Mathematics Applied to Science - In Memoriam Edward D. Conway

Front Cover

Mathematics Applied to Science: In Memoriam Edward D. Conway

Copyright Page

Table of Contents

Contributors

Preface

Biographical Sketch of Edward D. Conway

Scientific Biographical Sketch of Edward D. Conway

List of Articles by Edward D. Conway

CHAPTER 1. LARGE-TIME BEHAVIOR OF MODEL GASES WITH A DISCRETE SET OF VELOCITIES

1. INTRODUCTION

2. FUNDAMENTAL PROPERTIES

3. ESTIMATES IN HIGHER NORMS

4. ASYMPTOTIC BEHAVIOR IN L

5. CONCLUSION

REFERENCES

CHAPTER 2. APPLICATIONS OF OPERATOR SPLITTING METHODS TO THE NUMERICAL SOLUTION OF NONLINEAR PROBLEMS IN CONTINUUM MECHANICS AND PHYSICS

ABSTRACT

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

6. CONCLUSION

ACKNOWLEDGEMENTS

REFERENCES

CHAPTER 3. ON AN ASYMPTOTIC MODEL FOR MACH STEM FORMATION IN PLANAR DETONATIONS

1. INTRODUCTION

2. THE MAJDA-ROSALES SCHEME

3. ANALYTICAL RESULTS

REFERENCES

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

5. AN EXAMPLE

REFERENCES

CHAPTER 5. SOLVENT INDUCED RELAXATION OF EXCITED STATE VIBRATIONAL POPULATIONS OF DIATOMICS: A MIXED QUANTUM-CLASSICAL SIMULATION

ABSTRACT

I. INTRODUCTION

II. THEORY

3. RESULTS AND DISCUSSION

4. SUMMARY

ACKNOWLEDGEMENT

REFERENCES

CHAPTER 6. MOVING MESH METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

ABSTRACT

1. INTRODUCTION

2. SOFTWARE DESIGN

3. TIME DISCRETIZATION

4. DYNAMIC REZONING

5. MESH REGULARITY

6. NUMERICAL EXAMPLE

7. CONCLUSIONS

ACKNOWLEDGMENTS

REFERENCES

CHAPTER 7. OSCILLATORY SOLUTIONS OF PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS

ACKNOWLEDGEMENTS

REFERENCES

8. THE QUANTUM-MECHANICAL HARTREE-FOCK STAIRCASE METHOD FOR MOLECULAR ELECTRONIC ENERGIES

ABSTRACT

I. INTRODUCTION

2. HARTREE-FOCK STAIRCASE METHOD

3. ANALYSIS OF THE STAIRCASE METHOD

4. AN OPEN MATHEMATICAL QUESTION AND CONCLUDING REMARKS

REFERENCES

CHAPTER 9. ELECTRON DENSITY FUNCTIONALS FROM THE GRADIENT EXPANSION OF THE DENSITY MATRIX: THE TROUBLE WITH LONG-RANGE INTERACTIONS

ABSTRACT

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

REFERENCES

CHAPTER 10. DYNAMICS OF SYSTEMS IN CLOSE-TO-CONTINUUM CONDITIONS

ABSTRACT

1. OUTLINE OF THE METHOD

2. APPLICATIONS (Summary)

REFERENCES

CHAPTER 11. HAMILTONIAN DYNAMICS OF RIEMANN ELLIPSOIDS

1. INTRODUCTION

2. RIEMANN ELLIPSOIDS

3. OBSERVABLES

4. EULER EQUATIONS

5. LAGRANGE FORMULATION

6. HAMILTONIAN FORMULATION

7. S-TYPE RIEMANN ELLIPSOIDS

8. GEOMETRIC QUANTIZATION

9. CONCLUSION

REFERENCES

CHAPTER 12. ASYMMETRIC SOLUTIONS OF PROBLEMS WITH SYMMETRY

1. INTRODUCTION

2. POSITIVE SOLUTIONS OF THE DIRICHLET PROBLEM

3. GENERAL BOUNDARY CONDITIONS; A UNIVERSALITY THEOREM

REFERENCES

CHAPTER 13. THE MATHEMATICS IN CLIMATE CHANGE

1. INTRODUCTION

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

REFERENCES