26,030 research outputs found
Multicritical Points of Potts Spin Glasses on the Triangular Lattice
We predict the locations of several multicritical points of the Potts spin
glass model on the triangular lattice. In particular, continuous multicritical
lines, which consist of multicritical points, are obtained for two types of
two-state Potts (i.e., Ising) spin glasses with two- and three-body
interactions on the triangular lattice. These results provide us with numerous
examples to further verify the validity of the conjecture, which has succeeded
in deriving highly precise locations of multicritical points for several spin
glass models. The technique, called the direct triangular duality, a variant of
the ordinary duality transformation, directly relates the triangular lattice
with its dual triangular lattice in conjunction with the replica method.Comment: 18 pages, 2, figure
Whirling Hexagons and Defect Chaos in Hexagonal Non-Boussinesq Convection
We study hexagon patterns in non-Boussinesq convection of a thin rotating
layer of water. For realistic parameters and boundary conditions we identify
various linear instabilities of the pattern. We focus on the dynamics arising
from an oscillatory side-band instability that leads to a spatially disordered
chaotic state characterized by oscillating (whirling) hexagons. Using
triangulation we obtain the distribution functions for the number of pentagonal
and heptagonal convection cells. In contrast to the results found for defect
chaos in the complex Ginzburg-Landau equation and in inclined-layer convection,
the distribution functions can show deviations from a squared Poisson
distribution that suggest non-trivial correlations between the defects.Comment: 4 mpg-movies are available at
http://www.esam.northwestern.edu/~riecke/lit/lit.html submitted to New J.
Physic
Vectorial Loading of Processive Motor Proteins: Implementing a Landscape Picture
Individual processive molecular motors, of which conventional kinesin is the
most studied quantitatively, move along polar molecular tracks and, by exerting
a force on a tether, drag cellular cargoes, {\em in
vivo}, or spherical beads, {\em in vitro}, taking up to hundreds of
nanometer-scale steps. From observations of velocities and the dispersion of
displacements with time, under measured forces and controlled fuel supply
(typically ATP), one may hope to obtain insight into the molecular motions
undergone in the individual steps. In the simplest situation, the load force
may be regarded as a scalar resisting force, , acting
parallel to the track: however, experiments, originally by Gittes {\em et al.}
(1996), have imposed perpendicular (or vertical) loads, , while more
recently Block and coworkers (2002, 2003) and Carter and Cross (2005) have
studied {\em assisting} (or reverse) loads, , and also sideways (or
transverse) loads
Pressure coefficients of Raman modes of carbon nanotubes resolved by chirality: Environmental effect on graphene sheet
Studies of the mechanical properties of single-walled carbon nanotubes are
hindered by the availability only of ensembles of tubes with a range of
diameters. Tunable Raman excitation spectroscopy picks out identifiable tubes.
Under high pressure, the radial breathing mode shows a strong environmental
effect shown here to be largely independent of the nature of the environment .
For the G-mode, the pressure coefficient varies with diameter consistent with
the thick-wall tube model. However, results show an unexpectedly strong
environmental effect on the pressure coefficients. Reappraisal of data for
graphene and graphite gives the G-mode Grueuneisen parameter gamma = 1.34 and
the shear deformation parameter beta = 1.34.Comment: Submitted to Physical Review
Theta Vectors and Quantum Theta Functions
In this paper, we clarify the relation between Manin's quantum theta function
and Schwarz's theta vector in comparison with the kq representation, which is
equivalent to the classical theta function, and the corresponding coordinate
space wavefunction. We first explain the equivalence relation between the
classical theta function and the kq representation in which the translation
operators of the phase space are commuting. When the translation operators of
the phase space are not commuting, then the kq representation is no more
meaningful. We explain why Manin's quantum theta function obtained via algebra
(quantum tori) valued inner product of the theta vector is a natural choice for
quantum version of the classical theta function (kq representation). We then
show that this approach holds for a more general theta vector with constant
obtained from a holomorphic connection of constant curvature than the simple
Gaussian one used in the Manin's construction. We further discuss the
properties of the theta vector and of the quantum theta function, both of which
have similar symmetry properties under translation.Comment: LaTeX 21 pages, give more explicit explanations for notions given in
the tex
A ferromagnet with a glass transition
We introduce a finite-connectivity ferromagnetic model with a three-spin
interaction which has a crystalline (ferromagnetic) phase as well as a glass
phase. The model is not frustrated, it has a ferromagnetic equilibrium phase at
low temperature which is not reached dynamically in a quench from the
high-temperature phase. Instead it shows a glass transition which can be
studied in detail by a one step replica-symmetry broken calculation. This spin
model exhibits the main properties of the structural glass transition at a
solvable mean-field level.Comment: 7 pages, 2 figures, uses epl.cls (included
Quasinormal Modes of Dirty Black Holes
Quasinormal mode (QNM) gravitational radiation from black holes is expected
to be observed in a few years. A perturbative formula is derived for the shifts
in both the real and the imaginary part of the QNM frequencies away from those
of an idealized isolated black hole. The formulation provides a tool for
understanding how the astrophysical environment surrounding a black hole, e.g.,
a massive accretion disk, affects the QNM spectrum of gravitational waves. We
show, in a simple model, that the perturbed QNM spectrum can have interesting
features.Comment: 4 pages. Published in PR
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