Stephanos Venakides | Scholars@Duke

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=58729

Office Hours

Tuesday and Thursday 3:00-4:00pm

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 27708-0320
ven@math.duke.edu (919) 660-2815
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
- Wave-breaking and Resonant Phenomena awarded by National Science Foundation 2012 - 2018
- Wave-breaking 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 Band-Gap Materials awarded by Army Research Office 1999 - 2003
- Propagation of Waves in Optical and Photonic Media awarded by Army Research Office 1996 - 2000
- (95-0206) Dispersive Shocks in Continuous and Discrete Media awarded by National Science Foundation 1995 - 1999
- (97-0433) Propagation of Waves in Optical and Photonic Media awarded by Army Research Office 1996 - 1998
- (96-0451) Propagation of Waves in Optical and Photonic Media awarded by Army Research Office 1996 - 1997
- (94-0403) The Generation and Propagation of Dispersive Oscillations in Non-linear Systems awarded by Army Research Office 1992 - 1995
- (95-0304) The Generation of Dispersive Oscillations In Non-linear Systems awarded by Army Research Office 1992 - 1995
- (94-0068) Generation and Propagation of Dispersive Waves in Integrable Systems awarded by National Science Foundation 1991 - 1994
- (92-0774) The Generation and Propagation of Dispersive Oscillations in Non-Linear Systems awarded by Army Research Office 1992 - 1993
- (92-0859) Generation and Propagation of Dispensive Waves in Integrable Systems awarded by National Science Foundation 1991 - 1993
- (91-0237) Generations and Propagation of Dispersive Waves in Integrable Systems awarded by National Science Foundation 1991 - 1992
- (92-0411) Dispersive Regularization of Shocks awarded by Army Research Office 1991 - 1992
- (91-0508) Dispersive Regularization of Shocks awarded by Army Research Office 1991
- (89-0480) Nonlinear Oscillations/ Completely Integrable Systems awarded by National Science Foundation 1987 - 1990
- (88-0164) Nonlinear Oscillations/ Completely Integrable Systems awarded by National Science Foundation 1987 - 1989
- (87-0215) Nonlinear Oscillations/ Completely Integrable Systems awarded by National Science Foundation 1987 - 1988
Publications & Artistic Works
Selected Publications
- Academic Articles
  - Komineas, S., C. Melcher, and S. Venakides. “Traveling domain walls in chiral ferromagnets.” Nonlinearity 32, no. 7 (May 30, 2019): 2392–2412. https://doi.org/10.1088/1361-6544/ab1430.
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  - Pérez-Arancibia, C., S. P. Shipman, C. Turc, and S. Venakides. “Domain decomposition for quasi-periodic scattering by layered media via robust boundary-integral equations at all frequencies.” Communications in Computational Physics 26, no. 1 (January 1, 2019): 265–310. https://doi.org/10.4208/cicp.OA-2018-0021.
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  - Aristotelous, A. C., J. M. Crawford, G. S. Edwards, D. P. Kiehart, and S. Venakides. “Mathematical models of dorsal closure..” Progress in Biophysics and Molecular Biology 137 (September 2018): 111–31. https://doi.org/10.1016/j.pbiomolbio.2018.05.009.
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  - Perez-Arancibia, C., S. Shipman, C. Turc, and S. Venakides. “DDM solutions of quasiperiodic transmission problems in layered media via robust boundary integral equations at all frequencies.” Communications in Computational Physics, May 25, 2018.
  - Bruno, Oscar P., Stephen P. Shipman, Catalin Turc, and Venakides Stephanos. “Three-dimensional quasi-periodic shifted Green function throughout the spectrum, including Wood anomalies..” Proceedings. Mathematical, Physical, and Engineering Sciences 473, no. 2207 (November 2017). https://doi.org/10.1098/rspa.2017.0242.
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  - Kiehart, Daniel P., Janice M. Crawford, Andreas Aristotelous, Stephanos Venakides, and Glenn S. Edwards. “Cell Sheet Morphogenesis: Dorsal Closure in Drosophila melanogaster as a Model System..” Annual Review of Cell and Developmental Biology 33 (October 2017): 169–202. https://doi.org/10.1146/annurev-cellbio-111315-125357.
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  - Bruno, O. P., S. P. Shipman, C. Turc, and S. Venakides. “Superalgebraically convergent smoothly windowed lattice sums for doubly periodic Green functions in three-dimensional space.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2191 (July 1, 2016). https://doi.org/10.1098/rspa.2016.0255.
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  - Komineas, S., S. P. Shipman, and S. Venakides. “Lossless polariton solitons.” Physica D: Nonlinear Phenomena 316 (February 15, 2016): 43–56. https://doi.org/10.1016/j.physd.2015.10.018.
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  - Komineas, S., S. P. Shipman, and S. Venakides. “Continuous and discontinuous dark solitons in polariton condensates.” Physical Review B Condensed Matter and Materials Physics 91, no. 13 (April 9, 2015). https://doi.org/10.1103/PhysRevB.91.134503.
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  - Belov, S., and S. Venakides. “Long-time limit studies of an obstruction in the g-function mechanism for semiclassical focusing NLS,” 2015.
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  - Belov, S., and S. Venakides. “Smooth parametric dependence of asymptotics of the semiclassical focusing NLS.” Analysis and Pde 8, no. 2 (January 1, 2015): 257–88. https://doi.org/10.2140/apde.2015.8.257.
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  - Jackson, Aaron D., Da Huang, Daniel J. Gauthier, and Stephanos Venakides. “Destructive impact of imperfect beam collimation in extraordinary optical transmission..” Journal of the Optical Society of America. A, Optics, Image Science, and Vision 30, no. 6 (June 2013): 1281–90. https://doi.org/10.1364/josaa.30.001281.
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  - Shipman, S. P., and S. Venakides. “An exactly solvable model for nonlinear resonant scattering.” Nonlinearity 25, no. 9 (September 1, 2012): 2473–2501. https://doi.org/10.1088/0951-7715/25/9/2473.
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  - Tovbis, A., and S. Venakides. “Semiclassical limit of the scattering transform for the focusing nonlinear Schrödinger equation.” International Mathematics Research Notices 2012, no. 10 (May 21, 2012): 2212–71. https://doi.org/10.1093/imrn/rnr092.
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  - Tovbis, A., and S. Venakides. “Nonlinear steepest descent asymptotics for semiclassical limit of Integrable systems: Continuation in the parameter space.” Communications in Mathematical Physics 295, no. 1 (February 1, 2010): 139–60. https://doi.org/10.1007/s00220-009-0984-0.
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  - Layton, Anita T., Yusuke Toyama, Guo-Qiang Yang, Glenn S. Edwards, Daniel P. Kiehart, and Stephanos Venakides. “Drosophila morphogenesis: tissue force laws and the modeling of dorsal closure..” Hfsp Journal 3, no. 6 (December 15, 2009): 441–60. https://doi.org/10.2976/1.3266062.
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  - Lefew, W. R., S. Venakides, and D. J. Gauthier. “Accurate description of optical precursors and their relation to weak-field coherent optical transients.” Physical Review a Atomic, Molecular, and Optical Physics 79, no. 6 (June 29, 2009). https://doi.org/10.1103/PhysRevA.79.063842.
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  - Tovbis, A., and S. Venakides. “Determinant form of the complex phase function of the steepest descent analysis of Riemann-Hilbert problems and its application to the focusing nonlinear schrödinger equation.” International Mathematics Research Notices 2009, no. 11 (February 1, 2009): 2056–80. https://doi.org/10.1093/imrn/rnp011.
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  - Tovbis, A., and S. Venakides. “Determinant form of modulation equations for the semiclassical focusing Nonlinear Schr\" odinger equation,” 2009.
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  - Ptitsyna, N., S. P. Shipman, and S. Venakides. “Fano resonance of waves in periodic slabs.” Mathematical Methods in Electromagnetic Theory, Mmet, Conference Proceedings, September 19, 2008, 73–78. https://doi.org/10.1109/MMET.2008.4580900.
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  - Tovbis, A., S. Venakides, and X. Zhou. “Semiclassical focusing nonlinear schrödinger equation i: Inverse scattering map and its evolution for radiative initial data.” International Mathematics Research Notices 2007 (December 1, 2007). https://doi.org/10.1093/imrn/rnm094.
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  - Buckingham, R., and S. Venakides. “Long-time asymptotics of the nonlinear Schrödinger equation shock problem.” Communications on Pure and Applied Mathematics 60, no. 9 (September 1, 2007): 1349–1414. https://doi.org/10.1002/cpa.20179.
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  - Peralta, X. G., Y. Toyama, M. S. Hutson, R. Montague, S. Venakides, D. P. Kiehart, and G. S. Edwards. “Upregulation of forces and morphogenic asymmetries in dorsal closure during Drosophila development..” Biophysical Journal 92, no. 7 (April 2007): 2583–96. https://doi.org/10.1529/biophysj.106.094110.
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  - Peralta, X. G., Y. Toyama, M. S. Hutson, R. Montague, S. Venakides, D. P. Kiehartand, and G. S. Edwards. “Resiliency, coordination, and synchronization of dorsal closure during Drosophila morphogenesis.” Biophysical Journal 92 (April 2007): 2583–96.
  - Tovbis, A., S. Venakides, and X. Zhou. “On the long-time 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 (January 1, 2006): 1379–1432. https://doi.org/10.1002/cpa.20142.
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  - Shipman, Stephen P., and Stephanos Venakides. “Resonant transmission near nonrobust periodic slab modes..” Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 71, no. 2 Pt 2 (February 23, 2005). https://doi.org/10.1103/physreve.71.026611.
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  - Tovbis, A., S. Venakides, and X. Zhou. “On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation.” Communications on Pure and Applied Mathematics 57, no. 7 (July 1, 2004): 877–985. https://doi.org/10.1002/cpa.20024.
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  - Lipton, R. P., S. P. Shipman, and S. Venakides. “Optimization of Resonances in Photonic Crystal Slabs.” Proceedings of Spie the International Society for Optical Engineering 5184 (December 1, 2003): 168–77.
  - Shipman, S. P., and S. Venakides. “Resonance and bound states in photonic crystal slabs.” Siam Journal on Applied Mathematics 64, no. 1 (October 1, 2003): 322–42. https://doi.org/10.1137/S0036139902411120.
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  - Hutson, M Shane, Yoichiro Tokutake, Ming-Shien Chang, James W. Bloor, Stephanos Venakides, Daniel P. Kiehart, and Glenn S. Edwards. “Forces for morphogenesis investigated with laser microsurgery and quantitative modeling..” Science (New York, N.Y.) 300, no. 5616 (April 2003): 145–49. https://doi.org/10.1126/science.1079552.
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  - Haider, M. A., S. P. Shipman, and S. Venakides. “Boundary-integral calculations of two-dimensional electromagnetic scattering in infinite photonic crystal slabs: Channel defects and resonances.” Siam Journal on Applied Mathematics 62, no. 6 (July 1, 2002): 2129–48. https://doi.org/10.1137/S003613990138531X.
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  - El, G. A., A. L. Krylov, and S. Venakides. “Unified approach to KdV modulations.” Communications on Pure and Applied Mathematics 54, no. 10 (October 1, 2001): 1243–70. https://doi.org/10.1002/cpa.10002.
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  - Deift, P., T. Kriecherbauer, K. R. McLaughlin, S. Venakides, and X. Zhou. “A riemann-Hilbert approach to asymptotic questions for orthogonal polynomials.” Journal of Computational and Applied Mathematics 133, no. 1–2 (August 1, 2001): 47–63. https://doi.org/10.1016/S0377-0427(00)00634-8.
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  - El, G. A., A. L. Krylov, S. A. Molchanov, and S. Venakides. “Soliton turbulence as a thermodynamic limit of stochastic soliton lattices.” Physica D: Nonlinear Phenomena 152–153 (May 15, 2001): 653–64. https://doi.org/10.1016/S0167-2789(01)00198-1.
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  - Georgieva, A., T. Kriecherbauer, and S. Venakides. “1:2 resonance mediated second harmonic generation in a 1-D nonlinear discrete periodic medium.” Siam Journal on Applied Mathematics 61, no. 5 (January 1, 2001): 1802–15. https://doi.org/10.1137/S0036139999365341.
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  - Tovbis, A., and S. Venakides. “The eigenvalue problem for the focusing nonlinear Schrödinger equation: New solvable cases.” Physica D: Nonlinear Phenomena 146, no. 1–4 (November 15, 2000): 150–64. https://doi.org/10.1016/S0167-2789(00)00126-3.
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  - Venakides, S., M. A. Haider, and V. Papanicolaou. “Boundary integral calculations of two-dimensional electromagnetic scattering by photonic crystal Fabry-Perot structures.” Siam Journal on Applied Mathematics 60, no. 5 (May 1, 2000): 1686–1706.
  - VENAKIDES, S. “Boundary integral calculations of two-dimensional electromagnetic scattering by photonic crystal Fabri-Peror structures.” Siam J. Appl. Math. 60 (2000): 1686–1706. https://doi.org/10.1137/S0036139999350779.
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  - Beaky, M. M., J. B. Burk, H. O. Everitt, M. A. Haider, and S. Venakides. “Two-dimensional photonic crystal fabry-perot resonators with lossy dielectrics.” Ieee Transactions on Microwave Theory and Techniques 47, no. 11 (December 1, 1999): 2085–91. https://doi.org/10.1109/22.798003.
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  - Filip, A. M., and S. Venakides. “Existence and modulation of traveling waves in particle chains.” Communications on Pure and Applied Mathematics 52, no. 6 (June 1, 1999): 693–735.
  - Cheng, P. J., S. Venakides, and X. Zhou. “Long-time asymptotics for the pure radiation solution of the sine-Gordon equation.” Communications in Partial Differential Equations 24, no. 7–8 (January 1, 1999): 1195–1262. https://doi.org/10.1080/03605309908821464.
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  - Deift, P., T. Kriecherbauer, K. T. R. McLaughlin, S. Venakides, and X. Zhou. “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 (January 1, 1999): 1335–1425. https://doi.org/10.1002/(SICI)1097-0312(199911)52:11<1335::AID-CPA1>3.0.CO;2-1.
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  - Deift, P., T. Kriecherbauer, K. T. R. Mclaughlin, S. Venakides, and X. Zhou. “Strong asymptotics of orthogonal polynomials with respect to exponential weights.” Communications on Pure and Applied Mathematics 52, no. 12 (January 1, 1999): 1491–1552. https://doi.org/10.1002/(SICI)1097-0312(199912)52:12<1491::AID-CPA2>3.0.CO;2-#.
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  - Georgieva, A., T. Kriecherbauer, and S. Venakides. “Wave propagation and resonance in a one-dimensional nonlinear discrete periodic medium.” Siam Journal on Applied Mathematics 60, no. 1 (January 1, 1999): 272–94. https://doi.org/10.1137/S0036139998340315.
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  - Deift, P., S. Venakides, and X. Zhou. “An extension of the steepest descent method for Riemann-Hilbert problems: the small dispersion limit of the Korteweg-de Vries (KdV) equation..” Proceedings of the National Academy of Sciences of the United States of America 95, no. 2 (January 1998): 450–54. https://doi.org/10.1073/pnas.95.2.450.
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  - McDonald, M. A., and S. Venakides. “Renormalization of the τ-functions for integrable systems: A model problem.” Communications on Pure and Applied Mathematics 51, no. 8 (January 1, 1998): 937–66. https://doi.org/10.1002/(SICI)1097-0312(199808)51:8<937::AID-CPA3>3.0.CO;2-6.
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  - Deift, P., S. Venakides, and X. Zhou. “New Results in Small Dispersion KdV by an Extension of the Steepest Descent Method for Riemann-Hilbert Problems.” International Mathematics Research Notices, no. 6 (December 1, 1997): 284–99.
  - Deift, P., T. Kriecherbauer, K. T. R. McLaughlin, S. Venakides, and X. Zhou. “Asymptotics for Polynomials Orthogonal with Respect to Varying Exponential Weights.” International Mathematics Research Notices, no. 16 (December 1, 1997).
  - Bonilla, L. L., M. Kindelan, M. Moscoso, and S. Venakides. “Periodic generation and propagation of traveling fronts in dc voltage biased semiconductor superlattices.” Siam Journal on Applied Mathematics 57, no. 6 (January 1, 1997): 1588–1614. https://doi.org/10.1137/S0036139995288885.
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  - Deift, P., S. Venakides, and X. Zhou. “New results in small dispersion kdV by an extension of the steepest descent method for Riemann-Hilbert problems.” International Mathematics Research Notices, no. 6 (1997): 285–99.
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  - Deift, P., T. Kriecherbauer, K. T. R. McLaughlin, S. Venakides, and X. Zhou. “Asymptotics for polynomials orthogonal with respect to varying exponential weights.” International Mathematics Research Notices, no. 16 (1997): 759–82.
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  - Deift, P., T. Kriecherbauer, and S. Venakides. “Forced lattice vibrations: Part I.” Communications on Pure and Applied Mathematics 48, no. 11 (January 1, 1995): 1187–1249. https://doi.org/10.1002/cpa.3160481102.
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  - Deift, P., T. Kriecherbauer, and S. Venakides. “Forced lattice vibrations: Part II.” Communications on Pure and Applied Mathematics 48, no. 11 (January 1, 1995): 1251–98. https://doi.org/10.1002/cpa.3160481103.
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  - Bonilla, L. L., F. J. Higuera, and S. Venakides. “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 (January 1, 1994): 1521–41. https://doi.org/10.1137/S0036139992236554.
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  - Deift, P., S. Venakides, and X. Zhou. “The collisionless shock region for the long‐time behavior of solutions of the KdV equation.” Communications on Pure and Applied Mathematics 47, no. 2 (January 1, 1994): 199–206. https://doi.org/10.1002/cpa.3160470204.
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  - Zhang, T., and S. Venakides. “Periodic limit of inverse scattering.” Communications on Pure and Applied Mathematics 46, no. 6 (January 1, 1993): 819–65. https://doi.org/10.1002/cpa.3160460603.
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  - Venakides, S., P. Deift, and R. Oba. “The toda shock problem.” Communications on Pure and Applied Mathematics 44, no. 8–9 (January 1, 1991): 1171–1242. https://doi.org/10.1002/cpa.3160440823.
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  - Reed, M. C., S. Venakides, and J. J. Blum. “Approximate traveling waves in linear reaction-hyperbolic equations.” Siam Journal on Applied Mathematics 50, no. 1 (January 1, 1990): 167–80. https://doi.org/10.1137/0150011.
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  - 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): 335–61. https://doi.org/10.1002/cpa.3160430303.
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  - Venakides, S. “The continuum limit of theta functions.” Communications on Pure and Applied Mathematics 42, no. 6 (January 1, 1989): 711–28. https://doi.org/10.1002/cpa.3160420602.
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  - 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): 3–17. https://doi.org/10.1002/cpa.3160410103.
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  - Venakides, S. “The Zero Dispersion Limit of the Korteweg-Devries Equation with Periodic Initial Data.” Transactions of the American Mathematical Society 301, no. 1 (May 1987): 189–226. https://doi.org/10.2307/2000334.
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  - Venakides, S. “The zero dispersion limit of the korteweg-de vries equation with periodic initial data.” Transactions of the American Mathematical Society 301, no. 1 (January 1, 1987): 189–226. https://doi.org/10.1090/S0002-9947-1987-0879569-7.
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  - Venakides, S. “Long time asymptotics of the korteweg-de vries equation.” Transactions of the American Mathematical Society 293, no. 1 (January 1, 1986): 411–19. https://doi.org/10.1090/S0002-9947-1986-0814929-0.
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  - Venakides, S. “Long-Time Asymptotics of the Korteweg-Devries Equation.” Transcations of the American Mathematical Society 293, no. 1 (January 1986): 411–19. https://doi.org/10.2307/2000288.
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  - 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): 883–909. https://doi.org/10.1002/cpa.3160380616.
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  - 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): 125–55. https://doi.org/10.1002/cpa.3160380202.
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  - Belov, Sergey, and Stephanos Venakides. “Perturbation of Riemann-Hilbert jump contours: smooth parametric dependence with application to semiclassical focusing NLS,” n.d.
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  - Deift, Percy, Thomas Kriecherbauer, and Stephanos Venakides. “Forced Lattice Vibrations -- A Videotext,” n.d.
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- Conference Papers
  - Tovbis, A., S. Venakides, and X. Zhou. “Semiclassical Focusing Nonlinear Schrodinger equation in the pure radiation case: Riemann-Hilbert Problem approach.” In Integrable Systems and Random Matrices: In Honor of Percy Deift, 458:117–44, 2008.
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  - Buckingham, R., A. Tovbis, S. Venakides, and X. Zhou. “The semiclassical focusing nonlinear Schrodinger equation.” In Recent Advances in Nonlinear Partial Differential Equations and Applications, 65:47–80, 2007.
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  - Peralta, X. G., Y. Toyama, A. Wells, Y. Tokutake, M. S. Hutson, S. Venakides, D. P. Kiehart, and G. S. Edwards. “Force regulation during dorsal closure in Drosophila.” In Molecular Biology of the Cell, 15:403A-403A. American Society for Cell Biology, 2004.
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  - Hutson, S., Y. Tokutake, M. Chang, J. W. Bloor, S. Venakides, D. P. Kiehart, and G. S. Edwards. “Measuring the forces that drive morphogenesis: Laser-microsurgery and quantitative modeling applied to dorsal closure in Drosophila.” In Molecular Biology of the Cell, 13:476A-476A. American Society for Cell Biology, 2002.
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  - Reed, D., and S. Venakides. “Studying the asymptotics of Selberg-type integrals.” In Applied and Industrial Mathematics, Venice 2, 1998, 187–98, 2000.
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  - Venakides, S. “The Korteweg-Devries Equation with Small Dispersion - Higher-Order Lax Levermore Theory.” In Journal of Applied and Industrial Mathematics, 56:255–62, 1991.
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  - Venakides, S. “The Small Dispersion Limit of the Korteweg-Devries Equation.” In Differential Equations, 118:725–37, 1989.
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- Applied ARP hiring committee. December 2018 - February 2019 2018 - 2019

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