Explanipedia

Spectrum of the Maxwell Equations for a Flat Interface Between Homogeneous Dispersive Media Open

Malcolm Brown, Tomáš Dohnal, Michael Plum, Ian Wood · 2024

The paper determines and classifies the spectrum of a non-self-adjoint operator pencil generated by the time-harmonic Maxwell problem with a nonlinear dependence on the frequency for the case of two homogeneous materials joined at a planar…

On the physical significance of non-local material parameters in optical metamaterials Open

Ramakrishna Venkitakrishnan, Yannick Augenstein, Benedikt Zerulla, Fatima Z. Goffi, Michael Plum , et al. · 2023

When light interacts with a material made from subwavelength periodically arranged constituents, non-local effects can emerge. They occur because of either a complicated response of the constituents or possible lattice interactions. In low…

Boltzmann's Billiard Systems: Computation of the Billiard Mapping and Some Numerical Results Open

Michael Plum, Airi Takeuchi, Lei Zhao · 2023

L. Boltzmann proposed a billiard model with a planar central force problem reflected against a line not passing through the center. He asserted that such a system is ergodic, which thus illustrates his ergodic hypothesis. However, it has b…

Breathers and rogue waves for semilinear curl-curl wave equations Open

Michael Plum, Wolfgang Reichel · 2023

We consider localized solutions of variants of the semilinear curl-curl wave equation $$s(x) \partial _t^2 U +\nabla \times \nabla \times U + q(x) U \pm V(x) \vert U \vert ^{p-1} U = 0$$ for $$(x,…

Dynamics of the black soliton in a regularized nonlinear Schrodinger equation Open

Dmitry E. Pelinovsky, Michael Plum · 2023

We consider a family of regularized defocusing nonlinear Schrodinger (NLS) equations proposed in the context of the cubic NLS equation with a bounded dispersion relation. The time evolution is well-posed if the black soliton is perturbed b…

Breathers and rogue waves for semilinear curl-curl wave equations Open

Michael Plum, Wolfgang Reichel · 2022

We consider localized solutions of variants of the semilinear curl-curl wave equation $s(x) \partial_t^2 U +\nabla\times\nabla\times U + q(x) U \pm V(x) |U|^{p-1} U = 0$ for $(x,t)\in \mathbb{R}^3\times\mathbb{R}$ and arbitrary $p>1$. Depe…

Eigenvalue analysis of the Lax operator for the one-dimensional cubic nonlinear defocusing Schrödinger equation Open

Xian Liao, Michael Plum · 2022

We characterize the location and number of eigenvalues for the Lax operator associated to the one-dimensional cubic nonlinear defocusing Schrödinger equation. With the help of a newly discovered unitary matrix, the analysis reduces to the …

Spectrum of the Maxwell Equations for a Flat Interface between Homogeneous Dispersive Media Open

Malcolm Brown, Tomáš Dohnal, Michael Plum, Ian Wood · 2022

The paper determines and classifies the spectrum of a non-self-adjoint operator pencil generated by the time-harmonic Maxwell problem with a nonlinear dependence on the frequency for the case of two homogeneous materials joined at a planar…

Stability of black solitons in optical systems with intensity-dependent dispersion Open

Dmitry E. Pelinovsky, Michael Plum · 2022

Black solitons are identical in the nonlinear Schrödinger (NLS) equation with intensity-dependent dispersion and the cubic defocusing NLS equation. We prove that the intensity-dependent dispersion introduces new properties in the stability…

Approximate nonradial solutions for the Lane-Emden problem in the ball Open

Borbála Fazekas, Filomena Pacella, Michael Plum · 2021

In this paper we provide a numerical approximation of bifurcation branches from nodal radial solutions of the Lane Emden Dirichlet problem in the unit ball in ℝ 2 , as the exponent of the nonlinearity varies. We consider solutions with two…

Higher order constitutive relations and interface conditions for metamaterials with strong spatial dispersion Open

Fatima Z. Goffi, Andrii Khrabustovskyi, Ramakrishna Venkitakrishnan, Carsten Rockstuhl, Michael Plum · 2021

Operator estimates for homogenization of the Robin Laplacian in a perforated domain Open

Andrii Khrabustovskyi, Michael Plum · 2021

Let $\varepsilon>0$ be a small parameter. We consider the domain $Ω_\varepsilon:=Ω\setminus D_\varepsilon$, where $Ω$ is an open domain in $\mathbb{R}^n$, and $D_\varepsilon$ is a family of small balls of the radius $d_\varepsilon=o(\varep…

Lower limits for the homogenization of periodic metamaterials made from electric dipolar scatterers Open

Ramakrishna Venkitakrishnan, Timon Höß, Taavi Repän, Fatima Z. Goffi, Michael Plum , et al. · 2021

Nonlocal constitutive relations promise to homogenize metamaterials even though the ratio of period over operational wavelength is not much smaller than unity. However, this ability has not yet been verified, as frequently only discrete st…

Towards more general constitutive relations for metamaterials: A checklist for consistent formulations Open

Fatima Z. Goffi, Karim Mnasri, Michael Plum, Carsten Rockstuhl, Andrii Khrabustovskyi · 2020

When the period of unit-cells constituting metamaterials is no longer much smaller than the wavelength but only smaller, local material laws fail to describe the propagation of light in such composite media when considered at the effective…

Computer-assisted Existence Proofs for One-dimensional Schrödinger-Poisson Systems Open

Jonathan Wunderlich, Michael Plum · 2020

Motivated by the three-dimensional time-dependent Schrödinger-Poisson system we prove the existence of non-trivial solutions of the one-dimensional stationary Schrödinger-Poisson system using computer-assisted methods. Starting from a nume…

Die Ansprechpartnerinnen und Ansprechpartner der DMV Open

Hinrich Lorenzen, U Oldenburg, Daniel Grieser, Anke Pohl, Michael Plum , et al. · 2019

Retrieving effective material parameters of metamaterials characterized by nonlocal constitutive relations Open

Karim Mnasri, Andrii Khrabustovskyi, Michael Plum, Carsten Rockstuhl · 2019

The parameter retrieval is a procedure in which effective material properties\nare assigned to a given metamaterial. A widely used technique bases on the\ninversion of reflection and transmission from a metamaterial slab. Thus far,\nlocal …

Gap Localization of TE-Modes by arbitrarily weak defects - multiband case Open

B. M. Brown, Vu Hoang, Michael Plum, Maria Radosz, Ian Wood · 2019

This paper considers the propagation of TE-modes in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a periodic background medium. Both the periodic background problem and the perturbed problem are …

Surface plasmon polaritons sustained at the interface of a nonlocal metamaterial Open

Joshua Feis, Karim Mnasri, Andrii Khrabustovskyi, Christian Stohrer, Michael Plum , et al. · 2018

Studying basic physical effects sustained in metamaterials characterized by specific constitutive relation is a research topic with a long standing tradition. Besides intellectual curiosity, it derives its importance from the ability to pr…

Beyond local effective material properties for metamaterials Open

Karim Mnasri, Andrii Khrabustovskyi, Christian Stohrer, Michael Plum, Carsten Rockstuhl · 2018

To discuss the properties of metamaterials on physical grounds and to consider them in applications, effective material parameters are usually introduced and assigned to a given metamaterial. In most cases, only weak spatial dispersion is …

Orbital Stability of Domain Walls in Coupled Gross--Pitaevskii Systems Open

Andres Contreras, Dmitry E. Pelinovsky, Michael Plum · 2018

Domain walls are minimizers of energy for coupled one-dimensional Gross--Pitaevskii systems with nontrivial boundary conditions at infinity. It has been shown that these solutions are orbitally stable in the space of complex $\dot{H}^1$ fu…

Interface conditions for a metamaterial with strong spatial dispersion Open

Andrii Khrabustovskyi, Karim Mnasri, Michael Plum, Christian Stohrer, Carsten Rockstuhl · 2017

Local constitutive relations, i.e. a weak spatial dispersion, are usually considered in the effective description of metamaterials. However, they are often insufficient and effects due to a nonlocality, i.e. a strong spatial dispersion, ar…

Interface conditions for a metamaterial with strong spatial dispersion Open

Andrii Khrabustovskyi, Karim Mnasri, Michael Plum, Christian Stohrer, Carsten Rockstuhl · 2017

Local constitutive relations, i.e. a weak spatial dispersion, are usually considered in the effective description of metamaterials. However, they are often insufficient and effects due to a nonlocality, i.e. a strong spatial dispersion, ar…

A computer-assisted existence proof for Emden’s equation on an unbounded L-shaped domain Open

Filomena Pacella, Michael Plum, Dagmar Rütters · 2017

We prove existence, non-degeneracy, and exponential decay at infinity of a non-trivial solution to Emden's equation -Δu = |u|3 on an unbounded L-shaped domain, subject to Dirichlet boundary conditions. Besides the direct value of this resu…

Gap localization of TE-modes by arbitrarily weak defects Open

B. M. Brown, Vu Hoang, Michael Plum, Maria Radosz, Ian Wood · 2017

This paper considers the propagation of TE-modes in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a periodic background medium. Both the periodic background problem and the perturbed problem are …

A computer-assisted existence proof for Emden's equation on an unbounded L-shaped domain Open

Filomena Pacella, Michael Plum, Dagmar Rütters · 2016

We prove existence, non-degeneracy, and exponential decay at infinity of a non-trivial solution to Emden's equation [Formula: see text] on an unbounded [Formula: see text]-shaped domain, subject to Dirichlet boundary conditions. Besides th…

A breather construction for a semilinear curl-curl wave equation with\n radially symmetric coefficients Open

Michael Plum, Wolfgang Reichel · 2016

We consider the semilinear curl-curl wave equation $s(x) \\partial_t^2 U\n+\\nabla\\times\\nabla\\times U + q(x) U \\pm V(x) |U|^{p-1} U = 0 \\mbox{ for }\n(x,t)\\in \\mathbb{R}^3\\times\\mathbb{R}$. For any $p>1$ we prove the existence of…

Ground states of a nonlinear curl-curl problem in cylindrically symmetric media Open

Thomas Bartsch, Tomáš Dohnal, Michael Plum, Wolfgang Reichel · 2016

Rigorous numerical enclosures for positive solutions of Lane-Emden's equation with sub-square exponents Open

Kazuaki Tanaka, Michael Plum, Kouta Sekine, Masahide Kashiwagi, Shin’ichi Oishi · 2016

The purpose of this paper is to obtain rigorous numerical enclosures for solutions of Lane-Emden's equation $-Δu=|u|^{p-1} u$ with homogeneous Dirichlet boundary conditions. We prove the existence of a nondegenerate solution $u$ nearby a n…

Verified numerical computation for semilinear elliptic problems with lack of Lipschitz continuity of the first derivative Open

Kazuaki Tanaka, Michael Plum, Kouta Sekine, Masahide Kashiwagi, Shin’ichi Oishi · 2016

In this paper, we propose a numerical method for verifying solutions to the semilinear elliptic equation -{\Delta}u=f(u) with homogeneous Dirichlet boundary condition. In particular, we consider the case in which the Frechet derivative of …

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