Table Of ContentPulling Rabbits Out of Hats
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Pulling Rabbits Out of Hats
Using Mathematical Modeling in the Material, Biophysical, Fluid Mechanical, and Chemical Sciences
David Wollkind, Bonni J. Dichone
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Pulling Rabbits Out of Hats
Using Mathematical Modeling in the
Material, Biophysical, Fluid Mechanical,
and Chemical Sciences
David Wollkind
Washington State University
with
Bonni Dichone
Gonzaga University
First edition published 2022
by CRC Press
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and by CRC Press
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© 2022 David Wollkind, Bonni J. Dichone
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Library of Congress Cataloging-in-Publication Data
Names: Wollkind, David J., 1942- author. | Dichone, Bonni, author.
Title: Pulling rabbits out of hats : using mathematical modeling in the material,
biophysical, fluid mechanical, and chemical sciences/David Wollkind with Bonni
Dichone.
Description: Boca Raton : CRC Press, 2021. | Includes bibliographical
references and index.
Identifiers: LCCN 2021021531 (print) | LCCN 2021021532 (ebook) | ISBN
9781032047874 (hardback) | ISBN 9781032050072 (paperback) | ISBN
9781003195603 (ebook)
Subjects: LCSH: Mathematical models. | Mathematical analysis.
Classification: LCC QA401 .W74 2021 (print) | LCC QA401 (ebook) | DDC
511/.8--dc23
LC record available at https://lccn.loc.gov/2021021531
LC ebook record available at https://lccn.loc.gov/2021021532
ISBN: 9781032047874 (hbk)
ISBN: 9781032050072 (pbk)
ISBN: 9781003195603 (ebk)
DOI: 10.1201/9781003195603
Typeset in CMR10 font
by KnowledgeWorks Global Ltd.
For Juan, Natasha, and Olli; Niki, Jonathan, and Jeremy; and
in memory of Edward Pate and thesis advisor Lee Segel.
David J. Wollkind
For my husband Paulo, daughter Georgina, and mother Gloria
Kealy.
Bonni Dichone
Contents
Alternate chapter arrangement by analysis topic (see Preface: Scope): Chapters 1, 4, 16, 5,
17, 6, 15, 3, 2, 8, 7, 12, 9, 10, 11, 14, 13, 18.
Foreword ix
Preface xi
Acknowledgements xv
1 Introduction 1
2 Solidification and Melting of Dilute Binary Alloys: Longitudinal and
Hexagonal Planform Nonlinear Stability Analyses 7
3 Chemically Driven Convection of Dissociating Gases: Longitudinal Plan-
form Nonlinear Stability Analysis 47
4 Temperature-Dependent Predator-Prey Mite Interaction on Apple Tree
Foliage: Dynamical Systems Analysis 81
5 Multi-Layer Fluid Phenomena: Rayleigh-B´enard-Marangoni Convection
and Kelvin-Helmholtz Rock Folding: Linear Stability Analyses 127
6 Two-Phase Fluid Flow of Aerosols and Convection in Planetary Atmo-
spheres: Longitudinal Planform Nonlinear Stability Analyses 163
7 Chemical Turing Patterns and Diffusive Instabilities: Hexagonal Plan-
form Nonlinear Stability Analysis 203
8 Evolution Equation Phenomenon I: Lubrication Theory of Liquids:
Hexagonal Planform Nonlinear Stability Analysis 233
9 Evolution Equation Phenomenon II: Ion-Sputtering of Solids: Hexagonal
and Rhombic Planform Nonlinear Stability Analyses 259
10 Evolution Equation Phenomenon III: Nonlinear Optical Pattern Forma-
tion: Hexagonal and Rhombic Planform Nonlinear Stability Analyses 297
11 Evolution Equation Phenomenon IV: Nonlinear Vegetative Pattern For-
mation: Hexagonal and Rhombic Planform Nonlinear Stability Analyses 331
12 Diffusive Versus Differential Flow Instabilities I: Dryland Turing Pattern
Formation: Hexagonal and Square Planform Nonlinear Stability Analy-
ses 365
vii
viii Contents
13 DiffusiveVersusDifferentialFlowInstabilitiesII:MusselBedTuringPat-
tern Formation: Hexagonal and Rhombic Planform Nonlinear Stability
Analyses 403
14 Root Suction Driven Vegetative Rhombic Pattern Formation: Rhombic
Planform Nonlinear Stability Analysis 433
15 Subcritical Behavior of a Model Interaction-Dispersion Equation: Longi-
tudinal Planform Nonlinear Stability Analysis 455
16 Non-Cytopathic Viral-Target Cell Dynamical System Interaction: Dy-
namical Systems Analysis 473
17 Jeans’ Criterion for Gravitational Instabilities with Uniform Rotation:
Linear Stability Analysis 487
18 Conclusions 503
Bibliography 519
Index 537
Foreword
It was Fall of 2007. I was at graduate school orientation at Washington State University
(WSU). I already had a Master’s degree in Mathematics from Eastern Washington Uni-
versity and had spent the last two years lecturing at other universities, but colleagues had
convinced me to go back to school and pursue a Ph.D. I was hesitant to do so, because I
thoughtIwasnot“goodenough”atmathematicsandhadbeenoutofthatkindofin-depth
study for too long. But, somehow I found myself at WSU, terrified of what lay ahead of me
and certain I would fail.
It was during this orientation that I first met Dr. David J. Wollkind or just “Wollkind,”
as I still call him. He came into orientation and gave a presentation on his research and
the courses he taught. He was extremely intense, talked very quickly, and disseminated in-
formation at a rapid speed, while pacing and clicking through slides being projected (from
one of those old-fashioned projectors that had a wheel of literal film slides) at an alarming
and aggressive rate. Being in the state of mind that I was, you would have thought such
a presentation from this clearly intelligent and entirely formidable mathematician would
haveintimidatedmebutinsteadIwasintriguedandfascinated.Iapproachedhimafterthe
session and he said, in the most matter of a fact way, “Bonni, you should sign up for my
ContinuumMechanicscoursethisFall.”WhichIdidandeverycoursehetaught,thereafter.
LectureswithWollkindwereunique.Heusedaveryspecificsetofcoloredchalk,inaddition
to white chalk, along with a yard stick, all of which he used to draw very detailed pictures
and graphs up on the board, well before class would begin. I learned very quickly that one
needed to arrive at least 10 minutes before class to copy said figures down, as there was no
time during his lecture to copy them when he referenced them. He would lecture rapidly
andhishandwriting,whilequitelegiblecomparedtootherprofessors,degradedashewould
go, with t’s, x’s, and z’s all looking nearly the same by the end of class, not to speak of his
useofξ’s,ζ’s,andthelike.Eachlecturewasjam-packedwithmathematicaltechniqueand
its applications, relayed in the most carefully planned out and truly beautiful and artistic
way. Every class felt like a master class in the topic being presented, from the master, him-
self. Sprinkled throughout the complex mathematics, he would often relay these anecdotal
stories of when and how he learned the mathematics or discovered the techniques he was
presenting.Ialwayslookedforwardtotheseaccounts,becausehewouldgetatwinkleinhis
eye and usually include some kind of sarcastic joke or comment, which was always funny
and also gave me a chance to catch up in my note taking.
One semester in, I asked him to be my thesis advisor and the rest, as they say, is history
(see Chapter 12 and onward). Throughout my time at WSU, we formed a very close work-
ing relationship and a great friendship, which has continued to this day. He shepherded
me through my qualifying exams, doctoral exams, dissertation defense, publications, and
presentations. In so doing, he built my confidence as a mathematician and I successfully
graduated with my Ph.D. and, after a Post-Doctoral position, was hired in a tenure-track
position, as one of the first Applied Mathematicians, at Gonzaga University (GU). Our
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