## A Celebration of Mathematical Modeling: The Joseph B. Keller Anniversary VolumeJoseph Bishop Keller, Dan Givoli, Marcus J. Grote, George Papanicolaou 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. |

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### Contents

MONTE CARLO SIMULATION FOR AMERICAN OPTIONS | 1 |

SOME PROBLEMS IN ELECTROMAGNETICS | 17 |

NONLINEAR ASPECTS | 33 |

HIGHORDER TREATMENT | 53 |

NONREFLECTING BOUNDARY CONDITIONS FOR TIME DEPENDENT WAVES | 73 |

WEAK SHOCK REFLECTION | 93 |

BIFURCATION THEORY SYMMETRY BREAKING AND HOMOGENIZATION IN CONTINUUM MECHANICS DESCRIPTIONS OF DNA | 113 |

### Other editions - View all

A Celebration of Mathematical Modeling Dan Czamanski,Marcus Grote,George Papanicolaou No preview available - 2014 |

### Common terms and phrases

Acoust American options analysis antenna applied approximation Bifurcation Theory boundary layer Brownian bridge coefficients Comm computational constant contact angle contact line curvature Darrieus-Landau denotes density dependent derived Differential Equations Diffraction diffusion domain dynamics effective eigenvalues eikonal elastic Electromagnetic example expansion finite flame speed relation flow field Fluid Mech function geometrical optics Givoli hydrodynamic inner solution instability integral interface inverse problems J.B. Keller jump conditions leading order Legendre transform length scale limiting configurations Mach reflection Math mathematical model Matkowsky method Miksis Monte Carlo motion nonreflecting boundary condition NRBC numerical solution obtain parameter pattern perturbation Phys plane Proc Pure Appl Random reaction region Revs Reynolds number Scattering sequence shock reflection SIAM simulation singular ray supersonic surface tension tangential Theory of Diffraction Ting tion triple point twist two-dimensional Vanden-Broeck variables velocity viscous wave equation wave number Wave Propagation wavefront weak shock weakly nonlinear

### Popular passages

Page 236 - The ray theory of ship waves and the class of streamlined ships. "J. Fluid Mech. Vol.91 pp.465-487 (1979) 4 Yim,B." A ray theory for non-linear ship waves and wave resistance.

Page 236 - Rottman, JW 1980 Some new highest-wave solutions for deep-water waves of permanent form J. Fluid Mech. 100.