Scholars@Duke
Stephanos Venakides

Stephanos Venakides

Professor of Mathematics
Mathematics
ven@math.duke.edu
Box 90320, Durham, NC 27708-0320
120 Science Drive, Durham, NC 27708, Durham, NC 27708
Office hours Tuesday and Thursday 3:00-4:00pm  

Selected Publications

Chiral skyrmions of large radius

Journal Article Physica D: Nonlinear Phenomena · April 1, 2021 Featured Publication We study the structure of an axially symmetric magnetic skyrmion in a ferromagnet with the Dzyaloshinskii–Moriya interaction. We examine the regime of large skyrmions and we identify rigorously the critical value of the dimensionless parameter at which the ... Full text Open Access Cite

The profile of chiral skyrmions of small radius

Journal Article Nonlinearity · July 1, 2020 Chiral skyrmions are stable particle-like solutions of the Landau-Lifshitz equation for ferromagnets with the Dzyaloshinskii-Moriya (DM) interaction, characterized by a topological number. We study the profile of an axially symmetric skyrmion and give exac ... Full text Cite

Traveling domain walls in chiral ferromagnets

Journal Article Nonlinearity · May 30, 2019 We show that chiral symmetry breaking enables traveling domain wall solution for the conservative Landau-Lifshitz equation of a uniaxial ferromagnet with Dzyaloshinskii-Moriya interaction. In contrast to related domain wall models including stray-field bas ... Full text Cite

Domain decomposition for quasi-periodic scattering by layered media via robust boundary-integral equations at all frequencies

Journal Article Communications in Computational Physics · January 1, 2019 We develop a non-overlapping domain decomposition method (DDM) for scalar wave scattering by periodic layered media. Our approach relies on robust boundary-integral equation formulations of Robin-to-Robin (RtR) maps throughout the frequency spectrum, inclu ... Full text Cite

Mathematical models of dorsal closure.

Journal Article Progress in biophysics and molecular biology · September 2018 Dorsal closure is a model cell sheet movement that occurs midway through Drosophila embryogenesis. A dorsal hole, filled with amnioserosa, closes through the dorsalward elongation of lateral epidermal cell sheets. Closure requires contributions from 5 dist ... Full text Cite

Cell Sheet Morphogenesis: Dorsal Closure in Drosophila melanogaster as a Model System.

Journal Article Annual review of cell and developmental biology · October 2017 Dorsal closure is a key process during Drosophila morphogenesis that models cell sheet movements in chordates, including neural tube closure, palate formation, and wound healing. Closure occurs midway through embryogenesis and entails circumferential elong ... Full text Cite

Superalgebraically convergent smoothly windowed lattice sums for doubly periodic Green functions in three-dimensional space

Journal Article Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences · July 1, 2016 This work, part I in a two-part series, presents: (i) a simple and highly efficient algorithm for evaluation of quasi-periodic Green functions, as well as (ii) an associated boundary-integral equation method for the numerical solution of problems of scatte ... Full text Cite

Lossless polariton solitons

Journal Article Physica D: Nonlinear Phenomena · February 15, 2016 Photons and excitons in a semiconductor microcavity interact to form exciton-polariton condensates. These are governed by a nonlinear quantum-mechanical system involving exciton and photon wavefunctions. We calculate all non-traveling harmonic soliton solu ... Full text Cite

Continuous and discontinuous dark solitons in polariton condensates

Journal Article Physical Review B - Condensed Matter and Materials Physics · April 9, 2015 Bose-Einstein condensates of exciton-polaritons are described by a Schrödinger system of two equations. Nonlinearity due to exciton interactions gives rise to a frequency band of dark soliton solutions, which are found analytically for the lossless zero-ve ... Full text Cite

Long-time limit studies of an obstruction in the g-function mechanism for semiclassical focusing NLS

Journal Article · 2015 We consider the long-time properties of the an obstruction in the Riemann-Hilbert approach to one dimensional focusing Nonlinear Schr\"odinger equation in the semiclassical limit for a one parameter family of initial conditions. For certain values of the p ... Link to item Cite

Smooth parametric dependence of asymptotics of the semiclassical focusing NLS

Journal Article Analysis and PDE · January 1, 2015 We consider the one-dimensional focusing (cubic) nonlinear Schrödinger equation (NLS) in the semiclassical limit with exponentially decaying complex-valued initial data, whose phase is multiplied by a real parameter. We prove smooth dependence of the asymp ... Full text Cite

Destructive impact of imperfect beam collimation in extraordinary optical transmission.

Journal Article Journal of the Optical Society of America. A, Optics, image science, and vision · June 2013 We investigate the difference between analytic predictions, numerical simulations, and experiments measuring the transmission of energy through subwavelength, periodically arranged holes in a metal film. At normal incidence, theory predicts a sharp transmi ... Full text Cite

An exactly solvable model for nonlinear resonant scattering

Journal Article Nonlinearity · September 1, 2012 This work analyses the effects of cubic nonlinearities on certain resonant scattering anomalies associated with the dissolution of an embedded eigenvalue of a linear scattering system. These sharp peak-dip anomalies in the frequency domain are often called ... Full text Cite

Semiclassical limit of the scattering transform for the focusing nonlinear Schrödinger equation

Journal Article International Mathematics Research Notices · May 21, 2012 The semiclassical limit of the focusing Nonlinear (cubic) Schr ̈ odinger Equation corresponds to the singularly perturbed Zakharov-Shabat (ZS) system that defines the direct and inverse scattering transforms (IST). In this paper, we derive explicit expressi ... Full text Cite

Perturbation of Riemann-Hilbert jump contours: smooth parametric dependence with application to semiclassical focusing NLS

Journal Article · August 25, 2011 A perturbation of a class of scalar Riemann-Hilbert problems (RHPs) with the jump contour as a finite union of oriented simple arcs in the complex plane and the jump function with a zlog⁡z type singularity on the jump contour is considered. The jump fun ... Link to item Cite

Nonlinear steepest descent asymptotics for semiclassical limit of Integrable systems: Continuation in the parameter space

Journal Article Communications in Mathematical Physics · February 1, 2010 The initial value problem for an integrable system, such as the Nonlinear Schrödinger equation, is solved by subjecting the linear eigenvalue problem arising from its Lax pair to inverse scattering, and, thus, transforming it to a matrix Riemann-Hilbert pr ... Full text Cite

Drosophila morphogenesis: tissue force laws and the modeling of dorsal closure.

Journal Article HFSP journal · December 2009 Dorsal closure, a stage of Drosophila development, is a model system for cell sheet morphogenesis and wound healing. During closure, two flanks of epidermal tissue progressively advance to reduce the area of the eye-shaped opening in the dorsal surface, wh ... Full text Cite

Accurate description of optical precursors and their relation to weak-field coherent optical transients

Journal Article Physical Review A - Atomic, Molecular, and Optical Physics · June 29, 2009 We study theoretically the propagation of a step-modulated optical field as it passes through a dispersive dielectric made up of a dilute collection of oscillators characterized by a single narrow-band resonance. The propagated field is given in terms of a ... Full text Cite