arXiv research

Study proves interaction of three impulsive gravitational waves, showing local solution and Lipschitz continuity.

Study axisymmetric waves on extremal Kerr spacetime using physical-space estimates.

Study proves well-posedness and scattering for wave equations on hyperbolic spaces with singular data.

Second paper in series solves Einstein vacuum equations for three impulsive waves.

Simulation-based inference speeds up gravitational wave data analysis.

Geometric focusing affects dispersive estimates for Schrödinger and wave equations.

The paper establishes scattering theory for wave equations on Schwarzschild spacetime.

Study dispersive estimates for Schrödinger and wave equations on a cone with specific metric.

Study examines wave equation decay and Strichartz estimates on conic manifolds.

We consider the problem of recovering material parameters in a transversely isotropic medium from the qP and qSV waves' travel times, given the axis of isotropy and the material parameters associated to the qSH wave speed. The operators obtained from the pseudolinearization argument are of parabolic type, and so we dis…

Paper proves stability of multi-dimensional rarefaction waves in gas dynamics.

This paper addresses parameter estimation for wave equations with Markovian switching.

New method finds precise late-time behavior of wave equations.

In a previous paper on coupled gravitational and electromagnetic perturbations of Reissner-Nordström spacetime in a polarized setting, we derived a system of wave equations for two independent quantities, one related to the Weyl curvature and one related to the Ricci curvature of the perturbed spacetime. We analyze her…

New method predicts wave height exceedance probabilities.

Novel approach to wave equations near null infinity in flat spacetimes.

Deep learning helps remove secondary $B$-mode polarization to detect primordial gravitational waves.

WAVE improves stability in reinforcement learning by adaptively weighting critic's loss.

Proves energy estimates for tensorial wave equations, decoupling components for stability proof.

Neural networks improve gravitational-wave parameter estimation.

We study the following problem: Given initial data on a compact Cauchy horizon, does there exist a unique solution to wave equations on the globally hyperbolic region? Our main results apply to any spacetime satisfying the null energy condition and containing a compact Cauchy horizon with surface gravity that can be no…

In this paper, we investigate the problem of blow up and sharp upper bound estimates of the lifespan for the solutions to the semilinear wave equations, posed on asymptotically Euclidean manifolds. Here the metric is assumed to be exponential perturbation of the spherical symmetric, long range asymptotically Euclidean …

Study proves global existence and decay for complex wave equations.

A nonlinear wave alternative for the standard Black-Scholes option-pricing model is presented. The adaptive-wave model, representing 'controlled Brownian behavior' of financial markets, is formally defined by adaptive nonlinear Schrödinger (NLS) equations, defining the option-pricing wave function in terms of the stock…

Estimates classical potential from stock price data using quantum mechanics.

New criterion for wave operators on Kato-Ricci manifolds.

New approach simplifies proof of wave equations on black holes.

The commuting vector fields approach, devised for strichartz estimates in [13], was developed for proving the local well-posedness in the Sobolev spaces $H^s$ with $s>2+\frac{2-\sqrt{3}}{2}$ for general quasi-linear wave equation in ${\mathbb R}^{1+3}$ by Klainerman and Rodnianski. Via this approach they obtained the l…

In recent work, we have proven uniform decay bounds for solutions of the wave equation $\Box_gφ=0$ on a Schwarzschild exterior, in particular, the uniform pointwise estimate $|φ|\le Cv_+^{-1}$, which holds throughout the domain of outer communications, where $v$ is an advanced Eddington-Finkelstein coordinate, $v_+=\ma…

The Einstein equations in wave map gauge are a geometric second order system for a Lorentzian metric. To study existence of solutions of this hyperbolic quasi diagonal system with initial data on a characteristic cone which are not zero in a neighbourhood of the vertex one can appeal to theorems due to Cagnac and Dossa…

Deep learning speeds up gravitational wave analysis.

We explore a model of dark matter called wave dark matter (also known as scalar field dark matter and boson stars) which has recently been motivated by a new geometric perspective by Bray. Wave dark matter describes dark matter as a scalar field which satisfies the Einstein-Klein-Gordon equations. These equations rely …

The mixture of Gaussian distributions, a soft version of k-means , is considered a state-of-the-art clustering algorithm. It is widely used in computer vision for selecting classes, e.g., color, texture, and shapes. In this algorithm, each class is described by a Gaussian distribution, defined by its mean and covarianc…

With millimeter wave wireless communications, the resulting radiation reflects on most visible objects, creating rich multipath environments, namely in urban scenarios. The radiation captured by a listening device is thus shaped by the obstacles encountered, which carry latent information regarding their relative posit…

Kolmogorov-Arnold network improves GW catalog posterior construction.

We prove a dynamical wave trace formula for asymptotically hyperbolic (n+1) dimensional manifolds with negative (but not necessarily constant) sectional curvatures which equates the renormalized wave trace to the lengths of closed geodesics. A corollary of this dynamical trace formula is a dynamical resonance-wave trac…

Gravitational-wave data analysis is rapidly absorbing techniques from deep learning, with a focus on convolutional networks and related methods that treat noisy time series as images. We pursue an alternative approach, in which waveforms are first represented as weighted sums over reduced bases (reduced-order modeling)…

Full Wave Inversion (FWI) imaging scheme has many applications in engineering, geoscience and medical sciences. In this paper, a surrogate deep learning FWI approach is presented to quantify properties of materials using stress waves. Such inverse problems, in general, are ill-posed and nonconvex, especially in cases w…

We study the Cauchy problem for the wave equation on extreme Kerr backgrounds under axisymmetry. Specifically, we consider regular axisymmetric initial data prescribed on a Cauchy hypersurface S which connects the future event horizon with spacelike or null infinity, and we solve the linear wave equation on the domain …

Study shows how electromagnetic and gravitational waves can form trapped surfaces.

The complex wave representation (CWR) converts unsigned 2D distance transforms into their corresponding wave functions. Here, the distance transform S(X) appears as the phase of the wave function φ(X)---specifically, φ(X)=exp(iS(X)/τwhere τis a free parameter. In this work, we prove a novel result using the higher-orde…

New Galilean spacetimes found as pp-wave reductions.

Estimates high-dimensional posterior densities by marginal distributions and neural networks.

Global existence and decay for quasilinear wave equations on various spacetimes, including Kerr black holes.

Analyzes Gerstner's trochoidal waves and their geometric properties.

Wave fronts on certain surfaces become dense.

Analyzes properties of stiffness tensors for elastic wave imaging.

New method for efficient inference over complex parameter spaces.