Related papers: Fundamental Limits of Characteristic Mode Slopes
The idea of the modal expansion in electromagnetics is derived from the research on electromagnetic resonators, which play an essential role in developments in nanophotonics. All of the electromagnetic resonators share a common property:…
Band structure analysis is central to understanding wave propagation in periodic media; however, it becomes challenging in open systems owing to energy leakage. Photonic crystal (PhC) slabs exemplify such systems, featuring periodicity in…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
Wave steepness is a key geometric variable for describing breaking occurrence and its consequences, including energy dissipation and air entrainment. Using three laboratory campaigns under varying spectral conditions and co-flowing wind…
The eigenvalues of matrices representing the structure of large-scale complex networks present a wide range of applications, from the analysis of dynamical processes taking place in the network to spectral techniques aiming to rank the…
Sub-photospheric acoustic resonators allow for the formation of standing p-mode oscillations by reflecting acoustic waves with frequencies below the acoustic cut-off frequency. We employ the Klein-Gordon equation with a piecewise acoustic…
Modes generally provide an economical description of waves, reducing complicated wave functions to finite numbers of mode amplitudes, as in propagating fiber modes and ideal laser beams. But finding a corresponding mode description for…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
We derive two methods for simultaneously controlling the resonance frequency, linewidth and multipolar nature of the resonances of radially symmetric structures. Firstly, we formulate an eigenvalue problem for a global shift in the…
Structured latent attribute models (SLAMs) are a special family of discrete latent variable models widely used in social and biological sciences. This paper considers the problem of learning significant attribute patterns from a SLAM with…
We consider bounded width CNF-formulas where the width is measured by popular graph width measures on graphs associated to CNF-formulas. Such restricted graph classes, in particular those of bounded treewidth, have been extensively studied…
The synthesis of antenna arrays in presence of mutual coupling using generalized scattering matrices in terms of characteristic modes is proposed. For the synthesis, the array is built of synthetic elements that are described by their modal…
Frequency-domain analysis has emerged as a powerful paradigm for time series analysis, offering unique advantages over traditional time-domain approaches while introducing new theoretical and practical challenges. This survey provides a…
Temporal or spatial structures are readily extracted from complex data by modal decompositions like Proper Orthogonal Decomposition (POD) or Dynamic Mode Decomposition (DMD). Subspaces of such decompositions serve as reduced order models…
In many CAD-based applications, complex geometries are defined by a high number of design parameters. This leads to high-dimensional design spaces that are challenging for downstream engineering processes like simulations, optimization, and…
We associate a sequence of variational eigenvalues to any Radon measure on a compact Riemannian manifold. For particular choices of measures, we recover the Laplace, Steklov and other classical eigenvalue problems. In the first part of the…
Shape-constrained optimization arises in a wide range of problems including distributionally robust optimization (DRO) that has surging popularity in recent years. In the DRO literature, these problems are usually solved via reduction into…
This article aims to present a general study of the Helmholtz problem in slowly varying waveguides. This work is of particular interest at locally resonant frequencies, where a phenomenon close to the tunnel effect for Schr\"odinger…
A spatially localized initial condition for an energy-conserving wave equation with periodic coefficients disperses (spatially spreads) and decays in amplitude as time advances. This dispersion is associated with the continuous spectrum of…
We develop a modal method that solves Maxwell's equations in the presence of the linearized hydrodynamic correction. Using this approach, it is now possible to calculate the full diffraction for structures with period of the order of the…