Pulling Rabbits Out of Hats: Using Mathematical Modeling in the Material, Biophysical, Fluid Mechanical, and Chemical Sciences (Advances in Biochemistry and Biophysics)

Pulling Rabbits Out of Hats: Using Mathematical Modeling in the Material, Biophysical, Fluid Mechanical, and Chemical Sciences focuses on those assumptions made during applied mathematical modeling in which the phenomenological data and the model predictions are self-consistent. This comprehensive reference demonstrates how to employ a variety of mathematical techniques to quantify a number of problems from the material, biophysical, fluid mechanical, and chemical sciences. In doing so, methodology of modelling, analysis, and result generation are all covered. Key Features: Includes examples on such cases as solidification of alloys, chemically-driven convection of dissociating gases, temperature-dependent predator-prey mite systems, multi-layer and two-phase fluid phenomena, viral-target cell interactions, diffusive and gravitational instabilities, and chemical, material science, optical, and ecological Turing patterns. Aims to make the process of quantification of scientific phenomena transparent. Is a hybrid semi-autobiographical account of research results and a monograph on pattern formation. This book is for everyone with an interest in how both scientific contributions are made and mathematical modelling is developed from first principles in STEM fields. For errata, please visit the author's website. Cover Half Title Series Page Title Page Copyright Page Dedication Contents Foreword Preface Acknowledgements 1. Introduction 2. Solidification and Melting of Dilute Binary Alloys: Longitudinal and Hexagonal Planform Nonlinear Stability Analyses 3. Chemically Driven Convection of Dissociating Gases: Longitudinal Planform Nonlinear Stability Analysis 4. Temperature-Dependent Predator-Prey Mite Interaction on Apple Tree Foliage: Dynamical Systems Analysis 5. Multi-Layer Fluid Phenomena: Rayleigh-Benard-Marangoni Convection and Kelvin-Helmholtz Rock Folding: Linear Stability Analyses 6. Two-Phase Fluid Flow of Aerosols and Convection in Planetary Atmospheres: Longitudinal Planform Nonlinear Stability Analyses 7. Chemical Turing Patterns and Diffusive Instabilities: Hexagonal Planform Nonlinear Stability Analysis 8. Evolution Equation Phenomenon I: Lubrication Theory of Liquids: Hexagonal Planform Nonlinear Stability Analysis 9. Evolution Equation Phenomenon II: Ion-Sputtering of Solids: Hexagonal and Rhombic Planform Nonlinear Stability Analyses 10. Evolution Equation Phenomenon III: Nonlinear Optical Pattern Formation: Hexagonal and Rhombic Planform Nonlinear Stability Analyses 11. Evolution Equation Phenomenon IV: Nonlinear Vegetative Pattern Formation: Hexagonal and Rhombic Planform Nonlinear Stability Analyses 12. Diffusive Versus Differential Flow Instabilities I: Dryland Turing Pattern Formation: Hexagonal and Square Planform Nonlinear Stability Analyses 13. Diffusive Versus Differential Flow Instabilities II: Mussel Bed Turing Pattern Formation: Hexagonal and Rhombic Planform Nonlinear Stability Analyses 14. Root Suction Driven Vegetative Rhombic Pattern Formation: Rhombic Planform Nonlinear Stability Analysis 15. Subcritical Behavior of a Model Interaction-Dispersion Equation: Longitudinal Planform Nonlinear Stability Analysis 16. Non-Cytopathic Viral-Target Cell Dynamical System Interaction: Dynamical Systems Analysis 17. Jeans' Criterion for Gravitational Instabilities with Uniform Rotation: Linear Stability Analysis 18. Conclusions Bibliography Index