相关论文: Self-force and radial fall: new integration method…

We establish the existence of gravity water waves by applying a mountain pass theorem to a singular perturbation of the Alt-Caffarelli functional associated with the two-dimensional water wave equations. Our approach is formulated entirely…

I present an overview of the methods involved in the computation of the scalar, electromagnetic, and gravitational self-forces acting on a point particle moving in a curved spacetime. For simplicity, the focus here will be on the scalar…

We present a practical method for calculating the gravitational self-force, as well as the electromagnetic and scalar self forces, for a particle in a generic orbit around a Kerr black hole. In particular, we provide the values of all the…

We consider the semilinear wave equation with a power nonlinearity in the radial case. Given $r_0>0$, we construct a blow-up solution such that the solution near $(r_0,T(r_0))$ converges exponentially to a soliton. Moreover, we show that…

We derive an expression for the second-order gravitational self-force that acts on a self-gravitating compact-object moving in a curved background spacetime. First we develop a new method of derivation and apply it to the derivation of the…

The electromagnetic force on a polarizable particle is calculated in a covariant framework. Local equilibrium temperatures for the electromagnetic field and the particle's dipole moment are assumed, using a relativistic formulation of the…

A partially first-order form of the characteristic formulation is introduced to control the accuracy in the computation of gravitational waveforms produced by highly distorted single black hole spacetimes. Our approach is to reduce the…

We present a new approach for boundary integral equations for the wave equation with zero initial conditions. Unlike previous attempts, our mathematical formulation allows us to prove that the associated boundary integral operators are…

In a recent work, we provided a standardized and exact analytical formalism for computing in the semiclassical regime the radiation force experienced by a two-level atom interacting with any number of plane waves with arbitrary intensities,…

We propose a self-adaptive absorbing technique for quasilinear ultrasound waves in two- and three-dimensional computational domains. As a model for the nonlinear ultrasound propagation in thermoviscous fluids, we employ Westervelt's wave…

Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of…

If we want to deform a compact Riemannian manifold with boundary using Ricci flow, we first need to decide on appropriate boundary conditions. We would like these conditions to reflect the geometric nature of the flow and allow for a…

An embedding method for solving the time-dependent Schr\"odinger equation is developed using the Dirac-Frenkel variational principle. Embedding allows the time-evolution of the wavefunction to be calculated explicitly in a limited region of…

We show that gravitational waves can act as waveguides for electromagnetic radiation, that is if the latter is initially aligned with the gravitational waves, then the alignment will survive during the propagation. The analysis is performed…

The wavefunction of a particle is obtained from its intermediate states and interaction processes considered as happening concurrently. When the interaction is described by a potential, the energy of the particle is equal to its total…

We present a characteristic initial value approach to calculating the Green function of the Regge-Wheeler and Zerilli equations. We combine well-known numerical methods with newly derived initial data to obtain a scheme which can in…

In this study, singular diffusion operator with jump conditions is considered. Integral representations have been derived for solutions that satisfy boundary conditions and jump conditions. Some properties of eigenvalues and eigenfunctions…

We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the…

We consider Waveform Relaxation (WR) methods for partitioned time-integration of surface-coupled multiphysics problems. WR allows independent time-discretizations on independent and adaptive time-grids, while maintaining high…

The gravitational waves emitted by binary systems with extreme mass ratios carry unique astrophysical information expected to be probed by the next generation of gravitational wave detectors such as LISA. The detection of these binaries…