Related papers: Anomalies of the tides
Gravitational waves are minute ripples in spacetime, first predicted by Einstein's general theory of relativity in 1916. Gravitational waves from rapidly-rotating neutron stars, whose shape deviates from perfect axisymmetry, are a potential…
In the first part of this paper (mainly a review) we present general and formal (simple) introductions to the ordinary gaussian waves and to the Bessel waves, by explicitly separating the cases of the beams from the cases of the pulses;…
To study the geometry of Gerstner's water wave model, we analyse the velocity of his fluid particles in a reference frame that moves with the wave. Gerstner wave profiles are cycloidal, curtate (flattened) trochoids, or prolate (extended)…
Just 100 years ago, Nekrasov published the widely cited paper \cite{N1}, in which he derived the first of his two integral equations describing steady periodic waves on the free surface of water. We examine how Nekrasov arrived at these…
There is compelling evidence for subsurface water oceans among the three outer Galilean satellites, and evidence for an internal magma ocean in the innermost moon, Io. Tidal forces from Jupiter periodically deform these bodies, causing…
We present a short communication on the recent direct measurements of gravitational waves, made possible by the joint efforts of the LIGO and the Virgo projects. These notes are devoted to a broad audience. In the first part we will present…
The concept of walking wave is introduced from classical relativistic positions. One- and three-dimensional walking waves considered with their wave equations and dispersion equations. It is shown that wave characteristics (de Broglie's and…
The LIGO results are among the greatest experimental achievements of all times. Time and again scientists have compared this feat to Galileo pointing his telescope to the sky, offering instead an 'ear' to the cosmos. After the remarkable…
This chapter provides an overview of gravitational wave (GW) astronomy, providing background material that underpins the other, more specialized chapters in this handbook. It starts with a brief historical review of the development of GW…
Wave catastrophes are characterized by logarithmic phase singularities. Examples are light at the horizon of a black hole, sound in transsonic fluids, waves in accelerated frames, light in singular dielectrics and slow light close to a zero…
A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…
An unexpected wave is defined by Gemmrich & Garrett (2008) as a wave that is much taller than a set of neighboring waves. Their definition of "unexpected" refers to a wave that is not anticipated by a casual observer. Clearly, unexpected…
This is an overview article of the mathematics of gravitational waves. We explain the mathematics and physics of these waves in general relativity theory, discuss the gravitational wave experiment aLIGO and their detection of gravitational…
We consider Stokes' conjecture concerning the shape of the extremal two-dimensional water wave. By new geometric methods including a nonlinear frequency formula, we prove Stokes' conjecture in the original variables. Our results do not rely…
Using non-excessively-technical language and written in informal style, this article introduces the reader to the concepts of electromagnetic and gravitational waves and recounts the prediction of existence of these waves by Maxwell and…
When light is incident upon a diffraction grating, images of the grating appear at periodic intervals behind the grating. This phenomenon and the associated self-imaging distance were named after Talbot who first observed them in the…
Gravitational-wave astronomy will soon become a new tool for observing the Universe. Detecting and interpreting gravitational waves will require deep theoretical insights into astronomical sources. The past three decades have seen…
This is a review (in Italian) on aperiodic tilings of the plane intended for a general audience. First, we recall some basic results about lattices and periodic tilings. Then, we move on to one-dimensional (domino) tilings and Wang tilings.…
Ocean rogue waves are large and suddenly appearing surface gravity waves, which may cause severe damage to ships and other maritime structures. Despite years of research, the exact origin of rogue waves is still disputed. Linear…
Quantifying tidal effects on giant planets has recently made significant advances, thanks in particular to the Cassini space probe. During its thirteen-year orbit around Saturn, numerous measurements from different instruments made it…