相关论文: Anomalies of the tides
In 1680 Cassini proposed oval curves as alternative trajectories for the visible planets around the sun. The Cassini ovals were of course overshadow by the Kepler's first law (1609), namely the planets move around the sun describing conic…
In this essay we give an overview on the problem of rogue or freak wave formation in the ocean. The matter of the phenomenon is a sporadic occurrence of unexpectedly high waves on the sea surface. These waves cause serious danger for…
In this paper, we study the (normalized) Ricci flow on surfaces with conical singularities. Long time existence is proved for cone angle smaller than $2\pi$. In this case, convergence results are obtained if the Euler number is nonpositive.
Work published in Sky and Telescope in 2004 discusses Galileo's observations of the star Mizar. These observations raise questions regarding Galileo's assumptions about the universe and the conclusions he drew from his observations. Galileo…
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…
This paper is a continuation of a series of works, devoted to various aspects of the 1908 Tunguska event. In the late June - early July, 1908 there were various optical anomalies in the atmosphere. Early the Author already considered…
The classical theory of modulation instability (MI) attributed to Bespalov-Talanov in optics and Benjamin-Feir for water waves is just a linear approximation of nonlinear effects and has limitations that have been corrected using the exact…
This article presents a comprehensive analysis of the physics of gravitational waves, exploring both the theoretical foundations and the most recent experimental advances. After a general introduction to the theory of general relativity and…
Following theoretical and experimental work of Maas et al we consider a linearized model for internal waves in effectively two dimensional aquaria. We provide a precise description of singular profiles appearing in long time wave evolution…
Sunspots have been known in the West since Galileo Galilei and Thomas Harriot first used telescopes to observe the Sun nearly four centuries ago; they have been known to the Chinese for more than two thousand years. They appear as…
This article provides a survey on some main results and recent developments in the mathematical theory of water waves. More precisely, we briefly discuss the mathematical modeling of water waves and then we give an overview of local and…
A 1934 paper by Leray posed the question of the regularity of solutions of the dynamical equations for incompressible inviscid fluids with smooth initial data. Since there has been many attempts to answer this question. Leray examined the…
The first decade of the new millenium should see the first direct detections of gravitational waves. This will be a milestone for fundamental physics and it will open the new observational science of gravitational wave astronomy. But…
In this paper, we analyze various types of critical phenomena in one-dimensional gas flows described by Euler equations. We give a geometrical interpretation of thermodynamics with a special emphasis on phase transitions. We use ideas from…
This document is an announcement and preview of a memoir whose full version is available on the Open Math Notes repository of the American Mathematical Society (OMN:202109.111309). In this memoir, I try to provide a fairly comprehensive…
This paper studies the classical water wave problem with vorticity described by the Euler equations with a free surface under the influence of gravity over a flat bottom. Based on fundamental work \cite{ConstantinStrauss}, we first obtain…
An axiomatic theory of classical nondissipative waves is proposed that is constructed based on the definition of a wave as a multidimensional oscillator. Waves are represented as abstract vectors $|\psi\rangle$ in the appropriately defined…
Encyclopedic article covering shallow water wave models used in oceanography and atmospheric science. Sections: Definition of the Subject; Introduction and Historical Perspective; Completely Integrable Shallow Water Wave Equations; Shallow…
We establish several quantitative results about singular Ricci flows, including estimates on the curvature and volume, and the set of singular times.
An approach to special relativity is outlined which emphasizes the wave and field mechanisms which physically produce the relativistic effects, with the goal of making them seem more natural to students by connecting more explicitly with…