1st Edition

Pulling Rabbits Out of Hats Using Mathematical Modeling in the Material, Biophysical, Fluid Mechanical, and Chemical Sciences

By David Wollkind, Bonni J. Dichone Copyright 2022
    554 Pages 56 Color & 156 B/W Illustrations
    by CRC Press

    554 Pages 56 Color & 156 B/W Illustrations
    by CRC Press

    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.

    1. Introduction

    2. Solidification and Melting of Dilute Binary Alloys

    3. Chemically Driven Convection of Dissociating Gases

    4. Temperature-Dependent Predator-Prey Mite Interaction on Apple Tree Foliage

    5. Multi-Layer Fluid Phenomena: Rayleigh-Bénard-Marangoni Convection and Kelvin- Helmholtz Rock Folding

    6. Two-Phase Fluid Flow of Aerosols and Convection in Planetary Atmospheres

    7. Chemical Turing Patterns and Diffusive Instabilities

    8. Evolution Equation Phenomenon I: Lubrication Theory of Liquids

    9. Evolution Equation Phenomenon II: Ion-Sputtering of Solids

    10. Evolution Equation Phenomenon III: Nonlinear Optical Pattern Formation

    11. Evolution Equation Phenomenon IV: Nonlinear Vegetative Pattern Formation

    12. Diffusive Versus Differential Flow Instabilities I: Dryland Turing Pattern Formation

    13. Diffusive Versus Differential Flow Instabilities II: Mussel Bed Turing Pattern Formation

    14. Root Suction Driven Vegetative Rhombic Pattern Formation

    15. Subcritical Behavior of a Model Interaction-Dispersion Equation

    16. Non-Cytopathic Viral-Target Cell Dynamical System Interaction

    17. Jeans’ Criterion for Gravitational Instabilities with Uniform Rotation

    18. Conclusions


    David J. Wollkind is Professor Emeritus at Washington State University, USA. Bonni Dichone, is an Associate Professor at Gonzaga University, USA.