Long range bond-bond correlations in dense polymer solutions

The scaling of the bond-bond correlation function P1(s) along linear polymer chains is investigated with respect to the curvilinear distance s along the flexible chain and the monomer density rho via Monte Carlo and molecular dynamics simulations. Surprisingly, the correlations in dense three-dimensional solutions are found to decay with a power law P1(s) approximately s(-omega) with omega=3/2 and the exponential behavior commonly assumed is clearly ruled out for long chains. In semidilute solutions, the density dependent scaling of P1(s) approximately g(-omega(0))(s/g)(-omega) with omega(0)=2-2nu=0.824 (nu=0.588 being Flory's exponent) is set by the number of monomers g(rho) in an excluded volume blob. Our computational findings compare well with simple scaling arguments and perturbation calculation. The power-law behavior is due to self-interactions of chains caused by the chain connectivity and the incompressibility of the melt.     

Thermodynamics of phase equilibrium of binary alloys containing nanprecipitates

A model of phase equilibrium in binary alloys has been developed taking into account the formation of phase precipitates of arbitrary (including nanometer) size. It has been shown that the phase composition of alloys substantially depends on the size of phase precipitates and, in the case of the formation of nano-precipitates, the phase composition can differ by a factor of several times from the phase composition of macroscopic precipitates. The proposed model has been used for calculating the dependence of the phase composition of some binary alloys (α-Fe-Cr at the temperature T = 773 K and Zr-Nb at the temperature T = 853−873 K) on the size of precipitates. The results of the calculation agree with experimental data obtained by other authors.     

On the chiral anomaly in non-Riemannian spacetimes

Thetranslation Chern-Simons type three-formcoframe∧torsion on a Riemann-Cartan spacetime is related (by differentiation) to the Nieh-Yan fourform. Following Chandia and Zanelli, two spaces with nontrivial translational Chern-Simons forms are discussed. We then demonstrate, first within the classical Einstein-Cartan-Dirac theory and second in the quantum heat kernel approach to the Dirac operator, how the Nieh-Yan form surfaces in both contexts, in contrast to what has been assumed previously.     

Solar image recovery with a weak filling of the spectral plane by the method of projections onto convex sets

This paper is devoted to the problem of solar image recovery in synthesizing radio brightness maps in the case of an incomplete filling of the spectral region (the Fourier data are bounded by a cone with an angle much smaller than 180 deg.) The image was recovered by the method of projection onto closed convex sets (PCCS). Brief theoretical postulates which formed the basis for this method are presented. A comparative characteristic with the CLEAN method is given. The results of using this method for the model data and real data (recovery of the solar radio image obtained in the knife-edge beams of the SSRT) are presented.     

Integrability of Einstein–Weyl Equations for Spatially Homogeneous Models of Type III by Bianchi

This paper deals with nonisotropic spatially homogeneous models for a self-consistent system of Einstein–Weyl equations with a spinor field. It is shown that for spaces of type III by Bianchi the system of Einstein–Weyl equations is integrable.     

Stäckel electrovacuum spaces with isotropic complete sets. Integration of field equations for the metric generalizing a space of type (1.1)

A system of Einstein-Maxwell equations is integrated for the metric that generalizes the metric of a space with full set of type (1.1). This is necessary for carrying out the classification of the corresponding Stäckel electrovacuum spaces. An algebraic classification of the solutions obtained is carried out.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 17–20, December, 1987.     

A complete classification of Stäckel spaces of type (2.1) in the Brans-Dicke theory

In the paper the complete classification of vacuum stäckel spaces of type (2.1) in the Brans-Dicke theory is completed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 93–96, February, 1992.     

Special Stâckel spaces of the electrovacuum

The investigation of the problem of classifying the spaces of the electrovacuum that admit a complete separation of variables in the Hamilton-Jacobi equation for a charged test particle is completed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 20–22, August, 1984.     

Stekkel space of electrovacuum with isotropic complete sets of the type (1.1)

A complete classification of the Stekkel spaces of the electrovacuum, admitting one isotropic Killing vector field and two Killing tensor fields, is presented. All solutions of the Einstein-Maxwell equations found refer to the Petrov type N.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 79–83, October, 1988.In conclusion we note that all solutions presented above are of the Petrov type N.