Vered Rom-Kedar The Estrin Family Chair of Computer Science and Applied Mathematics Department of computer science and applied mathematics The Weizmann Institute, Rehovot, Israel 76100. Chair of the Moross Research school of mathematics and computer science Tel: 972 8 9343170 Fax: 972 8 9344122 office: 211 Zyskind E-mail : Vered.Rom-Kedar At weizmann.ac.il Courses Fall 2012: Mathematical  modelling in Biology and Medicine   Wednesday, 1100-1300, Ziskind, Rm 1 Topics in Applied Mathematics (Rothchild program for Highschool teachers) Thursday, 1100-1230, FGS, Rm A Students Editorials Seminars The ACM bi-annual workshops CV

Publications   News:   Preprints/recently published               Press release 12/9/12          See Research interests and publications for  summary and motivation for each subject.  Publication list (chronological order) Selected publications: Fluid Mixing Medicine Billiards Near-integrable Hamiltonians

Selected Publications:

Medicine:

• [with  R. Malka, B. Wolach, R. Gavrieli and  E. Shochat] Evidence for bistable bacteria-neutrophil interaction and its clinical implications  J. Clin Invest. doi:10.1172/JCI59832, 2012.  See also commentary ,  Press release 12/9/12 . 
• [with  R. Malka] Bacteria--Phagocytes Dynamics, Axiomatic Modelling and Mass-Action Kinetics, Mathematical Biosciences and Engineering, 8(2) 475--502, 2011.
• [with R. Malka and E. Shochat]  Bistability and Bacterial Infections, 2010,  PLoS ONE 5(5) .
• [with E. Shochat]  Novel strategies for G-CSF treatment of high-risk severe neutropenia suggested by mathematical modeling, Clinical Cancer Research 14, 6354-6363, October 15, 2008. See also the Supplement. 
• [with E. Shochat and L. Segel]  G-CSF control of neutrophils dynamics in the blood, Bull. Math. Biology , 69(7), 2299-2338, 2007.

Far from integrable limit - Billiards with Steep Potentials, Fermi accelerators:

• [with V. Gelfreich, D. Turaev]  "Fermi acceleration and adiabatic invariants for non-autonomous billiards", Chaos 22, 033116 (2012); http://dx.doi.org/10.1063/1.4736542 (21 pages).
• [with D. Turaev]  "Billiards: a singular perturbation limit of smooth Hamiltonian flows", Chaos 22, 026102 (2012); http://dx.doi.org/10.1063/1.4722010 (21 pages)
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• [with V. Gelfreich, K. Shah, D. Turaev]  Robust exponential accelerators, PRL  106, 074101, 2011
• [with K. Shah and  D. Turaev]  Exponential energy growth in a Fermi accelerator,  Phys. Rev. E 81, 056205, 2010. 
• [with D.Turaev] Big islands in dispersing billiard-like potentials. Physica D, 130:187-210, 1999.
• [with A. Rapoport and D. Turaev] Stability in high dimensional steep repelling potentials, Comm. Math. Phys., 279, 497-534, 2008.
• [with A. Rapoport] Chaotic scattering by steep potentials, Phys. Rev E., 77, 016207, 2008.

Near Integrable Hamiltonians:

• [with E. Shlizermann] Classification of  solutions of the forced periodic nonlinear Schr\"{o}dinger equation,  Nonlinearity 23 (9), 2183-2218,2010. Selected to be on Nonlinearity Highly Downloaded Collection for 2010

• [with  D. Turaev] The symmetric Parabolic Resonance Instability, Nonlinearity 23 1325-1351, 2010.
• [with E. Shlizermann]  Parabolic Resonance: A Route to Hamiltonian Spatio-Temporal Chaos, Physical Review Letters, 102, 033901, 2009.
• [with E. Shlizermann] Three types of chaos in the forced nonlinear Schrodinger equation, Physical Review Letters, 96, 024104, 2006.
• Parabolic resonances and instabilities. Chaos, 7(1):148-158, 1997.
• [with A. Litvak-Hinenzon] On energy surfaces and the resonance web, SIAM J. Appl. Dyn. Syst. 3(4), 525—573, 2004.
• [with S. Wiggins] Transport in two-dimensional maps. Archive for Rational Mech. and Anal., 109(3):239-298, 1990.
• Homoclinic tangles - classification and applications. Nonlinearity, 7:441-473, 1994.

Fluid Mixing:

• Rotem Aharon, Vered Rom-Kedar, and Hezi Gildor, "When complexity leads to simplicity: ocean surface mixing simplified by vertical convection", Phys. Fluids 24, 056603 (2012); http://dx.doi.org/10.1063/1.4719147. ON THE COVER.
• D. F. Carlson, E. Fredj, H. Gildor, V. Rom-Kedar, Deducing an upper bound to the horizontal eddy diffusivity using a stochastic Lagrangian model, Environmental Fluid Mechanics, 1567-7419 (Print) 1573-1510 (Online),  2010
• [with A.C. Poje] Universal properties of chaotic transport in the presence of diffusion. Phys. Fluids 11 (8) (1999) 2044-2057, 1999.
• [with A. Leonard and S. Wiggins] An analytical study of transport, mixing and chaos in an unsteady vortical flow.  J.  Fluid Mech., 214:347-394, 1990.

נושאי מחקר עיקריים

ראו סדרת הרצאות לקהל הרחב

*בעיות בסיסיות בטבע הקשורות בתופעת הכאוס  ראו קורס מתוקשב שפותח לתלמידי תיכון ע"י קלריסה ברקוביץ

*בעיות הקשורות במערכת החיסונית.

* חקירת תופעות אלו מלווה בשימוש ופיתוח תיאוריות ושיטות מתימטיות בתחום מערכות דינמיות