A High-Order Perturbation of Envelopes (HOPE) Method for Vector Electromagnetic Scattering by Periodic Inhomogeneous Media: Joint Analyticity: A high-order perturbation of envelopes (HOPE) method for vector electromagnetic scattering by periodic inhomogeneous media: joint analyticity

Authors: David P. Nicholls, Liet Vo

Source: SIAM Journal on Applied Mathematics. 85:755-778

Subject Terms: Spectral, collocation and related methods applied to problems in optics and electromagnetic theory, high-order spectral methods, Boundary value problems for second-order elliptic equations, Maxwell equations, inhomogeneous media, high-order perturbation of envelopes methods, linear wave scattering, Spectral, collocation and related methods for boundary value problems involving PDEs, layered media, PDEs in connection with optics and electromagnetic theory, PDEs in connection with geophysics, Diffraction, scattering

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Access URL: https://zbmath.org/8035693
https://doi.org/10.1137/24m1643189

Stabilization of walls in notched ferromagnetic nanowires

Authors: Gilles Carbou, David Sanchez

Contributors: Sanchez, David

Source: ESAIM: Mathematical Modelling and Numerical Analysis. 59:925-954

Subject Terms: Landau-Lifshitz equation, nanowire, Nonlinear parabolic equations, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], stability, PDEs in connection with optics and electromagnetic theory, ferromagnetism

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Access URL: https://zbmath.org/8028643
https://doi.org/10.1051/m2an/2025008
https://hal.science/hal-01810144v2
https://doi.org/10.1051/m2an/2025008
https://hal.science/hal-01810144v2/document

Geometry-Based Approximation of Waves in Complex Domains: Geometry-based approximation of waves in complex domains

Authors: Davide Pradovera, Monica Nonino, Ilaria Perugia

Source: SIAM Journal on Applied Mathematics. 85:224-248

Subject Terms: 101014 Numerical mathematics, scattering, geometrical theory of diffraction, wave propagation, Numerical Analysis (math.NA), 101014 Numerische Mathematik, 01 natural sciences, surrogate modeling, Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs, Model reduction in optics and electromagnetic theory, FOS: Mathematics, Wave equation, 35L05, 35Q60, 65M25, 78A45, 78M34, Mathematics - Numerical Analysis, Initial-boundary value problems for second-order hyperbolic equations, 0101 mathematics, PDEs in connection with optics and electromagnetic theory, Diffraction, scattering

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Access URL: http://arxiv.org/abs/2301.13613
https://zbmath.org/8008453
https://doi.org/10.1137/23m1611300
https://ucrisportal.univie.ac.at/de/publications/a134d4c7-4109-4b86-9d30-4a7a723fe292

A Novel PML-Type Technique for Acoustic Scattering Problems Based on a Real Coordinate Transformation: A novel PML-type technique for acoustic scattering problems based on a real coordinate transformation

Authors: Jiangxing Wang, Li-Lian Wang, Bo Wang

Source: SIAM Journal on Scientific Computing. 47:A153-A180

Subject Terms: Roundoff error, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, real coordinate transformation, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, oscillation, perfectly matched layer, time-harmonic wave scattering, Pattern formations in context of PDEs, substitution, FOS: Mathematics, Helmholtz equation, Mathematics - Numerical Analysis, Waves and radiation in optics and electromagnetic theory, PDEs in connection with optics and electromagnetic theory, Diffraction, scattering

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Access URL: http://arxiv.org/abs/2401.15573
https://zbmath.org/7967117
https://doi.org/10.1137/24m1628554

A Highly Accurate PML-BIE Solver for the Electromagnetic Scattering Problem in a Multilayered Medium: A highly accurate PML-BIE solver for the electromagnetic scattering problem in a multilayered medium

Authors: Gang Bao, Wangtao Lu, Tao Yin, Lu Zhang

Source: SIAM Journal on Scientific Computing. 46:A3849-A3872

Subject Terms: perfectly matched layer, Integral representations, integral operators, integral equations methods in higher dimensions, electromagnetic scattering, Integral representations of solutions to PDEs, boundary integral equation, Numerical methods for integral equations, layered media, PDEs in connection with optics and electromagnetic theory

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Access URL: https://zbmath.org/7959779
https://doi.org/10.1137/24m1650703

Measure-valued solutions to a generalized Landau–Lifshitz–Bloch equation: Measure-valued solutions to a generalized Landau-Lifshitz-Bloch equation

Authors: Chahid Ayouch, Driss Meskine, Mouhcine Tilioua

Source: Zeitschrift für Analysis und ihre Anwendungen. 44:1-15

Subject Terms: Initial-boundary value problems for systems of nonlinear higher-order PDEs, Statistical mechanics of magnetic materials, Young measures, Existence problems for PDEs: global existence, local existence, non-existence, PDEs with measure, Weak solutions to PDEs, Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations, PDEs in connection with optics and electromagnetic theory, Landau-Lifshitz-Bloch equation, measure-valued solutions

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Access URL: https://zbmath.org/8021679
https://doi.org/10.4171/zaa/1783

Approximations of Euler-Maxwell systems by drift-diffusion equations through zero-relaxation limits near the non-constant equilibrium

Authors: Jin, Rui, Li, Yachun, Zhao, Liang

Source: Science China Mathematics. 68:1051-1078

Subject Terms: Euler-Maxwell system, Mathematics - Analysis of PDEs, Initial value problems for second-order parabolic systems, Euler-Poisson system, Asymptotic behavior of solutions to PDEs, non-constant equilibrium state, global convergence rate, Initial value problems for first-order hyperbolic systems, PDEs in connection with optics and electromagnetic theory, zero-relaxation limit, Singular perturbations in context of PDEs, 35B25, 35L45, 35Q60, 35K45

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Access URL: http://arxiv.org/abs/2312.07314
https://zbmath.org/8029232
https://doi.org/10.1007/s11425-023-2286-7

On the Regularity of Time-Harmonic Maxwell Equations with Impedance Boundary Conditions: On the regularity of time-harmonic Maxwell equations with impedance boundary conditions

Authors: Chen, Zhiming

Source: Communications on Applied Mathematics and Computation. 7:759-770

Subject Terms: Maxwell equations, Smoothness and regularity of solutions to PDEs, impedance boundary condition, \(H^2\) regularity, Weak solutions to PDEs, PDEs in connection with optics and electromagnetic theory

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Access URL: https://zbmath.org/8034298
https://doi.org/10.1007/s42967-024-00386-x

Global Solutions for the Rotating Magnetohydrodynamics System in the Scaling Critical Sobolev Space: Global solutions for the rotating magnetohydrodynamics system in the scaling critical Sobolev space

Authors: Takada, Ryo, Yoneda, Keiji

Source: Funkcialaj Ekvacioj. 67:29-59

Subject Terms: global-in-time existence, dispersive Coriolis force, uniqueness, Magnetohydrodynamics and electrohydrodynamics, General theory of rotating fluids, homogeneous Sobolev space, PDEs in connection with fluid mechanics, initial value problem, global energy estimate, PDEs in connection with optics and electromagnetic theory

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A High–Order Perturbation of Envelopes (HOPE) method for vector electromagnetic scattering by periodic inhomogeneous media: Analytic continuation: A high-order perturbation of envelopes (HOPE) method for vector electromagnetic scattering by periodic inhomogeneous media: analytic continuation

Authors: David P. Nicholls, Liet Vo

Source: Journal of Differential Equations. 422:106-151

Subject Terms: Spectral, collocation and related methods applied to problems in optics and electromagnetic theory, high-order spectral methods, Composite media, random media in optics and electromagnetic theory, Perturbations in context of PDEs, 4. Education, inhomogeneous media, Analyticity in context of PDEs, Numerical Analysis (math.NA), Best approximation, Chebyshev systems, analytic continuation, Mathematics - Analysis of PDEs, Boundary value problems for second-order elliptic equations, Maxwell equations, high-order perturbation of envelopes methods, FOS: Mathematics, Spectral, collocation and related methods for boundary value problems involving PDEs, Mathematics - Numerical Analysis, Waves and radiation in optics and electromagnetic theory, layered media, PDEs in connection with optics and electromagnetic theory, Numerical methods for discrete and fast Fourier transforms, Diffraction, scattering, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2407.03351

Criterion of singularity formation for radial solutions of the pressureless Euler-Poisson equations in exceptional dimension

Authors: Olga S. Rozanova

Source: Journal of Mathematical Analysis and Applications. 548:129394

Subject Terms: Mathematics - Analysis of PDEs, isochronous oscillations, FOS: Mathematics, FOS: Physical sciences, Euler-Poisson equations, singularity formation, Mathematical Physics (math-ph), Primary 35Q60, Secondary 35L60, 35L67, 34M10, PDEs in connection with optics and electromagnetic theory, Mathematical Physics, Singularity in context of PDEs, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2408.13794
https://zbmath.org/8028656
https://doi.org/10.1016/j.jmaa.2025.129394

On the distribution of Born transmission eigenvalues in the complex plane

Authors: Hovsepyan, Narek

Source: Asymptotic Analysis. 136:27-60

Subject Terms: Born approximation, Eigenvalues, singular values, and eigenvectors, inverse scattering, 01 natural sciences, transmission eigenvalues, eigenvalue-free regions, Mathematics - Analysis of PDEs, Scattering theory for PDEs, FOS: Mathematics, Inverse problems (including inverse scattering) in optics and electromagnetic theory, spherically stratified medium, 0101 mathematics, PDEs in connection with optics and electromagnetic theory, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2304.09470

Existence of multi‐dimensional contact discontinuities for the ideal compressible magnetohydrodynamics: Existence of multi-dimensional contact discontinuities for the ideal compressible magnetohydrodynamics

Authors: Wang, Yanjin, Xin, Zhouping

Source: Communications on Pure and Applied Mathematics. 77:583-629

Subject Terms: uniform highest-order tangential energy estimate, inviscid limit, uniqueness, FOS: Physical sciences, Mathematical Physics (math-ph), PDEs in connection with fluid mechanics, Sobolev space, 01 natural sciences, Mathematics - Analysis of PDEs, well-posedness, 0103 physical sciences, FOS: Mathematics, Magnetohydrodynamics and electrohydrodynamics, Rayleigh-Taylor instability, 0101 mathematics, PDEs in connection with optics and electromagnetic theory, local existence, Mathematical Physics, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2112.08580
https://zbmath.org/7782035
https://doi.org/10.1002/cpa.22148

Coherent Manipulation of Optical Soliton in Four Level N-type Atomic Medium: Coherent manipulation of optical soliton in four level N-type atomic medium

Authors: Khan, Shehzad, Saeed, Muhammad, Khan, Meraj Ali, Aldosary, Saud Fahad, Ahmad, Shabir

Source: International Journal of Theoretical Physics. 63

Subject Terms: Quantum optics, Soliton equations, optical solitons, Soliton solutions, dark soliton, bright soliton, Lasers, masers, optical bistability, nonlinear optics, mixed-type solitons, atomic medium, PDEs in connection with optics and electromagnetic theory, PDEs in connection with quantum mechanics, Atomic physics

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Access URL: https://zbmath.org/7898345
https://doi.org/10.1007/s10773-024-05712-w

Semiclassical states for the curl–curl problem: Semiclassical states for the curl-curl problem

Authors: Bartosz Bieganowski, Adam Konysz, Jarosław Mederski

Source: Nonlinear Analysis. 255:113756

Subject Terms: semiclassical limit, Variational methods for second-order elliptic equations, NLS equations (nonlinear Schrödinger equations), Asymptotic behavior of solutions to PDEs, variational methods, Existence problems for PDEs: global existence, local existence, non-existence, Lasers, masers, optical bistability, nonlinear optics, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, time-harmonic waves, Variational methods applied to PDEs, Mathematics - Analysis of PDEs, Maxwell equations, FOS: Mathematics, nonlinear Schrödinger equation, PDEs in connection with optics and electromagnetic theory, Critical points of functionals in context of PDEs (e.g., energy functionals), singular potential, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2312.03658
https://zbmath.org/8018056
https://doi.org/10.1016/j.na.2025.113756

Solitons in the semi-infinite ferromagnets with the different types of anisotropy

Authors: V.V. Kiselev, A.A. Raskovalov

Source: Annals of Physics. 475:169933

Subject Terms: crystallographic magnetic anisotropy, Soliton equations, Soliton solutions, Landau-Lifshitz equation, solitons, spin pinning, breather, PDEs in connection with optics and electromagnetic theory

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An Infinite Sequence of Localized Semiclassical States for Nonlinear Maxwell–Dirac System: An infinite sequence of localized semiclassical states for nonlinear Maxwell-Dirac system

Authors: Zhang, Jian, Zhang, Ying

Source: The Journal of Geometric Analysis. 34

Subject Terms: Variational methods applied to PDEs, unbounded sequence of bound states, Covariant wave equations in quantum theory, relativistic quantum mechanics, Time-dependent Schrödinger equations and Dirac equations, Motion of charged particles, degenerate potential, Existence of solutions for minimax problems, nonlinear Maxwell-Dirac system, localized semiclassical states, PDEs in connection with optics and electromagnetic theory, PDEs in connection with quantum mechanics, Selfadjoint operator theory in quantum theory, including spectral analysis

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Optical soliton noninteraction transmission in optical communication systems

Authors: Zhang, Xin, Li, Xiaofeng, Ma, Guoli

Source: Applied Mathematics Letters. 162:109383

Subject Terms: solitons interactions, optical solitons, Soliton solutions, NLS equations (nonlinear Schrödinger equations), Time-dependent Schrödinger equations and Dirac equations, higher-order nonlinear effects, Lasers, masers, optical bistability, nonlinear optics, nonlinear Schrödinger equation, PDEs in connection with optics and electromagnetic theory, Solutions to PDEs in closed form

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Influence of initial conditions on data-driven model identification and information entropy for ideal mhd problems: Influence of initial conditions on data-driven model identification and information entropy for ideal MHD problems

Authors: Gina Vasey, Daniel Messenger, David Bortz, Andrew Christlieb, Brian O'Shea

Source: Journal of Computational Physics. 524:113719

Subject Terms: Inverse problems for PDEs, ideal MHD, Fluid Dynamics (physics.flu-dyn), FOS: Physical sciences, Physics - Fluid Dynamics, Computational Physics (physics.comp-ph), Physics - Plasma Physics, Plasma Physics (physics.plasm-ph), Physics - Data Analysis, Statistics and Probability, 35Q60, 35R30, 76W05, 85A30, data-driven, Shannon information entropy, Magnetohydrodynamics and electrohydrodynamics, PDEs in connection with optics and electromagnetic theory, Hydrodynamic and hydromagnetic problems in astronomy and astrophysics, Physics - Computational Physics, Data Analysis, Statistics and Probability (physics.data-an), weak sparse identification of nonlinear dynamics

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Access URL: http://arxiv.org/abs/2312.05339
https://zbmath.org/7996133
https://doi.org/10.1016/j.jcp.2025.113719

A constructible conductivity cloak via homogenisation*: A constructible conductivity cloak via homogenisation

Authors: Yves Capdeboscq, Eleanor Gemida

Source: Inverse Problems. 41:035001

Subject Terms: Technical applications of optics and electromagnetic theory, Homogenization in optics and electromagnetic theory, Inverse problems for PDEs, homogenisation, Electromagnetic theory (general), Composite media, random media in optics and electromagnetic theory, laminate composites, Inverse problems (including inverse scattering) in optics and electromagnetic theory, Spectral theory and eigenvalue problems for partial differential equations, approximate cloaking, Homogenization in context of PDEs, PDEs in media with periodic structure, PDEs in connection with optics and electromagnetic theory

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Access URL: https://zbmath.org/7988271
https://doi.org/10.1088/1361-6420/adaa98