Guy Baruch

Scientific interests:

I am an applied mathematician, with academic background in Mathematics, Physics and Computer Science. I am mainly interested in the mathematical modeling and investigation of scientific and engineering problems, using asymptotic, numeric, and analytic methods.

Here is my detailed research statement, and research statement abstract:

Currently, I'm a Ph.D. student in Prof. Gadi Fibich's group at the Applied Mathematics department of the Tel Aviv University. We collaborate with Prof. Semyon V. Tsynkov from North-Carolina State University.
In the bulk of my PhD research I studied the nonlinear Helmholtz (NLH) equation, which models intense laser beams in nonlinear optics. The standard model in nonlinear optics is based on the simpler nonlinear Schrodinger equation (NLS), but it predicts nonphysical singularity formation. We have shown, for the first time ever, that solutions to the 3D cubic NLH exist under boundary-conditions which lead to singularity formation in the NLS, thereby closing a question which had been open since 1965. We have also investigated the 2D NLH, showing the existence of very narrow solitons and modeling counter-propagating beams (both cases are beyond the limits of the NLS model). Numerically, this work required the solution of a nonlinear, non self-adjoint boundary-value problem, the development of high-order schemes with material discontinuities, and nonlocal absorbing boundary conditions.

I have also investigated the bi-harmonic NLS (BNLS) equation. We found and characterized new peak-type and ring-type singular solutions of the BNLS and show rigorously that, in the L²-critical case, all singular solutions are self-similar.

I obtained my M.Sc. in experimental plasma Physics at the Weizmann Institute, where we used X-ray spectroscopy to investigate unstable plasma in stagnating Z-Pinches. Z-Pinch based X-ray sources may be used to achieve viable energy-production via inertial confinement fusion.

Previously, I have worked for four years as an algorithm developer in an industrial start-up called Verisity (since acquired by Cadence). In the course of my work, we applied mathematical constraint-solving techniques to the modeling and application of hardware-verification. In that work, I co-invented two patents.

Scientific publications:

1. G. Baruch, G. Fibich, E. Mandelbaum
   "New ring-type singular solutions of the biharmonic NLS", work in progress.
2. G. Baruch, G. Fibich, E. Mandelbaum
   "Singular solutions of the biharmonic NLS", work in progress.
3. G. Baruch, G. Fibich, N. Gavish
   Singular standing-ring solutions of nonlinear partial differential equations, submitted.
4. G. Baruch, G. Fibich, S. V. Tsynkov
   High-Order Numerical Method for the Nonlinear Helmholtz Equation in Multidimensional Layered Media, Journal of Computational Physics, 228 10 (Feb. 2009) pp. 3789--3815. (arXiv)
5. G. Baruch, G. Fibich, S. V. Tsynkov
   Simulations of the Nonlinear Helmholtz Equation: Arrest of Beam Collapse, Nonparaxial Solitons, and Counter-Propagating Beams, Optics Express Vol. 16 Issue 17, pp.13323-13329 (2008). (arXiv)
6. G. Baruch, G. Fibich, S. V. Tsynkov, E. Turkel
   Fourth Order Schemes for Time-Harmonic Wave Equations with Discontinuous Coefficients,
   Communications in Computational Physics 5 (2-4) (Feb. 2009) pp. 442-455 .
7. G. Baruch, G. Fibich and S. V. Tsynkov
   High-order numerical method for the nonlinear Helmholtz equation with material discontinuities in one space dimension
   Journal of Computational Physics, 227 1 (Nov. 2007) pp. 820-850 (arXiv). It has associated scripts.
8. G. Baruch, G. Fibich and S. V. Tsynkov
   High-Order Numerical Solution of the Nonlinear Helmholtz Equation with Axial Symmetry
   Journal of Computational and Applied Mathematics 204: 477-492, 2007.

Applied Math student seminar

Together with Nir Gavish, we organized the 2008 Applied Math student seminar here at TAU.

CV

Here are my CV and list of publications and patents.

contact info:

email: mailto:guy.baruch@math.tau.ac.il.
Tel.: 972-3-6406210

Lab:

Room 025, ground floor, Schreiber building.

Dead-tree address:

Guy Baruch
School of Mathematical Sciences
Tel Aviv University
Tel Aviv 69978
Israel