Sentences with phrase «wave equations used»

Kadri says the typical water wave equations used to characterize ocean wave interactions do not apply to acoustic - gravity waves, as they do not factor in compressibility and gravity effects.

Not exact matches

«When the physical model of wave - motion in a material medium had to be abandoned in physics», writes Mary Hesse, «it left its traces in the kind of mathematics which was used, for this was still a mathematical language derived from the wave equations of fluid motion, and so, for the mathematician, it carried some of the imaginative associations of the original physical picture.»

Polkinghorne's scientific background is everywhere evident; often he uses examples from the laboratory: the historical appearance of Jesus in the world is seen in terms of the apparently undramatic discovery of penicillin on a windowsill; the two natures in Christ find a possible parallel in the wave / particle duality of light, and Dirac's equation concerning quantum mechanics is used in reference to the doctrine of the Trinity.

This relation of the Schrödinger equation to classical waves is already revealed in the way that a variant called the nonlinear Schrödinger equation is commonly used to describe other classical wave systems — for example in optics and even in ocean waves, where it provides a mathematical picture of unusually large and robust «rogue waves.»

Schrödinger drew on his deep knowledge of classical mechanics, and his equation in many ways resembles those used for ordinary waves.

In this story, and in his latest book, 17 Equations that Changed the World, Ian Stewart uses Maxwell's equation for electromagnetic waves propagating in a vacuum.

The seven I focus on here — the wave equation, Maxwell's four equations, the Fourier transform and Schrödinger's equation — illustrate how empirical observations have led to equations that we use both in science and in everyday life.

In the accompanying video, we use the longer version of the equation that doesn't depend on the waves moving through a vacuum.

Perhaps most importantly, the approach used can be applied to other physical phenomena that are described by wave equations, such as acoustics.

Simmons, with the help of the Arctic Region Supercomputer Center, which is part of the UAF Geophysical Institute, used math equations to make detailed numerical simulations, or high - resolution models, of under - ocean wave processes.

First, they spotted clusters of waves that tend to roll along together, then they analyzed each cluster's length and height, and they finally used a combination of statistics and dynamical equations to determine which of those clusters was most likely to go rogue.

«Using data and equations, we've determined for any given sea state the wave groups that can evolve into rogue waves,» Sapsis says.

Propagation of waves through an astrophysical disk can be understood using Schrödinger's equation - a cornerstone of quantum mechanics.

An engaging activity introducing students to the wave equation, giving them an understanding of some of the vocabulary and concepts used.

The equations for Rossby waves (Calculation of the Meridional Wave Number, Physics of the Parameter, and Calculation of the Amplitudes) show that this can occur if a set of necessary conditions are met: u ¯ > 0 in the midlatitude region; the highest value of l within the waveguide is in the range of the meridional wave numbers lm dominantly contributing to the external forcing with a given m, which provides closeness of the k waves to respective m waves not only in terms of the zonal but also the meridional wave numbers, favoring the QRA of the m waves; the total latitudinal width of the waveguide is no less than the characteristic spatial scale of the relevant Airy function (25), which is used as the boundary condition at its southern and northern boundaries; and latitudinal distribution of l is sufficiently smooth in the waveguide, and both TPs lie within a midlatitude region of ∼ 25 ° N — 30 ° N and ∼ 65 ° N − 70 ° N, as the necessary condition for the application of quasilinear Wentzel − Kramers − Brillouin (WKB) method (25) when solving the equations for Rossby waves.

To obtain the equation for A˜m, b, we use the parameterization of the wave activity A during the wave breaking proposed in ref.