Description
Mathematics Applied to Science: In Memoriam Edward D. Conway presents a compilation of articles as a lasting tribute to Edward Conway III. This book covers a variety of topics, including molecular electronic energies, partial differential equations, density matrix, electron density functional, and climate change.
Organized into 13 chapters, this book begins with an overview of the large-time behavior of one-dimensional motion in a model gas whose particles have a discrete set of allowed velocities. This text then explores the operator splitting techniques for the solution of time dependent differential equations. Other chapters describe a Monte Carlo simulation procedure for evaluating the relaxation rate of an excited state vibrational population of a diatomic in a simple solvent. This book discusses as well the numerical solution of nonlinear differential equations. The final chapter deals with the physical, thermal, and dynamical properties near the surface of the Earth.
This book is a valuable resource for mathematicians.
Chapter
List of Articles by Edward D. Conway
CHAPTER 1. LARGE-TIME BEHAVIOR OF MODEL GASES WITH A DISCRETE SET OF VELOCITIES
2. FUNDAMENTAL PROPERTIES
3. ESTIMATES IN HIGHER NORMS
4. ASYMPTOTIC BEHAVIOR IN L
CHAPTER 2. APPLICATIONS OF OPERATOR SPLITTING METHODS TO THE NUMERICAL SOLUTION OF NONLINEAR PROBLEMS IN CONTINUUM MECHANICS AND PHYSICS
1. GENERALITIES AND SYNOPSIS
2. DESCRIPTION OF SOME BASIC OPERATOR SPLITTING METHODS FOR TIME DEPENDENT PROBLEMS
3. APPLICATION TO THE NAVIER-STOKES EQUATIONS FOR INCOMPRESSIBLE VISCOUS FLUIDS
4. APPLICATION TO LINEAR AND NONLINEAR EIGENVALUE PROBLEMS
5. APPLICATION TO LIQUID CRYSTAL CALCULATIONS
CHAPTER 3. ON AN ASYMPTOTIC MODEL FOR MACH STEM FORMATION IN PLANAR DETONATIONS
2. THE MAJDA-ROSALES SCHEME
CHAPTER 4. GROWTH OF CELL POPULATIONS VIA ONE-PARAMETER SEMIGROUPS OF POSITIVE OPERATORS
1. AN EQUATION DESCRIBING CELL SIZE DISTRIBUTION AS A CONCRETE AND ABSTRACT CAUCHY PROBLEM
2. WELL-POSED ABSTRACT CAUCHY PROBLEMS AND STRONGLY CONTINUOUS SEMIGROUPS
3. ASYMPTOTIC BEHAVIOR OF STRONGLY CONTINUOUS SEMIGROUPS
4. ASYMPTOTIC BEHAVIOR OF POSITIVE SEMIGROUPS
CHAPTER 5. SOLVENT INDUCED RELAXATION OF EXCITED STATE VIBRATIONAL POPULATIONS OF DIATOMICS: A MIXED QUANTUM-CLASSICAL SIMULATION
3. RESULTS AND DISCUSSION
CHAPTER 6. MOVING MESH METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
CHAPTER 7. OSCILLATORY SOLUTIONS OF PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS
8. THE QUANTUM-MECHANICAL HARTREE-FOCK STAIRCASE METHOD FOR MOLECULAR ELECTRONIC ENERGIES
2. HARTREE-FOCK STAIRCASE METHOD
3. ANALYSIS OF THE STAIRCASE METHOD
4. AN OPEN MATHEMATICAL QUESTION AND CONCLUDING REMARKS
CHAPTER 9. ELECTRON DENSITY FUNCTIONALS FROM THE GRADIENT EXPANSION OF THE DENSITY MATRIX: THE TROUBLE WITH LONG-RANGE INTERACTIONS
1. DENSITY FUNCTIONAL THEORY
2. KINETIC AND EXCHANGE ENERGIES
3. DENSITY MATRIX AND ITS GRADIENT EXPANSION
4. GRADIENT EXPANSION OF THE EXCHANGE ENERGY
5. INCONCLUSIVE NUMERICAL EXPERIMENT ON THE GRADIENT COEFFICIENT
6. DERIVATIONS FROM LINEAR-RESPONSE THEORY
CHAPTER 10. DYNAMICS OF SYSTEMS IN CLOSE-TO-CONTINUUM CONDITIONS
2. APPLICATIONS (Summary)
CHAPTER 11. HAMILTONIAN DYNAMICS OF RIEMANN ELLIPSOIDS
6. HAMILTONIAN FORMULATION
7. S-TYPE RIEMANN ELLIPSOIDS
8. GEOMETRIC QUANTIZATION
CHAPTER 12. ASYMMETRIC SOLUTIONS OF PROBLEMS WITH SYMMETRY
2. POSITIVE SOLUTIONS OF THE DIRICHLET PROBLEM
3. GENERAL BOUNDARY CONDITIONS; A UNIVERSALITY THEOREM
CHAPTER 13. THE MATHEMATICS IN CLIMATE CHANGE
2. THE THINGS THAT NEED TO BE EXPLAINED
3. THE OVERALL PHILOSOPHY OF THE PRESENT APPROACH
ORGANIZATION OF THE RAMAINDER OF THIS PAPER
5. THE ORIGIN OF THE PLEISTOCENE ICE AGE
5. CLIMATES WITHIN THE OCEAN
6. ABRUPT CLIMATIC EVENTS
Mathematics Applied to Science
：In Memoriam Edward D. Conway
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