Related papers: Numerical evolution of Brill waves
The real number system is geometrically extended to include three new anticommuting square roots of plus one, each such root representing the direction of a unit vector along the orthonormal coordinate axes of Euclidean 3-space. The…
We consider optimal control of the scalar wave equation where the control enters as a coefficient in the principal part. Adding a total variation penalty allows showing existence of optimal controls, which requires continuity results for…
The subject of this paper is multigrid solvers for Helmholtz operators with large wave numbers. Algorithms presented here are variations of the wave-ray solver which is modified to allow efficient solutions for operators with constant,…
Numerical solutions to hyperbolic partial differential equations, involving wave propagations in one direction, are subject to several specific errors, such as numerical dispersion, dissipation or aliasing. In multi-dimensions, where the…
We present the first results in a new program intended to make the best use of all available technologies to provide an effective understanding of waves from inspiralling black hole binaries in time for imminent observations. In particular,…
The analysis of wave propagation problems in linear damped media must take into account both propagation features and attenuation process. To perform accurate numerical investigations by the finite differences or finite element method, one…
Properties of the geometric phase for a nonstatic coherent light-wave arisen in a static environment are analyzed from various angles. The geometric phase varies in a regular nonlinear way, where the center of its variation increases…
Given the absence of observations of black hole binaries, it is critical that the full range of accessible parameter space be explored in anticipation of future observation with gravitational wave detectors. To this end, we compile the…
An implicit, fully characteristic, numerical scheme for solving the field equations of a cosmic string coupled to gravity is described. The inclusion of null infinity as part of the numerical grid allows us to apply suitable boundary…
We present a study of the gravitational waveforms from a series of spinning, equal-mass black hole binaries focusing on the harmonic content of the waves and the contribution of the individual harmonics to the signal-to-noise ratio. The…
We subject the stationary solutions of inviscid and axially symmetric rotational accretion to a time-dependent radial perturbation, which includes nonlinearity to any arbitrary order. Regardless of the order of nonlinearity, the equation of…
The stationary background flow in the spherically symmetric infall of a compressible fluid, coupled to the space-time defined by the static Schwarzschild metric, has been subjected to linearized perturbations. The perturbative procedure is…
Traveling waves are ubiquitous in nature and control the speed of many important dynamical processes, including chemical reactions, epidemic outbreaks, and biological evolution. Despite their fundamental role in complex systems, traveling…
In this text, we prove the existence of an asymptotic growth rate of the number of dominating sets (and variants) on finite rectangular grids, when the dimensions of the grid grow to infinity. Moreover, we provide, for each of the variants,…
The numerical integration of the Schr\"odinger equation by discretization of time is explored for the curved manifolds arising from finite representations based on evolving basis states. In particular, the unitarity of the evolution is…
Recent developments in string theory have brought forth a considerable interest in time-dependent hair on extended objects. This novel new hair is typically characterized by a wave profile along the horizon and angular momentum quantum…
A code to evolve boson stars in 3D is presented as the starting point for the evolution of scalar field systems with arbitrary symmetries. It was possible to reproduce the known results related to perturbations discovered with 1D numerical…
We consider some of the methods that can be used to reveal the general features of how wave functions evolve with time in the harmonic oscillator. We first review the periodicity properties over each multiple of a quarter of the classical…
We present new results from two open source codes, using finite differencing and pseudo-spectral methods for the wave equations in (3+1) dimensions. We use a hyperboloidal transformation which allows direct access to null infinity and…
In physics, timbre is a complex phenomenon, like color. Musical timbres are given by the superposition of sinusoidal signals, corresponding to longitudinal acoustic waves. Colors are produced by the superposition of transverse…