Zoi Rapti
J.L. Doob Research Assistant Professor

Department of Mathematics University of Illinois at Urbana Champaign 1409 W. Green Street Urbana, Illinois 61801, USA

Office: 366 Altgeld Hall Phone: (217) 333-6625 FAX: (217) 333-9576 e-mail: zrapti@math.uiuc.edu

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Research

My principal research interests lie in Differential Equations and Mathematical Biology. In Differential Equations , my work to date has been primarily concerned with the study of stability of solutions to nonlinear evolution equations and the study of the spectrum of certain perturbed linear Schrodinger Equations. In Mathematical Biology , I have been investigating the relation between the thermal denaturation profiles of DNA sequences and the location of promoters -- regions of DNA providing a control point for regulated gene transcription-- and other significant regulatory regions.

Grants

NSF Grant DMS 0708421

Positions

• 2005-present, J.L. Doob Research Assistant Professor, University of Illinois at Urbana-Champaign.
• June-August 2005/ November 2005-present, Visiting Scientist/ Consultant, Beth Israel Deaconess Medical Center - teaching hospital of Harvard Medical School.
• 2004-2005, Visitor, Institute for Advanced Study at Princeton.
• June-July 2004, October-November, and July 2005 Affiliated, Center for Nonlinear Studies, Los Alamos National Laboratory.

Publications

• Healing Length and Bubble Formation in DNA (with A. Smerzi, K.O. Rasmussen, A.R. Bishop, C.H. Choi and A. Usheva), Phys. Rev. E. Vol. 73, 051902 (2006).
• Lengthscales and Cooperativity in DNA Bubble Formation (with A. Smerzi, K.O. Rasmussen, A.R. Bishop, C.H. Choi and A. Usheva), Europhysics Letters, Vol. 74 (2006) 540-546.
• Modulational Instabilities for Nonlinear Schrodinger Equations With a Periodic Potential (with J. C. Bronski), Dynamics of PDE, Vol. 2 (2005) 335-355.
• Transient Radiative Behavior of Hamiltonian Systems in Finite Domains (with M.I. Weinstein and P.G. Kevrekidis), Physics Letters A, Vol. 345 (2005) 1-9.
• A Variational Approach to the Modulational Instability (with A. Smerzi, P.G. Kevrekidis and A.R. Bishop), Phys. Rev. E 69,017601 (2004).
• Modulational and Parametric Instabilities of the Disrete Nonlinear Schrodinger Equation (with P.G. Kevrekidis, A. Smerzi and A. R. Bishop), J. Phys. B: At. Mol. Opt. Phys. 37, (2004) S257-264.
• On the Modulational Instability of the Nonlinear Schrodinger Equation with Dissipation (with P.G. Kevrekidis, D.J. Frantzeskakis and B.A. Malomed), Phys. Scr. Vol. T 113, (2004) 74.
• Modulational Instability in Coupled Disrete Nonlinear Schrodinger Equations (with A. Trombettoni, P.G. Kevrekidis, D.J. Frantzeskakis, B.A. Malomed and A. R. Bishop), Physics Letters A Vol. 330, (2004) 95.
• Modulational Instability in Bose-Einstein Condensates under Feshbach Resonance Management (with G. Theocharis, P.G. Kevrekidis, D.J. Frantzeskakis and B.A. Malomed), Phys. Scr. Vol. T 107, (2004) 27.
• On the Modulational Stability of Gross-Pittaevskii Type Equations in 1+1 Dimensions (with G. Theocharis, P.G. Kevrekidis, D.J. Frantzeskakis and V.V. Konotop), Phys. Rev. A 67, 063610 (2003).
• On the Modulational Stability of Gross-Pittaevskii Type Equations in 1+1 Dimensions (with P.G. Kevrekidis and V.V. Konotop), Proceedings of the Third Conference on Localization and Energy Transfer in Nonlinear Systems, San Lorenzo de El Escorial Madrid, (2002).
• An Exterior Mixed Boundary Value Problem for the Helmholtz Equation (with K. Kiriaki), Bull. of the Greek Math. Soc. 45 (2001), 43-55.

Teaching

Math 181. A Mathematical World

Math 385. Introduction to Differential Equations
Math 441. Differential Equations

Math 181. A Mathematical World (formerly Math 118).

Math 118. A Mathematical World.
Math 489. Differential Equations II.

Math 230.Calculus II.
Math 489. Differential Equations II.

Math 230. Calculus II.