2,991 research outputs found
Superdiffusivity of asymmetric exclusion process in dimensions one and two
We prove that the diffusion coefficient for the asymmetric exclusion process
diverges at least as fast as in dimension and
in . The method applies to nearest and non-nearest neighbor asymmetric
exclusion processes
Temperature dependent photoluminescence of organic semiconductors with varying backbone conformation
We present photoluminescence studies as a function of temperature from a
series of conjugated polymers and a conjugated molecule with distinctly
different backbone conformations. The organic materials investigated here are:
planar methylated ladder type poly para-phenylene, semi-planar polyfluorene,
and non-planar para hexaphenyl. In the longer-chain polymers the
photoluminescence transition energies blue shift with increasing temperatures.
The conjugated molecules, on the other hand, red shift their transition
energies with increasing temperatures. Empirical models that explain the
temperature dependence of the band gap energies in inorganic semiconductors can
be extended to explain the temperature dependence of the transition energies in
conjugated molecules.Comment: 8 pages, 9 figure
Superdiffusivity of Finite-Range Asymmetric Exclusion Processes on
We consider finite-range asymmetric exclusion processes on with
non-zero drift. The diffusivity is expected to be of . We prove that in the weak (Tauberian) sense
that as . The proof employs the resolvent method to make a direct comparison with the
totally asymmetric simple exclusion process, for which the result is a
consequence of the scaling limit for the two-point function recently obtained
by Ferrari and Spohn. In the nearest neighbor case, we show further that
is monotone, and hence we can conclude that in the usual sense.Comment: Version 3. Statement of Theorem 3 is correcte
Algebraic Torsion in Contact Manifolds
We extract a nonnegative integer-valued invariant, which we call the "order
of algebraic torsion", from the Symplectic Field Theory of a closed contact
manifold, and show that its finiteness gives obstructions to the existence of
symplectic fillings and exact symplectic cobordisms. A contact manifold has
algebraic torsion of order zero if and only if it is algebraically overtwisted
(i.e. has trivial contact homology), and any contact 3-manifold with positive
Giroux torsion has algebraic torsion of order one (though the converse is not
true). We also construct examples for each nonnegative k of contact 3-manifolds
that have algebraic torsion of order k but not k - 1, and derive consequences
for contact surgeries on such manifolds. The appendix by Michael Hutchings
gives an alternative proof of our cobordism obstructions in dimension three
using a refinement of the contact invariant in Embedded Contact Homology.Comment: 53 pages, 4 figures, with an appendix by Michael Hutchings; v.3 is a
final update to agree with the published paper, and also corrects a minor
error that appeared in the published version of the appendi
Phase Segregation Dynamics in Particle Systems with Long Range Interactions I: Macroscopic Limits
We present and discuss the derivation of a nonlinear non-local
integro-differential equation for the macroscopic time evolution of the
conserved order parameter of a binary alloy undergoing phase segregation. Our
model is a d-dimensional lattice gas evolving via Kawasaki exchange dynamics,
i.e. a (Poisson) nearest-neighbor exchange process, reversible with respect to
the Gibbs measure for a Hamiltonian which includes both short range (local) and
long range (nonlocal) interactions. A rigorous derivation is presented in the
case in which there is no local interaction. In a subsequent paper (part II),
we discuss the phase segregation phenomena in the model. In particular we argue
that the phase boundary evolutions, arising as sharp interface limits of the
family of equations derived in this paper, are the same as the ones obtained
from the corresponding limits for the Cahn-Hilliard equation.Comment: amstex with macros (included in the file), tex twice, 20 page
Feed-Forward Chains of Recurrent Attractor Neural Networks Near Saturation
We perform a stationary state replica analysis for a layered network of Ising
spin neurons, with recurrent Hebbian interactions within each layer, in
combination with strictly feed-forward Hebbian interactions between successive
layers. This model interpolates between the fully recurrent and symmetric
attractor network studied by Amit el al, and the strictly feed-forward
attractor network studied by Domany et al. Due to the absence of detailed
balance, it is as yet solvable only in the zero temperature limit. The built-in
competition between two qualitatively different modes of operation,
feed-forward (ergodic within layers) versus recurrent (non- ergodic within
layers), is found to induce interesting phase transitions.Comment: 14 pages LaTex with 4 postscript figures submitted to J. Phys.
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Beagle 2: Mission to Mars — current status
Beagle 2, developed in the UK, was launched on June 2, 2003. It landed on Mars on December 25th, 2003 in Isidis Planitia, a large sedimentary basin. To date, the team is awaiting signals from the Beagle 2 lander. Current status of the mission will be reported
Manifolds with 1/4-pinched flag curvature
We say that a nonnegatively curved manifold has quarter pinched flag
curvature if for any two planes which intersect in a line the ratio of their
sectional curvature is bounded above by 4. We show that these manifolds have
nonnegative complex sectional curvature. By combining with a theorem of Brendle
and Schoen it follows that any positively curved manifold with strictly quarter
pinched flag curvature must be a space form. This in turn generalizes a result
of Andrews and Nguyen in dimension 4. For odd dimensional manifolds we obtain
results for the case that the flag curvature is pinched with some constant
below one quarter, one of which generalizes a recent work of Petersen and Tao
Hyperholomorpic connections on coherent sheaves and stability
Let be a hyperkaehler manifold, and a torsion-free and reflexive
coherent sheaf on . Assume that (outside of its singularities) admits a
connection with a curvature which is invariant under the standard SU(2)-action
on 2-forms. If the curvature is square-integrable, then is stable and its
singularities are hyperkaehler subvarieties in . Such sheaves (called
hyperholomorphic sheaves) are well understood. In the present paper, we study
sheaves admitting a connection with SU(2)-invariant curvature which is not
necessarily square-integrable. This situation arises often, for instance, when
one deals with higher direct images of holomorphic bundles. We show that such
sheaves are stable.Comment: 37 pages, version 11, reference updated, corrected many minor errors
and typos found by the refere
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