Convection in the Melt

A physical problem involving the melting/freezing of a phase-change material (PCM) is the applied setting of this research. The development of models that couple the partial differential equations for energy transport and fluid motion with phases of differing densities is a primary goal of the research. In Chapter 2, a general framework is developed for the formulation of conservation laws that admit interfaces. A notion of weak solution is developed and its relation with classical and other weak formulations is discussed. Conditions that hold across various kinds of interfaces are also developed. The formulation is examined for the conservation of mass, momentum and energy in Chapter 3. In Chapter 4, a numerical method for the solution of conservation law equations is given. The method uses a Crank-Nicolson time discretization and solves the implicit equations with a Newton/Approximate Factorization technique. The method captures interfaces and is consistent with the control volume weak formulations of Chapter 2. The numerical solution converges to the distributional solution of the conservation law. In Chapter 5, three applications of the theory are developed and numerical computations are presented. First, a one dimensional problem is studied involving conservation of mass. momentum and energy in a phase-change material with a liquid density larger than that of the solid. The second application is a suction problem in two dimensions. The bulk movement of a liquid and void are simulated with and without the effects of surface tension. The third application is to a three-dimensional simulation of the heating of a cylindrical canister of PCM in 1-g and 0-g. For this simulation the Marangoni stress is the important driving force on the flow

Mathematical source references

This list of references is intended to be a convenient reference source for those interested in the historical origin of common mathematical ideas, The topics mentioned are mostly those met in a degree course in mathematics. For each entry the list attempts to give an exact source reference with comments about priority. There are now available other historical reference sources for mathematics on the internet but with a different style of presentation.<br/

Analysis and Computation of Equilibria and Regions of Stability, With Applications in Chemistry, Climatology, Ecology, Economics

This record has been put together in a limited time for prompt distribution. It is not a proceedings volume. Rather it is a collection of all memoranda, diagrams, and literature references that were circulated before the workshop, used to support presentations during the workshop, or written down to preserve some ideas and some outcomes of computations that arose from the workshop. The only organizing principle is the temporal sequence in which the materials were presented or prepared

Research in nonlinear structural and solid mechanics

Nonlinear analysis of building structures and numerical solution of nonlinear algebraic equations and Newton's method are discussed. Other topics include: nonlinear interaction problems; solution procedures for nonlinear problems; crash dynamics and advanced nonlinear applications; material characterization, contact problems, and inelastic response; and formulation aspects and special software for nonlinear analysis

Functional analysis and aspects of non-linear control theory

This thesis studies the state reconstruction problem for a class of non-linear systems. This class is that of perturbed linear systems. The properties of the linear part are used to arrive at results for the complete system. Whilst this is a common technique in mathematics and physics its use in non-linear infinite dimensional systems theory has not been extensively investigated. The present work makes such an investigation with a view to indicating the successes, and limitations, of such a treatment. As to contribution, as far as the author is aware, many of the results are new both in precise statement and general approach. Chapter 1 introduces, and motivates, the formulation adopted. Chapter 2 provides some useful information on linear infinite dimensional control theory. Chapter 3 gives, subject to certain, perhaps restrictive, conditions, a rigorous statement, and proof, of the basic theorems. Here, as elsewhere, the standard fixed point results are used. Parts of this chapter are extracts from, as yet unpublished, joint work with A.J. Pritchard and M.D. Quinn. Chapter 4 relaxes some of the conditions in 3 and applies the same techniques to other areas. Chapter 5 surveys, in a formal fashion the more constructive, numerical aspects of the preceding results with a view to indicating directions for this important area of further research. It is concluded that the "perturbed linear" approach used here can give results that are both theoretically and computationally useful. The strength of the requirements placed on the linear part, however, indicates a challenging area for future investigations: a constructive approach to intrins1cally non-linear problems

Control and Coordination in Hierarchical Systems

This book presents the applied theory of control and cooordination in hierarchical systems which are those where decision making has been divided in a certain way. It concentrates on various aspects of optimal control in large scale systems and covers a range of topics from multilevel methods for optimizing by interactive feedback procedures to methods for sequential, hierarchical control in large dynamic systems

Proceedings of the Flat-plate Solar Array Project Research Forum on the High-speed Growth and Characterization of Crystals for Solar Cells

Theoretical and experimental phenomena, applications, and characterization including stress/strain and other problem areas that limit the rate of growth of crystals suitable for processing into efficient, cost-effective solar cells are discussed. Melt spinning, ribbon growth, rapid solidification, laser recrystallization, and ignot growth of silicon and metals are also discussed

Mathematical Optimization Techniques

The papers collected in this volume were presented at the Symposium on Mathematical Optimization Techniques held in the Santa Monica Civic Auditorium, Santa Monica, California, on October 18-20, 1960. The objective of the symposium was to bring together, for the purpose of mutual education, mathematicians, scientists, and engineers interested in modern optimization techniques. Some 250 persons attended. The techniques discussed included recent developments in linear, integer, convex, and dynamic programming as well as the variational processes surrounding optimal guidance, flight trajectories, statistical decisions, structural configurations, and adaptive control systems. The symposium was sponsored jointly by the University of California, with assistance from the National Science Foundation, the Office of Naval Research, the National Aeronautics and Space Administration, and The RAND Corporation, through Air Force Project RAND

Second Microgravity Fluid Physics Conference

The conference's purpose was to inform the fluid physics community of research opportunities in reduced-gravity fluid physics, present the status of the existing and planned reduced gravity fluid physics research programs, and inform participants of the upcoming NASA Research Announcement in this area. The plenary sessions provided an overview of the Microgravity Fluid Physics Program information on NASA's ground-based and space-based flight research facilities. An international forum offered participants an opportunity to hear from French, German, and Russian speakers about the microgravity research programs in their respective countries. Two keynote speakers provided broad technical overviews on multiphase flow and complex fluids research. Presenters briefed their peers on the scientific results of their ground-based and flight research. Fifty-eight of the sixty-two technical papers are included here