Geometrical acoustics approximation for surface waves

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 3, pp. 69–73, May–June, 1992.     

Asymptotic expansions of solutions of equations with a deviating argument in Banach spaces

For the equation $$Lu = \frac{1}{i}\frac{{du}}{{dt}}\sum\nolimits_{j = 0}^m {A_j u} (l - h_j^0 - h_j^1 (t)) = f(t),$$ whereh ₀ ^o =0,h ₀ ¹ =0 (t) ≡ 0,h _j ^o = const > 0,h ₁ ^j (t),j= 1, ...,m are nonnegative continuously differentiable functions in [0, ∞), Aj are bounded linear operators, under conditions on the resolvent and on the right hand sidef(t), we have obtained an asymptotic formula for any solution u(t) from L₂ in terms of the exponential solutions u_k(t), k=1, ..., n, of the equation $$\frac{1}{i}\frac{{du}}{{dt}} - A_0 u - \sum\nolimits_{j = 0}^m {A_j u} (t - h_j^0 ) = 0,$$ connected with the poles λ_k, k=1, ..., n, of the resolvent R_λ in a certain strip.     

Structural and dynamic aspects of hydrogen-bonded complexes and inclusion compounds containing alpha,omega-dicyanoalkanes and urea, investigated by solid-state 13C and 2H NMR techniques

Solid-state 13C NMR and 2H NMR techniques have been used to investigate structural and dynamic properties of the 1,4-dicyanobutane/urea and 1,5-dicyanopentane/urea 1:1 hydrogen-bonded complexes and the 1,6-dicyanohexane/urea inclusion compound. The pure crystalline phase of urea has also been investigated. The 13C NMR studies have focused on 13C chemical shift anisotropy and second-order quadrupolar effects (arising from 13C-14N interaction) for the urea molecules and the cyano groups of the alpha,omega-dicyanoalkanes. Parameters describing these interactions are derived and are discussed in relation to the known structural properties of these materials. Comparison of 13C chemical shift anisotropies of the cyano carbons and rates of 13C dipolar dephasing suggest that 1,4-dicyanobutane and 1,5-dicyanopentane are effectively static, whereas 1,6-dicyanohexane has greater mobility. 2H NMR line shape analysis for the 1,4-dicyanobutane/urea-d4 and 1,5-dicyanopentane/urea-d4 complexes indicates that the only motion of the urea molecules that is effective on the 2H NMR time scale is a rapid libration about the C=O bond over an angular range of about 26 degrees . For the 1,6-dicyanohexane/urea-d4 inclusion compound, the 2H NMR line shape is consistent with a motion comprising 180 degrees jumps about the C=O bond at rates that are intermediate on the 2H NMR time scale. In addition, rapid libration about the C=O bond also occurs over an angular range of about 20 degrees . The dynamic properties of the urea molecules in these materials are compared with those of urea molecules in other crystalline environments.     

Molecular relaxation processes in the salt systems containing anions of various configurations

We present in this paper a comparative analysis of the spectral and molecular-relaxation parameters of the ionic salts in the region of solid-liquid phase transition and in the molten state depending on the anion symmetry (thiocyanate (SCN-), a linear rotor, C(infinity v); nitrate (NO3-), a symmetrical top, D3h; and perrhenate (ReO4-), a spherical top, Td), size and charge of the cation, and temperature. We also present new results of the investigations on molecular relaxation in thiocyanate ion in several crown-etheric complexes.     

Another approach to protons with constricted mobility in white matter: pilot studies using wideline and high-resolution NMR spectroscopy

We report a new approach for the identification of an independent method of studying the semi-solid pool of protons, i.e., protons with constrained motion as a result of being bound to lipid and protein matrices. These protons cannot be observed using conventional imaging techniques since their transverse relaxation times are much shorter than the minimum echo times that are currently available on clinical scanners. In this pilot study, in vitro multicomponent transverse relaxation experiments were made on human white matter slices, fixed in formalin (7 normal and 5 with multiple sclerosis). The transverse relaxation decay curves were multiexponential and were decomposed to yield three primary components. The shortest T(2) component that we obtained (a component too short to be seen by in vivo methods) was of the order of microseconds. We hypothesize that this might correspond to the macromolecular pool of lipid protons trapped within the myelin sheaths. To our knowledge, this is the first attempt at extracting this ultra short T(2) component from human white matter. Subsequently, an attempt was made to directly detect the lipid protons in a proton NMR spectrum and, if possible, measure their concentration in some of the tissues, using the technique of magic angle spinning.     

Effect of a magnetic field on the thermal and kinetic properties of the Sm<Subscript>0.55</Subscript>Sr<Subscript>0.45</Subscript>MnO<Subscript>3.02</Subscript> manganite

The temperature and magnetic-field dependences of the heat capacity, thermal conductivity, thermopower, and electrical resistivity of the Sm_0.55Sr_0.45MnO_3.02 ceramic material are studied in the temperature range 77–300 K and in magnetic fields up to 26 kOe. It is revealed that the quantities under investigation exhibit anomalous behavior due to a magnetic phase transition at the Curie temperature T_C. An increase in the magnetic field strength H leads to an increase in the Curie temperature T_C and a jump in the heat capacity ΔC_p at T_C. The temperature dependences of the measured quantities are characterized by hystereses that are considerably suppressed in a magnetic field of 26 kOe and depend neither on the thermocycling range nor on the rate of change in the temperature. The thermal conductivity K at temperatures above T_C shows unusual behavior for crystalline solids (dK/dT>0) and, upon the transition to a ferromagnetic state, drastically increases as a result of a decrease in the phonon scattering by Jahn-Teller distortions. It is demonstrated that the hystereses of the studied properties of the Sm_0.55Sr_0.45MnO_3.02 manganite are caused by a jumpwise change in the critical temperature due to variations in the lattice parameters upon the magnetic phase transition.     

Transform-Limited Pulses Are Not Optimal for Resonant Multiphoton Transitions

Maximizing nonlinear light-matter interactions is a primary motive for compressing laser pulses to achieve ultrashort transform limited pulses. Here we show how, by appropriately shaping the pulses, resonant multiphoton transitions can be enhanced significantly beyond the level achieved by maximizing the pulse's peak intensity. We demonstrate the counterintuitive nature of this effect with an experiment in a resonant two-photon absorption, in which, by selectively removing certain spectral bands, the peak intensity of the pulse is reduced by a factor of 40, yet the absorption rate is doubled. Furthermore, by suitably designing the spectral phase of the pulse, we increase the absorption rate by a factor of 7.