102 research outputs found
Exact result for the effective conductivity of a continuum percolation model
Journal ArticleA random two-dimensional checkerboard of squares of conductivities 1 and 8 in proportions p and 1 - p is considered. Classical duality implies that the effective conductivity obeys o* = V8 at p = 1/2. It is rigorously found here that to leading order as 8--0, this exact result holds for all p in the interval (1- pc,pc), where pc=0.59 is the site percolation probability, not just at p = 1/2. In particular, o*(p,8)=78+O (8), as 8 -- 0. which is argued to hold for complex 8 as well. The analysis is based on the identification of a "symmetric" backbone, which is statistically invariant under interchange of the components for any pE(1--pc,pc), like the entire checkerboard at p =1/2. This backbone is defined in terms of "choke points" for the current, which have been observed in an experiment
Heat balance of the Earth
Results of improved calculations of the heat balance components of Earth's surface are reported for yearly average conditions. The technique used to determine the heat-balance components from land- and sea-based actinometric observations as well as from satellite data on the radiation balance of the Earth-atmosphere system is described, with special attention given to short-wavelength solar radiation on the continents, effective radiation from the land surface, the radiation balance of the ocean surface, heat expended by both evaporation from the ocean surface, and turbulent heat transfer between the ocean surface and the atmosphere. World maps of heat-balance components show yearly average values of total radiation, radiation balance, heat expended by evaporation, the turbulent heat flow between Earth's surface and atmosphere, and heat transfer between the ocean surface and underlying waters. The global surface heat balance is estimated along with global values of the various components and the heat-balance components for different latitude zones
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
Ginzburg-Landau model with small pinning domains
We consider a Ginzburg-Landau type energy with a piecewise constant pinning
term in the potential . The function is different from
1 only on finitely many disjoint domains, called the {\it pinning domains}.
These pinning domains model small impurities in a homogeneous superconductor
and shrink to single points in the limit ; here, \v is the inverse of
the Ginzburg-Landau parameter. We study the energy minimization in a smooth
simply connected domain with Dirichlet boundary
condition on \d \O, with topological degree {\rm deg}_{\d \O} (g) = d
>0. Our main result is that, for small \v, minimizers have distinct
zeros (vortices) which are inside the pinning domains and they have a degree
equal to 1. The question of finding the locations of the pinning domains with
vortices is reduced to a discrete minimization problem for a finite-dimensional
functional of renormalized energy. We also find the position of the vortices
inside the pinning domains and show that, asymptotically, this position is
determined by {\it local renormalized energy} which does not depend on the
external boundary conditions.Comment: 39 page
Are the Tails of Percolation Thresholds Gaussians ?
The probability distribution of percolation thresholds in finite lattices
were first believed to follow a normal Gaussian behaviour. With increasing
computer power and more efficient simulational techniques, this belief turned
to a stretched exponential behaviour, instead. Here, based on a further
improvement of Monte Carlo data, we show evidences that this question is not
yet answered at all.Comment: 7 pages including 3 figure
Efficient Monte Carlo algorithm and high-precision results for percolation
We present a new Monte Carlo algorithm for studying site or bond percolation
on any lattice. The algorithm allows us to calculate quantities such as the
cluster size distribution or spanning probability over the entire range of site
or bond occupation probabilities from zero to one in a single run which takes
an amount of time scaling linearly with the number of sites on the lattice. We
use our algorithm to determine that the percolation transition occurs at
occupation probability 0.59274621(13) for site percolation on the square
lattice and to provide clear numerical confirmation of the conjectured
4/3-power stretched-exponential tails in the spanning probability functions.Comment: 8 pages, including 3 postscript figures, minor corrections in this
version, plus updated figures for the position of the percolation transitio
Effective Viscosity of Dilute Bacterial Suspensions: A Two-Dimensional Model
Suspensions of self-propelled particles are studied in the framework of
two-dimensional (2D) Stokesean hydrodynamics. A formula is obtained for the
effective viscosity of such suspensions in the limit of small concentrations.
This formula includes the two terms that are found in the 2D version of
Einstein's classical result for passive suspensions. To this, the main result
of the paper is added, an additional term due to self-propulsion which depends
on the physical and geometric properties of the active suspension. This term
explains the experimental observation of a decrease in effective viscosity in
active suspensions.Comment: 15 pages, 3 figures, submitted to Physical Biolog
Chiral tunneling in single and bilayer graphene
We review chiral (Klein) tunneling in single-layer and bilayer graphene and
present its semiclassical theory, including the Berry phase and the Maslov
index. Peculiarities of the chiral tunneling are naturally explained in terms
of classical phase space. In a one-dimensional geometry we reduced the original
Dirac equation, describing the dynamics of charge carriers in the single layer
graphene, to an effective Schr\"odinger equation with a complex potential. This
allowed us to study tunneling in details and obtain analytic formulas. Our
predictions are compared with numerical results. We have also demonstrated
that, for the case of asymmetric n-p-n junction in single layer graphene, there
is total transmission for normal incidence only, side resonances are
suppressed.Comment: submitted to Proceedings of Nobel Symposium on graphene, May 201
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