Related papers: A rigorous solution concept for geodesic and geode…
We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…
Generalized solitary waves with exponentially small non-decaying far field oscillations have been studied in a range of singularly-perturbed differential equations, including higher-order Korteweg-de Vries (KdV) equations. Many of these…
The dynamics of metric perturbations is explored in the gravity theory with anomaly-induced quantum corrections. Our first purpose is to derive the equation for gravitational waves in this theory on the general homogeneous and isotropic…
This paper is devoted to the proof of a global existence result for the water waves equation with smooth, small, and decaying at infinity Cauchy data. We obtain moreover an asymptotic description in physical coordinates of the solution,…
There exists a two parameter action, the variation of which produces both the geodesic equation and the geodesic deviation equation. In this paper it is shown that this action can be quantized by the canonical method, resulting in equations…
We propose a general convex optimization problem for computing regularized geodesic distances. We show that under mild conditions on the regularizer the problem is well posed. We propose three different regularizers and provide analytical…
We develop a high order accurate numerical method for solving the elastic wave equation in second-order form. We hybridize the computationally efficient Cartesian grid formulation of finite differences with geometrically flexible…
The geodesic deviation equation (`GDE') provides an elegant tool to investigate the timelike, null and spacelike structure of spacetime geometries. Here we employ the GDE to review these structures within the…
Rogue waves are extreme ocean events characterized by the sudden formation of anomalously large crests, and remain an important subject of investigation in oceanography and mathematics. A central problem is to quantify the probability of…
We consider the problem of optimally stopping a general one-dimensional stochastic differential equation (SDE) with generalised drift over an infinite time horizon. First, we derive a complete characterisation of the solution to this…
Exact solutions of Einstein's vacuum equations are considered which describe gravitational waves with distinct wavefronts. A family of such solutions presented recently in which the wavefronts have various geometries and which propagate…
Geometric quantiles are popular location functionals to build rank-based statistical procedures in multivariate settings. They are obtained through the minimization of a non-smooth convex objective function. As a result, the singularity of…
We present a mathematical approach that simplifies the theoretical treatment of electromagnetic localization in random media and leads to closed form analytical solutions. Starting with the assumption that the dielectric permittivity of the…
In this paper, we prove a convergence theorem for singular perturbations problems for a class of fully nonlinear parabolic partial differential equations with ergodic structures. The limit function is represented as the viscosity solution…
We discuss an approach to gravitational waves based on Geometric Algebra and Gauge Theory Gravity. After a brief introduction to Geometric Algebra (GA), we consider Gauge Theory Gravity, which uses symmetries expressed within the GA of flat…
The Korteweg-de Vries (KdV) equation is known as a universal equation describing various long waves in dispersive systems. In this article, we prove that in a certain scaling regime, a large class of rough solutions to the Boussinesq…
Gravitational waves are investigated in Intrinsic Time Geometrodynamics. This theory has a non-vanishing physical Hamiltonian generating intrinsic time development in our expanding universe, and four-covariance is explicitly broken by…
We report an analytical example of the gravitational wave memory effect in exact plane wave spacetimes. A square pulse profile is chosen which gives rise to a curved wave region sandwiched between two flat Minkowski spacetimes. Working in…
In this paper we investigate the gravitational waves emission by stellar dynamical structures as complex systems in the quadrupole approximation considering bounded and unbounded orbits. Precisely, after deriving analytical expressions for…
We study the wave form emitted by a particle moving along an arbitrary (in general open) geodesic of the Schwarzschild geometry. The mathematical problem can be phrased in terms of quantities in ${\cal N}=2$ supersymmetric gauge theories…