Particle Modeling

ISBN-13: 9780817639853 / Angielski / Twarda / 1997 / 274 str.

Donald Greenspan

Opis

A reference for the field of particle modelling - the study of dynamical behaviour of solids and fluids in response to external forces, with the solids and fluids modelled as systems of atoms and molecules.

Spis treści

I. Mathematical, Physical and Numerical Considerations.- 1. Particle Modeling: What It Is and What It Is Not.- 1.1 Introduction.- 1.2 Classical Molecular Forces.- 1.3 General Modeling Principles.- 2. Numerical Methodology.- 2.1 Introduction.- 2.2 The Leap Frog Method.- 2.3 Completely Conservative.- Numerical Methodology.- 2.4 Remarks.- II. Qualitative Newtonian Modeling.- 3. Elastic Strings and Solitons.- 3.1 Introduction.- 3.2 Discrete Strings.- 3.3 Example.- 3.4 String Solitons.- 3.5 Heavy Strings and Strings with One Fixed End.- 3.6 Remark.- 4. Elastic Snap Through.- 4.1 Introduction.- 4.2 An Arch.- 4.3 Elastic Snap Through.- 4.4 Unstable Mode Approximation.- 4.5 Remarks.- 5. Minimal Surfaces.- 5.1 Introduction.- 5.2 Computer Examples.- 6. Biological Self Reorganization.- 6.1 Introduction.- 6.2 Computer Examples.- 6.3 Remarks.- 7. Cavity Flow.- 7.1 Introduction.- 7.2 Computer Example.- 7.3 Additional Examples.- 8. Turbulent and Nonturbulent Vortices.- 8.1 Introduction.- 8.2 Basic Definitions.- 8.3 Examples.- 8.4 Remark.- 9. Liquid Drop Formation, Fall, and Collision.- 9.1 Introduction.- 9.2 Drop Generation.- 9.3 Drop Fall.- 9.4 Drop Collision.- 10. Conservative Motion of Tops and Gyroscopes.- 10.1 Introduction.- 10.2 A Discrete, Rigid Tetrahedral Top.- 10.3 Dynamical Equations.- 10.4 Numerical Method.- 10.5 Examples.- 10.6 Extensions.- 10.7 A Discrete, Rigid Hexahedral Gyroscope.- 10.8 Dynamical Equations.- 10.9 Numerical Method.- 10.10 Examples.- 10.11 Remark.- III. Quantitative Modeling.- 11. Stress Wave Propagation in Slender Bars.- 11.1 Introduction.- 11.2 Force Formula Development.- 11.3 Particle Model of a Slender Bar.- 11.4 Examples.- 12. Colliding Microdrops of Water.- 12.1 Introduction.- 12.2 Mathematical and Physical Considerations.- 12.3 Examples.- 13. Crack Development in a Stressed Copper Plate.- 13.1 Introduction.- 13.2 Formular Derivation.- 13.3 Examples.- 14. Liquid Drop Formation on a Solid Surface.- 14.1 Introduction.- 14.2 Local Force Formulas.- 14.3 Dynamical Equations.- 14.4 Drop and Slab Stabilization.- 14.5 Sessile Drop Formation.- 15. Fluid Bubbles and Jiggling Gels.- 15.1 Introduction.- 15.2 Fluid Models.- 15.3 Basin Stabilization.- 15.4 Motion of CO2 Bubbles.- 15.5 Jiggling Gels.- 16. Melting Points.- 16.1 Introduction.- 16.2 Formula Development.- 16.3 Noble Gas Calculations.- 16.4 Helium (26atm).- 16.5 Homogeneous, Diatomic Molecular Solids.- 17. Special Relativistic Motion.- 17.1 Introduction.- 17.2 Inertial Frames.- 17.3 The Lorentz Transformation.- 17.4 Rod Contraction and Time Dilation.- 17.5 Relativistic Particle Motion.- 17.6 Covariance.- 17.7 Relativistic Motion.- 17.8 Numerical Methodology.- 17.9 Relativistic Harmonic Oscillation.- 17.10 Computational Covariance.- 18. A Speculative Model of the Diatomic Molecular Bond.- 18.1 Introduction.- 18.2 Classical Simulation of the Hydrogen Molecule.- 18.3 Modification of the Classical Model.- 18.4 Extension to Li2B2C2N2and O2.- References and Sources for Further Reading.- Appendices — FORTRAN Programs and Related Formulas.- A1. Stress. For.- A2. Drop. For.- A3. Morse. For.- A4. Ghexa. For.- A5. Newtonian Iteration Formulas.