Journal ArticlePhysica D: Nonlinear Phenomena · April 1, 2021
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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 ...
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Journal ArticleNonlinearity · 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 ...
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Journal ArticleNonlinearity · 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 ...
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Journal ArticleCommunications 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 ...
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Journal ArticleProgress 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 ...
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Journal ArticleAnnual 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 ...
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Journal ArticleProceedings 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 ...
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Journal ArticlePhysica 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 ...
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Journal ArticlePhysical 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 ...
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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 ...
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Journal ArticleAnalysis 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleNonlinearity · 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 ...
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Journal ArticleInternational 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 ...
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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 $z\log z$ type singularity on the jump contour is
considered. The jump fun ...
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Journal ArticleCommunications 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 ...
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Journal ArticleHFSP 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticleInternational Mathematics Research Notices · February 1, 2009
We derive a determinant formula for the g-function that plays a key role in the steepest descent asymptotic analysis of the solution of 2 × 2 matrix Riemann-Hilbert problems (RHPs) and is closely related to a hyperelliptic Riemann surface. We formulate a s ...
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Journal Article · 2009
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-H ...
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Journal ArticleMathematical Methods in Electromagnetic Theory, MMET, Conference Proceedings · September 19, 2008
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 n ...
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Journal ArticleInternational Mathematics Research Notices · December 1, 2007
We consider the semiclassical limit for the focusing nonlinear (cubic) Schrödinger 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 cl ...
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Journal ArticleCommunications on Pure and Applied Mathematics · September 1, 2007
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 pha ...
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Journal ArticleBiophysical Journal · April 2007
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
mult ...
Cite
Journal ArticleBiophysical journal · April 2007
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, whi ...
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Journal ArticleCommunications on Pure and Applied Mathematics · January 1, 2006
In a previous paper [13] we calculated the leading-order term q 0(x, t, ε) of the solution of q(x, t, ε), the focusing nonlinear (cubic) Schrödinger (NLS) equation in the semiclassical limit (ε → 0) for a certain one-parameter family of initial conditions. ...
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Journal ArticlePhysical review. E, Statistical, nonlinear, and soft matter physics · February 2005
We present a precise theoretical explanation and prediction of certain resonant peaks and dips in the electromagnetic transmission coefficient of periodically structured slabs in the presence of nonrobust guided slab modes. We also derive the leading asymp ...
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Journal ArticleCommunications on Pure and Applied Mathematics · July 1, 2004
We calculate the leading-order term of the solution of the focusing nonlinear (cubic) Schrödinger equation (NLS) in the semiclassical limit for a certain one-parameter family of initial conditions. This family contains both solitons and pure radiation. In ...
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Journal ArticleSIAM Journal on Applied Mathematics · October 1, 2003
Using boundary-integral projections for time-harmonic electromagnetic (EM) fields, and their numerical implementation, we analyze EM resonance in slabs of two-phase dielectric photonic crystal materials. We characterize resonant frequencies by a complex Fl ...
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Journal ArticleScience (New York, N.Y.) · April 2003
We investigated the forces that connect the genetic program of development to morphogenesis in Drosophila. We focused on dorsal closure, a powerful model system for development and wound healing. We found that the bulk of progress toward closure is driven ...
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Journal ArticleProceedings of SPIE - The International Society for Optical Engineering · January 1, 2003
Variational methods are applied to the design of a two-dimensional lossless photonic crystal slab to optimize resonant scattering phenomena. The method is based on varying properties of the transmission coefficient that are connected to resonant behavior. ...
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Journal ArticleSIAM Journal on Applied Mathematics · July 1, 2002
We compute the transmission of two-dimensional (2D) electromagnetic waves through a square lattice of lossless dielectric rods with a channel defect. The lattice is finite in the direction of propagation of the incident wave and periodic in a transverse di ...
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Journal ArticleCommunications on Pure and Applied Mathematics · October 1, 2001
We develop a unified approach to integrating the Whitham modulation equations. Our approach is based on the formulation of the initial-value problem for the zero-dispersion KdV as the steepest descent for the scalar Riemann-Hilbert problem [6] and on the m ...
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Journal ArticleJournal of Computational and Applied Mathematics · August 1, 2001
A few years ago the authors introduced a new approach to study asymptotic questions for orthogonal polynomials. In this paper we give an overview of our method and review the results which have been obtained in Deift et al. (Internat. Math. Res. Notices (1 ...
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Journal ArticlePhysica D: Nonlinear Phenomena · May 15, 2001
We use the recently introduced notion of stochastic soliton lattice for quantitative description of soliton turbulence. We consider the stochastic soliton lattice on a special band-gap scaling of the spectral surface of genus N so that the integrated densi ...
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Journal ArticleSIAM Journal on Applied Mathematics · January 1, 2001
We derive traveling wave solutions in a nonlinear diatomic particle chain near the 1:2 resonance (κ*, ω*), where ω* = D(κ*), 2ω* = D(2κ*) and ω = D(κ) is the linear dispersion relation. To leading order, the waves have form ±εsin(κn - ωt) + δsin(2κn - 2ωt) ...
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Journal ArticlePhysica D: Nonlinear Phenomena · November 15, 2000
In this paper, we study the semi-classical limit of the Zakharov-Shabat eigenvalue problem for the focusing of NLS with some specific initial data. In all these cases, the eigenvalue problem is reduced to connection problems for the hypergeometric equation ...
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Journal ArticleSIAM Journal on Applied Mathematics · January 1, 2000
We compute the transmission properties of two-dimensional (2-D) electromagnetic transverse magnetic (TM) waves that are normally incident on a Fabry-Perot structure with mirrors consisting of photonic crystals. We use a boundary integral formulation with q ...
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Journal ArticleIEEE Transactions on Microwave Theory and Techniques · December 1, 1999
Square and triangular lattice two-dimensional (2-D) photonic crystals (PC's) composed of lossy dielectric rods in air were constructed with a microwave bandgap between 4-8 GHz. Fabry-Perot resonators of varying length were constructed from two of these PC' ...
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Journal ArticleCommunications on Pure and Applied Mathematics · January 1, 1999
We consider asymptotics of orthogonal polynomials with respect to weights w(x)dx = e-Q(x)dx on the real line, where Q(x) = Σ2mk=0qkxk, q2m > 0, denotes a polynomial of even order with positive leading coefficient. The orthogonal polynomial problem is formu ...
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Journal ArticleCommunications on Pure and Applied Mathematics · January 1, 1999
We consider asymptotics for orthogonal polynomials with respect to varying exponential weights wn(x)dx = e-nV(x)dx on the line as n → ∞. The potentials V are assumed to be real analytic, with sufficient growth at infinity. The principle results concern Pla ...
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Journal ArticleSIAM Journal on Applied Mathematics · January 1, 1999
We consider wave propagation in a nonlinear infinite diatomic chain of particles as a discrete model of propagation in a medium whose properties vary periodically in space. The particles have alternating masses M1 and M2 and interact in accordance to a gen ...
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Journal ArticleCommunications on Pure and Applied Mathematics · January 1, 1999
We consider an infinite particle chain whose dynamics are governed by the following system of differential equations: q̈n = V′ (qn-1 - qn) - V′ (qn - qn+1), n = 1,2, . . . , where qn(t) is the displacement of the nth particle at time t along the chain axis ...
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Journal ArticleCommunications on Pure and Applied Mathematics · January 1, 1998
We introduce a renormalization procedure for the τ-function of integrable systems. We illustrate the procedure using the supercritical Toda shock problem as a model problem. We start with a finite chain and take the limit of the solution as the number of p ...
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Journal ArticleProceedings of the National Academy of Sciences of the United States of America · January 1998
This paper extends the steepest descent method for Riemann-Hilbert problems introduced by Deift and Zhou in a critical new way. We present, in particular, an algorithm, to obtain the support of the Riemann-Hilbert problem for leading asymptotics. Applying ...
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Journal ArticleSIAM Journal on Applied Mathematics · January 1, 1997
The continuum limit of a recently proposed model for charge transport in resonant-tunneling semiconductor superlattices (SLs) is analyzed. It is described by a nonlinear hyperbolic integrodifferential equation on a one-dimensional spatial support, suppleme ...
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Journal ArticleCommunications on Pure and Applied Mathematics · January 1, 1995
This is the First part of a two‐part series on forced lattice vibrations in which a semi‐infinite lattice of one‐dimensional particles {xn}n≧1 (Formula Presented.) is driven from one end by a particle x0. This particle undergoes a given, periodically pertu ...
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Journal ArticleCommunications on Pure and Applied Mathematics · January 1, 1995
This is the second part of a two‐part series on forced lattice vibrations in which a semi‐infinite lattice of one‐dimensional particles {xn}n≧1, (Formula Presented.) is driven from one end by a particle x0. This particle undergoes a given, periodically per ...
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Journal Article · September 26, 1994
We begin with a description of recent numerical and analytical results that
are closely related to the results of this paper. ...
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Journal ArticleSIAM Journal on Applied Mathematics · January 1, 1994
A linear stability analysis of the stationary solution of a one-dimensional drift-diffusion model used to describe the Gunn effect in GaAs is performed. It is shown that for long semiconductor samples under dc voltage bias conditions, and small diffusivity ...
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Journal ArticleCommunications on Pure and Applied Mathematics · January 1, 1993
I t is well known that a p‐periodic potential Q(x) can be reconstructed from spectral data of the corresponding Hill operator −(d2/dx2) + Q(x) in terms of a Riemann θ‐function. We regard the periodic potential Q(x) as the pointwise limit of a scattering po ...
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Journal ArticleSIAM Journal on Applied Mathematics · January 1, 1990
Linear reaction-hyperbolic equations of a general type arising in certain physiological problems do not have traveling wave solutions, but numerical computations have shown that they possess approximate traveling waves. Using singular perturbation theory, ...
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Journal ArticleTransactions of the American Mathematical Society · January 1, 1987
We study the initial value problem for the Korteweg-de Vries equation (FORMULA PRESENTED) in the limit of small dispersion, i.e., 0. When the unperturbed equation (FORMULA PRESENTED) develops a shock, rapid oscillations arise in the solution of the perturb ...
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Journal ArticleTransactions of the American Mathematical Society · January 1, 1986
We study the long time evolution of the solution to the Korteweg- de Vries equation with initial data u(x) which satisfy lim y(.x) = -1, lim U(x) = 0. (Formula presented) We show that as t →∞the step emits a wavetrain of solitons which asymptotically have ...
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Journal ArticleCommunications on Pure and Applied Mathematics · January 1, 1985
The inverse scattering method is used to determine the distribution limit as ϵ → 0 of the solution u(x, t, ϵ) of the initial value problem. Ut − 6uux + ϵ2uxxx = 0, u(x, 0) = v(x), where v(x) is a positive bump which decays sufficiently fast as x x→±α. The ...
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