Related papers: Towards a classification of wave catastrophes
Let $X$ be a manifold with boundary, endowed with a metric with conic singularities at the boundary components of $X$. Let $u$ be a solution to the wave equation on $\mathbb{R} \times X$. When a singularity of $u$ strikes a cone point of…
We determine the phase portrait of a Hamiltonian system of equations describing the motion of the particles in linear deep-water waves. The particles experience in each period a forward drift which decreases with greater depth.
The theoretical properties of the black holes (BHs) and of the universe were derived from a unified relativistic theory based on a generalization of local relativity for nonlocal cases in gravitational fields and a quantized standing wave…
The event horizon of black holes and white holes can be achieved in the context of analogue gravity. It was proven for a sonic case that if these two horizons are close to each other their dynamics resemble a laser, a black hole laser,…
Extreme or rogue waves are large and unexpected waves appearing with higher probability than predicted by Gaussian statistics. Although their formation is explained by both linear and nonlinear wave propagation, nonlinearity has been…
We classify all possible singularities in the electronic dispersion of two-dimensional systems that occur when the Fermi surface changes topology, using catastrophe theory. For systems with up to seven control parameters (i.e., pressure,…
Here we examine the quantum-mechanical decay of a Schwarzschild-like black hole, formed by gravitational collapse, into almost-flat space-time and weak radiation at a very late time, in order to evaluate quantum amplitudes (not just…
We present a scenario for fast growth of cosmological perturbations; $\delta(t) \sim a(t)^s$, $a(t)$ being the scale factor, with $s > 10$ for the numerical examples reported in this article. The basic ingredients of the scenario are an…
The amplitude equation for an unstable electrostatic wave is analyzed using an expansion in the mode amplitude $A(t)$. In the limit of weak instability, i.e. $\gamma\to 0^+$ where $\gamma$ is the linear growth rate, the nonlinear…
A variety of solitary waves, such as solitons, vortex rings, solitonic vortices, and more complex entities, have recently been predicted to exist. They can move in superfluid ultracold gases along elongated traps. The theoretical…
We consider a tsunami wave equation with singular coefficients and prove that it has a very weak solution. Moreover, we show the uniqueness results and consistency theorem of the very weak solution with the classical one in some appropriate…
We consider two- and three-dimensional gravity and gravity-capillary solitary water waves in infinite depth. Assuming algebraic decay rates for the free surface and velocity potential, we show that the velocity potential necessarily behaves…
I formalize the ontology of apocalyptic events as synchronized morphogenetic manifolds within the framework of Thom's catastrophe theory. Local catastrophes (folds, cusps, umbilici) are extended to higher-order systemic collapses through…
Assuming that general relativity is the correct theory of gravity in the strong field limit, can gravitational wave observations distinguish between black hole and other compact object sources? Alternatively, can gravitational wave…
A precise electromagnetic measurement of the sky coordinates and redshift of a coalescing black hole binary holds the key for using its gravitational wave (GW) signal to constrain cosmological parameters and to test general relativity. Here…
The event horizon of a black hole in general relativity absorbs all infalling radiation. Any observation of the contrary would immediately challenge the expectation that astrophysical black holes are described by the vacuum Kerr geometry.…
Bulk motion Comptonization utilizes properties of both matter and radiation close to the horizon of a black hole. Computation with these considerations produce hard tails of energy spectral slope $\sim 1.5-1.7$. These are the most direct…
A detailed description of how black holes grow in full, non-linear general relativity is presented. The starting point is the notion of dynamical horizons. Expressions of fluxes of energy and angular momentum carried by gravitational waves…
We analyze the scattering of a planar monochromatic electromagnetic wave incident upon a Schwarzschild black hole. We obtain accurate numerical results from the partial wave method for the electromagnetic scattering cross section, and show…
A summary of how black holes grow in full, non-linear general relativity is presented. Specifically, a notion of "dynamical horizons" is introduced and expressions of fluxes of energy and angular momentum carried by gravitational waves…