About

Stephanos Venakides is a Professor of Mathematics at Duke University, holding his position since 1991 within the Trinity College of Arts & Sciences. His research spans the fields of pure and applied mathematics, physics, and biology, with specific focus on differential equations, integrable systems, acoustic and electromagnetic scattering—particularly transmission anomalies and resonances—photonic crystals, exciton polaritons, and micromagnetics. Venakides has been recognized for his contributions to the field, notably being invited as one of the three Abel lecturers during the award of the Abel Prize to Peter Lax by the Norwegian Academy of Science and Letters in May 2005. His work includes studying the structure of magnetic skyrmions, traveling domain walls in chiral ferromagnets, and analyzing wave-breaking and resonant phenomena through various grants from the National Science Foundation. Venakides holds a Ph.D. from New York University, an M.S. from Georgia Tech, and a B.S. from the National Technical University of Athens.

Research topics

• Quantum electrodynamics
• Condensed matter physics
• Quantum mechanics
• Physics

Selected publications

• Chiral magnetic skyrmions across length scales

  New Journal of Physics · 2023 · 9 citations

  Senior authorCorresponding
  • Physics
  • Condensed matter physics
  • Quantum electrodynamics

  Abstract The profile, radius, and energy of chiral skyrmions, found in magnetic materials with the Dzyaloshinskii–Moriya (DM) interaction and easy-axis anisotropy perpendicular to the film, have been previously calculated in the asymptotic limits of small and large skyrmion radius, as functions of the model parameter. We extend the asymptotic analysis to the case of an external field or a combination of anisotropy and external field. The formulae for the skyrmion radius and energy are then modified, by the use of fitting techniques, into very good approximations through almost the entire range of skyrmion radii, from zero to infinity. We include a study of the effect of the magnetostatic field on the skyrmion profile in two cases. We compare the profile of magnetic bubbles, stabilized without the chiral DM interaction to that of a chiral skyrmion.

  PublisherOA PDFDOI

• Chiral magnetic skyrmions across length scales

  arXiv (Cornell University) · 2022-06-09 · 1 citations

  preprintOpen accessSenior author

  The profile and energy of chiral skyrmions, found in magnetic materials with the Dzyaloshinskii-Moriya interaction, can be approximated by formulae obtained through asymptotic analysis in the limits of small and large skyrmion radius. Using fitting techniques, we modify these formulae so that their validity extends to almost the entire range of skyrmion radii. Such formulae are obtained for skyrmions that are stabilised in the presence of an external field or easy-axis anisotropy or a combination of these. We further study the effect of the magnetostatic field on the skyrmion profile. We compare the profile of magnetic bubbles, stabilized without the chiral Dzyaloshinskii-Moriya interaction to that of a chiral skyrmion.

  PublisherOA PDFDOI

• Chiral skyrmions of large radius

  Physica D Nonlinear Phenomena · 2021-01-11 · 3 citations

  preprintOpen accessSenior author
  PublisherOA PDFDOI

• The profile of chiral skyrmions of large radius

  arXiv (Cornell University) · 2019-10-10 · 1 citations

  preprintOpen accessSenior author

  We study the profile of an axially symmetric magnetic skyrmion in a ferromagnet with the Dzyaloshinskii-Moriya interaction (DMI). We give exact formulas for the solution of the Landau-Lifshitz equation in the asymptotic limit that the dimensionless DMI parameter approaches a critical value $\epsilon\to\epsilon_0$ and the skyrmion radius becomes large and diverges to infinity. We give the profile field at the skyrmion core, the far field and the field of the skyrmion domain wall. An asymptotic formula for the skyrmion radius as a function of the DMI constant is obtained.

  Publisher

• Traveling domain walls in chiral ferromagnets

  Nonlinearity · 2019-05-30 · 4 citations

  articleOpen accessSenior author

  Abstract 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 based anisotropy, traveling wave solutions are not found in closed form. For the construction we follow a topological approach and provide details of solutions by means of numerical calculations.

  PublisherOA PDFDOI

• Mathematical models of dorsal closure

  Progress in Biophysics and Molecular Biology · 2018-05-28 · 11 citations

  reviewSenior author
  PublisherDOI

• Three-dimensional quasi-periodic shifted Green function throughout the spectrum, including Wood anomalies

  Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2017-11-01 · 11 citations

  articleOpen accessSenior author

  This work, part II in a series, presents an efficient method for evaluation of wave scattering by doubly periodic diffraction gratings at or near what are commonly called 'Wood anomaly frequencies'. At these frequencies, there is a grazing Rayleigh wave, and the quasi-periodic Green function ceases to exist. We present a modification of the Green function by adding two types of terms to its lattice sum. The first type are transversely shifted Green functions with coefficients that annihilate the growth in the original lattice sum and yield algebraic convergence. The second type are quasi-periodic plane wave solutions of the Helmholtz equation which reinstate certain necessary grazing modes without leading to blow-up at Wood anomalies. Using the new quasi-periodic Green function, we establish, for the first time, that the Dirichlet problem of scattering by a smooth doubly periodic scattering surface at a Wood frequency is uniquely solvable. We also present an efficient high-order numerical method based on this new Green function for scattering by doubly periodic surfaces at and around Wood frequencies. We believe this is the first solver able to handle Wood frequencies for doubly periodic scattering problems in three dimensions. We demonstrate the method by applying it to acoustic scattering.

  PublisherOA PDFDOI

• Cell Sheet Morphogenesis: Dorsal Closure in<i>Drosophila melanogaster</i>as a Model System

  Annual Review of Cell and Developmental Biology · 2017-10-06 · 105 citations

  reviewOpen access

  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 elongation of lateral epidermal cell sheets that close a dorsal hole filled with amnioserosa cells. Signaling pathways regulate the function of cellular structures and processes, including Actomyosin and microtubule cytoskeletons, cell-cell/cell-matrix adhesion complexes, and endocytosis/vesicle trafficking. These orchestrate complex shape changes and movements that entail interactions between five distinct cell types. Genetic and laser perturbation studies establish that closure is robust, resilient, and the consequence of redundancy that contributes to four distinct biophysical processes: contraction of the amnioserosa, contraction of supracellular Actomyosin cables, elongation (stretching?) of the lateral epidermis, and zipping together of two converging cell sheets. What triggers closure and what the emergent properties are that give rise to its extraordinary resilience and fidelity remain key, extant questions.

  PublisherOA PDFDOI

• 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 · 2016-07-01 · 20 citations

  articleOpen accessSenior author

  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 scattering of waves by doubly periodic arrays of scatterers in three-dimensional space. Except for certain 'Wood frequencies' at which the quasi-periodic Green function ceases to exist, the proposed approach, which is based on smooth windowing functions, gives rise to tapered lattice sums which converge superalgebraically fast to the Green function-that is, faster than any power of the number of terms used. This is in sharp contrast to the extremely slow convergence exhibited by the lattice sums in the absence of smooth windowing. (The Wood-frequency problem is treated in part II.) This paper establishes rigorously the superalgebraic convergence of the windowed lattice sums. A variety of numerical results demonstrate the practical efficiency of the proposed approach.

  PublisherOA PDFDOI

• Continuous and discontinuous dark solitons in polariton condensates

  Physical Review B · 2015-04-09 · 7 citations

  articleOpen accessSenior author

  Bose-Einstein condensates of exciton-polaritons are described by a Schr\"odinger 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-velocity case. The soliton's far-field value varies from zero to infinity as the operating frequency varies across the band. For positive detuning (photon frequency higher than exciton frequency), the exciton wave function becomes discontinuous when the operating frequency exceeds the exciton frequency. This phenomenon lies outside the parameter regime of validity of the Gross-Pitaevskii (GP) model. Within its regime of validity, we give a derivation of a single-mode GP model from the initial Schr\"odinger system and compare the continuous polariton solitons and GP solitons using the healing length notion.

  PublisherOA PDFDOI

Recent grants

• Nonlinear Waves in Uniform and Periodic Media

  NSF · $239k · 2002–2008

• Wave-breaking and Resonant Phenomena

  NSF · $480k · 2007–2014

• Wave-breaking and Resonant Phenomena

  NSF · $510k · 2012–2018

Frequent coauthors

• Percy Deift

  Courant Institute of Mathematical Sciences

  26 shared

• Stephen P. Shipman

  Louisiana State University

  20 shared

• Xin Zhou

  Cornell University

  16 shared

• Thomas Kriecherbauer

  14 shared

• Daniel P. Kiehart

  Duke University

  12 shared

• Stavros Komineas

  University of Crete

  12 shared

• Alexander Tovbis

  11 shared

• K. T-R McLaughlin

  9 shared

Awards & honors

• Invited as one of the three Abel lecturers in the award of t…