A Mushy Region in a Stefan Problem

In the melting of a pure metal by volume heating, when superheatingdoes not occur, there will be a region in which the metal isneither pure liquid nor pure solid, called a mushy region. Agrain or dendrite model is proposed to describe the microstructureof the metal in this situation, and its stability is discussed.The explicit solution for the one-dimensional version of themodel is obtained and has a different form in three regions;near the pure solid boundary, in the mush, and near the pureliquid boundary. An appropriate average of this solution forthe microstructure is shown to reduce to the weak solution forthe microstructure is shown to reduce to the weak solution forthe macroscopic problem proposed by Atthey (1974). Propertiesof the solution for more general grain geometries are also discussed.     

Motion of Discrete Interfaces Through Mushy Layers

We study the geometric motion of sets in the plane derived from the homogenization of discrete ferromagnetic energies with weak inclusions. We show that the discrete sets are composed by a ‘bulky’ part and an external ‘mushy region’ composed only of weak inclusions. The relevant motion is that of the bulky part, which asymptotically obeys to a motion by crystalline mean curvature with a forcing term, due to the energetic contribution of the mushy layers, and pinning effects, due to discreteness. From an analytical standpoint, it is interesting to note that the presence of the mushy layers implies only a weak and not strong convergence of the discrete motions, so that the convergence of the energies does not commute with the evolution. From a mechanical standpoint it is interesting to note the geometrical similarity of some phenomena in the cooling of binary melts.     

Inertia Effects in Squeeze Flows of Viscoplastic Fluids

A squeeze flow of a viscoplastic fluid through a narrow clearance between two coaxial surfaces of revolution is considered. The problem is described by boundary-layer equations. With the use of the method of integral approaches, formulas for the pressure distribution are obtained. Generally, the flow of viscoplastic fluids given by the nonlinear Shulman model is considered. The flows of viscoplastic fluids given by the Herschel, Bulkley, Bingham, Ostwald-de Waele, and Newton models are discussed in detail. Numerical examples of pressure distributions in the clearance between parallel disks are presented.     

Squeeze flow of multiply-connected fluid domains in a Hele-Shaw cell

Summary. The theory of algebraic curves and quadrature domains is used to construct exact solutions to the problem of the squeeze flow of multiply-connected fluid domains in a Hele-Shaw cell. The solutions are exact in that they can be written down in terms of a finite set of time-evolving parameters. The method is very general and applies to fluid domains of any finite connectivity. By way of example, the evolution of fluid domains with two and four air holes are calculated explicitly. For simply connected domains, the squeeze flow problem is well posed. In contrast, the squeeze flow problem for a multiply connected domain is not necessarily well-posed and solutions can break down in finite time by the formation of cusps on the boundaries of the enclosed air holes. Received September 20, 2000; accepted September 10, 2001 Online publication November 5, 2001     

数列极限迫敛性定理的推广(英文)

极限论是微积分中基础和重要的概念.数列极限的迫敛性定理既能判断数列的收敛性,也给出其极限值。通过对数列极限迫敛性定理的条件加以改进,得到了它的推论,并用一个例子说明了该推论的应用。     

Negative modal schemes

We deal with the question of whether solutions of modal propositional negative schemes are definable on Kripke models. It is shown that there exists a formula by which a solution of such a scheme is defined in every Kripke model with the ascending chain condition, in which the solution exists. We present an algorithm for constructing such a defining formula. Supported by RFFR grant No. 96-01-01552. Translated fromAlgebra i Logika, Vol. 37, No. 3, pp. 329–337, May–June, 1998.     

Continuous Accumulation Games in Continuous Regions

In a continuous accumulation game on a continuous region, a Hider distributes material over a continuous region at each instant of discrete time, and a Seeker examines the region. If the Seeker locates any of the material hidden, the Seeker confiscates it. The goal of the Hider is to accumulate a certain amount of material before a given time, and the goal of the Seeker is to prevent this. In previous works, we have studied accumulation games involving discrete objects and continuous material over discrete locations. The issues raised when the region is continuous are substantially different. In this paper, we study accumulation of continuous material over two types of continuous regions: the interval and the circle.     

否定非对合剩余格的BF-理想

为了深入研究否定非对合剩余格的结构特征,引入否定非对合剩余格的BF-理想概念并考察其性质.证明了BF-理想的BF-交集、同态像和同态原像也是BF-理想.同时,给出了BF-理想的BF-并集成为BF-理想的条件.     

相互粒子系统中的负相关(英文)

主要研究相互粒子系统中概率测度的负相关.我们得到判定概率测度是负相关的一个充分必要条件.最后证明了具有负相关的概率测度的线性组合及乘积测度仍是负相关的.     

Brittle Thin Films

A two-dimensional model for brittle thin films is obtained from a three-dimensional fracture model for elastic material. Γ -convergence techniques are used to identify the limiting effective energy as the thickness of the sample approaches zero. Accepted 27 March 2001. Online publication 9 August 2001.     

Cellulose-Based Composite Films

The mechanical and optical properties of cellulose-based composite films are investigated.It is shown that the use of toluene diisocyanate as a coupling agent and Avicel fibers as reinforcing elements give films with the highest mechanical characteristics. Using differential scanning calorimetry, it is also found that the glass transition temperature T _g of all the materials studied is below the room temperature and that the T _g increased with cross-linking and introduction of Avicel.     

Central Regions and Dependency

The paper introduces an approach to the ordering of dependence which is based on central regions. A d-variate probability distribution is described by a nested family of sets, called central regions. Those regions are affine equivariant, compact and starshaped and concentrate about a properly defined center. They can be seen as level sets of a depth function. Special cases are Mahalanobis, zonoid, and likelihood regions. A d-variate distribution is called more dependent than another one if the volume of each central region is smaller with the first distribution. This dependence order is characterized by an inequality between determinants of certain parameter matrices if either (i) F and G are arbitrary distributions and the central regions are Mahalanobis or (ii) F and G belong to an elliptical family of distributions and the central regions are arbitrary. If the regions are zonoid regions, the dependence order implies the ordering of lift zonoid volumes. Alternatively, the dependence order is applied to the copulae of the given distributions. Generalized correlation indices are proposed which are increasing with the dependence orders.     

存在滑移时两圆球间的幂律流体挤压流动

基于Reynolds润滑理论分析了壁面滑移对任意圆球颗粒间幂律流体的挤压流动的影响。研究表明有壁面滑移时挤压流动的粘性力可通过引进本文定义的滑移修正系数分离出无滑移解。推导出的挤压力滑移修正系数是一积分表达式，依赖于滑移参数、幂律指数、球间隙和积分上限。一般地壁面滑移导致粘性力减小，粘性力的减小量随幂律指数的增大而增大，表明壁面滑移对剪切增稠流变材料有更大的影响；粘性力的减小量还随着滑移参数的增大而增加，而这恰与假设相符合；粘性力的减小量又随球间隙减小或积分上限的增大（从液桥情况到完全浸渍）而减小直到趋于常数，这一特性在离散元模拟时可以有效地减少计算量。     

Negative Dense Linear Orders

Considering dense linear orders, we establish their negative representability over every infinite negative equivalence, as well as uniformly computable separability by computable gaps and the productivity of the set of computable sections of their negative representations. We construct an infinite decreasing chain of negative representability degrees of linear orders and prove the computability of locally computable enumerations of the field of rational numbers.     

Conditionally Negative Definite Functions

Let \(f:[0,\infty )\rightarrow [0,\infty )\) be an operator monotone function and \(g: \mathbb {R}\rightarrow [0,\infty )\) be a conditionally negative definite(in short cnd) function. We obtain that \(f\circ g:\mathbb {R}\rightarrow [0,\infty )\) is also conditionally negative definite. This generalizes and subsumes several existing results. A versatile direct connection between cnd functions and functions having Weierstrass factorization is established and consequently a reasonable account for cnd functions is presented.     

Negative Beantwortung einer Approximationsfrage

Ohne Zusammenfassung