Characteristics and design procedure of hyperbolic dies

Nozzle profiles capable of generating constant extensional strain rates are termed hyperbolic dies. When used in polymer extrusion, they exhibit greater potential in inducing and retaining polymer molecular orientation than conventional capillary dies. Most mathematical expressions found in the literature involve several processing variables in describing and designing such nozzle profiles. This report reveals that a hyperbolic die profile, although rather complicated, can be expressed with equations in terms of two ordinary geometrical parameters—the exit diameter and the hyperbolic length. This finding greatly simplifies the design procedure of hyperbolic dies. The extensional strain rate of a hyperbolic die can be related to the length-to-diameter ratio for any given exit diameter. Examples of various types of die profiles are presented and their constant extensional strain-rate characteristics are discussed.     

Simultaneous multiphoton ionization by two radiation fields. Effects of the statistical properties of the radiation

Summary We report on calculations of differential and total ionization cross-sections of hydrogen atoms irradiated by two radiation fields with different properties. One of the fields is of low intensity and relatively high frequency, the other is of low frequency and high intensity. In particular, we show that the inclusion of the multimode structure of the low-frequency laser field modifies considerably the shape of the angular distribution of the photoelectrons and the rates of ionization into the different channels characterized by the number of low-frequency photons exchanged. Further, we find that the average energy exchanged between the photoelectrons and the low-frequency radiation field is independent of the statistical properties of the low-frequency laser field.     

Molecular beam epitaxy

Molecular beam epitaxy (MBE) is a process for growing thin, epitaxial films of a wide variety of materials, ranging from oxides to semiconductors to metals. It was first applied to the growth of compound semiconductors. That is still the most common usage, in large part because of the high technological value of such materials to the electronics industry. In this process beams of atoms or molecules in an ultra-high vacuum environment are incident upon a heated crystal that has previously been processed to produce a nearly atomically clean surface. The arriving constituent atoms form a crystalline layer in registry with the substrate, i.e., an epitaxial film. These films are remarkable because the composition can be rapidly changed, producing crystalline interfaces that are almost atomically abrupt. Thus, it has been possible to produce a large range of unique structures, including quantum well devices, superlattices, lasers, etc., all of which benefit from the precise control of composition during growth. Because of the cleanliness of the growth environment and because of the precise control over composition, MBE structures closely approximate the idealized models used in solid state theory.

This discussion is intended as an introduction to the concept and the experimental procedures used in MBE growth. The refinement of experimental procedures has been the key to the successful fabrication of electronically significant devices, which in turn has generated the widespread interest in the MBE as a research tool. MBE experiments have provided a wealth of new information bearing on the general mechanisms involved in epitaxial growth, since many of the phenomena initially observed during MBE have since been repeated using other crystal growth processes. We also summarize the general types of layered structures that have contributed to the rapid expansion of interest in MBE and its various offshoots. Finally we consider some of the problems that remain in the growth of heteroepitaxial structures, specifically, the problem of mismatch in lattice constant between layers and between layer and substrate. The discussion is phenomenological, not theoretical; MBE has been primarily an experimental approach based on simple concepts.     

关于双特征Beltrami方程

该文研究空间Ｂｅｌｔｒａｍｉ方程的推广形式，即双特征Ｂｅｌｔｒａｍｉ方程．利用外微分形式与矩阵的外代数等工具，将双特征Ｂｅｌｔｒａｍｉ方程转化为一个非齐次的狆 调和方程，转化过程中只用到加于特征矩阵的一致椭圆型条件．然后验证了算子犃满足的条件：Ｌｉｐｓｃｈｉｔｚ型条件、单调不等式、齐次性条件以及算子犅满足的控制增长条件．并利用得到的狆 调和方程，给出了双特征Ｂｅｌｔｒａｍｉ方程广义解分量函数的弱单调性结果．     

HLS储存环束流发射度研究

 研究了合肥光源(HLS)储存环束流发射度与其长直线节消色散条件之间的关系；在考虑到H函数的匹配时，计算了储存环最低束流发射度；为光源多种运行模式提供了理论依据。     

Multi-sample cluster analysis using Akaike's Information Criterion

Summary Multi-sample cluster analysis, the problem of grouping samples, is studied from an information-theoretic viewpoint via Akaike's Information Criterion (AIC). This criterion combines the maximum value of the likelihood with the number of parameters used in achieving that value. The multi-sample cluster problem is defined, and AIC is developed for this problem. The form of AIC is derived in both the multivariate analysis of variance (MANOVA) model and in the multivariate model with varying mean vectors and variance-covariance matrices. Numerical examples are presented for AIC and another criterion calledw-square. The results demonstrate the utility of AIC in identifying the best clustering alternatives. This research was supported by Office of Naval Research Contract N00014-80-C-0408, Task NR042-443 and Army Research Office Contract DAAG 29-82-K-0155, at the University of Illinois at Chicago.     

Models of a structural phase transition with general anharmonicity and disorder

It is shown how the self-consistent phonon Ansatz leads to a new class of exactly soluble models of a structural phase transition. Both nonpolynomial anharmonicity and disorder are analyzed in detail. In the classical limit, the thermodynamics is obtained and sufficient conditions on the anharmonicity are given to ensure a soft-mode phase transition. Diagonal disorder has been studied numerically. It is found that in three dimensions a pronounced mobility edge, separating localized and delocalized phonon states, may exist.     

方位偏振 Be s s e 一 Ga u s s光束的传输特性研究`

利用 o C il sn 衍射积分公式,给出了方 位偏 振 e B s el一G au s 光 束通过 A B C D 轴 对称 光学系统的解析 表达式.对其通过 自由空 间和付里 叶变换系统特殊情况的传输作 了分析和 讨论.     

非线性等重码的一个上界

本文给出等重码的一个上界，并且举例说明这个上界是可以达到的，作为直接推论，我们推导出等重等距码的几个结果。     

On parallel asynchronous high-order solutions of parabolic PDEs

In achieving significant speed-up on parallel machines, a major obstacle is the overhead associated with synchronizing the concurrent processes. This paper presents high-orderparallel asynchronous schemes, which are schemes that are specifically designed to minimize the associated synchronization overhead of a parallel machine in solving parabolic PDEs. They are asynchronous in the sense that each processor is allowed to advance at its own speed. Thus, these schemes are suitable for single (or multi) user shared memory or (message passing) MIMD multiprocessors. Our approach is demonstrated for the solution of the multidimensional heat equation, of which we present a spatial second-order Parametric Asynchronous Finite-Difference (PAFD) scheme. The well-known synchronous schemes are obtained as its special cases. This is a generalization and expansion of the results in [5] and [7]. The consistency, stability and convergence of this scheme are investigated in detail. Numerical tests show that although PAFD provides the desired order of accuracy, its efficiency is inadequate when performed on each grid point.In an alternative approach that uses domain decomposition, the problem domain is divided among the processors. Each processor computes its subdomain mostly independently, while the PAFD scheme provides the solutions at the subdomains' boundaries. We use high-order finite-difference implicit scheme within each subdomain and determine the values at subdomains' boundaries by the PAFD scheme. Moreover, in order to allow larger time-step, we use remote neighbors' values rather than those of the immediate neighbors. Numerical tests show that this approach provides high efficiency and in the case which uses remote neighbors' values an almost linear speedup is achieved. Schemes similar to the PAFD can be developed for other types of equations [3].This research was supported by the fund for promotion of research at the Technion.