相关论文: A Parametrix Construction for the Wave Equation wi…
The structure function is a useful quantity to characterize wavefront distortions. We derive expressions for the structure functions of the averaged wavefront phase and slopes. The expressions are valid within the inertial range of…
Many problems in areas such as compressive sensing and coding theory seek to design a set of equal-norm vectors with large angular separation. This idea is essentially equivalent to constructing a frame with low coherence. The elements of…
We present a lightweight, flexible, and high-performance framework for inferring the properties of gravitational-wave events. By combining likelihood heterodyning, automatically-differentiable and accelerator-compatible waveforms, and…
In analogy to a characterisation of operator matrices generating $C_0$-semigroups due to R. Nagel (\cite{[Na89]}), we give conditions on its entries in order that a $2\times 2$ operator matrix generates a cosine operator function. We apply…
We consider the parametric excitation of a Langmuir wave and an electromagnetic wave by gravitational radiation, in a thin plasma on a Minkowski background. We calculate the coupling coefficients starting from a kinetic description, and the…
Folding uncertainty in theoretical models into Bayesian parameter estimation is necessary in order to make reliable inferences. A general means of achieving this is by marginalizing over model uncertainty using a prior distribution…
A parabolic equation for the propagation of periodic internal waves over varying bottom topography is derived using the multiple-scale perturbation method. Some computational aspects of the numerical implementation are discussed. The…
Laguerre-Gauss (LG) modes represent an orthonormal basis set of solutions of the paraxial wave equation. LG are characterized by two integer parameters $n$ and $\ell$ that are related to the radial and azimuthal profile of the beam. The…
We establish a decoupling result for the $P$ and $S$ waves of linear, isotropic elasticity, in the setting of twice-differentiable Lam\'e parameters. Precisely, we show that the $P\leftrightarrow S$ components of the wave propagation…
Detection of gravitational waves(GW) involves using the network of GW telescopes to observe a large sky region. However, owing to the arrangement of the GW telescopes, even with aLIGO- aVirgo-KAGRA network,parameter estimation accuracy…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
One may associate several frames to a given polytope, such as its collection of vertices, edges, or facet normal vectors. In this note, we use these frames to generate geometric inequalities for the simplex in $\mathbb{R}^d$ and polytopes…
We investigate the potential and limitations of the wave generation by disturbances moving at the bottom. More precisely, we assume that the wavemaker is composed of an underwater object of a given shape which can be displaced according to…
In a recent work the first named author, Levitin and Vassiliev have constructed the wave propagator on a closed Riemannian manifold $M$ as a single oscillatory integral global both in space and in time with a distinguished complex-valued…
A global weak solution of the biharmonic wave map equation in the energy space for spherical targets is constructed. The equation is reformulated as a conservation law and solved by a suitable Ginzburg-Landau type approximation.
In this paper, we investigate the stability of the linear wave equation where one part of the boundary, which is seen as a lower-dimensional Riemannian manifold, is governed by a coupled wave equation, while the other part is subject to a…
We consider the wave equation with uncertain initial data and medium, when the wavelength $\varepsilon$ of the solution is short compared to the distance traveled by the wave. We are interested in the statistics for quantities of interest…
In the present study, the authors introduce a geometrically improved model inspired by the mammalian basilar membrane's properties and special vibratory behavior while conducting a parametric investigation. The goal of this model is to…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
We discuss a geometrical method to define a preferred reference frame for precessing binary systems and the gravitational waves they emit. This minimal-rotation frame is aligned with the angular-momentum axis and fixes the rotation about…