79 research outputs found
Current percolation and anisotropy in polycrystalline MgB
The influence of anisotropy on the transport current in MgB
polycrystalline bulk samples and wires is discussed. A model for the critical
current density is proposed, which is based on anisotropic London theory, grain
boundary pinning and percolation theory. The calculated currents agree
convincingly with experimental data and the fit parameters, especially the
anisotropy, obtained from percolation theory agree with experiment or
theoretical predictions.Comment: 5 pages, accepted for publication in Physical Review Letters
(http://prl.aps.org/
Superfluid-insulator transition and BCS-BEC crossover in dirty ultracold Fermi gas
Superfluid-insulator transition in an ultracold Fermi gas in the external
disorder potential of the amplitude is studied as a function of the
concentration of the gas and magnetic field in the presence of the
Feshbach resonance. We find the zero temperature phase diagrams in the plane
() at a given and in the plane at a given . Our
results for BEC side of the diagram are also valid for the superfluid-insulator
transition in a Bose gas.Comment: Reference added, typos correcte
Critical dynamics of ballistic and Brownian particles in a heterogeneous environment
The dynamic properties of a classical tracer particle in a random, disordered
medium are investigated close to the localization transition. For Lorentz
models obeying Newtonian and diffusive motion at the microscale, we have
performed large-scale computer simulations, demonstrating that universality
holds at long times in the immediate vicinity of the transition. The scaling
function describing the crossover from anomalous transport to diffusive motion
is found to vary extremely slowly and spans at least 5 decades in time. To
extract the scaling function, one has to allow for the leading universal
corrections to scaling. Our findings suggest that apparent power laws with
varying exponents generically occur and dominate experimentally accessible time
windows as soon as the heterogeneities cover a decade in length scale. We
extract the divergent length scales, quantify the spatial heterogeneities in
terms of the non-Gaussian parameter, and corroborate our results by a thorough
finite-size analysis.Comment: 14 page
Percolation with excluded small clusters and Coulomb blockade in a granular system
We consider dc-conductivity of a mixture of small conducting and
insulating grains slightly below the percolation threshold, where finite
clusters of conducting grains are characterized by a wide spectrum of sizes.
The charge transport is controlled by tunneling of carriers between neighboring
conducting clusters via short ``links'' consisting of one insulating grain.
Upon lowering temperature small clusters (up to some -dependent size) become
Coulomb blockaded, and are avoided, if possible, by relevant hopping paths. We
introduce a relevant percolational problem of next-nearest-neighbors (NNN)
conductivity with excluded small clusters and demonstrate (both numerically and
analytically) that decreases as power law of the size of excluded
clusters. As a physical consequence, the conductivity is a power-law function
of temperature in a wide intermediate temperature range. We express the
corresponding index through known critical indices of the percolation theory
and confirm this relation numerically.Comment: 7 pages, 6 figure
A Numerical Study of Transport and Shot Noise at 2D Hopping
We have used modern supercomputer facilities to carry out extensive Monte
Carlo simulations of 2D hopping (at negligible Coulomb interaction) in
conductors with the completely random distribution of localized sites in both
space and energy, within a broad range of the applied electric field and
temperature , both within and beyond the variable-range hopping region. The
calculated properties include not only dc current and statistics of localized
site occupation and hop lengths, but also the current fluctuation spectrum.
Within the calculation accuracy, the model does not exhibit noise, so
that the low-frequency noise at low temperatures may be characterized by the
Fano factor . For sufficiently large samples, scales with conductor
length as , where , and
parameter is interpreted as the average percolation cluster length. At
relatively low , the electric field dependence of parameter is
compatible with the law which follows from directed
percolation theory arguments.Comment: 17 pages, 8 figures; Fixed minor typos and updated reference
Anisotropic generalization of Stinchcombe's solution for conductivity of random resistor network on a Bethe lattice
Our study is based on the work of Stinchcombe [1974 \emph{J. Phys. C}
\textbf{7} 179] and is devoted to the calculations of average conductivity of
random resistor networks placed on an anisotropic Bethe lattice. The structure
of the Bethe lattice is assumed to represent the normal directions of the
regular lattice. We calculate the anisotropic conductivity as an expansion in
powers of inverse coordination number of the Bethe lattice. The expansion terms
retained deliver an accurate approximation of the conductivity at resistor
concentrations above the percolation threshold. We make a comparison of our
analytical results with those of Bernasconi [1974 \emph{Phys. Rev. B}
\textbf{9} 4575] for the regular lattice.Comment: 14 pages, 2 figure
Percolative properties of hard oblate ellipsoids of revolution with a soft shell
We present an in-depth analysis of the geometrical percolation behavior in
the continuum of random assemblies of hard oblate ellipsoids of revolution.
Simulations where carried out by considering a broad range of aspect-ratios,
from spheres up to aspect-ratio 100 plate-like objects, and with various
limiting two particle interaction distances, from 0.05 times the major axis up
to 4.0 times the major axis. We confirm the widely reported trend of a
consistent lowering of the hard particle critical volume fraction with the
increase of the aspect-ratio. Moreover, assimilating the limiting interaction
distance to a shell of constant thickness surrounding the ellipsoids, we
propose a simple relation based on the total excluded volume of these objects
which allows to estimate the critical concentration from a quantity which is
quasi-invariant over a large spectrum of limiting interaction distances.
Excluded volume and volume quantities are derived explicitly.Comment: 11 pages, 8 figure
Unusual thermoelectric behavior of packed crystalline granular metals
Loosely packed granular materials are intensively studied nowadays.
Electrical and thermal transport properties should reflect the granular
structure as well as intrinsic properties. We have compacted crystalline
based metallic grains and studied the electrical resistivity and the
thermoelectric power as a function of temperature () from 15 to 300K. Both
properties show three regimes as a function of temperature. It should be
pointed out : (i) The electrical resistivity continuously decreases between 15
and 235 K (ii) with various dependences, e.g. at low ,
while (iii) the thermoelectric power (TEP) is positive, (iv) shows a bump near
60K, and (v) presents a rather unusual square root of temperature dependence at
low temperature. It is argued that these three regimes indicate a competition
between geometric and thermal processes, - for which a theory seems to be
missing in the case of TEP. The microchemical analysis results are also
reported indicating a complex microstructure inherent to the phase diagram
peritectic intricacies of this binary alloy.Comment: to be published in J. Appl. Phys.22 pages, 8 figure
Transport properties of heterogeneous materials derived from Gaussian random fields: Bounds and Simulation
We investigate the effective conductivity () of a class of
amorphous media defined by the level-cut of a Gaussian random field. The three
point solid-solid correlation function is derived and utilised in the
evaluation of the Beran-Milton bounds. Simulations are used to calculate
for a variety of fields and volume fractions at several different
conductivity contrasts. Relatively large differences in are observed
between the Gaussian media and the identical overlapping sphere model used
previously as a `model' amorphous medium. In contrast shows little
variability between different Gaussian media.Comment: 15 pages, 14 figure
Critical Exponents for Diluted Resistor Networks
An approach by Stephen is used to investigate the critical properties of
randomly diluted resistor networks near the percolation threshold by means of
renormalized field theory. We reformulate an existing field theory by Harris
and Lubensky. By a decomposition of the principal Feynman diagrams we obtain a
type of diagrams which again can be interpreted as resistor networks. This new
interpretation provides for an alternative way of evaluating the Feynman
diagrams for random resistor networks. We calculate the resistance crossover
exponent up to second order in , where is the spatial
dimension. Our result verifies a
previous calculation by Lubensky and Wang, which itself was based on the
Potts--model formulation of the random resistor network.Comment: 27 pages, 14 figure
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