Stephanos Venakides
Professor of Mathematics
Fields of work: Pure and applied mathematics, physics and biology. Specific areas: Differential equations, integrable systems, acoustic and electromagnetic scattering (especially transmission anomalies and resonances), photonic crystals, exciton polaritons and recently micromagnetics.
Invited as one of the three Abel lecturers in the award of the Abel Prize to Peter Lax, The Norwegian Academy of Science and Letters, Oslo, Norway, May 2005
http://www.abelprize.no/c57575/seksjon/vis.html?tid=58729Current Research Interests
INTEGRABLE SYSTEMS
Worked on the semiclassical focusing Nonlinear Schroedinger equation (NSF supported work) towards resolving the longstanding problem of the mechanism of the second break, making substantial progress. I believe that the problem will be solved in the coming year.
MATHEMATICAL BIOLOGY: DORSAL CLOSURE
Participant of the Dorsal Closure project of the Kiehart lab. In collaboration with the Kiehart group:
1) Review of of dorsal closure, the biological part published, the mathematical modeling part on preparation,
2) Advanced mathematical model of dorsal closure in progress.
ACOUSTIC AND ELECTROMAGNETIC SCATTERING: THEORETICAL AND COMPUTATIONAL
Collaborative work on the scattering from scatterers with spatially periodic geometry.
1) Paper published. For the first time, the paper overcomes theoretical and computational difficulties at certain frequencies associated with the wellknown Wood anomalies (NSF supported work),
2) Paper, that utilizes the approach of the above work, to be submitted in the current or next week (NSF supported work).
MICROMAGNETICS
This area of physics deals with the prediction of magnetic behaviors at submicrometer length scales. Although little mathematical work has been done in this field, its physical and technological importance is obvious. From wikipedia: “Apart from conventional magnetic domains and domainwalls, the theory also treats the statics and dynamics of topological line and point configurations, e.g. magnetic vortex and antivortex states or even 3dBloch points,^{ } where, for example, the magnetization leads radially into all directions from the origin, or into topologically equivalent configurations. Thus in space, and also in time, nano (and even pico)scales are used. The corresponding topological quantum numbers^{ } are thought to be used as information carriers, to apply the most recent, and already studied, propositions in information technology .”
I entered this area, working collaboratively in June 2017. Two papers are in preparation. By analyzing the related LandauLifschitsGilbert equation, both works prove for the first time the existence of traveling domain walls under different circumstances in each case. In one of the papers, the proof utilizes a topological argument.
Office Hours
Current Appointments & Affiliations
 Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 1991
Contact Information
 104 Physics Bldg, Durham, NC 27708
 Box 90320, Durham, NC 277080320
 ven@math.duke.edu (919) 6602815
 http://www.math.duke.edu/~ven
 Background

Education, Training, & Certifications
 Ph.D., New York University 1982
 M.S., Georgia Institute of Technology 1979
 B.S., National Technical University of Athens (Greece) 1969

Duke Appointment History
 Associate Professor with Tenure, Mathematics, Trinity College of Arts & Sciences 1986  1991
 Director of Graduate Studies, Mathematics, Trinity College of Arts & Sciences 1987  1989

Academic Positions Outside Duke
 Assistant Professor, Stanford University. 1982  1986
 Research

Selected Grants
 Wavebreaking and Resonant Phenomena awarded by National Science Foundation 2012  2018
 Wavebreaking and Resonant Phenomena awarded by National Science Foundation 2007  2014
 Nonlinear Waves in Uniform and Periodic Media awarded by National Science Foundation 2002  2008
 Conference on Recent Advances in Nonlinear Partial Differential Equations awarded by National Science Foundation 2006  2007
 Wave Propagation in Linear and Nonlinear Photonic BandGap Materials awarded by Army Research Office 1999  2003
 Propagation of Waves in Optical and Photonic Media awarded by Army Research Office 1996  2000
 (950206) Dispersive Shocks in Continuous and Discrete Media awarded by National Science Foundation 1995  1999
 (970433) Propagation of Waves in Optical and Photonic Media awarded by Army Research Office 1996  1998
 (960451) Propagation of Waves in Optical and Photonic Media awarded by Army Research Office 1996  1997
 (940403) The Generation and Propagation of Dispersive Oscillations in Nonlinear Systems awarded by Army Research Office 1992  1995
 (950304) The Generation of Dispersive Oscillations In Nonlinear Systems awarded by Army Research Office 1992  1995
 (940068) Generation and Propagation of Dispersive Waves in Integrable Systems awarded by National Science Foundation 1991  1994
 (920774) The Generation and Propagation of Dispersive Oscillations in NonLinear Systems awarded by Army Research Office 1992  1993
 (920859) Generation and Propagation of Dispensive Waves in Integrable Systems awarded by National Science Foundation 1991  1993
 (910237) Generations and Propagation of Dispersive Waves in Integrable Systems awarded by National Science Foundation 1991  1992
 (920411) Dispersive Regularization of Shocks awarded by Army Research Office 1991  1992
 (910508) Dispersive Regularization of Shocks awarded by Army Research Office 1991
 (890480) Nonlinear Oscillations/ Completely Integrable Systems awarded by National Science Foundation 1987  1990
 (880164) Nonlinear Oscillations/ Completely Integrable Systems awarded by National Science Foundation 1987  1989
 (870215) Nonlinear Oscillations/ Completely Integrable Systems awarded by National Science Foundation 1987  1988
 Publications & Artistic Works

Selected Publications

Academic Articles
 Aristotelous, AC, Crawford, JM, Edwards, GS, Kiehart, DP, and Venakides, S. "Mathematical models of dorsal closure." Progress in Biophysics and Molecular Biology 137 (September 2018): 111131. (Review) Full Text
 PerezArancibia, C, Shipman, S, Turc, C, and Venakides, S. "DDM solutions of quasiperiodic transmission problems in layered media via robust boundary integral equations at all frequencies (In preparation)." (December 31, 2017).
 Bruno, OP, Shipman, SP, Turc, C, and Venakides, S. "Threedimensional quasiperiodic shifted Green function throughout the spectrum, including Wood anomalies." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2207 (November 1, 2017). Full Text
 Kiehart, DP, Crawford, JM, Aristotelous, A, Venakides, S, and Edwards, GS. "Cell Sheet Morphogenesis: Dorsal Closure in Drosophila melanogaster as a Model System." Annual Review of Cell and Developmental Biology 33 (October 2017): 169202. (Review) Full Text
 Bruno, OP, Shipman, SP, Turc, C, and Venakides, S. "Superalgebraically convergent smoothly windowed lattice sums for doubly periodic Green functions in threedimensional space." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2191 (July 1, 2016). Full Text
 Komineas, S, Shipman, SP, and Venakides, S. "Lossless polariton solitons." Physica D: Nonlinear Phenomena 316 (February 15, 2016): 4356. Full Text
 Komineas, S, Shipman, SP, and Venakides, S. "Continuous and discontinuous dark solitons in polariton condensates." Physical Review B 91, no. 13 (April 2015). Full Text
 Belov, S, and Venakides, S. "Longtime limit studies of an obstruction in the gfunction mechanism for semiclassical focusing NLS." (2015). Link to Item
 Belov, S, and Venakides, S. "Smooth parametric dependence of asymptotics of the semiclassical focusing NLS." Analysis and PDE 8, no. 2 (January 1, 2015): 257288. Full Text
 Jackson, AD, Huang, D, Gauthier, DJ, and Venakides, S. "Destructive impact of imperfect beam collimation in extraordinary optical transmission." Journal of the Optical Society of America A: Optics and Image Science, and Vision 30, no. 6 (2013): 12811290. Full Text
 Shipman, SP, and Venakides, S. "An exactly solvable model for nonlinear resonant scattering." Nonlinearity 25, no. 9 (2012): 24732501. Full Text
 Tovbis, A, and Venakides, S. "Semiclassical limit of the scattering transform for the focusing nonlinear Schrödinger equation." International Mathematics Research Notices 2012, no. 10 (2012): 22122271. Full Text
 Tovbis, A, and Venakides, S. "Nonlinear steepest descent asymptotics for semiclassical limit of Integrable systems: Continuation in the parameter space." Communications in Mathematical Physics 295, no. 1 (2010): 139160. Full Text
 Layton, AT, Toyama, Y, Yang, GQ, Edwards, GS, Kiehart, DP, and Venakides, S. "Drosophila morphogenesis: tissue force laws and the modeling of dorsal closure." HFSP J 3, no. 6 (December 2009): 441460. Full Text Link to Item
 Lefew, WR, Venakides, S, and Gauthier, DJ. "Accurate description of optical precursors and their relation to weakfield coherent optical transients." Physical Review A  Atomic, Molecular, and Optical Physics 79, no. 6 (2009). Full Text
 Tovbis, A, and Venakides, S. "Determinant form of the complex phase function of the steepest descent analysis of RiemannHilbert problems and its application to the focusing nonlinear schrödinger equation." International Mathematics Research Notices 2009, no. 11 (2009): 20562080. Full Text
 Tovbis, A, and Venakides, S. "Determinant form of modulation equations for the semiclassical focusing Nonlinear Schr\" odinger equation." (2009). Link to Item
 Peralta, XG, Toyama, Y, Hutson, MS, Montague, R, Venakides, S, Kiehart, DP, and Edwards, GS. "Upregulation of forces and morphogenic asymmetries in dorsal closure during Drosophila development." Biophysical Journal 92, no. 7 (April 2007): 25832596. Full Text
 Peralta, XG, Toyama, Y, Hutson, MS, Montague, R, Venakides, and S, Kiehart and, DP, Edwards, GS. "Resiliency, coordination, and synchronization of dorsal closure during Drosophila morphogenesis." Biophysical Journal 92 (April 2007): 25832596. (Academic Article)
 Buckingham, R, and Venakides, S. "Longtime asymptotics of the nonlinear Schrödinger equation shock problem." Communications on Pure and Applied Mathematics 60, no. 9 (2007): 13491414. Full Text
 Tovbis, A, Venakides, S, and Zhou, X. "Semiclassical focusing nonlinear schrödinger equation i: Inverse scattering map and its evolution for radiative initial data." International Mathematics Research Notices 2007 (2007). Full Text
 Tovbis, A, Venakides, S, and Zhou, X. "On the longtime limit of semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation: Pure radiation case." Communications on Pure and Applied Mathematics 59, no. 10 (2006): 13791432. Full Text
 Shipman, SP, and Venakides, S. "Resonant transmission near nonrobust periodic slab modes." Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 71, no. 2 Pt 2 (February 23, 2005): 026611null. Full Text Open Access Copy
 Tovbis, A, Venakides, S, and Zhou, X. "On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation." Communications on Pure and Applied Mathematics 57, no. 7 (2004): 877985. Full Text
 Hutson, MS, Tokutake, Y, Chang, MS, Bloor, JW, Venakides, S, Kiehart, DP, and Edwards, GS. "Forces for morphogenesis investigated with laser microsurgery and quantitative modeling." Science (New York, N.Y.) 300, no. 5616 (April 2003): 145149. Full Text
 Lipton, RP, Shipman, SP, and Venakides, S. "Optimization of Resonances in Photonic Crystal Slabs." Proceedings of SPIE  The International Society for Optical Engineering 5184 (2003): 168177.
 Shipman, SP, and Venakides, S. "Resonance and bound states in photonic crystal slabs." SIAM Journal on Applied Mathematics 64, no. 1 (2003): 322342. Full Text
 Haider, MA, Shipman, SP, and Venakides, S. "Boundaryintegral calculations of twodimensional electromagnetic scattering in infinite photonic crystal slabs: Channel defects and resonances." SIAM Journal on Applied Mathematics 62, no. 6 (2002): 21292148. Full Text
 Deift, P, Kriecherbauer, T, McLaughlin, KTR, Venakides, S, and Zhou, X. "A Riemann–Hilbert approach to asymptotic questions for orthogonal polynomials." Journal of Computational and Applied Mathematics 133, no. 12 (August 2001): 4763. Full Text
 El, GA, Krylov, AL, Molchanov, SA, and Venakides, S. "Soliton turbulence as a thermodynamic limit of stochastic soliton lattices." Physica D: Nonlinear Phenomena 152153 (2001): 653664. Full Text
 El, GA, Krylov, AL, and Venakides, S. "Unified approach to KdV modulations." Communications on Pure and Applied Mathematics 54, no. 10 (2001): 12431270. Full Text
 Georgieva, A, Kriecherbauer, T, and Venakides, S. "1:2 resonance mediated second harmonic generation in a 1D nonlinear discrete periodic medium." SIAM Journal on Applied Mathematics 61, no. 5 (2001): 18021815. Full Text
 Tovbis, A, and Venakides, S. "The eigenvalue problem for the focusing nonlinear Schrödinger equation: New solvable cases." Physica D: Nonlinear Phenomena 146, no. 14 (2000): 150164. Full Text
 VENAKIDES, S. "Boundary integral calculations of twodimensional electromagnetic scattering by photonic crystal FabriPeror structures." SIAM J. Appl. Math. 60 (2000): 16861706. Full Text
 Venakides, S, Haider, MA, and Papanicolaou, V. "Boundary integral calculations of twodimensional electromagnetic scattering by photonic crystal FabryPerot structures." SIAM Journal on Applied Mathematics 60, no. 5 (2000): 16861706.
 Deift, P, Kriecherbauer, T, McLaughlin, KTR, Venakides, S, and Zhou, X. "Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory." Communications on Pure and Applied Mathematics 52, no. 11 (November 1999): 13351425. Full Text
 Beaky, MM, Burk, JB, Everitt, HO, Haider, MA, and Venakides, S. "Twodimensional photonic crystal fabryperot resonators with lossy dielectrics." IEEE Transactions on Microwave Theory and Techniques 47, no. 11 (1999): 20852091. Full Text
 Cheng, PJ, Venakides, S, and Zhou, X. "Longtime asymptotics for the pure radiation solution of the sineGordon equation." Communications in Partial Differential Equations 24, no. 78 (1999): 11951262.
 Deift, P, Kriecherbauer, T, Mclaughlin, KTR, Venakides, S, and Zhou, X. "Strong asymptotics of orthogonal polynomials with respect to exponential weights." Communications on Pure and Applied Mathematics 52, no. 12 (January 1, 1999): 14911552. Full Text
 Filip, AM, and Venakides, S. "Existence and modulation of traveling waves in particle chains." Communications on Pure and Applied Mathematics 52, no. 6 (1999): 693735.
 Georgieva, A, Kriecherbauer, T, and Venakides, S. "Wave propagation and resonance in a onedimensional nonlinear discrete periodic medium." SIAM Journal on Applied Mathematics 60, no. 1 (1999): 272294.
 Deift, P, Venakides, S, and Zhou, X. "An extension of the steepest descent method for RiemannHilbert problems: the small dispersion limit of the Kortewegde Vries (KdV) equation." Proc Natl Acad Sci U S A 95, no. 2 (January 20, 1998): 450454. Link to Item
 McDonald, MA, and Venakides, S. "Renormalization of the τfunctions for integrable systems: A model problem." Communications on Pure and Applied Mathematics 51, no. 8 (January 1, 1998): 937966. Full Text
 Bonilla, LL, Kindelan, M, Moscoso, M, and Venakides, S. "Periodic generation and propagation of traveling fronts in dc voltage biased semiconductor superlattices." SIAM Journal on Applied Mathematics 57, no. 6 (1997): 15881614.
 Deift, P, Kriecherbauer, T, McLaughlin, KTR, Venakides, S, and Zhou, X. "Asymptotics for Polynomials Orthogonal with Respect to Varying Exponential Weights." International Mathematics Research Notices , no. 16 (1997): X782.
 Deift, P, Kriecherbauer, T, McLaughlin, KTR, Venakides, S, and Zhou, X. "Asymptotics for polynomials orthogonal with respect to varying exponential weights." International Mathematics Research Notices , no. 16 (1997): 759782. Link to Item
 Deift, P, Venakides, S, and Zhou, X. "New Results in Small Dispersion KdV by an Extension of the Steepest Descent Method for RiemannHilbert Problems." International Mathematics Research Notices , no. 6 (1997): 284299.
 Deift, P, Venakides, S, and Zhou, X. "New results in small dispersion kdV by an extension of the steepest descent method for RiemannHilbert problems." International Mathematics Research Notices , no. 6 (1997): 285299. Link to Item
 Deift, P, Kriecherbauer, T, and Venakides, S. "Forced lattice vibrations: Part I." Communications on Pure and Applied Mathematics 48, no. 11 (January 1, 1995): 11871249. Full Text
 Deift, P, Kriecherbauer, T, and Venakides, S. "Forced lattice vibrations: Part II." Communications on Pure and Applied Mathematics 48, no. 11 (January 1, 1995): 12511298. Full Text
 DEIFT, P, VENAKIDES, S, and ZHOU, X. "THE COLLISIONLESS SHOCK REGION FOR THE LONGTIME BEHAVIOR OF SOLUTIONS OF THE KDV EQUATION." COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS 47, no. 2 (February 1994): 199206. Full Text Link to Item
 Bonilla, LL, Higuera, FJ, and Venakides, S. "Gunn effect: Instability of the steady state and stability of the solitary wave in long extrinsic semiconductors." SIAM Journal on Applied Mathematics 54, no. 6 (1994): 15211541.
 Zhang, T, and Venakides, S. "Periodic limit of inverse scattering." Communications on Pure and Applied Mathematics 46, no. 6 (January 1, 1993): 819865. Full Text
 Venakides, S, Deift, P, and Oba, R. "The toda shock problem." Communications on Pure and Applied Mathematics 44, no. 89 (January 1, 1991): 11711242. Full Text
 Reed, MC, Venakides, S, and Blum, JJ. "Approximate traveling waves in linear reactionhyperbolic equations." SIAM Journal on Applied Mathematics 50, no. 1 (1990): 167180.
 Venakides, S. "The korteweg‐de vries equation with small dispersion: Higher order lax‐levermore theory." Communications on Pure and Applied Mathematics 43, no. 3 (January 1, 1990): 335361. Full Text
 Venakides, S. "The continuum limit of theta functions." Communications on Pure and Applied Mathematics 42, no. 6 (January 1, 1989): 711728. Full Text
 Venakides, S. "The infinite period limit of the inverse formalism for periodic potentials." Communications on Pure and Applied Mathematics 41, no. 1 (January 1, 1988): 317. Full Text
 Venakides, S. "The Zero Dispersion Limit of the KortewegDevries Equation with Periodic Initial Data." Transactions of the American Mathematical Society 301, no. 1 (May 1987): 189226. Full Text Link to Item
 Venakides, S. "The zero dispersion limit of the Kortewegde Vries equation with periodic initial data." Transactions of the American Mathematical Society 301, no. 1 (January 1, 1987): 189189. Full Text
 Venakides, S. "Long time asymptotics of the Kortewegde Vries equation." Transactions of the American Mathematical Society 293, no. 1 (January 1, 1986): 411411. Full Text
 Venakides, S. "LongTime Asymptotics of the KortewegDevries Equation." Transcations of the American Mathematical Society 293, no. 1 (January 1986): 411419. Full Text Link to Item
 Venakides, S. "The generation of modulated wavetrains in the solution of the Korteweg—de vries equation." Communications on Pure and Applied Mathematics 38, no. 6 (January 1, 1985): 883909. Full Text
 Venakides, S. "The zero dispersion limit of the korteweg‐de vries equation for initial potentials with non‐trivial reflection coefficient." Communications on Pure and Applied Mathematics 38, no. 2 (January 1, 1985): 125155. Full Text
 Belov, S, and Venakides, S. "Perturbation of RiemannHilbert jump contours: smooth parametric dependence with application to semiclassical focusing NLS." Link to Item
 Deift, P, Kriecherbauer, T, and Venakides, S. "Forced Lattice Vibrations  A Videotext." Link to Item
 PerezArancibia, C, Shipman, SP, Turc, C, and Venakides, S. "Domain decomposition for quasiperiodic scattering by layered media via robust boundaryintegral equations at all frequencies (In preparation)."
 Ptitsyna, N, Shipman, SP, and Venakides, S. "FanoType Resonance of Waves in Periodic Slabs." Link to Item

Conference Papers
 Tovbis, A, Venakides, S, and Zhou, X. "Semiclassical Focusing Nonlinear Schrodinger equation in the pure radiation case: RiemannHilbert Problem approach." 2008. Link to Item
 Buckingham, R, Tovbis, A, Venakides, S, and Zhou, X. "The semiclassical focusing nonlinear Schrodinger equation." 2007. Link to Item
 Peralta, XG, Toyama, Y, Wells, A, Tokutake, Y, Hutson, MS, Venakides, S, Kiehart, DP, and Edwards, GS. "Force regulation during dorsal closure in Drosophila." American Society for Cell Biology, November 2004. Link to Item
 Hutson, S, Tokutake, Y, Chang, M, Bloor, JW, Venakides, S, Kiehart, DP, and Edwards, GS. "Measuring the forces that drive morphogenesis: Lasermicrosurgery and quantitative modeling applied to dorsal closure in Drosophila." American Society for Cell Biology, November 2002. Link to Item
 Reed, D, and Venakides, S. "Studying the asymptotics of Selbergtype integrals." 2000. Link to Item
 Venakides, S. "The KortewegDevries Equation with Small Dispersion  HigherOrder Lax Levermore Theory." 1991. Link to Item
 Venakides, S. "The Small Dispersion Limit of the KortewegDevries Equation." 1989. Link to Item

 Teaching & Mentoring

Recent Courses
 Scholarly, Clinical, & Service Activities

Presentations & Appearances
 Lossless Polariton Solitons. Challenges in Nonlinear Systems. Universidad Carlos III de Madrid. July 2017  July 7, 2017 2017
 Universality formulae for resonant scattering by open periodic waveguides. PDEs in Physics and Material Sciences. Institute of Applied and Computational Mathematics, FORTH, Crete, Greece. June 12, 2017  June 14, 2017 2017
 Abel lecturer . Abel Prize award to Peter Lax. The Norwegian Academy of Science and Letters. May 2005 2005

Service to the Profession
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