A Celebration of Mathematical Modeling

1. Front Matter

   Pages i-xxxix

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2. Monte Carlo Simulation for American Options

   • Russel E. Caflisch, Suneal Chaudhary

   Pages 1-16

3. Some Problems in Electromagnetics

   • Margaret Cheney

   Pages 17-32

4. Pattern Formation in a Suspension of Swimming Microorganisms: Nonlinear Aspects

   • S. Childress, E. A. Spiegel

   Pages 33-52

5. Non-Reflecting Boundaries: High-Order Treatment

   • Dan Givoli

   Pages 53-72

6. Nonreflecting Boundary Conditions for Time Dependent Waves

   • Marcus J. Grote

   Pages 73-92

7. Weak Shock Reflection

   • John K. Hunter, Allen M. Tesdall

   Pages 93-112

8. Bifurcation Theory, Symmetry Breaking and Homogenization in Continuum Mechanics Descriptions of DNA

   • John H. Maddocks

   Pages 113-136

9. On Flames as Discontinuity Surfaces in Gasdynamic Flows

   • Bernard J. Matkowsky

   Pages 137-160

10. Contact Lines

    • Michael J. Miksis

    Pages 161-180

11. Eikonal Functions: Old and New

    • Jacob Rubinstein, Gershon Wolansky

    Pages 181-198

12. Physical Insight, Mathematical Modeling and Asymptotics

    • Ting Lu

    Pages 199-220

13. Waves, Bubbles and Jets

    • J.-M. Vanden-Broeck

    Pages 221-238

14. Back Matter

    Pages 239-241

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ThisvolumecelebratestheeightiethbirthdayofJosephB. Keller. The authors who contributed to this volume belong to what can be called the “Keller school of applied mathematics. ” They are former students, postdoctoral fellows and visiting scientists who have collaborated with Joe (some of them still do) during his long career. They all look at Joe as their ultimate (role) model. JoeKeller’sdistinguishedcareerhasbeendividedbetweentheCourant Institute of Mathematical Sciences at New York University, where he received all his degrees (his PhD adviser being the great R. Courant himself) and served as a professor for 30 years, and Stanford University, where he has been since 1978. The appended photos highlight some scenes from the old days. Those who know Joe Keller’s work have been always amazed by its diversity and breadth. It is considered a well-known truth that there is not a single important area in applied mathematics or physics which Keller did not contribute to. This can be appreciated, for example, by glancing through his list of publication included in this volume. App- priately, the papers in this book, written with Joe’s inspiration, cover a variety of application areas; together they span the broad subject of mathematical modeling. The models discussed in the book describe the behavior of various systems such as those related to ?nance, waves, - croorganisms, shocks, DNA, ?ames, contact, optics, ?uids, bubbles and jets. Joe’s activity includes many more areas, which unfortunately are not represented here.

• Mathematica
• bifurcation
• mathematical modeling
• mechanics
• modeling

• Department of Aerospace Engineering, Technion — Israel Institute of Technology, Haifa, Israel

  Dan Givoli

• Department of Mathematics, University of Basel, Basel, Switzerland

  Marcus J. Grote

• Department of Mathematics, Stanford University, Stanford, USA

  George C. Papanicolaou

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