Related papers: Discrete resonant Rossby/drift wave triads: an exp…
Observations by recent space missions reported the detection of Rossby waves (r-modes) in light curves of many stars (mostly A, B, and F spectral types) with outer radiative envelope. This paper aims to study the theoretical dynamics of…
We consider the long-term dynamics of nonlinear dispersive waves in a finite periodic domain. The purpose of the work is to show that the statistical properties of the wave field rely critically on the structure of the discrete resonant…
We formalise the concept of near resonance for the rotating Navier-Stokes equations, based on which we propose a novel way to approximate the original PDE. The spatial domain is a three-dimensional flat torus of arbitrary aspect ratios. We…
We consider a diatomic chain characterized by a cubic anharmonic potential. After diagonalizing the harmonic case, we study in the new canonical variables, the nonlinear interactions between the acoustical and optical branches of the…
In this paper, we consider the resonance problem for the cubic nonlinear Helmholtz equation in the subwavelength regime. We derive a discrete model for approximating the subwavelength resonances of finite systems of high-contrast resonators…
We establish a well-posedness and error-estimation framework that solves Hamilton-Jacobi equations by minimizing the least-squares residual of monotone finite-difference discretizations. This approach also applies naturally to second-order…
Let $0<\alpha<1$. We obtain the boundedness of the discrete fractional Hardy-Littlewood maximal operators ${\mathcal M}_\alpha$ on discrete weighted Lebesgue spaces. From this and a discrete version of Whitney decomposition theorem, we…
We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. We introduce a new abstract framework to analyze the convergence of domain truncations and discretizations.…
Accurate and fast calculations of localized surface plasmon resonances (LSPR) in metallic nanoparticles is essential for applications in sensing, nano-optics, and energy harvesting. Although full-wave numerical techniques such as the…
In storage rings, an accurate description of particle dynamics near third-integer resonance is crucial for various applications. The conventional approach is to extrapolate far-resonance dynamics to near-resonance, but difficulty arises…
A unidirectional reduction of the deep-water surface gravity wave problem is derived in physical space using real variables. By employing a near-identity canonical transformation, cubic interactions are eliminated from the Hamiltonian, with…
We describe an accelerated direct solver for the integral equations which model acoustic scattering from curved surfaces. Surfaces are specified via a collection of smooth parameterizations given on triangles, a setting which generalizes…
Triadic resonance is one mechanism via which internal waves dissipate their energy, often at locations away from their generation sites. In this paper, we perform a combined theoretical and numerical study of triadic resonance in internal…
In this work we consider the problem of identification and reconstruction of doubly-dispersive channel operators which are given by finite linear combinations of time-frequency shifts. Such operators arise as time-varying linear systems for…
In this paper, we focus on the finite difference approximation of nonlinear degenerate parabolic equations, a special class of parabolic equations where the viscous term vanishes in certain regions. This vanishing gives rise to additional…
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…
Adaptive mesh refinement efficiently facilitates the computation of gravitational waveforms in numerical relativity. However, determining precisely when, where, and to what extent to refine when solving the Einstein equations poses…
In this work, following the Discrete de Rham (DDR) paradigm, we develop an arbitrary-order discrete divdiv complex on general polyhedral meshes. The construction rests 1) on discrete spaces that are spanned by vectors of polynomials whose…
Fast radio bursts (FRBs) provide a sensitive probe of ionized baryons through their dispersion measure (DM). In addition to slowly evolving cosmological terms, at least two repeaters now show clear secular DM-decrease episodes:…
Three fundamental variational principles used for solving elastodynamic eigenvalue problems are studied within the context of elastic wave propagation in periodic composites (phononics). We study the convergence of the eigenvalue problems…