faculty

Faculty

List of faculty members:

Professor Saul Abarbanel
Professor Flavian Abramovici
Professor Alfred Inselberg
Dr. Adi Ditkowski
Professor Nira Dyn
Professor Gadi Fibich
Professor Nima Geffen
Dr. Arie Levant
Professor David Levin
Professor Joseph J. Roseman
Professor Philip Rosenau
Professor Steven Schochet (Chairman)
Professor Zeev Schuss
Professor Gregory Sivashinsky
Prof. Nir Sochen
Professor Eli Turkel

	Saul Abarbanel, Professor Ph.D.: 1959, MIT Research Interests: Hydrodynamics; Numerical methods for PDE; Computational fluid dynamics; Computational electromagnetics. Research Description: High order compact schemes with strict (temporal) stability. Strict temporal stability over irregular domains. Mathematical analysis of absorbing layers in Electromagnetics and fluid mechanics.

	Flavian Abramovici, Professor Ph.D.: 1964, Weizmann Institute Research Interests: Numerical analysis; Inverse problems; Theoretical geophysics; Synthetic seismograms. Research Description: Build a general computer code to handle all the cases of seismic 1-D models, continuous or discontinuous, elastic or visco-elastic,for which the final error of the computation is given in advance. Study, using the code described above, various special structures and peculiar behavior of seismic waves, like the elliptical-like particle motions of some S-waves. Extend the code described above to 2-D and 3-D structures, using stable and fast finite-difference algorithms. Finding a suitable mathematical model for the set of rules by which very strong earthquakes are predicted by the group headed by Prof. Keilis-Borok in Russia, rules based on the seismic history of the studied region and its characteristics.

	Alfred Inselberg, Visiting Professor Ph.D.: 1965, University of Illinois (Urbana-Champaign) Research Interests: Parallel Coordinates, Multidimensional Visualization and its applications.

	Adi Ditkowski, Senior Lecturer Ph.D.: Tel Aviv University Research Interests: Numerical Analysis of PDE's. Material Science.

	Nira Dyn, Professor Ph.D.: 1970, Weizmann Institute Research Interests: Approximation Theory, Curve and Surface Fitting,Computer Aided Geometric Design. Multivariate interpolation and approximation,Optimal Triangulations,Subdivision algorithms. Research Description: Construction of refinable vectors of functions which are bi-orthogonal to B-splines with multiple knots.This construction can be instrumental to the construction of wavelets of small support which are spline functions. Non-stationary subdivision schemes and signal processing This project introduces new methods for processing sound signals such as voice. The project consists of a theoretical study of the new tool, and of the algorithmic adaptation of the new tool to specific processing tasks. Non-linear interpolatory subdivision schemes for the approximation of univariate smooth functions with a finite number of discontinuities This project incorporates the idea of INO (introduced by A. Harten) to define non-linear interpolatory subdivision schemes that detect discontinuities of smoothunivariate functions with a finite number of discontinuities, and approximate such functions with the same order of approximation achieved by similar linear subdivision schemes applied to smooth functions.

	Gadi Fibich, Associate Professor Ph.D.: 1994, Courant Institute, NYU Research Interests: Mathematical modeling in medicine and biology,Mathematical modeling in economics,Nonlinear optics,Self-focusing in the nonlinear Schrodinger equation,Ultrashort laser-tissue interactions. Research Description: Model for blood flow in coronary capillaries. Optimal pricing strategies in the presence of reference-price effects. Asymptotic theory for analyzing the effect of small perturbations on critical self-focusing of laser beams (modulation theory). Adiabatic law for the blowup rate of solutions of the nonlinear Schrodinger equation. Showed that beam nonparaxiality arrests self-focusing of laser beams.

	Nima Geffen, Associate Professor Ph.D.: 1963, Cornell University Research Interests: PDE's of mixed type; variational,symmetry and geometric methods; Transonic aerodynamics;Bio-mathematics, bio-modeling. Research Description: Variational and symmetry analysis of fluids with shocks. Transonic flow revisited. A mathematical look at the motion of a unicellular organism:formulation, simulation, explanation and correlation with experiments.

	Arie Levant, Senior Lecturer Ph.D.: 1987, Institute for System Studies of the USSR Academy of Sciences, Moscow Research Interests: Nonlinear Control Theory, Tracking Systems, Variable Structure Systems, Higher Order Sliding Modes, Differential Equations with Discontinuous Right-Hand Sides, Image Processing, Singularity Theory of Differentiable Mappings Research Description: Universal output-feedback SISO controller. Arbitrary-order real-time exact robust differentiator. Arbitrary order sliding-mode controller with finite-time convergence. Higher-order sliding modes and their application in avionics, targeting and image processing. Classification of stability boundary singularities of ordinary differential equations depending on parameters.

	David Levin, Professor Ph.D.: 1975, Tel Aviv University Research Interests: Numerical Integration,Convergence Acceleration,Approximation methods,CAGD and Computer Graphics. Research Description: The d-transformation for convergence acceleration. Fast computation of rapidly oscillatory integrals. Analysis and computation of radial-basis-function approximation. Algorithms for data dependent triangulations. Analysis and applications of the moving-least-squares method. Set-valued interpolation and 3D morphing. Analysis and construction of subdivision schemes of many types - interpolatory, Hermite-type, matrix, etc. The Butterfly scheme for surface generation.

	Joseph J. Roseman, Associate Professor Ph.D.:1965, New York University Research Interests: Mathematical elasticity,Partial differential equations. Research Description: New results on the buckling states of elastic arches. Research is continuing on problems in mathematical elasticity and on decay theorems for partial differential equations.

	Philip Rosenau , Professor Ph.D.: 1976, Tel Aviv University Research Interests: Fluids and plasmas; Modeling and analysis of nonlinear phenomena, transport, solitons, coherent structures; Nonlinear methods of mathematical physics. Research Description: Mathematical modeling of complex processes. Dynamics of discrete systems. Formation of patterns. Nonlinear phenomena in plasma and fluids. Nonlinear dispersion, solitons, compactons.. Transport processes, kinetic theory of gases. Nonlinear dispersive-dissipative interactions.


	Steven Schochet , Professor Ph.D.: 1984, Courant Institute, NYU Research Interests: Nonlinear evolutionary partial differential equations Research Description: Fast singular limits of quasi-linear hyperbolic systems. Energy methods for quasi-linear diffusion equations. Vorticity in 2D incompressible Euler equations. Systems of conservation laws.

	Zeev Schuss, Professor Ph.D.: 1970, Northwestern University Research Interests: Stochastic processes;Partial differential equations; Molecular biophysics;Mathematical physics (solid state-, statistical-, chemical-,and quantum physics); Mathematical communications theory Research Description: Modeling and simulation of ionic channels in biological cell membranes. Problems in mathematical physics concerning nano structures, solid state physics, statistical physics, the physics of chemical reactions, problems In quantum physics including random media, quantum absorption and measurements. Filtering of signals from noisy measurements, synchronization and signal tracking in spread spectrum communications and RADAR. Escape problems in stochastic dynamics, asymptotics analysis of partial differential equations.


	Gregory Sivashinsky, Professor Ph.D.: 1973, Technion - Israel Institute of Technology Research Interests: Fluid Mechanics of Combustion;Hydrodynamic Instability and Turbulence; Asymptotic and Perturbation Methods in Differential Equations Research Description: Mathematical modeling of: Chaotic dynamics, self-fractalization and self-fragmentation in premixed gas flames, Spontaneous transition from deflagration to detonation in reactive gases, Flame propagation and extinction in turbulent flow-fields.

	Nir Sochen, Lecturer


	Eli Turkel, Professor Ph.D.: 1970, New York University Research Interests: Computational Fluid Dynamics;Computational Electrodynamics;Helmholtz Equations;Acoustics Research Description: Improving the acceleration to a steady state for computations of the Navier-Stokes equations. Improving the accuracy of the computational solution for the Navier-Stokes equations in aerodynamics. Construction of high-order methods for Maxwell's equations in in electrodynamics for general domains. Construction of high-order methods for the Helmholtz equations in general domains. Construction of absorbing boundary conditions for hyperbolic and elliptic partial differential equations.