Related papers: Making Waves
We present a variational wavefunction which explains the behaviour of the supersolid state formed by hard-core bosons on the triangular lattice. The wavefunction is a linear superposition of {\em only and all} configurations minimising the…
The properties of nonlinear PDEs that generate filtered solutions are explored with particular attention given to the constraints on the residual term. The analysis is carried out for nonlinear PDEs with an emphasis on evolution problems…
Support Vector Machines (SVMs) are an important tool for performing classification on scattered data, where one usually has to deal with many data points in high-dimensional spaces. We propose solving SVMs in primal form using feature maps…
In this paper, we introduce the prolate spheroidal wave functions (PSWFs) of real order $\alpha>-1$ on the unit ball in arbitrary dimension, termed as ball PSWFs. They are eigenfunctions of both a weighted concentration integral operator,…
In this paper, we present a semiclassical description of surface waves or modes in an elastic medium near a boundary, in spatial dimension three. The medium is assumed to be essentially stratified near the boundary at some scale comparable…
We study a class of localized solutions of the wave equation, called eigenwavelets, obtained by extending its fundamental solutions to complex spacetime in the sense of hyperfunctions. The imaginary spacetime variables y, which form a…
We introduce a class of probability measure-valued diffusions, coined polynomial, of which the well-known Fleming--Viot process is a particular example. The defining property of finite dimensional polynomial processes considered by Cuchiero…
We establish the exponential decay of the solutions of the damped wave equations in one-dimensional space where the damping coefficient is a nowhere-vanishing function of space. The considered PDE is associated with several dynamic boundary…
A review of light-cone, covariant and gauge-invariant wave-functions of mesons is presented. They are basic non-perturbative objects needed for hard exclusive processes and for the method of light-cone QCD sum rules. The emphasis is on the…
We investigate the generation of standing waves in the model provided by the inhomogeneous telegraph equation under different forcing conditions. We show that sustained standing waves arise only for a specific forcing that is spatially…
In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of phase-plane…
This paper investigates defining equations for secant varieties of the variety of reducible polynomials, which geometrically encode the notions of strength and slice rank of homogeneous polynomials. We present three main results. First, we…
In this work we study oceanic waves in a shallow water flow subject to strong wind forcing and rotation, and linearized around a inhomogeneous (non zonal) stationary profile. This extends the study \cite{CGPS}, where the profile was assumed…
We study linear programming and general LP-type problems in several big data (streaming and distributed) models. We mainly focus on low dimensional problems in which the number of constraints is much larger than the number of variables. Low…
We review various methods for the analysis of initial-value problems for integrable dispersive equations in the weak-dispersion or semiclassical regime. Some methods are sufficiently powerful to rigorously explain the generation of…
We consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The flow is continuously stratified, and the water layer is…
We generalize the pointwise decay estimates for large data solutions of the defocusing semilinear wave equations which we obtained earlier under restriction to spherical symmetry. Without the symmetry the conformal transformation we use…
The article presents an alternative approach to the definition of vector electrodynamic potential and its properties. It is shown that generally it has vortical and potential components. The system of differential equations of generalized…
We analyze the asymptotic behavior of solutions to wave equations with strong damping terms. If the initial data belong to suitable weighted $L^1$ spaces, lower bounds for the difference between the solutions and the leading terms in the…
We consider the coupled electromagnetic waves propagating in a waveguide array, which consists of alternating waveguides of positive and negative refraction indexes. Due to zigzag configuration there are interactions between both nearest…