Duality and Effective Conductivity of Two-dimensional Two-phase Systems

The possible functional forms of the effective conductivity sigma_{eff} of the randomly inhomogeneous two-phase system at arbitrary values of concentrations are discussed. A new functional equation, generalizing the duality relation, is deduced for systems with a finite maximal characteristical scale of the inhomogeneties and its solution is found. A hierarchical method of the construction of the model random inhomogeneous medium is proposed and one such simple model is constructed. Its effective conductivity at arbitrary phase concentrations is found in mean field like approximation. The derived formulas for the effective conductivity are different and also (1) satisfy all necessary inequalities and symmetries, including a dual symmetry; (2) reproduce the known formulas for sigma_{eff} in weakly inhomogeneous case. It means that in general sigma_{eff} of the two-phase randomly inhomogeneous systems may be a nonuniversal function and can depend on some details of the structure of the randomly inhomogeneous regions. The percolation limit is briefly discussed.Comment: 16 pages, latex-2e, 4 figures (3 eps-files added), small correction

Planar isotropic two-phase systemsin perpendicular magnetic field: effective conductivity

Three explicit approximate expressions for the effective conductivity sigma_e of various planar isotropic two-phase systems in a magnetic field are obtained using the dual linear fractional transformation, connecting sigma_e of these systems with and without magnetic field. The obtained results are applicable for two-phase systems (regular and nonregular as well as random), satisfying the symmetry and self-duality conditions, and allow to describe sigma_e of various two-dimensional and layered inhomogeneous media at arbitrary phase concentrations and magnetic fields. All these results admit a direct experimental checking.Comment: 10 pages, Latex2e, 3 figure

Duality and exact results for conductivity of 2D isotropic heterophase systems in magnetic field

Using a fact that the effective conductivity sigma_{e} of 2D random heterophase systems in the orthogonal magnetic field is transformed under some subgroup of the linear fractional group, connected with a group of linear transformations of two conserved currents, the exact values for sigma_{e} of isotropic heterophase systems are found. As known, for binary (N=2) systems a determination of exact values of both conductivities (diagonal sigma_{ed} and transverse Hall sigma_{et}) is possible only at equal phase concentrations and arbitrary values of partial conductivities. For heterophase (N > 2) systems this method gives exact values of effective conductivities, when their partial conductivities belong to some hypersurfaces in the space of these partial conductivities and the phase concentrations are pairwise equal. In all these cases sigma_e does not depend on phase concentrations. The complete, 3-parametric, explicit transformation, connecting sigma_e in binary systems with a magnetic field and without it, is constructedComment: 15 pages, 3 figures, Latex2

Relaxation rates and collision integrals for Bose-Einstein condensates

Near equilibrium, the rate of relaxation to equilibrium and the transport properties of excitations (bogolons) in a dilute Bose-Einstein condensate (BEC) are determined by three collision integrals, $\mathcal{G}^{12}$, $\mathcal{G}^{22}$, and $\mathcal{G}^{31}$. All three collision integrals conserve momentum and energy during bogolon collisions, but only $\mathcal{G}^{22}$ conserves bogolon number. Previous works have considered the contribution of only two collision integrals, $\mathcal{G}^{22}$ and $\mathcal{G}^{12}$. In this work, we show that the third collision integral $\mathcal{G}^{31}$ makes a significant contribution to the bogolon number relaxation rate and needs to be retained when computing relaxation properties of the BEC. We provide values of relaxation rates in a form that can be applied to a variety of dilute Bose-Einstein condensates.Comment: 18 pages, 4 figures, accepted by Journal of Low Temperature Physics 7/201

Large linear magnetoresistivity in strongly inhomogeneous planar and layered systems

Explicit expressions for magnetoresistance $R$ of planar and layered strongly inhomogeneous two-phase systems are obtained, using exact dual transformation, connecting effective conductivities of in-plane isotropic two-phase systems with and without magnetic field. These expressions allow to describe the magnetoresistance of various inhomogeneous media at arbitrary concentrations $x$ and magnetic fields $H$. All expressions show large linear magnetoresistance effect with different dependencies on the phase concentrations. The corresponding plots of the $x$- and $H$-dependencies of $R(x,H)$ are represented for various values, respectively, of magnetic field and concentrations at some values of inhomogeneity parameter. The obtained results show a remarkable similarity with the existing experimental data on linear magnetoresistance in silver chalcogenides $Ag_{2+\delta}Se.$ A possible physical explanation of this similarity is proposed. It is shown that the random, stripe type, structures of inhomogeneities are the most suitable for a fabrication of magnetic sensors and a storage of information at room temperatures.Comment: 12 pages, 2 figures, Latex2

Simplest random K-satisfiability problem

We study a simple and exactly solvable model for the generation of random satisfiability problems. These consist of $\gamma N$ random boolean constraints which are to be satisfied simultaneously by $N$ logical variables. In statistical-mechanics language, the considered model can be seen as a diluted p-spin model at zero temperature. While such problems become extraordinarily hard to solve by local search methods in a large region of the parameter space, still at least one solution may be superimposed by construction. The statistical properties of the model can be studied exactly by the replica method and each single instance can be analyzed in polynomial time by a simple global solution method. The geometrical/topological structures responsible for dynamic and static phase transitions as well as for the onset of computational complexity in local search method are thoroughly analyzed. Numerical analysis on very large samples allows for a precise characterization of the critical scaling behaviour.Comment: 14 pages, 5 figures, to appear in Phys. Rev. E (Feb 2001). v2: minor errors and references correcte

Statistical mechanics of the random K-SAT model

The Random K-Satisfiability Problem, consisting in verifying the existence of an assignment of N Boolean variables that satisfy a set of M=alpha N random logical clauses containing K variables each, is studied using the replica symmetric framework of diluted disordered systems. We present an exact iterative scheme for the replica symmetric functional order parameter together for the different cases of interest K=2, K>= 3 and K>>1. The calculation of the number of solutions, which allowed us [Phys. Rev. Lett. 76, 3881 (1996)] to predict a first order jump at the threshold where the Boolean expressions become unsatisfiable with probability one, is thoroughly displayed. In the case K=2, the (rigorously known) critical value (alpha=1) of the number of clauses per Boolean variable is recovered while for K>=3 we show that the system exhibits a replica symmetry breaking transition. The annealed approximation is proven to be exact for large K.Comment: 34 pages + 1 table + 8 fig., submitted to Phys. Rev. E, new section added and references update

Structural and magnetic properties of Mn3-xCdxTeO6 (x = 0, 1, 1.5 and 2)

Mn3TeO6 exhibits a corundum-related A3TeO6 structure and a complex magnetic structure involving two magnetic orbits for the Mn atoms [*]. Mn3-xCdxTeO6 (x=0, 1, 1.5 and 2) ceramics were synthesized by solid state reaction and investigated using X-ray powder diffraction, electron microscopy, calorimetric and magnetic measurements. Cd2+ replaces Mn2+ cations without greatly affecting the structure of the compound. The Mn and Cd cations were found to be randomly distributed over the A-site. Magnetization measurements indicated that the samples order antiferromagnetically at low temperature with a transition temperature that decreases with increasing Cd doping. The nuclear and magnetic structure of one specially prepared 114Cd containing sample: Mn1.5(114Cd)1.5TeO6, was studied using neutron powder diffraction over the temperature range 2 to 295 K. Mn1.5(114Cd)1.5TeO6 was found to order in an incommensurate helical magnetic structure, very similar to that of Mn3TeO6 [*]. However, with a lower transition temperature and the extension of the ordered structure confined to order 240(10) {\AA}. [*] S. A. Ivanov et al. Mater. Res. Bull. 46 (2011) 1870.Comment: 20 pages, 8 figure

The nature of slow dynamics in a minimal model of frustration-limited domains

We present simulation results for the dynamics of a schematic model based on the frustration-limited domain picture of glass-forming liquids. These results are compared with approximate theoretical predictions analogous to those commonly used for supercooled liquid dynamics. Although model relaxation times increase by several orders of magnitude in a non-Arrhenius manner as a microphase separation transition is approached, the slow relaxation is in many ways dissimilar to that of a liquid. In particular, structural relaxation is nearly exponential in time at each wave vector, indicating that the mode coupling effects dominating liquid relaxation are comparatively weak within this model. Relaxation properties of the model are instead well reproduced by the simplest dynamical extension of a static Hartree approximation. This approach is qualitatively accurate even for temperatures at which the mode coupling approximation predicts loss of ergodicity. These results suggest that the thermodynamically disordered phase of such a minimal model poorly caricatures the slow dynamics of a liquid near its glass transition

Evidence for "fragile" glass-forming behavior in the relaxation of Coulomb frustrated three-dimensional systems

We show by means of a Monte Carlo simulation study that three-dimensional models with long-range frustration display the generic phenomena seen in fragile glassforming liquids. Due to their properties (absence of quenched disorder, physical motivation in terms of structural frustration, and tunable fragility), these systems appear as promising minimal theoretical models for describing the glass transition of supercooled liquids.Comment: 4 pages, 4 figure