10,093 research outputs found
A homomorphism between link and XXZ modules over the periodic Temperley-Lieb algebra
We study finite loop models on a lattice wrapped around a cylinder. A section
of the cylinder has N sites. We use a family of link modules over the periodic
Temperley-Lieb algebra EPTL_N(\beta, \alpha) introduced by Martin and Saleur,
and Graham and Lehrer. These are labeled by the numbers of sites N and of
defects d, and extend the standard modules of the original Temperley-Lieb
algebra. Beside the defining parameters \beta=u^2+u^{-2} with u=e^{i\lambda/2}
(weight of contractible loops) and \alpha (weight of non-contractible loops),
this family also depends on a twist parameter v that keeps track of how the
defects wind around the cylinder. The transfer matrix T_N(\lambda, \nu) depends
on the anisotropy \nu and the spectral parameter \lambda that fixes the model.
(The thermodynamic limit of T_N is believed to describe a conformal field
theory of central charge c=1-6\lambda^2/(\pi(\lambda-\pi)).)
The family of periodic XXZ Hamiltonians is extended to depend on this new
parameter v and the relationship between this family and the loop models is
established. The Gram determinant for the natural bilinear form on these link
modules is shown to factorize in terms of an intertwiner i_N^d between these
link representations and the eigenspaces of S^z of the XXZ models. This map is
shown to be an isomorphism for generic values of u and v and the critical
curves in the plane of these parameters for which i_N^d fails to be an
isomorphism are given.Comment: Replacement of "The Gram matrix as a connection between periodic loop
models and XXZ Hamiltonians", 31 page
From solar-like to anti-solar differential rotation in cool stars
Stellar differential rotation can be separated into two main regimes:
solar-like when the equator rotates faster than the poles and anti-solar when
the polar regions rotate faster than the equator. We investigate the transition
between these two regimes with 3-D numerical simulations of rotating spherical
shells. We conduct a systematic parameter study which also includes models from
different research groups. We find that the direction of the differential
rotation is governed by the contribution of the Coriolis force in the force
balance, independently of the model setup (presence of a magnetic field,
thickness of the convective layer, density stratification). Rapidly-rotating
cases with a small Rossby number yield solar-like differential rotation, while
weakly-rotating models sustain anti-solar differential rotation. Close to the
transition, the two kinds of differential rotation are two possible bistable
states. This study provides theoretical support for the existence of anti-solar
differential rotation in cool stars with large Rossby numbers.Comment: 5 pages, 6 figures, accepted for publication in MNRA
What controls the large-scale magnetic fields of M dwarfs?
Observations of active M dwarfs show a broad variety of large-scale magnetic
fields encompassing dipole-dominated and multipolar geometries. We detail the
analogy between some anelastic dynamo simulations and spectropolarimetric
observations of 23 M stars. In numerical models, the relative contribution of
inertia and Coriolis force in the global force balance -estimated by the
so-called local Rossby number- is known to have a strong impact on the magnetic
field geometry. We discuss the relevance of this parameter in setting the
large-scale magnetic field of M dwarfs.Comment: 4 pages, 3 figures, conference proceeding, IAUS 302 'Magnetic Fields
Throughout the Stellar Evolution', (26-30 Aug 2013, Biarritz, France
M-dwarf stellar winds: the effects of realistic magnetic geometry on rotational evolution and planets
We perform three-dimensional numerical simulations of stellar winds of
early-M dwarf stars. Our simulations incorporate observationally reconstructed
large-scale surface magnetic maps, suggesting that the complexity of the
magnetic field can play an important role in the angular momentum evolution of
the star, possibly explaining the large distribution of periods in field dM
stars, as reported in recent works. In spite of the diversity of the magnetic
field topologies among the stars in our sample, we find that stellar wind
flowing near the (rotational) equatorial plane carries most of the stellar
angular momentum, but there is no preferred colatitude contributing to mass
loss, as the mass flux is maximum at different colatitudes for different stars.
We find that more non-axisymmetric magnetic fields result in more asymmetric
mass fluxes and wind total pressures (defined as the sum of
thermal, magnetic and ram pressures). Because planetary magnetospheric sizes
are set by pressure equilibrium between the planet's magnetic field and , variations of up to a factor of in (as found in the
case of a planet orbiting at several stellar radii away from the star) lead to
variations in magnetospheric radii of about 20 percent along the planetary
orbital path. In analogy to the flux of cosmic rays that impact the Earth,
which is inversely modulated with the non-axisymmetric component of the total
open solar magnetic flux, we conclude that planets orbiting M dwarf stars like
DT~Vir, DS~Leo and GJ~182, which have significant non-axisymmetric field
components, should be the more efficiently shielded from galactic cosmic rays,
even if the planets lack a protective thick atmosphere/large magnetosphere of
their own.Comment: 16 pages, 9 figures, to appear in MNRA
What controls the magnetic geometry of M dwarfs?
Context: observations of rapidly rotating M dwarfs show a broad variety of
large-scale magnetic fields encompassing dipole-dominated and multipolar
geometries. In dynamo models, the relative importance of inertia in the force
balance -- quantified by the local Rossby number -- is known to have a strong
impact on the magnetic field geometry. Aims: we aim to assess the relevance of
the local Rossby number in controlling the large-scale magnetic field geometry
of M dwarfs. Methods: we explore the similarities between anelastic dynamo
models in spherical shells and observations of active M-dwarfs, focusing on
field geometries derived from spectropolarimetric studies. To do so, we
construct observation-based quantities aimed to reflect the diagnostic
parameters employed in numerical models. Results: the transition between
dipole-dominated and multipolar large-scale fields in early to mid M dwarfs is
tentatively attributed to a Rossby number threshold. We interpret late M dwarfs
magnetism to result from a dynamo bistability occurring at low Rossby number.
By analogy with numerical models, we expect different amplitudes of
differential rotation on the two dynamo branches.Comment: 4 pages, 4 figures, accepted for publication in A&
Preferred levels for background ducking to produce esthetically pleasing audio for TV with clear speech
In audio production, background ducking facilitates speech intelligibility while allowing the background to fulfill its purpose, e.g., to create ambience, set the mood, or convey semantic cues. Technical details for recommended ducking practices are not currently documented in the literature. Hence, we first analyzed common practices found in TV documentaries. Second, a listening test investigated the preferences of 22 normal-hearing participants on the Loud- ness Difference (LD) between commentary and background during ducking. Highly personal preferences were observed, highlighting the importance of object-based personalization. Sta- tistically significant difference was found between non-expert and expert listeners. On average, non-experts preferred LDs that were 4 LU higher than the ones preferred by experts. A sta- tistically significant difference was also found between Commentary over Music (CoM) and Commentary over Ambience (CoA). Based on the test results, we recommend at least 10 LU difference for CoM and at least 15 LU for CoA. Moreover, a computational method based on the Binaural Distortion-Weighted Glimpse Proportion (BiDWGP) was found to match the median preferred LD for each item with good accuracy (mean absolute error = 1.97 LU ± 2.50)
Validity of the Adiabatic Approximation
We analyze the validity of the adiabatic approximation, and in particular the
reliability of what has been called the "standard criterion" for validity of
this approximation. Recently, this criterion has been found to be insufficient.
We will argue that the criterion is sufficient only when it agrees with the
intuitive notion of slowness of evolution of the Hamiltonian. However, it can
be insufficient in cases where the Hamiltonian varies rapidly but only by a
small amount. We also emphasize the distinction between the adiabatic {\em
theorem} and the adiabatic {\em approximation}, two quite different although
closely related ideas.Comment: 4 pages, 1 figur
Stochastic density functional theory
Linear-scaling implementations of density functional theory (DFT) reach their
intended efficiency regime only when applied to systems having a physical size
larger than the range of their Kohn-Sham density matrix (DM). This causes a
problem since many types of large systems of interest have a rather broad DM
range and are therefore not amenable to analysis using DFT methods. For this
reason, the recently proposed stochastic DFT (sDFT), avoiding exhaustive DM
evaluations, is emerging as an attractive alternative linear-scaling approach.
This review develops a general formulation of sDFT in terms of a
(non)orthogonal basis representation and offers an analysis of the statistical
errors (SEs) involved in the calculation. Using a new Gaussian-type basis-set
implementation of sDFT, applied to water clusters and silicon nanocrystals, it
demonstrates and explains how the standard deviation and the bias depend on the
sampling rate and the system size in various types of calculations. We also
develop basis-set embedded-fragments theory, demonstrating its utility for
reducing the SEs for energy, density of states and nuclear force calculations.
Finally, we discuss the algorithmic complexity of sDFT, showing it has CPU
wall-time linear-scaling. The method parallelizes well over distributed
processors with good scalability and therefore may find use in the upcoming
exascale computing architectures
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