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Panos Kevrekidis, Associate Professor |
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| Personal Webpage |
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| Office | LGRT 1524 | | Phone | (413) 577-1977 | | Fax | (413) 545-1801 | | Email | kevrekid <at> math.umass.edu | |
| Mailing Address |
| Department of Mathematics and Statistics |
| Lederle Graduate Research Tower |
| University of Massachusetts |
| Amherst, MA 01003-9305 |
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| Office Hours: W 2:00-4:00pm, Th 2:30-4:00 pm |
| Courses |
| Topics in Ordinary Differential Equations |
| Math 532H (TuTh 1:00 - 2:15 pm, LGRT 119) | | |
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| Education | | Ph.D. | Rutgers University, 2000 |
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| | M.S. | Rutgers University, 1998 |
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| | B.Sc. | University of Athens, 1996 |
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| Research Interests: Mathematical Physics; Nonlinear PDEs and DDEs; Dynamical Systems; Mathematical Biology |
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| Professor Kevrekidis studies a variety of systems chiefly stemming from the mathematical physics of optical systems (waveguide arrays and optical fibers), as well as from the soft-condensed matter setting of Bose-Einstein Condensates. The research mainly revolves around the existence, stability and dynamics of localized (solitary wave) structures in such one-, two- and three-dimensional setups, often described by equations of Nonlinear Schrodinger or Klein-Gordon type. While the settings under study are principally Hamiltonian in nature (often featuring external potentials, or being genuinely discrete and posed on, so-called, dynamical lattices), occasionally dissipative perturbations thereof are also considered. Besides this main thrust of research Professor Kevrekidis also maintains a wide variety of additional interests including mathematical biology [especially tumor angionesis, nephron dynamics and DNA models], simple cosmological models, the nucleation of liquid droplets in the atmosphere, gelation and related phase transition phenomena in polymers, aerosol dynamics in the atmosphere and in the human body [inhalation and desposition of particles in the respiratory tract], catalytic chemistry and reaction-diffusion models, and dynamics and energy landscapes of glassy materials among others. |
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| Selected Publications |
| N.J. Balmforth, R.V. Craster and P.G. Kevrekidis, Being Stable and Discrete, Physica 135D, 212-232 (2000) |
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| P.G. Kevrekidis and M.I. Weinstein, Dynamics of Lattice Kinks, Physica 142D, 113-152 (2000) |
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| T. Kapitula and P. Kevrekidis, Stability of Waves in Discrete Systems, Nonlinearity 14, 533-566 (2001). |
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| B.A. Malomed and P.G. Kevrekidis, Discrete Vortex Solitons, Phys. Rev. E 64, 026601, 6 pages (2001). |
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| P.G. Kevrekidis, K.O. Rasmussen and A.R. Bishop, The Discrete Nonlinear Schrodinger Equation: A Survey of Recent Results, Int. J. of Mod. Phys. B 15, 2833-2900 (2001). |
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| A. Smerzi, A. Trombettoni, P.G. Kevrekidis and A.R. Bishop, Superfluid-Insulator Transition in a Chain of Weakly Coupled Bose-Einstein Condensates, Phys. Rev. Lett. 89, 170402, 4 pages (2002) |
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| G.L. Alfimov, P.G. Kevrekidis, V.V. Konotop and M. Salerno, Wannier function analysis of the nonlinear Schrodinger equation with a periodic potential, Phys. Rev. E 66, 046608, 5 pages (2002) |
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| C.I. Siettos, I.G. Kevrekidis and P.G. Kevrekidis, Focusing Revisited: A Renormalization/Bifurcation Approach, Nonlinearity 16, 497-506 (2003). |
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| P.G. Kevrekidis, G. Theocharis, D.J. Frantzeskakis, and Boris A. Malomed, Feshbach Resonance Management for Bose-Einstein Condensates, Phys. Rev. Lett. 90, 230401 (2003). |
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| T.Kapitula, P.G. Kevrekidis and B. Sandstede, Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems, Physica D 195, 263-282 (2004). |
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| A. Stefanov and P.G. Kevrekidis, Asymptotic behavior of small solutions for the discrete nonlinear Schrodinger and Klein-Gordon equations, Nonlinearity 18, 1841-1857 (2005). |
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| D.E. Pelinovsky, P.G. Kevrekidis and D.J. Frantzeskakis, Stability of discrete solitons in Nonlinear Schrodinger Lattices, Physica D 212, 1-19 (2005). |
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| D.E. Pelinovsky, P.G. Kevrekidis and D.J. Frantzeskakis, Persistence and stability of discrete vortices in nonlinear Schrodinger lattices, Physica D 212, 20-53 (2005). |
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| X. Wang, Z. Chen and P.G. Kevrekidis, Observation of discrete solitons and soliton rotation in optically-induced periodic ring lattices, Phys. Rev. Lett. 96, 083904, 4 pages (2006). |
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| M. Centurion, M.A. Porter, P.G. Kevrekidis and D. Psaltis, Nonlinearity Management in Optics:
Experiment, Theory and Simulation, Phys. Rev. Lett. 97, 033903, 4 pages (2006). |
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