Short-wave asymptotic behavior of space-time creeping waves in elasticity theory

We consider the elastic space-time (ST) wave on an unstressed convex surface in a deep shadow zone. The uniform high-frequency asymptotic expansion of the wave field is constructed as the sum of the caustic expansion for the longitudinal (transverse) wave containing the Airy function and the space-time ray series for the transverse (longitudinal) wave. The contribution of the ray expansion with the transverse eikonal is comparable to the contribution of the longitudinal creeping wave to the wave field.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 148, pp. 176–189, 1985.I would like to thank V. M. Babich for suggesting the topic and for discussion of results.     

Effect of temperature on changes of tensile stress at constant elongation in certain human soft tissues

The nature and magnitude of the temperature-induced changes in the initial tensile stress at constant elongation have been investigated in relation to the human artery and vein walls, tendons, and muscle tissue. It has been established that for a cylindrical segment and a specimen of artery wall heated from 10 to 45°C the stress increases, whereas for the vein wall, the tendon, and the muscle tissue it decreases. This behavior of the artery and vein walls is attributed to their different biochemical composition. The difference in the stress-temperature dependence associated with age has been studied. The stresses in the walls of the human femoral artery and great saphenous vein have been determined during autopsy.     

Lateral strain coefficients of human compact bone tissue

The values of all the lateral strain coefficients of the compact bone tissue of the human tibia have been experimentally determined. The variation of these coefficients in six zones of the cross section have been studied at various stress levels, including the ultimate strengths in the corresponding directions. It has been established that the bone tissue possesses orthotropy of the elastic properties. The change in the volume of the bone tissue during deformation has been studied. The bulk moduli for both uniaxial and hydrostatic loading have been determined. A bulk deformation parameter characterizing the strain energy expended in producing a volume change of 100% is introduced. The coefficients of the rank correlation between the lateral strain coefficients and bulk moduli, on the one hand, and the concentrations of a number of biochemical substances found in bone tissue, on the other, are analyzed.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1089–1100, November–December, 1973.     

Investigation of the relations between the various mechanical properties and the biochemical composition of human bone tissue

Nondestructive and destructive methods have been used to establish a series of elastic and strength characteristics of the compact bone tissue in six zones of the cross section of the diaphysis of the human tibia. The quantity of five characteristic biochemical substances present in each zone has been determined. The experiments show that, from the standpoint of continuum mechanics, the compact bone tissue is an orthotropic material and that the bone is nonhomogeneous with respect to biochemical composition. The rank correlation coefficients between the mechanical characteristics and the biochemical concentrations are subjected to a detailed analysis. The important effect of the common glycoproteins on the elastic and strength properties of bone tissue in tension is established.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 138–145, January–February, 1973.     

Asymptotic behavior of the solutions of the Helmholtz equation in the caustic shadow domain. I

One makes use of the complex ray method in order to construct the uniform asymptotics of the wave field in the shadow zone beyond the caustic for the Helmholtz equation with an analytic refraction index. The complex eikonal is obtained as a result of the analytic continuation of the eikonal equation into the two-dimensional complex coordinate space. One considers a special example.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 128, pp. 172–185, 1983.The author expresses his gratitude to V. S. Buldyrev for the discussion of the results.     

Asymptotics of solutions of a differential equation of second order with two turning points and a complex parameter. II

Asymptotic formulas are constructed and rigorously justified for linearly independent solutions of a second-order differential equation with a coefficient possessing the property of finite smoothness and containing a complex parameter ζ (forTmζ=0 the equation has two real turning points). A perturbation method is applied which consists in extending the coefficient of the equation to the complex Z plane and approximating it in an ε-neighborhood of the real axis of this plane by a quadratic polynomial. It is proved that the leading terms of the constructed formulas expressed in terms of parabolic cylinder functions are uniform with respect to arg ζ and that the error admitted under the approximation indicated above can be estimated by the quantityO(K^?1/2, (K→∞ is the second parameter, in addition to S, on which the coefficient of the differential equation depends).     

Phonon singularities on volt-ampere curves of niobium point contacts

The volt-ampere curves and their second derivatives were studied for niobium point contacts at low temperatures in the voltage range corresponding to the characteristic phonon energies. It was found that while for the dirty contacts in the normal state no PC spectra of phonons could be detected, in the superconducting state there were singularities in the I–V curves corresponding to maxima either in the first or in the second derivatives. The singularities observed were due to the energy dependence of the excess current. We suppose that the origin of these singularities is due to the inelastic transitions of electrons between chemical potentials of Cooper pairs at both sides of the contact, which differ in energy by eV. These transitions are possible if ξ(0) ? d ≈ Λ_?, (ξ(0) being the coherence length; d, the contact diameter; $\text{Λ}{}_{\mathrm{?}}\text{= (l}{}_{\mathrm{i}}\text{·l}{}_{\mathrm{?}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, where l_i and l_? being the elastic and inelastic electron mean free paths, respectively).