194 research outputs found
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, ,
, and . All three collision integrals
conserve momentum and energy during bogolon collisions, but only conserves bogolon number. Previous works have considered the
contribution of only two collision integrals, and . In this work, we show that the third collision integral 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 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
and magnetic fields . All expressions show large linear
magnetoresistance effect with different dependencies on the phase
concentrations. The corresponding plots of the - and -dependencies of
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 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 random boolean constraints
which are to be satisfied simultaneously by 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
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