A Hamiltonian formulation of nonlinear, parallel propagating, travelling whistler waves is developed. The complete system of equations reduces to two coupled differential equations for the transverse electron speed u and a phase variable φ=φp − φe representing the difference in the phases of the transverse complex velocities of the protons and the electrons. Two integrals of the equations are o...

In the lecture notes on waves, we have shown that the waves on a plucked guitar string are transverse standing waves consisting of a linear superposition (i.e. sum) of harmonics of the fundamental (first harmonic) with the fundamental itself. A first-order mathematical description of the shape of the overall waveform of the transverse standing wave on a plucked guitar string is a triangle, or s...

We consider relativistic deformations of interfering paraxial waves moving in the transverse direction. Owing to superluminal transverse phase velocities, noticeable deformations of the interference patterns arise when the waves move with respect to each other with non-relativistic velocities. Similar distortions also appear on a mutual tilt of the interfering waves, which causes a phase delay ...

The critical subject of transverse crack detection in a rail head is treated in this paper. Conventional bulk wave ultrasonic techniques often fail because of shelling and other surface imperfections that shield the defects that lie below the shelling. A guided wave inspection technique is introduced here that can send ultrasonic energy along the rail under the shelling with a capability of fin...

We study transverse impacts of rigid objects on a free elastic membrane, using thin circular sheets of natural rubber as experimental models. After impact, two distinct axisymmetric waves propagate in and on the sheet. First a tensile wave travels at sound speed leaving behind the wave front a stretched domain. Then, a transverse wave propagates on the stretched area at a lower speed. In the st...

A zero index metamaterial (ZIM) can be utilized to block wave (super-reflection) or conceal objects completely (cloaking). The “super-reflection” device is realized by a ZIM with a perfect electric (magnetic) conductor inclusion of arbitrary shape and size for a transverse electric (magnetic) incident wave. In contrast, a ZIM with a perfect magnetic (electric) conductor inclusion for a transver...

The two-dimensional wave-breaking of relativistic plasma waves driven by a ultrashort high-power lasers, is described within a framework of cold 2-D fluid theory. It is shown that the transverse nonlinearity of the plasma wave results in temporally increasing transverse plasma oscillation in the wake of the laser pulse, inevitably inducing wave-breaking below the 1-D threshold. A condition for ...

The peculiarities of the propagating transverse waves observed in the solar corona with the Coronal Multi-channel Polarimeter (CoMP) indicate the existence of fine field structuring in the coronal density. We present results of numerical simulations studying the evolution of a localised transverse magneto-hydrodynamic wave in a uniform magnetic field. We consider two initial low plasma-beta equ...