Related papers: Space-time resonances
Two key types of inhomogeneous spatially dispersive media are described, both based on a spatially dispersive generalisation of the single resonance model of permittivity. The boundary conditions for two such media with different properties…
In this work, we prove global well-posedness and scattering for systems of quadratic nonlinear Schr\"odinger equations in the critical three-dimensional case, for small, localized data. For the terms corresponding to the nonlinearity…
This paper is concerned with the traveling wave solutions and asymptotic spreading of delayed lattice differential equations without quasimonotonicity. The spreading speed is obtained by constructing auxiliary equations and using the theory…
Space-time modulation of material parameters offers new possibilities for manipulating elastic wave propagation by exploiting time-reversal symmetry breaking. Here we propose and validate a general framework based on the multiple scattering…
A rotating cosmic string spacetime has a singularity along a timelike curve corresponding to a one-dimensional source of angular momentum. Such spacetimes are not globally hyperbolic: they admit closed timelike curves near the string. This…
Despite the abundance and importance of three-dimensional systems, relatively little progress has been made on spatiotemporal nonlinear optical waves compared to time-only or space-only systems. Here we study radiation emitted by…
Spatially dispersive (also known as non-local) electromagnetic media are considered where the parameters defining the permittivity relation vary periodically. Maxwell's equations give rise to a difference equation corresponding to the…
Energy conversion in a physical system requires time-translation invariance breaking according to Noether's theorem. Closely associated with this symmetry-conservation relation, the frequencies of electromagnetic waves are found to be…
During the last decade, possibilities to realize new phenomena and create new applications by varying system properties in time have gained increasing attention in many research fields, spanning a wide range from acoustics to optics. While…
We present simple classical dynamical models to illustrate the idea of introducing a stochasticity with non-locality into the time variable. For stochasticity in time, these models include noise in the time variable but not in the "space"…
Reciprocal space methods for solving Poisson's equation for finite charge distributions are investigated. Improvements to previous proposals are presented, and their performance is compared in the context of a real-space density functional…
With the advancement of GPS and remote sensing technologies, large amounts of geospatial and spatiotemporal data are being collected from various domains, driving the need for effective and efficient prediction methods. Given spatial data…
This paper presents a pulse compansion, i.e. compression or expansion, technique based on co-propagating space-time modulation. An engineered asymmetric space-time modulated medium, co-propagating with a pulse compands the pulse…
Explicit examples of scalar enhanced diffusion due to resonances between different transport mechanisms are presented. Their signature is provided by the sharp and narrow peaks observed in the effective diffusivity coefficients and, in the…
In this brief paper, we present a simple approach to estimate the variance of measurement noise with time-varying 1-D signals. The proposed approach exploits the relationship between the noise variance and the variance of the prediction…
In this manuscript we prove global existence and linear asymptotic behavior of small solutions to nonlinear wave equations. We assume that the quadratic part of the nonlinearity satisfies a non-resonant condition which is a generalization…
This work presents a generalized physical interpretation of unconventional dispersion asymmetries associated moving elastic solids. By shifting the notion from systems with time-variant material fields to physically traveling materials, the…
For odd anharmonic oscillators, it is well known that complex scaling can be used to determine resonance energy eigenvalues and the corresponding eigenvectors in complex rotated space. We briefly review and discuss various methods for the…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
The 'vertical modes and horizontal rays' method, commonly applied for simulating acoustic wave propagation in shallow water is advanced in this research. Our approach to this method involves the use of the so-called space-time rays, which…