3 citations · 13 across the 19 of their papers we have counts for
24 papers
The scattering matrix for the p-form Laplacian on asymptotically conic manifolds
Nelia Charalambous, Alden Waters
The Hodge decomposition at infinity gives rise to distinct tangential scattering channels for differential forms on asymptotically conic manifolds. We construct co-closed generaliz…
A Pöschl--Teller approximation to the wave equation outside a torus
Ronald Quirchmayr, Alden Waters
We prove dispersive estimates for an approximation to the wave equation in the exterior of a torus. Because no separation of variables into a basis of eigenfunctions and eigenvalue…
Dispersive Estimates for Maxwell's Equations in the Exterior of a Sphere
Alden Waters, Yan-Long Fang
The goal of this article is to establish general principles for high frequency dispersive estimates for Maxwell's equation in the exterior of a perfectly conducting ball. We constr…
Approximation of the non-linear water hammer problem by a Lax-Wendroff finite difference scheme
Hugo Carrillo-Lincopi, Alden Waters, Teke Xu
We study the water hammer problem in the case of a sudden closing of a valve upstream, and we consider a Lax-Wendroff finite difference scheme in order to obtain a numerical soluti…
The relative trace formula in electromagnetic scattering and boundary layer operators
Alexander Strohmaier, Alden Waters
This paper establishes trace-formulae for a class of operators defined in terms of the functional calculus for the Laplace operator on divergence-free vector fields with relative a…
The Birman-Krein formula for differential forms and electromagnetic scattering
Alexander Strohmaier, Alden Waters
We consider scattering theory of the Laplace Beltrami operator on differential forms on a Riemannian manifold that is Euclidean near infinity. Allowing for compact boundaries of lo…
Observability for Schrödinger equations with quadratic Hamiltonians
Alden Waters
We consider time dependent harmonic oscillators and construct a parametrix to the corresponding Schrödinger equation using Gaussian wavepackets. This parametrix of Gaussian wavepac…
Analytic properties of heat equation solutions and reachable sets
Alexander Strohmaier, Alden Waters
There recently has been some interest in the space of functions on an interval satisfying the heat equation for positive time in the interior of this interval. Such functions were…
A relative trace formula for obstacle scattering
Florian Hanisch, Alexander Strohmaier, Alden Waters
We consider the case of scattering of several obstacles in for . In this setting the absolutely continuous part of the Laplace operator with Dirichlet…
Geometric and Obstacle Scattering at Low Energy
Alexander Strohmaier, Alden Waters
We consider scattering theory of the Laplace Beltrami operator on differential forms on a Riemannian manifold that is Euclidean at infinity. The manifold may have several boundary…
Rank optimality for the Burer-Monteiro factorization
Irène Waldspurger, Alden Waters
When solving large scale semidefinite programs that admit a low-rank solution, an efficient heuristic is the Burer-Monteiro factorization: instead of optimizing over the full matri…
Asymptotics for optimal design problems for the Schrödinger equation with a potential
Alden Waters, Ekaterina Merkurjev
We study the problem of optimal observability and prove time asymptotic observability estimates for the Schrödinger equation with a potential in , with $Ω\subset \ma…
Unique Determination of Sound Speeds for Coupled Systems of Semi-linear Wave Equations
Alden Waters
We consider coupled systems of semi-linear wave equations with different sound speeds on a finite time interval and a bounded Lipschitz domain in , with b…
Low Regularity Ray Tracing for Wave Equations with Gaussian beams
Alden Waters
We prove observability estimates for oscillatory Cauchy data modulo a small kernel for -dimensional wave equations with space and time dependent and coefficients…
Recovery of the sound speed for the Acoustic wave equation from phaseless measurements
Joonas Ilmavirta, Alden Waters
We recover the higher order terms for the acoustic wave equation from measurements of the modulus of the solution. The recovery of these coefficients is reduced to a question of st…
Lower resolvent bounds and Lyapunov exponents
Semyon Dyatlov, Alden Waters
We prove a new polynomial lower bound on the scattering resolvent. For that, we construct a quasimode localized on a trajectory which is trapped in the past, but not in the fut…
Stability Analysis in Magnetic Resonance Elastography II
Heiko Gimperlein, Alden Waters
We consider the inverse problem of finding unknown elastic parameters from internal measurements of displacement fields for tissues. In the sequel to Ammari, Waters, Zhang (2015),…
A deterministic optimal design problem for the heat equation
Heiko Gimperlein, Alden Waters
For the heat equation on a bounded subdomain of , we investigate the optimal shape and location of the observation domain in observability inequalites. A new deco…
Stability Analysis for Magnetic Resonance Elastography
Habib Ammari, Alden Waters, Hai Zhang
We consider the inverse problem of finding unknown elastic parameters from internal measurements of displacement fields for tissues. The measurements are made on the entirety of a…
Stability estimate and the Aharonov-Bohm effect for the Klein-Gordon equation with time-dependent vector potentials
Ricardo Salazar, Alden Waters
We consider the relativistic Schrödinger (Gordon-Klein) equation with a time dependent vector and a scalar potential on a bounded cylindrical domain. Using a standard Geometric Opt…
Stability for Time Dependent X-ray Transforms and Applications
Alden Waters
We prove a logarithmic stability estimate for the time dependent X-ray transform on . To do so, we extend a known result by Begmatov for the stabi…
Stable determination of X-ray transforms of time dependent potentials from the dynamical Dirichlet-to-Neumann map
Alden Waters
We consider compact smooth Riemmanian manifolds with boundary of dimension greater than or equal to two. For the initial-boundary value problem for the wave equation with a lower o…
Spectral Rigidity for Periodic Schrödinger Operators in Dimension 2
Alden Waters
We consider two dimensional real-valued analytic potentials for the Schrödinger equation which are periodic over a lattice . Under certain assumptions on the form of the potenti…
A Parametrix Construction for the Wave Equation with Low Regularity Coefficients Using a Frame of Gaussians
Alden Waters
We construct a frame of complex Gaussians for the space of functions. When propagated along bicharacteristics for the wave equation, the frame can be used to bu…