Noise-assisted mound coarsening in epitaxial growth

Two types of mechanisms are proposed for mound coarsening during unstable epitaxial growth: stochastic, due to deposition noise, and deterministic, due to mass currents driven by surface energy differences. Both yield the relation H=(RWL)² between the typical mound height W, mound size L, and the film thickness H. An analysis of simulations and experimental data shows that the parameter R saturates to a value which discriminates sharply between stochastic () and deterministic () coarsening. We derive a scaling relation between the coarsening exponent 1/z and the mound-height exponent which, for a saturated mound slope, yields . Received: 11 November 1997 / Revised in final form: 28 November 1997 / Accepted: 28 November 1997     

Approximation in weighted Hardy spaces

This paper is concerned with several approximation problems in the weighted Hardy spacesH ^p(Ω) of analytic functions in the open unit disc D of the complex plane ℂ. We prove that ifX is a relatively closed subset of D, the class of uniform limits onX of functions inH ^p(Ω) coincides, moduloH ^p(Ω), with the space of uniformly continuous functions on a certain hull ofX which are holomorphic on its interior. We also solve the simultaneous approximation problems of describing Farrell and Mergelyan sets forH ^p(Ω), giving geometric characterizations for them. By replacing approximating polynomials by polynomial multipliers of outer functions, our results lead to characterizations of the same sets with respect to cyclic vectors in the classical Hardy spacesH ^p(D), 1 ⪯p < ∞. Dedicated to Professor Nácere Hayek on the occasion of his 75th birthday.     

Forced-air precooling of spherical foods in bulk: A parametric study

In this paper, a mathematical model for forced-air precooling of spherical food products in bulk is developed. The foods are arranged in horizontal layers stacked one above the other to form a rectangular parallelepiped with a vertical gap in between the product layers. The foods are cooled by chilled air blown along the height of the package. The governing equations for the conduction heat transfer in the foods, simultaneous heat and mass transfer at the food-air interface and in the air stream are solved numerically using finite-difference methods. A comprehensive numerical study is performed by varying the process parameters over a wide range. Typical results showing the variation of moist air properties along the height of the package and the effect of each parameter on the process time are presented. The ranges of parameters for advantageous operation of the precooling system are identified. Correlations are obtained for the process time based on the product center and mass-averaged temperatures in terms of process parameters.     

Positron annihilation in polycrystalline metals

The empirical relation θ _p ⁶ /I _p=aK (where θ _p is the limiting angle of the parabolic component in the angular distributions of annihilation photons in metals, I _p is the integrated contribution of this component, K=1, 2, 3, ... is an integer, and a is a constant independent of the type of metal) observed earlier has been tested on magnesium, aluminum, copper, zinc, lead, and bismuth samples. The validity of this relation has been substantiated. The value of the dimensionless constant a has been determined and was found to coincide within experimental error with the result obtained in previous measurements. It is shown that the value of K for the same metal but for different samples may be different. It is conjectured that this may be due to different defect concentrations in samples. Fiz. Tverd. Tela (St. Petersburg) 40, 600–602 (April 1998)     

The multiple-scale wave equation

An analytic and numerical study of the behavior of the linear nonhomogeneous wave equation of the form ε²u_tt = Δu + tf with high wave speed (ε 1) is carried out. This study was initially motivated by meteorological observations which have indicated the presence of large spatial scale gravity waves in the neighborhood of a number of summer and winter storms, mainly from visible images of ripples in clouds in satellite photos. There is a question as to whether the presence of these waves is caused by the nearby storms. Since the linear wave equation is an approximation to the full system describing pressure waves in the atmosphere, yet is considerably more tractable, we have chosen to analyze the behavior of the linear nonhomogeneous wave equation with high wave speed. The analysis is shown to be valid in one, two, and three space dimensions. Partly because of the high wave speed, the solution is known to consist of behavior which changes on two different time scales, one rapid and one slow. Additionally, because of the presence of the nonhomogeneous forcing term tf, we show that there is a component of the solution which will vary only on a very large spatial scale. Since even the linearized wave equation can give rise to persistent large spatial scale waves under the right conditions, the implication is that certain storms could be responsible for the generation of large-scale waves. Numerical simulations in one and two dimensions confirm analytic results.     

On Producing Multiple Solutions Using Repeated Trials

The number of trials that is required by an algorithm to produce a given fraction of the problem solutions with a specified level of confidence is analyzed. The analysis indicates that the number of trials required to find a large fraction of the solutions rapidly decreases as the number of solutions obtained on each trial by an algorithm increases. In applications where multiple solutions are sought, this decrease in the number of trials could potentially offset the additional computational cost of algorithms that produce multiple solutions on a single trial. The analysis framework presented is used to compare the efficiency of a homotopy algorithm to that of a Newton method by measuring both the number of trials and the number of calculations required to obtain a specified fraction of the solutions.     

Membrane introduction mass spectrometry

An overview of membrane introduction mass spectrometry (MIMS) is presented and comparisons are made with other direct sample introduction techniques. Special attention is given to the unique advantages and the limitations of newer variants on the MIMS technique, including affinity MIMS, reverse-phase and trap MIMS. The salient features of the interfaces used in MIMS are summarized and the various membrane materials commonly used are delineated. The applicability of MIMS is illustrated via discussion of

1. (i) bioreactor monitoring (represented by yeast fermentation),

2. (ii) environmental monitoring (illustrated by analysis of contaminated ground water samples) and

3. (iii) on-line chemical reaction monitoring (exemplified by the photolysis of aryl esters).

The applicability of MIMS to the analysis of environmental samples, including complex mixtures in water, air and soil, is noted.