2,114 research outputs found
Multiplicities of Periodic Orbit Lengths for Non-Arithmetic Models
Multiplicities of periodic orbit lengths for non-arithmetic Hecke triangle
groups are discussed. It is demonstrated both numerically and analytically that
at least for certain groups the mean multiplicity of periodic orbits with
exactly the same length increases exponentially with the length. The main
ingredient used is the construction of joint distribution of periodic orbits
when group matrices are transformed by field isomorphisms. The method can be
generalized to other groups for which traces of group matrices are integers of
an algebraic field of finite degree
Topological Expansion and Exponential Asymptotics in 1D Quantum Mechanics
Borel summable semiclassical expansions in 1D quantum mechanics are
considered. These are the Borel summable expansions of fundamental solutions
and of quantities constructed with their help. An expansion, called
topological,is constructed for the corresponding Borel functions. Its main
property is to order the singularity structure of the Borel plane in a
hierarchical way by an increasing complexity of this structure starting from
the analytic one. This allows us to study the Borel plane singularity structure
in a systematic way. Examples of such structures are considered for linear,
harmonic and anharmonic potentials. Together with the best approximation
provided by the semiclassical series the exponentially small contribution
completing the approximation are considered. A natural method of constructing
such an exponential asymptotics relied on the Borel plane singularity
structures provided by the topological expansion is developed. The method is
used to form the semiclassical series including exponential contributions for
the energy levels of the anharmonic oscillator.Comment: 46 pages, 22 EPS figure
Substrate Suppression of Thermal Roughness in Stacked Supported Bilayers
We have fabricated a stack of five 1,2-dipalmitoyl-sn-3-phosphatidylethanolamine (DPPE) bilayers supported on a polished silicon substrate in excess water. The density profile of these stacks normal to the substrate was obtained through analysis of x-ray reflectivity. Near the substrate, we find the layer roughness and repeat spacing are both significantly smaller than values found in bulk multilayer systems. The reduced spacing and roughness result from suppression of lateral fluctuations due to the flat substrate boundary. The layer spacing decrease then occurs due to reduced Helfrich repulsion.This work was partially supported by NSF Grants No.
DMR-0706369 and No. DMR-0706665. Use of the Advanced
Photon Sourcewas supported by theUSDepartment of Energy,
Office of Science, Office of Basic Energy Sciences, under
Contract No. DE-AC02-06CH11357. SKS and ANP wish
to acknowledge support from the Office of Basic Energy
Sciences, US Department of Energy, via Grant No. DE-FG02-
04ER46173. We would also like to thank Suresh Narayanan
for his support of the experimental work at Sector 8-ID
Noncompact chiral U(1) gauge theories on the lattice
A new, adiabatic phase choice is adopted for the overlap in the case of an
infinite volume, noncompact abelian chiral gauge theory. This gauge choice
obeys the same symmetries as the Brillouin-Wigner (BW) phase choice, and, in
addition, produces a Wess-Zumino functional that is linear in the gauge
variables on the lattice. As a result, there are no gauge violations on the
trivial orbit in all theories, consistent and covariant anomalies are simply
related and Berry's curvature now appears as a Schwinger term. The adiabatic
phase choice can be further improved to produce a perfect phase choice, with a
lattice Wess-Zumino functional that is just as simple as the one in continuum.
When perturbative anomalies cancel, gauge invariance in the fermionic sector is
fully restored. The lattice effective action describing an anomalous abelian
gauge theory has an explicit form, close to one analyzed in the past in a
perturbative continuum framework.Comment: 35 pages, one figure, plain TeX; minor typos corrected; to appear in
PR
Signed zeros of Gaussian vector fields-density, correlation functions and curvature
We calculate correlation functions of the (signed) density of zeros of
Gaussian distributed vector fields. We are able to express correlation
functions of arbitrary order through the curvature tensor of a certain abstract
Riemann-Cartan or Riemannian manifold. As an application, we discuss one- and
two-point functions. The zeros of a two-dimensional Gaussian vector field model
the distribution of topological defects in the high-temperature phase of
two-dimensional systems with orientational degrees of freedom, such as
superfluid films, thin superconductors and liquid crystals.Comment: 14 pages, 1 figure, uses iopart.cls, improved presentation, to appear
in J. Phys.
Bayesian Learning of Gas Transport in Three-Dimensional Fracture Networks
Modeling gas flow through fractures of subsurface rock is a particularly
challenging problem because of the heterogeneous nature of the material.
High-fidelity simulations using discrete fracture network (DFN) models are one
methodology for predicting gas particle breakthrough times at the surface, but
are computationally demanding. We propose a Bayesian machine learning method
that serves as an efficient surrogate model, or emulator, for these
three-dimensional DFN simulations. Our model trains on a small quantity of
simulation data and, using a graph/path-based decomposition of the fracture
network, rapidly predicts quantiles of the breakthrough time distribution. The
approach, based on Gaussian Process Regression (GPR), outputs predictions that
are within 20-30% of high-fidelity DFN simulation results. Unlike previously
proposed methods, it also provides uncertainty quantification, outputting
confidence intervals that are essential given the uncertainty inherent in
subsurface modeling. Our trained model runs within a fraction of a second,
which is considerably faster than other methods with comparable accuracy and
multiple orders of magnitude faster than high-fidelity simulations
Berry's phase and Quantum Dynamics of Ferromagnetic Solitons
We study spin parity effects and the quantum propagation of solitons (Bloch
walls) in quasi-one dimensional ferromagnets. Within a coherent state path
integral approach we derive a quantum field theory for nonuniform spin
configurations. The effective action for the soliton position is shown to
contain a gauge potential due to the Berry phase and a damping term caused by
the interaction between soliton and spin waves. For temperatures below the
anisotropy gap this dissipation reduces to a pure soliton mass renormalization.
The gauge potential strongly affects the quantum dynamics of the soliton in a
periodic lattice or pinning potential. For half-integer spin, destructive
interference between soliton states of opposite chirality suppresses nearest
neighbor hopping. Thus the Brillouin zone is halved, and for small mixing of
the chiralities the dispersion reveals a surprising dynamical correlation: Two
subsequent band minima belong to different chirality states of the soliton. For
integer spin, the Berry phase is inoperative and a simple tight-binding
dispersion is obtained. Finally it is shown that external fields can be used to
interpolate continuously between the Bloch wall dispersions for half-integer
and integer spin.Comment: 20 pages, RevTex 3.0 (twocolumn), to appear in Phys. Rev. B 53, 3237
(1996), 4 PS figures available upon reques
Impaired perception of facial motion in autism spectrum disorder
Copyright: © 2014 OâBrien et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.This article has been made available through the Brunel Open Access Publishing Fund.Facial motion is a special type of biological motion that transmits cues for socio-emotional communication and enables the discrimination of properties such as gender and identity. We used animated average faces to examine the ability of adults with autism spectrum disorders (ASD) to perceive facial motion. Participants completed increasingly difficult tasks involving the discrimination of (1) sequences of facial motion, (2) the identity of individuals based on their facial motion and (3) the gender of individuals. Stimuli were presented in both upright and upside-down orientations to test for the difference in inversion effects often found when comparing ASD with controls in face perception. The ASD groupâs performance was impaired relative to the control group in all three tasks and unlike the control group, the individuals with ASD failed to show an inversion effect. These results point to a deficit in facial biological motion processing in people with autism, which we suggest is linked to deficits in lower level motion processing we have previously reported
Vacuum decay in quantum field theory
We study the contribution to vacuum decay in field theory due to the
interaction between the long and short-wavelength modes of the field. The field
model considered consists of a scalar field of mass with a cubic term in
the potential. The dynamics of the long-wavelength modes becomes diffusive in
this interaction. The diffusive behaviour is described by the reduced Wigner
function that characterizes the state of the long-wavelength modes. This
function is obtained from the whole Wigner function by integration of the
degrees of freedom of the short-wavelength modes. The dynamical equation for
the reduced Wigner function becomes a kind of Fokker-Planck equation which is
solved with suitable boundary conditions enforcing an initial metastable vacuum
state trapped in the potential well. As a result a finite activation rate is
found, even at zero temperature, for the formation of true vacuum bubbles of
size . This effect makes a substantial contribution to the total decay
rate.Comment: 27 pages, RevTeX, 1 figure (uses epsf.sty
Vacuum decay in quantum field theory
We study the contribution to vacuum decay in field theory due to the
interaction between the long and short-wavelength modes of the field. The field
model considered consists of a scalar field of mass with a cubic term in
the potential. The dynamics of the long-wavelength modes becomes diffusive in
this interaction. The diffusive behaviour is described by the reduced Wigner
function that characterizes the state of the long-wavelength modes. This
function is obtained from the whole Wigner function by integration of the
degrees of freedom of the short-wavelength modes. The dynamical equation for
the reduced Wigner function becomes a kind of Fokker-Planck equation which is
solved with suitable boundary conditions enforcing an initial metastable vacuum
state trapped in the potential well. As a result a finite activation rate is
found, even at zero temperature, for the formation of true vacuum bubbles of
size . This effect makes a substantial contribution to the total decay
rate.Comment: 27 pages, RevTeX, 1 figure (uses epsf.sty
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