Observation of a superfluid component within solid helium

We demonstrate by neutron scattering that a localized superfluid component exists at high pressures within solid helium in aerogel. Its existence is deduced from the observation of two sharp phonon-roton spectra which are clearly distinguishable from modes in bulk superfluid helium. These roton excitations exhibit different roton gap parameters than the roton observed in the bulk fluid at freezing pressure. One of the roton modes disappears after annealing the samples. Comparison with theoretical calculations suggests that the model that reproduces the observed data best is that of superfluid double layers within the solid and at the helium-substrate interface.     

Light scattering from spin waves in superfluid3He-A

Summary We show that in theA-phase of superfluid³He one may expect the Mandelstam-Brillouin light scattering from spin waves. The scattering is caused by fluctuations of the magnetic susceptibility.

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Riassunto Si mostra che nella faseA del superfluido³He ci si può aspettare diffusione di luce di Mandelstam-Brillouin da onde di spin. La diffusione è caratterizzata da fluttuazioni della suscettibilità magnetica.

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Резюме Мы покаем, что ьА-qfазе сьерхтекучего³He μожно ожидать рассеяние света Мандельштама-Бриллюэна на спиновых волнах. Рассеяние обусповлено флуктациями магнитной восприимчивости.

     

Spectral theory of a string

In this survey, we present the principal results of Krein's spectral theory of a string and describe its development by other authors.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 155–176, March, 1994.     

The zonal linearization method for multidimensional mass transfer problems in porous media

A number of methods have been proposed in recent years for calculating the combined flows of immiscible and miscible liquids in strata to systems of boreholes. We propose a method which can naturally be called the zonal linearization method [1]. It is more compact than the usual finite-difference method and has high accuracy, in particular, in the neighborhood of a borehole, since it is closely similar to the method of characteristics. The method can be applied to both continuous and discontinuous flows and in principle makes it possible to investigate the formation and breakdown of discontinuities. As distinct from the method of characteristics, it is well suited to programming and implementation on a computer, and it also makes it possible to obtain an approximate analytic solution of the problem in many cases and to estimate the accuracy of the solution. The method is based on the zonal linearization of the equation for mass conservation in the total flow between chosen surfaces or contour lines (lines of equal saturation or concentration). Determination of the dynamics of the contour surfaces leads to a Cauchy problem for a system of integrodifferential equations involving partial derivatives. The zonal linearization method is a development of the scheme described in [2–4], and the method of solving the Cauchy problem is a generalization of the methods described in [4–13]. The essence of the method and its convergence are illustrated by means of two-dimensional problems in two-phase filtration.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 66–80, July–August, 1973.     

Vibrational enhancement of the effective donor-acceptor coupling

This letter deals with a simple three-site model for charge transfer phenomena in a one-dimensional donor (D)-bridge (B)-acceptor (A) system coupled with vibrational dynamics of the B site. It is found that, in a certain range of parameters, the vibrational coupling leads to an enhancement of the effective donor-acceptor electronic coupling as a result of the formation of the polaron on the B site. This enhancement of the charge transfer efficiency is maximum at the resonance, where the effective energy of the fluctuating B site coincides with the donor (acceptor) energy.     

Packing of molecules and hole formation in lyotropic systems

A vector field q (the order parameter of the molecular packing) describing the packing (specifically, the orientation) of membrane-forming amphiphilic molecules is introduced to describe the structures of lyotropic phases constructed from membranes. In the general case q·n≠0 (where n is the unit normal vector) and therefore the singularities of the vector field q are not determined uniquely by the topology of the surface. The condition q·n=0 signifies disruption of the packing of the molecules. This corresponds to holes, which can form in membranes when lyotropic systems are diluted. As an illustration, the simplest type of such singularities, in which the distribution of the field q around a hole is described by a part of an instanton with unit topological charge, is studied. It is shown that such a distribution guarantees the existence of a local minimum under the condition that the tension per unit length λ of the hole boundary is small compared with the deformation energy of the field q: λh/K≪l (K is the modulus of the orientational elasticity of the field q and h is the thickness of the membrane). The radius of the hole which is formed equals L≈2.52(K/λh)^1/3 and the energy E≈59.79K(λh/K)^1/3. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 575–580 (25 October 1996)     

Symmetry group of the kinetic equation and stationary distributions in a weakly turbulent plasma

A class of essentially non-equilibrium distributions characterized by the constant flux of one of the “integral of motion” (e.g. energy, number of particles or momentum) both for waves and particles is shown to exist in plasmas due to the symmetry of collision integrals (particle-wave interactions or Boltzmann's integral resp.). As a result, the non-equilibrium distributions can be obtained from a functional equation inferring that the projection of the stoss-integrand on the irreducible group representation should be equal to zero.