Linear Wave Equations
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Related Articles from SNS
3d Summation-by-Parts scheme for Linear Wave Equations on Hyperboloidal Slices
arXiv:2606.02051v1 Announce Type: cross Abstract: We derive a fully 3-dimensional Summation-By-Parts scheme for a class of linear wave equations on hyperboloidal slices that meet future null infinity on a Minkowski background. The scheme is derived in spherical polar coordinates, with a major strength being that it is provably stable and allows having grid points at the origin and on the $z$-axis, despite coordinate singularities, and at infinity, by introducing compactification followed by...
A high-order regularization of the non-linear shallow water equations with weakly singular shock waves and its approximation by finite volume methods
arXiv:2606.01200v1 Announce Type: cross Abstract: Considered herein is a high-order regularization of the nonlinear shallow water equations within the framework of water wave theory. The regularized system is Galilean invariant and its solutions maintain an energy level that closely matches that of the nonlinear shallow water equations.
Second-order bulk-surface splitting for the wave equation with kinetic boundary conditions
Announce Type: new Abstract: This paper is devoted to the numerical analysis of a second-order bulk--surface splitting scheme for the semi-linear wave equation with kinetic boundary conditions. The construction is based on the interpretation of the equations as coupled system and the implementation of different difference formulae for the discrete states depending on their exact position in the system equations. This results in a 4-step scheme which decouples bulk and surface dynamics.
A space-time sparse-grid method for the wave equation
arXiv:2606.09688v1 Announce Type: new Abstract: We develop a fast space-time numerical scheme for approximating solutions to the linear wave equation. The approach is based on the sparse-grid combination technique applied to a coercive space-time discretization. Designed for tensor-product space-time discretizations, the method enables efficient parallelization of the resulting solver.
Estimating Evolving Functions with Dynamic Gaussian Processes
arXiv:2606.06705v1 Announce Type: new Abstract: This paper develops the Dynamic Gaussian Process (DGP), a framework for estimating functions governed by integro-difference equations (IDEs). IDEs model continuous functions that evolve with discrete-time dynamics and arise naturally from time-discretization of linear partial differential equations (PDEs).
Evaluating Operators for Acoustic Wave Simulation Correction
arXiv:2606.08711v1 Announce Type: new Abstract: Correcting numerical dispersion artifacts from Finite Difference solvers is a well-identified challenge in computational wave physics, but existing approaches evaluate only a restricted family of CNN-based architectures and have been applied exclusively to the elastic wave equation. We instantiate the Deep Finite Difference framework on two-dimensional anisotropic acoustic wave propagation, pairing a fourth-order Finite Difference proxy with a...
Retarded Correlators of Charge Transport in a Magnetic Field
arXiv:2606.08139v1 Announce Type: cross Abstract: We study charge transport in a magnetized relativistic plasma using kinetic theory within the relaxation-time approximation. By exactly solving the linearized Boltzmann equation in a uniform magnetic field, we obtain an analytic solution for the distribution function in terms of Bessel functions. Using this solution, we compute the full set of retarded current-current correlators and verify the Ward identities.
On the instability of some upward propagating, exact, nonlinear mountain waves
Announce Type: replace Abstract: Using the short-wavelength instability method, we investigate the linear instability of an exact solution describing upward-propagating mountain waves, derived in A. Constantin, \emph{J. Phys. Theor.} (2023), under the assumption of a dry adiabatic flow. Within this approach, the stability problem reduces to analysing a system of ordinary differential equations along fluid trajectories.
Light-induced quantum friction of carbon nanotubes in water
Abstract Friction slows down moving objects at both macroscopic and microscopic scales1. At the electronic level, quantum friction describes direct transfer of momentum between a liquid and the electrons of a solid2. Owing to its microscopic nature, this phenomenon remains experimentally challenging to capture3.
Radial evolution of Alfv\'en wave Parametric Decay Instability in the near-Sun solar wind: Effects of Temperature Anisotropy
arXiv:2604.22489v3 Announce Type: replace-cross Abstract: Parametric decay instability (PDI) of Alfv\'en wave is thought to play an important role in the dissipation of the large-amplitude Alfv\'en waves and in the heating of magnetized plasmas. Temperature anisotropy is frequently observed by spacecraft, including Parker Solar Probe (PSP), in the near-Sun solar wind, yet its impact on PDI in the near-Sun solar wind has been understudied. We calculate the maximum growth rates of PDI,...