Disintegration of Cnoidal Waves over Smooth Topography

The transformation of cnoidal waves in a basin with smooth topography is studied in the frame of the variable-coefficient Korteweg–de Vries equation and the generalized Zakharov's system. It is shown that the cnoidal structure of the propagating nonlinear wave is destroyed if the topography contains a periodic component with a characteristic scale close to the nonlinearity length. Focusing on waves in intermediate depth, a simple analytical model based on a two-harmonic representation of the cnoidal wave demonstrates the main features of the process of disintegration of the cnoidal structure of the nonlinear wave. Numerical simulations of the interaction of several harmonics confirm the analytical conclusions.     

Periodic motions and resonances of impact oscillators

Bilinear oscillators – the oscillators whose springs have different stiffnesses in compression and tension – model a wide range of phenomena. A limiting case of bilinear oscillator with infinite stiffness in compression – the impact oscillator – is studied here. We investigate a special set of impact times – the eigenset, which corresponds to the solution of the homogeneous equation, i.e. the oscillator without the driving force. We found that this set and its subsets are stable with respect to variation of initial conditions. Furthermore, amongst all periodic sets of impact times with the period commensurate with the period of driving force, the eigenset is the only one which can support resonances, in particular the multi-‘harmonic’ resonances. Other resonances should produce non-periodic sets of impact times. This funding indicates that the usual simplifying assumption [e.g., S.W. Shaw, P.J. Holmes, A periodically forced piecewise linear oscillator, Journal of Sound and Vibration 90 (1983) 129–155] that the times between impacts are commensurate with the period of the driving force does not always hold. We showed that for the first sub-‘harmonic resonance’ – the resonance achieved on a half frequency of the main resonance – the set of impact times is asymptotically close to the eigenset. The envelope of the oscillations in this resonance increases as a square root of time, opposite to the linear increase characteristic of multi-‘harmonic’ resonances.     

2.1 Tesla permanent-magnet Faraday isolator for subkilowatt average power lasers

A Faraday isolator with one magneto-optical element providing 31 dB isolation ratio for 330 W average power lasers was produced and investigated in an experiment. These remarkable parameters were achieved by increasing the magnetic field and using a [0 0 1] oriented TGG crystal.     

Formation of a plasma with the determining role of radiative processes in thin foils irradiated by a pulse of the PEARL subpetawatt laser

A superbright X-ray source with a radiation temperature of ~1.2 keV making it possible to create a solid-state plasma whose kinetics is determined by the radiative processes has been implemented under the impact of a 170-TW pulse of the PEARL femtosecond laser facility on an aluminum target with submicron thickness. The diagnostics of the created plasma is performed by X-ray spectral methods using spectral transitions in hollow multicharged ions.     

Resonant scattering of nonequilibrium phonons (<Emphasis Type="Italic">λ</Emphasis><Subscript>ph</Subscript> = 10–50 nm) in nanostructured ceramics based on YSZ + Al<Subscript>2</Subscript>O<Subscript>3</Subscript> composites

Specific features of the transport of weakly nonequilibrium thermal phonons (λ _ph = 10–50 nm) in nanoscale ceramics at a transition from micro-to nanosizes have been investigated. On the basis of the model of spherical shells randomly distributed in space and modeling grain boundaries, whose elastic properties differ from the elastic properties of grains, features of the phonon spectrum in the wavelength range λ _ph ～ R _g have been studied. The conditions leading to the occurrence of a gap in the phonon spectrum of nanoscale materials are analyzed. It is shown that the position of the top gap edge in the phonon spectrum is determined to a large extent by the structure of phase boundaries, while the presence of inclusions (pores, other phases) with characteristic sizes smaller than that of grains of the main ceramic material shifts the gap to high frequencies in the phonon spectrum. Temperature dependences of the diffusion coefficient of nonequilibrium phonons near the top gap edge in the phonon spectrum have been measured for multiphase ceramics based on YSZ + 14.3% Al₂O₃ composites.     

Nonequilibrium acoustic phonons in Y3Al5O12-based nanocrystalline ceramics

The phonon transport processes in high-transparency nanocrystalline laser ceramics based on cubic Y₃Al₅O₁₂ garnet oxide were investigated by the heat-pulse technique. The propagation kinetics of nonequilibrium acoustic phonons was studied in the range of helium temperatures (1.7–3.8 K). The structural model is suggested for the intergrain layers, and their thickness is estimated.