Particle Modeling

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