| 1 |
Front Matter |
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Abstract
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| 2 |
,Internal Oxidation of Binary Alloys, |
Avner Friedman |
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Abstract
Alloys can be protected from corrosion by their ability, under some circumstances, to form a continuous thin metal-oxide layer at the alloy surface which acts as a barrier, separating the alloy from corrosive agents of the environment. This layer is called an external oxide scale; see Figure 1.1 (a).
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| 3 |
,Fundamental Problems in the Theory of Shaped-Charged Jets, |
Avner Friedman |
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Abstract
Shaped-charge jets were discussed in Chapter 16 of [1] (see also Chapter 16 of [2]). They are used primarily in armor penetration; other uses include welding. On October 27, 1989 Carl A. Nelson from Honeywell has presented the shaped-charge phenomenon. This explosive process can be divided into several sub-processes. He concentrated on the free boundary problem which arises as soon as the jet has formed, and on the free boundary problem which arises as the formed jet begins to penetrate the target. Interestingly enough, these two problems are very similar.
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| 4 |
,Mathematical Modeling of Dielectric Waveguides, |
Avner Friedman |
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Abstract
Devices that incorporate optical dielectric waveguides in their design now play a significant role in communications and signal processing. Optical fibers used in telephone communications are a familiar example of passive waveguides, but research activity is growing in the area of devices that actively switch or modulate light. The increasing interest in optical waveguides and the increasing complexity of waveguide devices have stimulated the development of mathematical tools for waveguide analysis. One set of important but difficult problems is characterizing propagation in inhomogeneous structures, i.e. waveguide structures that vary in the direction of propagation.
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| 5 |
,A diffusion problem from rock porosity measurements, |
Avner Friedman |
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Abstract
Disposing of nuclear waste is becoming a major environmental problem. Nuclear waste buried in the ground may migrate with water seeping through it. Research carried out at Los Alamos National Laboratory involves tracking the migration of nuclear waste. The goal is to understand the migration process in order to design safe burial sites, ensuring, in particular, that the nuclear waste will not enter into the water table.
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| 6 |
,Applications and modeling of diffractive optical elements, |
Avner Friedman |
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Abstract
Diffractive optics technology provides a new approach to optical design and fabrication using computer-aided design tools and integrated circuit manufacturing methods. With this approach, one creates an efficient holographic element in the form of a surface relief profile etched into an optical substrate. The appropriate interference fringe pattern is created on the surface with high resolution lithography. An accurate mathematical model of diffractive elements is essential for design development and performance prediction. A rigorous mathematical description is provided by solutions to Maxwell’s equations in .. with appropriate discontinuities across the surface relief profile. On November 17, 1989 Allen Cox from Honeywell has reviewed applications and modeling of devices with surface relief having periodic structure. He also discussed the mathematical problems which need to be addressed in order to improve the design of such devices.
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| 7 |
,An approach to optimal classification, |
Avner Friedman |
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Abstract
Classification of many objects is a problem which occurs both in industry and in the military. In complex industrial processes such as making plastic materials in a chemical factory, manufacturing electronics, building sensors for robots which are to be installed on the assembly line, or running nuclear plants, one is faced with an occasional failure. In order to correct it one must be able to identify a faulty component (or several) among the large number of components, by observing, often indirectly, the way the various components function. Similarly in military situations one is required to identify specific objects (e.g. ships or airplanes) among a large population of moving or still objects.
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| 8 |
,Polymer-dispersed liquid crystal films for light control, |
Avner Friedman |
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Abstract
Polymer-dispersed liquid crystal (PDLC) films, comprised of liquid crystal microdroplets dispersed in polymer matrices, are attractive for a variety of light control applications since they can be switched electrically from a light-scattering off-state to a transparent on-state [1]–[5]. On January 12, 1990 G. Paul Montgomery from General Motors Research Laboratories described the operating principles and the key electro-optic properties of PDLC films which govern their performance in such diverse applications as electronic information displays, signs, room dividers, and solar energy control in buildings and automobiles. Some of these properties could be improved if the light scattering properties of PDLC films were more fully understood. Montgomery reviewed current theoretical attempts to describe the light scattering properties of these films and compared these theories with experimental light scattering data. He concluded by identifying problems which require further research.
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| 9 |
,Singularity problems in the stress analysis of semiconductor packaging, |
Avner Friedman |
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Abstract
Years of empirical experimentation under the pressures of cost and competition has stimulated the developments of plastic packages for semiconductor chips that are simple, tough and cheap. As users of electronics demand fast introduction of new packages with proven reliability and much improved performance, the semiconductor producers are seeking rational design procedures for new or improved packages, using finite element stress. analysis. Small size and extreme cost constraints require the use of sharp edged components inside the plastic shell, and the sharp edges create stress fields that may cause cracks or delaminations in the plastic. Such stress fields can be treated as singularities to simplify the overall stress analysis of the effects of geometry and material properties, and to tie the overall analysis to the local stress fields that drive the failure mechanisms of the plastic. The mathematics of these singularities is still not connected well to the finite element stress analysis.
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| 10 |
,Pulse reflection from a randomly stratified medium, |
Avner Friedman |
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Abstract
Probing the earth, the ocean or the atmosphere is commonly performed by sending a pulse through the medium and then measuring the backscattered pulse as it is reflected back to the surface. The medium typically has complicated structure, so that some simplifying assumptions are usually made; for general reference on the subject see the articles in the book [1].
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| 11 |
,Theory of polymer melt viscoelasticity, |
Avner Friedman |
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Abstract
Polymers are long flexible chains of molecules. Under thermal motion in a polymer melt, chain entanglement will play a dominant role. Theoretical prediction of the dynamics of the system based upon first principles is an intracable many-body problem. On February 16, 1990 Young-Hwa Kim from 3M Corporation has reviewed the theory based on the reptation model of de-Gennes (1971) and the Doi-Edwards theory (1978) which relies upon this reptation model. He then pointed out some discrepancy between theory and experiment and suggested a more refined approach which will depend upon solving certain rather difficult mathematical problems.
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| 12 |
,The Advection Equation in Air Quality Modeling, |
Avner Friedman |
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Abstract
Air quality models are mathematical descriptions of atmospheric transport, diffusion and chemical reaction of pollutants. The unknown variables are concentrations of chemical species in the air. The aims are to be able to predict how peak concentrations will change in response to prescribed changes in meteorology and in the source of pollution. Ozone air quality modeling, commonly referred to as photochemical air quality modeling, has been one of the main areas of emphasis in the United States within the last twenty years. The developments in this area are described in an excellent review article by J.H. Seinfeld [1].
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| 13 |
,Diffusion in swelling media: modeling and applications, |
Avner Friedman |
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Abstract
On March 2, 1990 David S. Ross from Eastman Kodak Company presented a problem of 1-dimensional diffusion in a medium that swells as a function of the concentration of one or more of the diffusants. He described two applications: (1) dye transfer problem of thermal imaging, and (2) a process by which filter dyes are incorporated into photographic emulsion. He concluded by posing several mathematical problems.
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| 14 |
,Mathematical modeling of semiconductor lasers, |
Avner Friedman |
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Abstract
This chapter describes a coupled electrical and optical model for the conversion of electrial energy into coherent optical energy by solid state device. Such devices are used as exposure sources in photography and medicine, and in optical transmission lines for telephones. John Spence from Eastman Kodak has presented, on April 6, 1990, a solid state laser model, and discussed numerical results which he and Keith Kahen (from Eastman Kodak) have been developing. He concluded by presenting some mathematical problems.
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| 15 |
,Conformation of random polymers, |
Avner Friedman |
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Abstract
Homopolymers are polymers consisting of many identical monomers bonded sequentially. (In Chapter 10 we considered the entanglement problem for such polymers). Heteropolymers are polymers consisting of different groups of monomers. A protein is a heteropolymer; its monomers are amino-acids whose molecular structure is There are about 20 different amino-acids, each having a different radical ..
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| 16 |
,Current-voltage relations for electrolytic solutions, |
Avner Friedman |
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Abstract
A number of electrochemical systems that are of direct interest to the automobile industry — including batteries, sensors, and electrodeposition processes — could be improved if a more detailed knowledge of the charge-transfer reactions taking place at the electrode surface was available. In particular, it is desirable to have an efficient means of determining rate constants from current-voltage relations measured in the laboratory. These constants appear as parameters in boundary conditions for a system of nonlinear PDE’s that describe charge transport in electrolytic solutions. On April 20, 1990 Daniel Baker from General Motors Research Laboratories described the nonlinear system and discussed methods developed jointly with Mark Verbrugge (also from General Motors) for solving this system in order to determine the current distribution on the electrode. He concluded with some open problems.
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| 17 |
,Scaling and Optimization for List-Matching, |
Avner Friedman |
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Abstract
The list-matching problem is concerned with assigning . agents to . tasks in such a way that each task is assinged to precisely one agent. With each assignment . there is associated the cost ..(.) of performing the tasks. The goal is to choose . which minimizes the cost. As . increases the problem becomes increasingly complex. The time required to solve it grows polynomially with . The situation is quite similar to the one in the travelling salesman problem (TSP), although the time required to solve the TSP grows exponentially with .; the TSP is .-complete. This complexity has motivated Hopfield and Tank [1] to devise a neural network computational approach to the TSP.
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| 18 |
,Topics in Tomography, |
Avner Friedman |
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Abstract
In computerized tomography X-ray transmission measurements are recorded on a computer memory and a mathematical algorithm is applied to produce a numerical description of the tissue density as a function of position within a thin slice of the body. This function is then displayed visually. The X-ray machine projects several hundred parallel pencil beams in the plane of the slice, and the attenuation of each beam is recorded. This procedure is then repeated many times with a small change in the angle at each time. The mathematical problem is to devise an efficient algorithm for computing the density function from the X-ray measurements.
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| 19 |
,Solution to problems from Part 2, |
Avner Friedman |
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Abstract
We briefly describe, or give reference, to solutions of some of the open problems from Part 2 [1].
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| 20 |
Back Matter |
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Abstract
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