Cauchy problem for the Mathieu equation away from parametric resonance

Four solutions of the Cauchy problem for Mathieu’s equation away from parametric resonance domains are analytically constructed using an asymptotic averaging method in the fourth approximation. Three solutions occur near fractional parameter values at which slow combination phases exist. The fourth solution occurs in the absence of slow phases away from parametric resonance domains and the fractional parameter values.     

On Diffraction of a Sawtooth Nonlinear Wave by a Narrow Circular Aperture in a Screen

Acoustical Physics - The paper presents the experimental and theoretical studies of diffraction effects in intense acoustic beams diffracted by a narrow circular aperture in a screen. The...     

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Effect of the microstructure of epitaxial YBa2Cu3O7 − x films on their electrophysical and nonlinear microwave properties

The local nonlinear microwave response of YBa₂Cu₃O_{7 ? x} films was measured by near-zone field microscopy with a spatial resolution of 50 μm, and YBa₂Cu₃O_{7 ? x} film microbridges were locally studied by low-temperature scanning microscopy with a spatial resolution of 4 μm. The microstructure of epitaxial YBa₂Cu₃O_{7 ? x} films was examined using x-ray diffraction and electron microscopy. A correlation is detected between the average crystallite size and the half-widths of the temperature dependences of the third-harmonic power (W _TH) and the electron-beam-induced voltage (W _EBIV). The experimental results are described in terms of a model of a two-phase medium taking into account the nonlinear I-V characteristic of the superconductor. For large crystallites, the nonlinear microwave response is shown to be caused by intracrystallite vortex pinning. As the average crystallite size decreases, an additional contribution to the nonlinear response appears due to the pinning of a magnetic flux by the Josephson network of crystallite boundaries. Calculations show that a three-fold increase in the crystallite size decreases the nonlinearity coefficient of YBa₂Cu₃O_{7 ? x} films by two orders of magnitude.     

Excited classical oscillators under conditions of differing lifetime in the interaction space

The article considers the mechanism of interaction between oscillators and a high-frequency field, associated with differing lifetime of particles in the interaction space as a result of the fact that the drift velocity of the oscillators depends on their energy. Examples are given of interaction in which amplification results from the differing-lifetime mechanism.Translated from Izvestiya Vysshikh Uchebnyk Zavedenii, Radiofizika, Vol. 21, No. 12, pp. 1761–1765, December, 1978.     

Interaction between optical phonons and Josephson vortices in layered superconductors

The effect of optical phonons on the stability of the in-phase motion regime of Josephson vortices in a layered superconductor has been studied by using an expression for the dielectric constant of a layered high-temperature superconductor. The dispersion characteristics of linear waves have been analyzed. It has been shown that the in-phase motion regime of the Josephson vortices can be spontaneously established in the layered superconductor.