[1] Experimental observations of ELF/VLF waves generated using the dual‐beam heating capability of the High frequency Active Auroral Research Program (HAARP) HF transmitter in Gakona, Alaska, are compared with the predictions of an ionospheric HF heating model that accounts for the simultaneous propagation and absorption of multiple HF beams. The model output is used to assess three properties ...

Typically, MR-elastography (MRE) encodes the propagation of monochromatic acoustic waves in the MR-phase images via sinusoidal gradients characterized by a detection frequency equal to the frequency of the mechanical vibration. Therefore, the echo time of a conventional MRE sequence is typically longer than the vibration period which is critical for heart tissue exhibiting a short T(2). Thus, f...

In this paper, we develop for the first time to our knowledge an analytical theory of second harmonic generation (SHG) in a generic nonuniform χ 2 medium. It is shown that by varying the properties of the medium gradually enough, the system can enter an autoresonant state in which the phases of the fundamental pump and of the generated second harmonic wave are locked. The effect of autoresonanc...

Based on Feynman’s lifetime efforts on quantum mechanics and relativity, it is concluded that the basic difference between field theory and string theory is that field theory is based on running waves while string theory should deal with standing waves in the Lorentz-covariant regime. At the 1970 spring meeting of the American Physical Society held in Washington, DC, R. P. Feynman stunned the a...

In the process of optical second-harmonic generation an X-wave, travelling at the group velocity of the fundamental frequency, spontaneously forms. Its parameters, as well as the angular spectrum, are directly correlated to the group velocity mismatch and to the wavevector mismatch between the two harmonics. A novel mechanism for spatio-temporal localized waves generation is thus proposed. ∗Ele...

Consider the diffraction of a time-harmonic plane wave incident on a perfectly reflecting periodic surface. A continuation method on the wavenumber is developed for the inverse diffraction grating problem, which reconstructs the grating profile from measured reflected waves a constant distance away from the structure. Numerical examples are presented to show the validity and efficiency of the p...

We consider the scattering of time harmonic electromagnetic plane waves by a bounded, inhomogeneous, anisotropic dielectric medium and show that under certain assumptions a lower bound on the norm of the (matrix) index of refraction can be obtained from a knowledge of the smallest transmission eigenvalue corresponding to the medium. Numerical examples are given showing the efficaciousness of ou...

We consider the problem of determining either the surface impedance λ = λ(x) or surface conductivity η = η(x) from far field data corresponding to time-harmonic incident plane waves scattered by a coated infinite cylinder. We show that λ and η are uniquely determined from the far field data and provide a numerical algorithm for determining these quantities.

The uniqueness theorem is proved for the linearized problem describing radiation and scattering of time-harmonic water waves by a vertical shell having an arbitrary horizontal cross-section. The uniqueness holds for all frequencies, and various locations of the shell are possible: surface-piercing, totally immersed and bottom-standing. A version of integral equation technique is outlined for fi...

We survey some of the highlights of inverse scattering theory as it has developed over the past fifteen years, with emphasis on uniqueness theorems and reconstruction algorithms for time harmonic acoustic waves. Included in our presentation are numerical experiments using real data and numerical examples of the use of inverse scattering methods to detect buried objects.