An Introduction to Computer Simulation in Applied Science

1. Rationale for Computer Simulation in Materials Science.- I. Introduction.- II. Patterns of Science.- III. The Student and His Research.- IV. Examples of Systems Events in the Crystallization Area.- A. An Overview of the Scientific Subroutines.- B. Technological Understanding of Ingot Defects.- C. Solute Distribution in Pulled Crystals.- 2. Lectures on Large-Scale Finite Difference Computation of Incompressible Fluid Flows.- I. The Differential Equations.- A. Introduction.- B. Numerical Solution of Laplace's Equation.- C. The Inclusion of a Source Term and the Potential Solution.- D. The Time-Dependent Vorticity Field Due to Diffusion and Convection.- E. The Dynamic Equations and Scaling.- F. Suggested Reading.- II. Stability Analysis of the Difference Equations.- A. Introduction.- B. Stability Analysis of the Heat Conduction Equation.- C. Stability Analysis of Laplace's Equation.- D. Stability Analysis of the Nonlinear Convection Equation.- E. Suggested Reading.- III. Applications of the Numerical Program for Incompressible Flow.- A. Introduction.- B. The Differential Equations of Fluid Flow.- C. The Difference Equations.- D. Karman Vortex Street Flows.- E. The Benard Problem.- F. References.- IV. Description of the Numerical Program for Incompressible Flow.- A. Discussion of the Block Diagram.- B. Discussion of the Program Listings.- C. Suggested Reading.- Appendix: Computer Listings of the Hydrodynamic Programs.- 3. Computer Simulation of Diffusion Problems Using the Continuous System Modeling Program Language.- I. Introduction.- II. System/360 Continuous System Modeling Program (S/360 CSMP).- A. Types of Statements.- B. Elements of a Statement.- C. Important Features of S/360 CSMP.- D. The S/360 CSMP Library of Functions.- E. The S/360 CSMP Library of Data and Control Statements.- F. Integration Methods.- G. The MACRO Function.- H. The Structure of the Model.- I. Advantages of S/360 CSMP.- J. Sample Problem.- III. Heat Transfer in an Insulated Bar.- A. Finite Differencing the Heat Equation.- B. Finite Difference Approach in the Modeling.- C. Fourier Solution.- D. The S/360-CSMP Solution.- IV. The Freezing of a Liquid.- A. Finite Differencing the Governing Equations.- B. The S/360-CSMP Solution.- 4. Computer Simulation of Vapor Deposition on Two-Dimensional Lattices.- I. Basic Concepts of Physical Processes.- A. Introduction.- B. The Honig Model.- C. The Simulated Processes.- D. The Rate Equations.- II. The Computer Simulation Model.- A. Boundary Conditions.- B. Evaporation, Migration, and Nearest Neighbor Effects.- C. Initial Conditions.- III. Random Numbers and Simulation Strategy.- A. Monte Carlo Methods.- B. Generation of Random Numbers.- C. Gaussian Distribution Generated by Random Numbers.- D. Use of Random Numbers to Select Dynamic Processes- Simulation Strategy.- IV. Real and Simulated Time.- V. The VDS Programs.- VI. The Computer Simulation Results.- References.- Appendix: Fortran Code.- 5. Introduction to Computational Theoretical Chemistry.- I. Basic Concepts of Computational Theoretical Chemistry.- II. The Nature of the Problem.- A. The Hydrogen Atom (Ground Electronic State).- B. The Helium Atom (Ground Electronic State).- III. Real Molecular Systems.- A. Introduction.- B. The Method of Hartree and Hartree-Fock.- C. Multicenter Integrals.- IV. The Calculation of Quantum-Mechanical Two-Electron Multi-center Integrals via Transformation Theory.- A. Introduction.- B. General Theory.- V. Computational Results.- References.- Appendix: Fortran Code.- 6. Numerical Simulation of Weather.- I. Physical Phenomena.- A .Introduction.- B. Magnitude and Range of the Problem.- C. Scaling Approximations.- D. Fundamental Conservation Equations.- II. Numerical Methods.- A. Physical Considerations.- B. Finite Difference Solutions and Nonlinear Instability.- C. Existing General Circulation Models.- D. Nonfinite Difference Methods in Numerical Weather Calculations.- III. Computer Requirements.- A. High-Speed Computer Characteristics.- B. Need for Supercomputers.- C. Estimates of Computer Requirements in Meteorological Calculations.- D. Programming Considerations.- E. Future Outlook.- References.