Publications of Stephanos Venakides     :chronological  combined listing:

%% Papers Published   
@article{fds153395,
   Author = {N. Ptitsyna and S. P. Shipman and S. Venakides},
   Title = {Fano resonance of waves in periodic slabs},
   Journal = {Proceedings of the 12th International Conference on
             Mathematical Methods in Electrodynamic Theory (MMET08 Odesa)
             (2008) 73-78},
   Year = {2008},
   Abstract = {We investigate Fano-type anomalous transmission of energy of
             plane waves across lossless slab scatterers with periodic
             structure in the presence of non-robust guided modes. Our
             approach is based on rigorous analytic perturbation of the
             scattering problem near a guided mode and applies to very
             general structures, continuous and discrete.},
   Key = {fds153395}
}

@article{fds139791,
   Author = {X. G. Peralta and Y. Toyama and M. S. Hutson and R. Montague and S.
             Venakides, D. P. Kiehart and G. S. Edwards},
   Title = {Resiliency, coordination, and synchronization of dorsal
             closure during Drosophila morphogenesis},
   Journal = {Biophysical Journal},
   Volume = {92},
   Pages = {2583-2596},
   Year = {2007},
   Month = {April},
   Abstract = {Tissue dynamics during dorsal closure, a stage of Drosophila
             development, provide a model system for cell sheet
             morphogenesis and wound healing. Dorsal closure is
             characterized by complex cell sheet movements, driven by
             multiple tissue specific forces, which are coordinated in
             space, synchronized in time, and resilient to UV-laser
             perturbations. The mechanisms responsible for these
             attributes are not fully understood. We measured spatial,
             kinematic, and dynamic antero-posterior asymmetries to
             biophysically characterize both resiliency to laser
             perturbations and failure of closure in mutant embryos and
             compared them to natural asymmetries in unperturbed,
             wild-type closure. We quantified and mathematically modeled
             two processes that are upregulated to provide
             resiliency.contractility of the amnioserosa and formation of
             a seam between advancing epidermal sheets, i.e., zipping.
             Both processes are spatially removed from the laser-targeted
             site, indicating they are not a local response to
             laser-induced wounding and suggesting mechanosensitive
             and/or chemosensitive mechanisms for upregulation. In mutant
             embryos, tissue junctions initially fail at the anterior end
             indicating inhomogeneous mechanical stresses attributable to
             head involution, another developmental process that occurs
             concomitant with the end stages of closure. Asymmetries in
             these mutants are reversed compared to wild-type, and
             inhomogeneous stresses may cause asymmetries in wild-type
             closure.},
   Key = {fds139791}
}

@article{fds139802,
   Author = {A. Tovbis and S. Venakides and X. Zhou},
   Title = {Semiclassical Focusing Nonlinear Schrödinger Equation I:
             Inverse scattering map and its evolution for radiative
             initial data},
   Journal = {International Mathematics Research Notices},
   Volume = {2007},
   Number = {Article ID rnm094, 54 pages. doi:10.},
   Year = {2007},
   Abstract = {We consider the semiclassical limit for the focusing
             nonlinear (cubic) Schr ¨ odinger Equation (NLS) in the pure
             radiational case. We present a method of reconstructing the
             leading order terms of the solitonless initial data and of
             its evolution for a wide class of the corresponding
             reflection coefficients.},
   Key = {fds139802}
}

@article{fds139803,
   Author = {R. Buckingham and A. Tovbis and S. Venakides and X.
             Zhou},
   Title = {The semiclassical focusing nonlinear Schroedinger
             equation},
   Volume = {65,},
   Series = {Proceedings of Symposia in Applied Mathematics},
   Pages = {47-80},
   Booktitle = {"Recent Advances in Nonlinear Partial Differentila Equations
             and Applications''},
   Publisher = {American Mathematical Society},
   Editor = {L.L. Bonilla and A. Carpio and J.M. Vega and S. Venakides},
   Year = {2007},
   ISBN = {978-0-8218-4211-9},
   Key = {fds139803}
}

@article{fds139789,
   Author = {R. Buckingham and S. Venakides},
   Title = {Long-time asymptotics of the nonlinear {S}chr\"odinger
             equation shock problem},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {60},
   Number = {9},
   Pages = {1349--1414},
   Year = {2007},
   ISSN = {0010-3640},
   MRCLASS = {35Q55 (35B40 37K15)},
   MRNUMBER = {MR2337507},
   Abstract = {The long-time asymptotics of two colliding plane waves
             governed by the focusing nonlinear Schrödinger equation are
             analyzed via the inverse scattering method. We find three
             asymptotic regions in space-time: a region with the original
             wave modified by a phase perturbation, a residual region
             with a one-phase wave, and an intermediate transition region
             with a modulated two-phase wave. The leading-order terms for
             the three regions arecomputedwith error estimates using the
             steepest-descent method for Riemann-Hilbert problems. The
             nondecaying initial data requires a new adaptation of this
             method. A new breaking mechanisminvolvingacomplexconjugatepairofbranch
             points emerging from the real axis is observed between the
             residual and transition regions. Also, the effect of the
             collision is felt in the plane-wave state well beyond the
             shock fr ont at large times.},
   Key = {fds139789}
}

@article{fds139800,
   Author = {A. Tovbis and S. Venakides and X. Zhou},
   Title = {On the long time limit of semiclassical (zero dispersion
             limit) solutions of the focusing Nonlinear Schroedinger
             Equation: Pure radiation case.},
   Volume = {59},
   Number = {10},
   Pages = {1379 - 1432},
   Year = {2006},
   MRNUMBER = {MR2248894},
   Abstract = {In a previous paper [13] we calculated the leading-order
             term q0(x,t,) of the solution of q(x,t,), the focusing
             nonlinear (cubic) Schrödinger (NLS) equation in the
             semiclassical limit ( 0) for a certain one-parameter family
             of initial conditions. This family contains both solitons
             and pure radiation. In the pure radiation case, our result
             is valid for all times t 0. The aim of the present paper is
             to calculate the long-term behavior of the semiclassical
             solution q(x,t,) in the pure radiation case. As before, our
             main tool is the Riemann-Hilbert problem (RHP) formulation
             of the inverse scattering problem and the corresponding
             system of moment and integral conditions, known also as a
             system of modulation equations.},
   Key = {fds139800}
}

@article{fds41433,
   Author = {S. Shipman and S. Venakides},
   Title = {Resonant transmission near nonrobust periodic slab
             modes},
   Journal = {Phys. Rev. E},
   Volume = {71},
   Pages = {026611(1-10)},
   Year = {2005},
   Key = {fds41433}
}

@article{fds29381,
   Author = {A. Tovbis and S. Venakides and X Zhou},
   Title = {On semiclassical (zero dispersion limit) solutions of the
             focusing nonlinear {S}chr\"odinger equation},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {57},
   Number = {7},
   Pages = {877--985},
   Year = {2004},
   ISSN = {0010-3640},
   MRCLASS = {35Q55 (35C20 37K15 37K40)},
   MRNUMBER = {MR2044068 (2005c:35269)},
   Key = {fds29381}
}

@article{fds29380,
   Author = {Stephen Shipman and Stephanos Venakides},
   Title = {Resonance and bound states in photonic crystal
             slabs},
   Journal = {SIAM J. Appl. Math.},
   Volume = {64},
   Number = {1},
   Pages = {322-342},
   Year = {2003},
   Key = {fds29380}
}

@article{fds18208,
   Author = {M. Shane Hutson and Yoichiro Tokutake and Ming-Shien Chang and James
             W. Bloor and Stephanos Venakides and Daniel P. Kiehart and Glenn
             S. Edwards},
   Title = {Forces for Morphogenesis Investigated with Laser
             Microsurgery and Quantitative Modeling},
   Journal = {Science},
   Volume = {300},
   Pages = {145-149},
   Year = {2003},
   Key = {fds18208}
}

@article{fds10403,
   Author = {M.A. Haider and S.P. Shipman and S. Venakides},
   Title = {Boundary-integral calculations of two-dimensional
             electromagnetic scattering in infinite photonic crystal
             slabs: Channel defects and resonances},
   Journal = {SIAM Journal on Applied Mathematics, vol. 62, (2002), pp.
             2129-2148},
   Key = {fds10403}
}

@article{fds10162,
   Author = {El, G. A. and Krylov, A. L. and Venakides, S.},
   Title = {Unified approach to KdV modulations},
   Journal = {Comm. Pure Appl. Math. 54, no 10, (2001), pp.
             1243-1270.},
   Key = {fds10162}
}

@article{fds10163,
   Author = {El, G.A. and Krylov, A.L. and Molchanov, S.A. and Venakides,
             S.},
   Title = {Soliton turbulence as a thermodynamic limit of stochastic
             soliton lattices. In Advances in nonlinear mathematics and
             science.},
   Journal = {Physica D 152/153 (2001), 653--664},
   Key = {fds10163}
}

@article{fds10406,
   Author = {A. Georgieva and T. Kriecherbauer and Stephanos
             Venakides},
   Title = {1:2 Resonance Mediated Second Harmonic Generation in a 1-d
             Nonlinear Discrete Periodic Medium},
   Journal = {SIAM J. Appl. Math, vol 61 No 5 (2001) 1802-1815},
   Key = {fds10406}
}

@article{fds9748,
   Author = {Alexander Tovbis and Stephanos Venakides},
   Title = {The Eigenvalue Problem for the Focusing Nonlinear
             Schroedinger Equation: New Solvable Cases},
   Journal = {Physica D, vol. 146, (2000), pp. 150-164},
   Key = {fds9748}
}

@article{fds9749,
   Author = {S. Venakides and M. Haider and V. Papanicolaou},
   Title = {Boundary Integral Calculations of 2-d Electromagnetic
             Scattering by Photonic Crystal Fabry-Perot
             Structures},
   Journal = {SIAM J. Appl. Math. vol. 60/5, (2000), pp.
             1636-1706},
   Key = {fds9749}
}

@article{fds9751,
   Author = {P. Deift and T. Kriecherbauer and K. T-R McLaughlin and S. Venakides and X. Zhou},
   Title = {Uniform Asymptotics for Polynomials Orthogonal with respect
             to Varying Exponential Weights and Applications to
             Universality Questions in Random Matrix Theory},
   Journal = {CPAM vol. 52, (1999), pp. 1335-1425},
   Key = {fds9751}
}

@article{fds9752,
   Author = {A. Georgieva and T. Kriecherbauer and Stephanos
             Venakides},
   Title = {Wave Propagation and Resonance in a 1-d Nonlinear Discrete
             Periodic Medium},
   Journal = {SIAM J. Appl. Math., vol. 60/1, (1999), pp.
             272-294},
   Key = {fds9752}
}

@article{fds9753,
   Author = {P.J. Cheng and Stephanos Venakides and X. Zhou},
   Title = {Long-time Asymptotics for the Pure Radiation Solution of the
             Sine-Gordon Equation},
   Journal = {Comm. in PDE, vol. 24(7-8), (1999), pp. 1195-1262},
   Key = {fds9753}
}

@article{fds9411,
   Author = {M.M. Beaky and J.B. Burke and H.O. Everitt and M.A Haider and S.
             Venakides},
   Title = {Two Dimensional Photonic Crystal Fabry-Perot Resonators with
             Lossy Dielectrics},
   Journal = {IEEE Transactions on Microwave Theory, vol. 47 No. 9 (1999)
             pp. 2085-2091},
   Key = {fds9411}
}

@article{fds9506,
   Author = {P. Deift and T. Kriecherbauer and K. T-R McLaughlin and S. Venakides and X. Zhou},
   Title = {Strong Asymptotics of Orhtogonal Polynomials with Respect to
             Exponential Weights},
   Journal = {CPAM, vol.52 (1999) 1491-1552.},
   Key = {fds9506}
}

@article{fds9383,
   Author = {A. M. Filip and S. Venakides},
   Title = {Existence and Modulation of Traveling Waves in Particle
             Chains},
   Journal = {CPAM, Vol 51, 1998, 693-736.},
   Key = {fds9383}
}

@article{fds8925,
   Author = {M. McDonald and S. Venakides},
   Title = {Renormalization of the Tau Function for Integrable Systems:
             A Model Problem},
   Journal = {CPAM, Vol 51, 1998, 937-966.},
   Key = {fds8925}
}

@article{fds8924,
   Author = {P. Deift and S. Venakides and X. Zhou},
   Title = {An Extension of the Method of Steepest Descent for
             Riemann-Hilbert Problems: The Small Dispersion Limit of the
             Korteweg-de Vries (KdV) Equation},
   Journal = {Proc. Ntl. Acad. Sc. USA, vol. 95, Jan 1998,
             450-454.},
   Key = {fds8924}
}

@article{fds9390,
   Author = {P. Deift and S. Venakides and X. Zhou},
   Title = {New Results in the Small-Dispersion KdV by an Extension of
             the Method of Steepest Descent for Riemann-Hilbert
             Problems},
   Journal = {IMRN, 1997, N0. 6, 285-299.},
   Key = {fds9390}
}

@article{fds9391,
   Author = {L.L. Bonilla. M. Kindelan and M. Moscoso and S.
             Venakides},
   Title = {Periodic Generation and Propagation of Traveling Fronts in
             dc Voltage Biased Semiconductor Superlattices},
   Journal = {SIAM J. Appl. Math., Vol. 57, Number 6, 1997,
             1588-1614},
   Key = {fds9391}
}

@article{fds9389,
   Author = {P. Deift and T. Kriecherbauer and K. T-R McLaughlin and S. Venakides and X. Zhou},
   Title = {Asymptotics of Polynomials Orthogonal with Respect to
             Varying Exponential Weights},
   Journal = {IMRN, 1997 No 16, pp. 759-782},
   Key = {fds9389}
}

@article{fds9395,
   Author = {P. Deift and T. Kriecherbauer and S. Venakides},
   Title = {Forced Lattice Vibrations Part II},
   Journal = {Comm. Pure Appl. Math. 48, 1995, 1251-1298.},
   Key = {fds9395}
}

@article{fds9394,
   Author = {P. Deift and T. Kriecherbauer and S. Venakides},
   Title = {Forced Lattice Vibrations Part I},
   Journal = {Comm. Pure Appl. Math. 48,1995, 1187-1250.},
   Key = {fds9394}
}

@article{fds9410,
   Author = {L. L. Bonilla and F. Higuera and S. Venakides},
   Title = {The Stability of the Steady State of the Gunn
             Oscillator},
   Journal = {SIAM J. Appl. Math. vol. 54, No 6, (1994), pp.
             1521-1541.},
   Key = {fds9410}
}

@article{fds9409,
   Author = {P. Deift and S. Venakides and X. Zhou},
   Title = {The Collisionless Shock Region for the Long Time Behavior of
             the Solutions of the KdV Equation},
   Journal = {CPAM. vol. 47, (1994), pp. 199-206.},
   Key = {fds9409}
}

@article{fds9407,
   Author = {T. Zhang and S. Venakides},
   Title = {Periodic Limit of Inverse Scattering},
   Journal = {CPAM vol. 46 (1993), pp. 819-865.},
   Key = {fds9407}
}

@article{fds9408,
   Author = {P. D. Lax and C. D. Levermore and S. Venakides},
   Title = {The Generation and Propagation of Oscillations in Dispersive
             IVP's and their Limiting Behavior},
   Journal = {Important Developments in Soliton Theory 1980--1990}, T.
             Fokas and V.E. Zakharov eds., Springer-Verlag, Berlin
             (1992).},
   Key = {fds9408}
}

@article{fds9406,
   Author = {S. Venakides and P. Deift and R. Oba},
   Title = {The Toda shock problem},
   Journal = {CPAM vol 44 (1991), pp. 1171-1242.},
   Key = {fds9406}
}

@article{fds9405,
   Author = {S. Venakides},
   Title = {The Korteweg-de Vries equation with small dispersion: Higher
             order Lax-Levermore theory},
   Journal = {CPAM vol. 43 (1990), pp. 335-361.},
   Key = {fds9405}
}

@article{fds9404,
   Author = {M. Reed and S. Venakides and J. J. Blum},
   Title = {Approximate travelling waves in linear reaction-hyperbolic
             equations},
   Journal = {SIAP. 50, No 1 (1990), pp. 167-180. .},
   Key = {fds9404}
}

@article{fds9403,
   Author = {S. Venakides},
   Title = {The continuum limit of Theta functions},
   Journal = {CPAM, vol. 42, (1989) pp. 711-728.},
   Key = {fds9403}
}

@article{fds9402,
   Author = {S. Venakides},
   Title = {The Infinite Period Limit of the Inverse Formalism for
             Periodic Potentials},
   Journal = {CPAM, vol. 41, (1988) pp. 3-17.},
   Key = {fds9402}
}

@article{fds9401,
   Author = {S. Venakides},
   Title = {The small dispersion limit of the Korteweg-de Vries
             equation},
   Journal = {Proceedings of the Conference at M.S.R.I., in Berkeley in
             honor of P.D. Lax's 60th birthday, (editors A. J. Chorin, A.
             J. Majda) (1987) pp. 295-336.},
   Key = {fds9401}
}

@article{fds9400,
   Author = {S. Venakides},
   Title = {The zero dispersion limit of the Korteweg-de Vries equation
             with periodic initial data},
   Journal = {AMS Transactions, vol. 301 (1987), pp. 189-226.},
   Key = {fds9400}
}

@article{fds9399,
   Author = {S. Venakides},
   Title = {The solution of completely integrable systems in the
             continuum limit of the spectral data},
   Journal = {IMA Proceedings, vol. 2, (1986) pp. 337-356..},
   Key = {fds9399}
}

@article{fds9398,
   Author = {S. Venakides},
   Title = {Long-time asymptotics of the Korteweg-de Vries
             equation},
   Journal = {AMS Transactions 293 #1 (1986), pp. 411-419..},
   Key = {fds9398}
}

@article{fds9397,
   Author = {S. Venakides},
   Title = {The generation of modulated wavetrains in the solution of
             the Korteweg-de Vries Equation},
   Journal = {CPAM. 38, (1985), pp. 883-909..},
   Key = {fds9397}
}

@article{fds9396,
   Author = {S. Venakides},
   Title = {The zero-dispersion limit of the Korteweg-de Vries equation
             with non-trivial reflection coefficient},
   Journal = {Comm. Pure and Appl. Math. 38, pp. 125-155,
             1985.},
   Key = {fds9396}
}


%% Papers Submitted   
@article{fds153396,
   Author = {A. Tovbis and S. Venakides},
   Title = {Determinant form of modulation equations for the
             semiclassical focusing Nonlinear Schr\" odinger
             equation.},
   Journal = {International Mathematics Research Notices
             IMRN},
   Year = {2008},
   Abstract = {We derive a determinant formula for the WKB exponential of
             singularly perturbed Zakharov-Shabat system that corresponds
             to the semiclassical (zero dispersion) limit of the focusing
             Nonlinear Schr\" odinger equation. The derivation is based
             on the Riemann-Hilbert Problem (RHP) representation of the
             WKB exponential. We also prove its independence of the
             branchpoints of the corresponding hyperelliptic surface
             assuming that the modulation equations are
             satisfied.},
   Key = {fds153396}
}

@article{fds139804,
   Author = {W.R. Lefew and S. Venakides and D.J. Gauthier},
   Title = {Accurate description of optical precursors and their
             relation to weak-field coherent optical transients},
   Journal = {Phys. Rev. Lett.},
   Year = {2007},
   Abstract = {We study theoretically the propagation of a step-modulated
             optical field as it passes through a dispersive dielectric
             using two different approximate methods: an asymptotic
             approach and a method that assumes a slowly-varying field
             envelope. By improving the accuracy of the asymptotic
             approach soitis valid over a wider range ofparameters, we
             show thatthe two methods makeidentical predictions.
             Wedemonstratethatprecursors canpersistfor many nanoseconds
             and the chirp inthe instantaneous frequency of the precurors
             can manifest in beats in the transmitted intensity. Our work
             strongly suggests that precursors have been observed in many
             previous experiments.},
   Key = {fds139804}
}