Methods of statistical modeling in the process of sieve separation of heterogeneous particles

In the article we undertook the attempt of using the theory of random fields in the analysis of the separation process of particles in non-contiguous systems. The presentation of the complete model is a complicated problem. We can say that this article is start point of the theory, which will be supplemented gradually in the future. The separation process of particles on sieves is a phenomenon with random character. It is a result of random character of cleaned mixture and the nature of the separation process. Undoubtedly, an important part is played by the theory of random fields in which system-events, inherently not determined, are described in undetermined-probabilistic way. However, we can perceive one paradox in such actions – correctly constructed probabilistic models serve to impose deterministic frames on the given random process. We can say that stochastic models generate the matrix of the causal-consecutive dependence, which will give the ability of controlling a given process.     

Multi-Particle Processes with Reinforcements

We consider a multi-particle generalization of linear edge-reinforced random walk (ERRW). We observe that in absence of exchangeability, new techniques are needed in order to study the multi-particle model. We describe an unusual coupling construction associated with the two-point edge-reinforced process on ℤ and prove a form of recurrence: the two particles meet infinitely often a.s. This research was supported in part by NSF VIGRE Grant DMS 9983726 at UCLA.     

Supplier diversification under binomial yield

We consider supplier diversification in an EOQ type inventory setting with multiple suppliers and binomial yields. We characterize the optimal policy for the model and show that, in this case, it does not pay to diversify, in contrast to previous results in the random yield literature.     

Embedding with a Lipschitz function

We investigate a new notion of embedding of subsets of {?1,1}ⁿ in a given normed space, in a way which preserves the structure of the given set as a class of functions on {1, …, n}. This notion is an extension of the margin parameter often used in Nonparametric Statistics. Our main result is that even when considering “small” subsets of {?1, 1}ⁿ, the vast majority of such sets do not embed in a better way than the entire cube in any normed space that satisfies a minor structural assumption. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005     

Random graphs on surfaces

Counting labelled planar graphs, and typical properties of random labelled planar graphs, have received much attention recently. We start the process here of extending these investigations to graphs embeddable on any fixed surface S. In particular we show that the labelled graphs embeddable on S have the same growth constant as for planar graphs, and the same holds for unlabelled graphs. Also, if we pick a graph uniformly at random from the graphs embeddable on S which have vertex set {1,…,n}, then with probability tending to 1 as n→∞, this random graph either is connected or consists of one giant component together with a few nodes in small planar components.     

含有随机夹杂的统计非均匀弹性介质参数的分析

本文提出了随机点场理论用于研究含有随机夹杂的统计非均匀介质。本文不同于其它作者,一般均将随机理论建立在Eshelby的等效夹杂原理之上,而这里是建立在Kunin的微结构理论基础之上。作为理论的一个应用,本文对复合材料的有效模量及夹杂内部及周围微观场进行了计算。     

Effect of sequence distribution on the isothermal crystallization kinetics and successive self-nucleation and annealing (SSA) behavior of poly(ε-caprolactone-co-ε-caprolactam) copolymers

Two types of miscible poly(ε-caprolactone-co-ε-caprolactam) copolymers were studied. In both cases catalyzed hydrolytic ring-opening polymerization was employed. For the first type, the comonomers were added simultaneously to obtain random copolymers. For the second type, the comonomers were added sequentially to obtain block copolymers. Successive self-nucleation and annealing (SSA) and isothermal crystallization studies were performed to both types of copolymers. The SSA results reflect the differences in molecular microstructure: block versus random copolymers. In a wide composition range only the polycaprolactam sequences were capable of crystallization in the random copolymers. Avrami indexes of approximately 3-4 were obtained corresponding to the spherulitic crystallization of these units within the copolymers. The block copolymer samples experienced a relatively small reduction of crystallization kinetics with composition, and this was attributed to the dilution effect caused by the miscible non-crystalline polycaprolactone units. On the other hand, for the random copolymers, the rate of crystallization strongly increased with polycaprolactam content while the energy barrier for secondary nucleation decreased exponentially. The comparison between miscible block and random copolymers provides a unique opportunity to distinguish the dilution effect of the polycaprolactone units (a moderate effect) on the isothermal crystallization and melting of the polyamide phase from the molecular microstructural effect in the random copolymers case (a dramatically strong effect), where the polycaprolactam sequences are interrupted statistically by polycaprolactone sequences.     

Stationary point analysis of the one-dimensional lattice Landau gauge fixing functional, aka random phase XY Hamiltonian

We study the stationary points of what is known as the lattice Landau gauge fixing functional in one-dimensional compact U(1) lattice gauge theory, or as the Hamiltonian of the one-dimensional random phase XY model in statistical physics. An analytic solution of all stationary points is derived for lattices with an odd number of lattice sites and periodic boundary conditions. In the context of lattice gauge theory, these stationary points and their indices are used to compute the gauge fixing partition function, making reference in particular to the Neuberger problem. Interpreted as stationary points of the one-dimensional XY Hamiltonian, the solutions and their Hessian determinants allow us to evaluate a criterion which makes predictions on the existence of phase transitions and the corresponding critical energies in the thermodynamic limit.