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Motivated by the uniqueness problem for monostable semi-wavefronts, we propose a revised version of the Diekmann and Kaper theory of a nonlinear convolution equation. Our version of the Diekmann-Kaper theory allows 1) to consider new types…
General Relativity predicts the existence of quadratic quasi-normal modes at second order in perturbation theory. Building on our recent work, we compute the amplitudes and polarizations of these modes for non-rotating black holes, showing…
We investigate the formation of plasma cavities in unmagnetized relativistic pair shocks and demonstrate that these cavities emerge naturally as a nonlinear consequence of asymmetric Weibel instability. We provide an intuitive physical…
In this paper, we construct some non-normal Cayley graphs and explicitly provide their spectra and eigenspaces using representation theory of finite groups.
With a view towards studying the multitemporal wave equation on affine buildings recently introduced by Anker-R\'emy-Trojan [arXiv:2312.06860], we systematically develop the basic properties of the discrete wave equation on $\mathbb{Z}$ and…
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…
Electromagnetic cavity modes in photonic and plasmonic resonators offer rich and attractive regimes for tailoring the properties of light-matter interactions. Yet there is a disturbing lack of a precise definition for what constitutes a…
An effective surface equation, that encapsulates the detail of a microstructure, is developed to model microstructured surfaces. The equations deduced accurately reproduce a key feature of surface wave phenomena, created by periodic…
{We point out some obstacles raised by the lost of symmetry against the extension to the case of an interacting particle of the approach that {\sl deductively} establishes the Quantum Theory of a free particle according to the group…
Finite-element simulations of optical cavities are presented, showing frequency splittings in the resonance spectrum. These results support the theoretical framework and experimental observations presented in van Exter et al. (2022, Phys.…
Using ideas from paracontrolled calculus, we prove local well-posedness of a renormalized version of the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity forced by an additive space-time white noise on a…
The theory of admissible modules over symmetrizable anisotropic Kac-Moody superalgebras, introduced by Kac and Wakimoto in late 80's, is a well-developed subject with many applications, including representation theory of vertex algebras.…
We study multi-parameter solutions of the inhomogeneous paraxial wave equation in a linear and quadratic approximation which include oscillating laser beams in a parabolic waveguide, spiral light beams, and other important families of…
Cavity mode theory and analysis of open cavities and plasmonic particles is an essential component of optical resonator physics, offering considerable insight and efficiency for connecting to classical and quantum optical properties such as…
A tunable optical multistability scheme based on a single cavity mode coupled with two separate atomic transitions in an atom-cavity system is proposed and demonstrated. Under the collective strong coupling condition, multiple polariton…
In previous work, the authors have developed a geometric theory of fundamental strata to study connections on the projective line with irregular singularities of parahoric formal type. In this paper, the moduli space of connections that…
The quasicontinuum (QC) method, originally proposed by Tadmor, Ortiz and Phillips in 1996, is a computational technique that can efficiently handle regular atomistic lattices by combining continuum and atomistic approaches. In the present…
The objective of this paper is to construct geometrically Riemann $k$-wave solutions of the general form of first-order quasilinear hyperbolic systems of partial differential equations. To this end, we adapt and combine elements of two…
Nonlinear optical cavities are crucial both in classical and quantum optics; in particular, nowadays optical parametric oscillators are one of the most versatile and tunable sources of coherent light, as well as the sources of the highest…
We define a formal Gromov-Witten theory of the quintic 3-fold via localization on CP4. Our main result is a direct geometric proof of holomorphic anomaly equations for the formal quintic in precisely the same form as predicted by B-model…