1/2+V on l²(B), whereB is the Bethe lattice andV(x),x B, are i.i.d.r.v.'s with common probability distribution. It is shown that for distributions sufficiently close to the Cauchy distribution, the density of states(E) is analytic in a strip about the real axis.     

空间展布体系中由化学反应-扩散-热传导耦合导致的温度场对称破缺

分析了由于化学反应-扩散-热传导耦合而导致的非等温非均匀体系中温度场对称破缺.研究结果表明,在一定的边界条件下,甚至是单组分化学反应-扩散-热传导体系,温度场的这种自组织进程也不可避免.作为温度场结构的一个范例,进一步从解析解及计算机模拟两个方面研究了小展布非等温的Lindeman模型;结果表明,温度场出现时空自组织的阈值不仅与本征参数有关,而且与体系的边界条件及外控约束相关,揭示出了诱发或避免这种温度场时空自组织之途径.