19,405 research outputs found
Calculus on surfaces with general closest point functions
The Closest Point Method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys. 2008] and successfully applied to a variety of surface PDEs. In this paper we study the theoretical foundations of this method. The main idea is that surface differentials of a surface function can be replaced with Cartesian differentials of its closest point extension, i.e., its composition with a closest point function. We introduce a general class of these closest point functions (a subset of differentiable retractions), show that these are exactly the functions necessary to satisfy the above idea, and give a geometric characterization this class. Finally, we construct some closest point functions and demonstrate their effectiveness numerically on surface PDEs
An interacting spin flip model for one-dimensional proton conduction
A discrete asymmetric exclusion process (ASEP) is developed to model proton
conduction along one-dimensional water wires. Each lattice site represents a
water molecule that can be in only one of three states; protonated,
left-pointing, and right-pointing. Only a right(left)-pointing water can accept
a proton from its left(right). Results of asymptotic mean field analysis and
Monte-Carlo simulations for the three-species, open boundary exclusion model
are presented and compared. The mean field results for the steady-state proton
current suggest a number of regimes analogous to the low and maximal current
phases found in the single species ASEP [B. Derrida, Physics Reports, {\bf
301}, 65-83, (1998)]. We find that the mean field results are accurate
(compared with lattice Monte-Carlo simulations) only in the certain regimes.
Refinements and extensions including more elaborate forces and pore defects are
also discussed.Comment: 13pp, 6 fig
Phase Coexistence in Driven One Dimensional Transport
We study a one-dimensional totally asymmetric exclusion process with random
particle attachments and detachments in the bulk. The resulting dynamics leads
to unexpected stationary regimes for large but finite systems. Such regimes are
characterized by a phase coexistence of low and high density regions separated
by domain walls. We use a mean-field approach to interpret the numerical
results obtained by Monte-Carlo simulations and we predict the phase diagram of
this non-conserved dynamics in the thermodynamic limit.Comment: 4 pages, 3 figures. Accepted for publication on Phys. Rev. Let
Membrane paradigm and entropy of black holes in the Euclidean action approach
The membrane paradigm approach to black holes fixes in the vicinity of the
event horizon a fictitious surface, the stretched horizon, so that the
spacetime outside remains unchanged and the spacetime inside is vacuum. Using
this powerful method, several black hole properties have been found and
settled, such as the horizon's viscosity, electrical conductivity, resistivity,
as well as other properties. On the other hand the Euclidean action approach to
black hole spacetimes has been very fruitful in understanding black hole
entropy. Combining both the Euclidean action and membrane paradigm approaches a
direct derivation of the black hole entropy is given. In the derivation it is
considered that the only fields present are the gravitational and matter
fields, with no electric field.Comment: 13 page
Renormalised four-point coupling constant in the three-dimensional O(N) model with N=0
We simulate self-avoiding walks on a cubic lattice and determine the second
virial coefficient for walks of different lengths. This allows us to determine
the critical value of the renormalized four-point coupling constant in the
three-dimensional N-vector universality class for N=0. We obtain g* =
1.4005(5), where g is normalized so that the three-dimensional
field-theoretical beta-function behaves as \beta(g) = - g + g^2 for small g. As
a byproduct, we also obtain precise estimates of the interpenetration ratio
Psi*, Psi* = 0.24685(11), and of the exponent \nu, \nu = 0.5876(2).Comment: 16 page
Numerical Tests of the Chiral Luttinger Liquid Theory for Fractional Hall Edges
We report on microscopic numerical studies which support the chiral Luttinger
liquid theory of the fractional Hall edge proposed by Wen. Our calculations are
based in part on newly proposed and accurate many-body trial wavefunctions for
the low-energy edge excitations of fractional incompressible states.Comment: 12 pages + 1 figure, Revte
Exclusion process for particles of arbitrary extension: Hydrodynamic limit and algebraic properties
The behaviour of extended particles with exclusion interaction on a
one-dimensional lattice is investigated. The basic model is called -ASEP
as a generalization of the asymmetric exclusion process (ASEP) to particles of
arbitrary length . Stationary and dynamical properties of the -ASEP
with periodic boundary conditions are derived in the hydrodynamic limit from
microscopic properties of the underlying stochastic many-body system. In
particular, the hydrodynamic equation for the local density evolution and the
time-dependent diffusion constant of a tracer particle are calculated. As a
fundamental algebraic property of the symmetric exclusion process (SEP) the
SU(2)-symmetry is generalized to the case of extended particles
(1,4,7,10,13,16-HexaoxacycloÂoctaÂdecaÂne)dimethylÂindium(III) trifluoroÂmethaneÂsulfonate
In the title compound, [In(CH3)2(C12H24O6)](CF3O3S), two of the In—O distances within the cation are significantly shorter than the other four. The InIII atom is in a distorted hexaÂgonal–bipyramidal coordination geometry in which the C—In—C angle is 175.44 (12)°. The crystal structure is stabilized by weak interÂmolecular C—H⋯O hydrogen bonds
DC-transport properties of ferromagnetic (Ga,Mn)As semiconductors
We study the dc transport properties of (Ga,Mn)As diluted magnetic
semiconductors with Mn concentration varying from 1.5% to 8%. Both diagonal and
Hall components of the conductivity tensor are strongly sensitive to the
magnetic state of these semiconductors. Transport data obtained at low
temperatures are discussed theoretically within a model of band-hole
quasiparticles with a finite spectral width due to elastic scattering from Mn
and compensating defects. The theoretical results are in good agreement with
measured anomalous Hall effect and anisotropic longitudinal magnetoresistance
data. This quantitative understanding of dc magneto-transport effects in
(Ga,Mn)As is unparalleled in itinerant ferromagnetic systems.Comment: 3 pages, 3 figure
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