Rayleigh Approximation to Ground State of the Bose and Coulomb Glasses

Glasses are rigid systems in which competing interactions prevent simultaneous minimization of local energies. This leads to frustration and highly degenerate ground states the nature and properties of which are still far from being thoroughly understood. We report an analytical approach based on the method of functional equations that allows us to construct the Rayleigh approximation to the ground state of a two-dimensional (2D) random Coulomb system with logarithmic interactions. We realize a model for 2D Coulomb glass as a cylindrical type II superconductor containing randomly located columnar defects (CD) which trap superconducting vortices induced by applied magnetic field. Our findings break ground for analytical studies of glassy systems, marking an important step towards understanding their properties

Couette flow in channels with wavy walls

Summary. Three-dimensional Couette flows enclosed by a plane and by a wavy wall are addressed; the wave amplitude is proportional to the mean clearance of the channel multiplied by a small dimensionless parameter e. A perturbation expansion in terms of the powers of e of the full steady Navier-Stokes equations yields a cascade of boundary value problems which are solved at each step in closed form. The supremum value of e for which the expansion converges, is determined as a function of the Reynolds number Re: The analytical-numerical algorithm is applied to compute the velocity in the channel to O(e 4 ). Even in the first order approximation O(e), new results are obtained which complement the triple deck theory and its modifications. In particular, the incipient separation-detachment is discussed using the Prandtl-Schlichting criterion of starting eddies. The value e e for which eddies start in the channel, is analytically deduced as a function of Re as well as analytical formulas for the coordinates of the separation points. These analytical formulas show that e e in 3D channels is always less than e e in 2D channels. For non-smooth channels, a criterion of infinitesimally small e e is deduced. The critical value of e up to which bifurcation of the solutions can occur is estimated

Analytical methods for heat conduction in composites

Analytical methods unifying the study of heat conduction in various type of composite materials are described. Analytical formulas for the effective (macroscopic) conductivity tensor are presented