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I. Mathematical, Physical and Numerical Considerations.- 1. Particle Modeling: What It Is and What It Is Not.- 2. Numerical Methodology.- II. Qualitative Newtonian Modeling.- 3. Elastic Strings and Solitons.- 4. Elastic Snap Through.- 5. Minimal Surfaces.- 6. Biological Self Reorganization.- 7. Cavity Flow.- 8. Turbulent and Nonturbulent Vortices.- 9. Liquid Drop Formation, Fall, and Collision.- 10. Conservative Motion of Tops and Gyroscopes.- III. Quantitative Modeling.- 11. Stress Wave Propagation in Slender Bars.- 12. Colliding Microdrops of Water.- 13. Crack Development in a Stressed Copper Plate.- 14. Liquid Drop Formation on a Solid Surface.- 15. Fluid Bubbles and Jiggling Gels.- 16. Melting Points.- 17. Special Relativistic Motion.- 18. A Speculative Model of the Diatomic Molecular Bond.- 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.