Degeneracy In Ideal Chemical Equilibrium Problems

A single- or multi-phase chemical equilibrium problem may be though of as the problem of minimizing a particular nonlinear function (the free energy) of composition subject to the conditions that the composition vector be nonnegative and satisfy a system of linear equations (the mass-balance laws). It was pointed out in a previous paper (AD-706 018) that the free energy is convex and homogeneous of degree one, but that as a variable approaches zero, the free energy may behave badly. In this paper, the phase 'chemical equilibrium problem' refers only to a problem with a particular mathematical form. Problems of this form arise in many situations that are not classically denoted chemical equilibrium problems. (Author).

Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Theoretical Chemistry: Advances and Perspectives, Volume 5 covers articles concerning all aspects of theoretical chemistry. The book discusses the mean spherical approximation for simple electrolyte solutions; the representation of lattice sums as Mellin-transformed products of theta functions; and the evaluation of two-dimensional lattice sums by number theoretic means. The text also describes an application of contour integration; a lattice model of quantum fluid; as well as the computational aspects of chemical equilibrium in complex systems. Chemists and physicists will find the book useful.

This book differs from other thermodynamics texts in its objective which is to provide engineers with the concepts, tools, and experience needed to solve practical real-world energy problems. The presentation integrates computer tools (e.g., EES) with thermodynamic concepts to allow engineering students and practising engineers to solve problems they would otherwise not be able to solve. The use of examples, solved and explained in detail, and supported with property diagrams that are drawn to scale, is ubiquitous in this textbook. The examples are not trivial, drill problems, but rather complex and timely real world problems that are of interest by themselves. As with the presentation, the solutions to these examples are complete and do not skip steps. Similarly the book includes numerous end of chapter problems, both typeset and online. Most of these problems are more detailed than those found in other thermodynamics textbooks. The supplements include complete solutions to all exercises, software downloads, and additional content on selected topics. These are available at the book web site www.cambridge.org/KleinandNellis.