Bi-Annual Mini-Workshops on Applied and Computational Mathematics

Twenty fifth workshop    Bar-Ilan University, December 25, 2019

Twenty fourth workshop    Sessions at IMU meeting, June 13, 2019

Twenty third workshop    Hebrew University, December 25th, 2018

Twenty second workshop    Sessions at IMU meeting, May 24, 2018

Twenty first workshop    Ort Braude College, December 28, 2017

Twentieth workshop    Sessions at IMU meeting, May 25-28, 2017

Nineteenth workshop    Bar-Ilan University, December 29, 2016

Eighteenth workshop Sessions at IMU annual meeting, June 2-5, 2016

Seventeenth workshop Weizmann Institute, December 28, 2015

Sixteenth workshop Technion, December 30, 2014

Fifteenth workshop Ort Braude College, December 27, 2012

Fourteenth workshop Tel-Aviv University July 3, 2012

Thirteenth workshop Bar-Ilan University, December 29, 2011

Twelfth workshop               Ben Gurion University, December 31, 2009.

Eleventh workshop            Technion, July 2, 2009

Tenth workshop                  Tel-Aviv University, December 30, 2008

Ninth workshop                Hebrew University, July 3, 2008

Eightth workshop                Bar-Ilan, December 27, 2007

Seventh workshop             Weizmann, June 14, 2007

Sixth workshop                  Ben Gurion University, Jan 2007

Fifth workshop                  Technion, June 2006

Fourth workshop            Tel-Aviv University, January 3, 2006.

Third workshop                Hebrew University, June 7, 2005.

Second Workshop           Bar-Ilan University, December 23, 2004.

First workshop    Weizmann Institute, December 23, 2003.

Mini-Workshop on Applied Mathematics

Tuesday, December 23, 2003
Weizmann Institute, Zyskind 1

Organizers: Raz Kupferman (HU), Vered Rom-Kedar, Edriss Titi (WIS)

Few of us have thought about initiating informal one day meetings in Applied Mathematical Analysis and Computations. The idea is to have 2-3 such meeting per year. The suggested format is to have two one-hour plenary talks which are meant to be more of a review of a field of research and four half-hour talks by local participants (a balanced mixture of young and senior researchers). It will be fine if some speakers decide to report on some of their preliminary results. After all these are supposed to be informal meetings and the idea is to promote discussion and collaborations. In this first meeting we included several visitors who came for winter vacation to Israel - in the future we hope there will be more opportunity to local participants.

The first meeting includes a disscussion on the present and future directions of Applied mathematics in Israel.

We also intend to have a preprint/reprint table where people can display their recent works.

The participation in the mini-workshop is FREE. However, please register: Send e-mail to Carol, preferably now, but in any case before 18/12/03 if you plan to attend.
Please include details for a name tag and let us know if you plan to have lunch with us.

9:30-10:00	Coffee
10:00-11:00	Prof. G. Zaslavsky, NYU	Complexity of trajectories in Hamiltonian dynamics
11:00-11:30	Prof. N. Paldor, Hebrew U.	The Shallow Water Equations on the Rotating Spherical Earth: recent Advances
11:30-12:00	Dr. Boaz Ilan, U. of Colorado at Boulder	Optical light bullets in a pure Kerr medium
12:00-14:00	Lunch
14:00-15:00	Discussion on Applied Mathematics in Israel: wwww (what, why, where, where to)	Confirmed participants: Zvika Artstein (WIS), Matania Ben-Artzi (HU), Gadi Fibich (TAU), Ilan Kozma (Elta).
15:00-15:30	Prof. D. Turaev, BGU	On the richness of Hamiltonian chaos.
15:30-16:00	Coffee
16:00-16:30	Arkady Poliakovsky , Technion.	Singular perturbation problems and liftings in BV
16:30-17:30	Prof. G. Golub, Stanford	Numerical Methods for Solving Least Squares Problems with Constraints

We thank the Faculty of mathematics and computer science at Weizmann and the Belfer institute for their support.

Abstracts:

Prof. G. Zaslavsky, NYU

Complexity of trajectories in Hamiltonian dynamics

It is natural to introduce such a definition of the complexity that, from one side it provides " more complexity"
the more unpredictable is a trajectory, and, from another side, the complexity notion would be related to
such physical characteristics as entropy and transport. The existed notion of epsilon-complexity is insufficient
for this goal since it can't be applied to Hamiltonian dynamics with nonuniform hyperbolicity or with zero Lyapunov exponents.
We provide some examples of this difficulty and introduce new notions of the complexity function and entropy function.
Different features of the new notions will be described and the applications will be demonstrated.

Dr. Boaz Ilan, U. of Colorado at Boulder

Optical light bullets in a pure Kerr medium

Using a recent result on critical exponents of anisotropic NLS
equations, as well as numerical simulations, we show that small negative
fourth-order dispersion can arrest spatiotemporal collapse of ultrashort
laser pulses propagating in a planar waveguide having a pure Kerr
nonlinearity and anomalous dispersion, resulting in (2+1)D "optical
bullets". Similarly to solitons, these bullets undergo elastic
collisions. Since these bullets can self-trap from noisy Gaussian input
beams and propagate without power loss, this result may be used to
realize experimentally stable, non-dissipative optical bullets.
This is joint work with Gadi Fibich.

Prof. D. Turaev
Ben-Gurion University

On the richness of Hamiltonian chaos.

Abstract. We call a symplectic diffeomorphism of $R^{2n}$ universal, if
its iterations can be made arbitrarily close to any other symplectic
diffeomorphism by a smooth coordinate transformation. By definition, any
dynamical phenomenon, robust in the class of smooth 2n-simensional
symplectic diffeomorphisms, can be encountered in any universal symplectic
map of the same dimension. We prove that universal maps are dense in the
class of synmplectic maps which have at least one elliptic periodic
orbit. These results strongly suggest to expect an ultimate richness of
dynamics from any given Hamiltonian system with 2 or more degrees
of freedom without a uniform partially-hyperbolic structure.

Arkady Poliakovsky, Technion.

Singular perturbation problems and liftings in BV

The study of the asymptotic behavior of the minimizers $\{u_\e\}$, as $\e$
goes to zero, for the energy
$$
E_\e(u)=\int_\Omega \bigl\{|\nabla u|^2+
\frac{1}{\e²}W(u)\bigr\}\,dx\,,
$$
under a mass constraint $\int_\Omega u=m$, where $W$ is a double-well potential, is motivated
by the Van der Waals-Cahn-Hilliard theory of phase transitions.
We apply a generalization of the techniques developed by
Modica and Sternberg to a lifting problem in BV-spaces.
A function $u\in BV(\Omega,S¹)$ has many liftings in $BV(\Omega,\R)$ (by a {\em lifting}
we mean a function $\phi$ satisfying $u=e^{i\phi}$ a.e.~in $\Omega$), so it is natural
to look for an ``optimal'' lifting. Our approach consists of studying
the asymptotic behavior of the minimizers $\{\phi_\e\}$ for the energy
$$
E_\e(\phi)=\int_\Omega \bigl\{|\nabla\phi|^2+
\frac{1}{\e²}|u-e^{i\phi}|^2\bigr\}\,dx\,,
$$
for which we show the convergence to a lifting of $u$ with minimal BV-seminorm.

Prof. Gene H. Golub, Stanford University

Numerical Methods for Solving Least Squares Problems with Constraints

In this talk, we discuss the problem of solving linear least squares
problems and Total Least Squares problems with linear constraints
and/or a quadratic constraint. We are particularly interested in
developing stable numerical methods when the data matrix is singular
or near singular. Of particular interest are matrices which are large
and sparse and for which iterative methods must be employed. The
quadratically constrained problems arise in problems where
regularization is required. For such problems, a Lagrange multiplier
is required and that calculation may be quite intensive. The method we
propose will quickly yield an estimate of the parameter and allow for
finding the least squares solution.

Gene H. GOLUB, Computer Science Department, Stanford
University, Stanford, CA 94305, USA
golub@stanford.edu

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The Fifth Israeli Applied Math MiniWorkshop

Wednesday 7.6.06 at the Technion

********************************************************

This is the second announcement for the MiniWorkshop. We are pleased to

have a stellar lineup of speakers:

Ehud Yariv (Technion)

Avy Soffer (Rutgers)

Philip Rosenau (Tel Aviv)

Vered Rom-Kedar and Eliezer Shochat (Weizmann)

Alex and Michael Bronstein (Technion)

Matania Ben-Artzi (Jerusalem)