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We perform a statistical analysis of the binary black hole problem in the post-Newtonian approximation by systematically sampling and evolving the parameter space of initial configurations for quasi-circular inspirals. Through a principal…
The null-timelike initial-boundary value problem for a hyperbolic system of equations consists of the evolution of data given on an initial characteristic surface and on a timelike worldtube to produce a solution in the exterior of the…
We are concerned with solvability of the boundary value problem $$-\left[ \phi(u^{\prime}) \right] ^{\prime}=\nabla_u F(t,u), \quad \left ( \phi \left( u^{\prime }\right)(0), -\phi \left( u^{\prime }\right)(T)\right )\in \partial j(u(0),…
In this paper we construct periodic capillarity-gravity water waves with an arbitrary bounded vorticity distribution. This is achieved by reexpressing, in the height function formulation of the water wave problem, the boundary condition…
Future space-borne interferometers will be able to detect gravitational waves at $10^{-3}$ to $10^{-1}$ Hz. At this band extreme-mass-ratio inspirals (EMRIs) can be promising gravitational wave sources. In this paper, we investigate…
In standard treatments of stochastic filtering one first has to estimate the values of the parameters of the model. Simply running the filter without considering the reliability of this estimate does not take into account this additional…
This paper addresses deep-water gravity waves of finite amplitude generated by an initial disturbance to the water. It is assumed that the horizontal dimensions of the initially disturbed body of the water are much larger than the magnitude…
We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient…
We investigate stripe patterns formation far from threshold using a combination of topological, analytic, and numerical methods. We first give a definition of the mathematical structure of `multi-valued' phase functions that are needed for…
In order to solve an initial value problem by the variational iteration method, a sequence of functions is produced which converges to the solution under some suitable conditions. In the nonlinear case, after a few iterations the terms of…
Some basic concepts concerning systems of identical particles are discussed in the framework of a realist interpretation, where the wave function is the quantum object and |psi(r)|^2 d^3r is the probability that the wave function causes an…
Using a matched asymptotic expansion we analyze the two-dimensional, near- critical reflection of a weakly nonlinear, internal gravity wave from a sloping boundary in a uniformly stratified fluid. Taking a distinguished limit in which the…
Combining quantum and Bayesian principles leads to optimality in metrology, but the optimisation equations involved are often hard to solve. This work mitigates this problem with a novel class of measurement strategies for quantities…
We consider the concept of fundamental bias in gravitational wave astrophysics as the assumption that general relativity is the correct theory of gravity during the entire wave-generation and propagation regime. Such an assumption is valid…
We study the equations of motion for a barotropic fluid in spherical symmetric flow. Making use of the Riemann invariants we consider the characteristic form of these equations. In a first part, we show that the resulting constraint…
We propose Bell inequalities for discrete or continuous quantum systems which test the compatibility of quantum physics with an interpretation in terms of deterministic hidden-variable theories. The wave function collapse that occurs in a…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…
In this paper, we study the initial boundary value problem for the nonlinear wave equation with combined power-type nonlinearities with variable coefficients. The global behavior of the solutions with non-positive and sub-critical energy is…
A localised overpressure translating at a uniform speed greater than a critical value acts at the interface between two deep fluid layers with different densities. We analyse the resulting wave patterns using an initial-value problem…
Hamiltonian Boundary Value Methods (in short, HBVMs) is a new class of numerical methods for the efficient numerical solution of canonical Hamiltonian systems. In particular, their main feature is that of exactly preserving, for the…