We are pleased to invite the Israeli applied math community to participate in the Eighth Israeli Mini-Workshop in Applied and Computational Mathematics, to be held at Bar-Ilan University on Thursday December 27th, 2007.

These workshops have been held twice yearly for the last few years. For information on the last meeting click here. The idea is to create a forum for workers in applied mathematics, especially younger faculty and students, to get to know other members of the community, and promote discussion and collaboration.

**
We thank the Department of Mathematics, the Faculty of Exact Sciences
and the Office of the Vice-President for Research
at Bar-Ilan University for logistic and financial support.**

**
December 26th: Please note change in the workshop program!
**

Registration | Speakers and Schedule | Access and Parking | Abstracts |

9:00 | Reception | |

9:30 | Nir Sochen (Tel Aviv) | Fast GL(n)-invariant framework for tensor regularization |

10:00 | Daniel Freedman (RPI and Weizmann) | Measuring and localizing homology |

10:30 | Yair Zarmi (Ben Gurion) | Inelastic soliton interactions in the perturbed KdV equation |

11:00 | Break and refreshments | |

11:30 | Guy Baruch (Tel Aviv) | Solution of the nonlinear Helmholtz equation |

12:00 | Eitan Tadmor (University of Maryland) | Long time existence for the rapidly rotating shallow-water and Euler equations |

12:30 | Lunch and discussions | |

14:30 | Gershon Wolansky (Technion) | Incompressible, quasi-rigid deformations of 2-dimensional domains |

15:00 | Eli Shlizerman (Weizmann) | Chaos in the Pertubed Nonlinear Schrodinger Equation |

15:30 | Break and refreshments | |

15:50 | Fabio Ramos (Weizmann) | Statistical approximations of the Navier-Stokes equations |

16:20 | Reuven Cohen (Bar-Ilan) | Achieving convergence in mobile robot swarms |

(Joint work with Yaniv Gur and Ofer Pasternak.)

The solution of the perturbed equation is written as a sum of an elastic component and an inelastic one. The elastic component is described by the same perturbation series in the single- and multiple-soliton cases. In the multiple-soliton case, it preserves the elastic scattering character of the unperturbed solution.

The inelastic component is driven by that part in the perturbation, which represents the net effect of the difference between the single- and multiple-soliton solutions. This part corresponds to inelastic interactions amongst the solitons. It is highly localized in the x-t plane. The corrections it generates in the solution evolve along the characteristic lines of the original solitons. Hence, the soliton wave numbers and velocities are not affected. However, they do spoil the elastic character of the multiple-soliton solution.

The structure of the corrections included in the inelastic component depends on the initial data imposed on the solution. The common solution corresponds to solitary waves. Some initial data lead to the emergence of new types of corrections, including soliton-anti-soliton creation or annihilation, and soliton decay or amalgamation.

Its commonly-used parabolic approximation, the nonlinear Schrodinger equation (NLS), is known to possess singular solutions.

We therefore consider the question: do nonlinear Helmholtz solutions exists, under conditions for which the NLS solution becomes singular ? In other words, is the singularity removed in the elliptic model ?

In this work we develop a numerical method which produces such solutions in some cases.

Our study reveals a "nearby" periodic-in-time approximate solution in the small δ regime, upon which hinges the long time existence of the exact smooth solution. These results are in agreement with the close-to periodic dynamics observed in the "near inertial oscillation" (NIO) regime which follows oceanic storms.

A sensible definition of a deformation metric between 2-dimensional surfaces obtained from each other by an area preserving (incompressible) mapping is proposed. In addition, an algorithm for obtaining this metric, as well as the optimal deformation is suggested.

(Joint work with Vered Rom-Kedar.)

(Joint work with Edriss S. Titi and Boris Levant)

(Joint work with David Peleg.)