Uniform asymptotic formulas for curved solitons of the Kadomtsev-Petviashvili equations

A special class of solutions to the Kadomtsev-Petviashvili equations is investigated in the limit t . It is proved that these solutions split into an infinite series of curved solitons in the neighborhood of the wave front. Parameters of these solitons depend on the variable Y=y/t. Asymptotic formulas uniform in Y are obtained.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 108, No. 2, pp. 205–211, August, 1996.     

Effect of vibration frequency and sample composition on acoustic properties of Y?Ba?Cu?O high-Tc superconductors

Temperature dependences of absorption and velocity of longitudinal ultrasound in high-T_c ceramics Y Ba Cu O with different Y and Ba content at frequencies 100 kHz and 7.5 MHz are studied in the temperature range 6 to 300 K. For 100 kHz three peaks at 60, 140, and 230 K are observed in the temperature dependences of decrement. Temperature dependences of sound velocity show a broad hysteresis for thermocycling. The temperature boundaries of hysteresis and peak locations are almost independent of sample composition. Sizes of hysteresis and peak heights are very different in samples of various composition. For 7.5 MHz, a peak was found at 210 K in the temperature dependences of ultrasound absorption increment. It is shown that the acoustic anomalies are due to a structural phase transition of martensitic type. Thermoactivation parameters of the main microscopic mechanism responsible for the phase transition are estimated.     

Reactions of Podophyllotoxin with DDQ

Introduction 2, 3-Dichloro-5, 6-dicyanobenzoquinone (DDQ) can react with lignans of the mono- arylidene-butyrolactone1, aryltetralin2, dibenzylbutane3 and aryltetralin-butyrolactone4,5 series. We have studied the reactions of this reagent with podophyllotoxin 1, which is a well-known natural product on account of its long history of use in folk medicine and the biological activity of its many derivatives6. In particular, derivatives of 4-demethyl epipodophyllotoxin are used in cancer chemo…     

High amplitude dislocation damping in superconducting Pb and In

The amplitude dependence of ultrasound absorption due to dislocations, α, has been studied for single crystals of pure lead and indium as well as for lead doped with Tl, Sn or Bi, both in the superconducting and normal state and for a wide range of ultrasound amplitudes, ε₀. Pure and Tl-doped superconducting lead at large ε₀ displayed a maximum on the α(ε₀) dependence which became a plateau upon transition to the n-state. This is direct evidence for a change from static to dynamic dislocation hysteresis as a result of the increase in the electron drag constant. Limit values for the dislocation loop lengths have been estimated, viz. 2.4 × 10⁻⁴ cm < L_N < 10.4 × 10⁻⁴ cm. In other single crystals the dynamic hysteresis occurred both in the n- and s-state. In all the single crystals, α increased with the increase of ε₀ above the maximum amplitude and onset of the plateau which was observed in both states. The effect is associated with non-linear phenomena arising at significant loop flexures. The amplitude dependence of the losses due to this effect has been analysed, the results of the analysis being in good agreement with the experimental data.     

Variation of low temperature internal friction at microplastic deformation of high purity molybdenum single crystals

Amplitude and temperature spectra of ultrasound absorption in weakly deformed high purity molybdenum single crystals of different orientations were measured. The results were discussed in terms of parameter changes related to quasiparticle- or dislocation oscillations, respectively, dislocation-point defect interactions as well as defect generation at microplastic deformation.     

Unstable internal friction in Bismuth and Antimony single crystals

In the temperature range of 6 to 300 K an effect of the high amplitude ultrasound waves on amplitudedependences of decrement and modulus defects in the antimony and bismuth single crystals of different orientation is studied. The character of changes of the decrement and modulus defect amplitude dependences under the influence of the high amplitude ultrasound indicates that dislocation multiplication, obstacle break-through by dislocation pile-ups or deformation twinning may be observed in crystals depending on the ultrasound propagation direction and the temperature interval investigated.     

Anomalies of internal friction in CsI single crystal at liquid helium temperatures caused by plastic deformation

Acoustic relaxation in undeformed and plastically deformed CsI single crystal has been studied using the composite oscillator technique at frequencies (1–7) × 10⁵ Hz in the temperature range 2–15 K. Plastic deformation leads to appearance of an internal friction peak localized in the temperature interval 4–5 K. It is shown that the peak shifts towards higher temperatures when increasing the vibration frequency and corresponds to a thermally activated relaxation process with very low values of the activation energyU ≈ 1.9×10⁻³ eV and the attack frequencyν ₀≈6.7 × 10³ s⁻¹. Interaction of sound with dislocation kinks migrating in the second order Peierls relief is considered as a possible mechanism of the peak. Research was made possible in part by Grants U9T000 and U9T200 from the International Science Foundation and supported in part by the Fundamental Research Foundation of Ukraine (Project 2.4/156 “Bion”).