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 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.