BiAnnual MiniWorkshops on Applied and
Computational Mathematics
Nineteenth workshop BarIlan University,
December 29, 2016
Eighteenth
workshop Session at IMU annual meeting,
June 25, 2016
Seventeenth
workshop Weizmann Institute, December
28, 2015
Sixteenth
workshop Technion,
December 30, 2014
Fifteenth
workshop Ort Braude
College, December 27, 2012
Fourteenth
workshop TelAviv University July
3, 2012
Thirteenth
workshop BarIlan University,
December 29, 2011
Twelfth
workshop
Ben Gurion University, December 31, 2009.
Eleventh
workshop
Technion, July 2, 2009
Tenth
workshop
TelAviv University, December 30, 2008
Ninth
workshop
Hebrew University, July 3, 2008
Eightth
workshop
BarIlan, December 27, 2007
Seventh
workshop
Weizmann, June 14, 2007
Sixth
workshop
Ben Gurion University, Jan 2007
Fifth
workshop
Technion, June 2006
Fourth
workshop
TelAviv University, January 3, 2006.
Third
workshop
Hebrew University, June 7, 2005.
Second
Workshop
BarIlan
University, December 23, 2004.
First workshop
Weizmann Institute, December 23, 2003.
Few of us have thought about initiating informal one day meetings
in Applied Mathematical Analysis and Computations. The idea is to have
23 such meeting per year. The suggested format is to have two onehour
plenary talks which are meant to be more of a review of a field of
research and
four halfhour 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 miniworkshop is FREE. However,
please register: Send email 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.
9:3010:00

Coffee


10:0011:00

Prof. G. Zaslavsky, NYU

Complexity of trajectories in Hamiltonian
dynamics

11:0011:30

Prof. N. Paldor, Hebrew U.

The Shallow Water Equations on the Rotating
Spherical Earth:
recent Advances

11:3012:00

Dr. Boaz Ilan, U. of Colorado at Boulder

Optical light bullets in a pure Kerr medium 
12:0014:00

Lunch


14:0015:00

Discussion on Applied Mathematics in Israel:
wwww (what, why, where, where to)

Confirmed participants: Zvika Artstein
(WIS), Matania BenArtzi (HU),
Gadi
Fibich (TAU), Ilan Kozma (Elta).

15:0015:30

Prof. D. Turaev, BGU

On the richness of Hamiltonian chaos. 
15:3016:00

Coffee


16:0016:30

Arkady Poliakovsky , Technion. 
Singular perturbation problems and liftings in BV 
16:3017:30

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 epsiloncomplexity 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
fourthorder 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 selftrap from noisy Gaussian input
beams and propagate without power loss, this result may be used to
realize experimentally stable, nondissipative optical bullets.
This is joint work with Gadi Fibich.
Prof. D. Turaev
BenGurion 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 2nsimensional
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 partiallyhyperbolic 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
$$
E_\e(u)=\int_\Omega \bigl\{\nabla u^2+
\frac{1}{\e^{2}}W(u)\bigr\}\,dx\,,
$$
under a mass constraint $\int_\Omega u=m$, where $W$ is a doublewell
potential, is motivated
by the Van der WaalsCahnHilliard theory of phase transitions.
We apply a generalization of the techniques developed by
Modica and Sternberg to a lifting problem in BVspaces.
A function $u\in BV(\Omega,S^{1})$ 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
$$
E_\e(\phi)=\int_\Omega \bigl\{\nabla\phi^2+
\frac{1}{\e^{2}}ue^{i\phi}^2\bigr\}\,dx\,,
$$
for which we show the convergence to a lifting of $u$ with minimal
BVseminorm.
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

*******************************************************
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 RomKedar and Eliezer Shochat (Weizmann)
Alex and Michael Bronstein (Technion)
Matania BenArtzi (Jerusalem)
Avi Levy (Intel)
Dani Givoli (Technion)
A. As usual the MiniWorkshop will consists of 30 minutes talks.
B. Although there is no registration fee for this meeting, we ask all
those who plan to participate to inform the
organizer (Koby Rubinstein
koby@math.technion.ac.il)
by 20.5.06 in order to help make
suitable
local arrangements.
C. The meeting will conclude at an ApreMath party at the Camel beach
(Dado Darom).