3,030 research outputs found
Asymptotics of characters of symmetric groups, genus expansion and free probability
The convolution of indicators of two conjugacy classes on the symmetric group
S_q is usually a complicated linear combination of indicators of many conjugacy
classes. Similarly, a product of the moments of the Jucys--Murphy element
involves many conjugacy classes with complicated coefficients. In this article
we consider a combinatorial setup which allows us to manipulate such products
easily: to each conjugacy class we associate a two-dimensional surface and the
asymptotic properties of the conjugacy class depend only on the genus of the
resulting surface. This construction closely resembles the genus expansion from
the random matrix theory. As the main application we study irreducible
representations of symmetric groups S_q for large q. We find the asymptotic
behavior of characters when the corresponding Young diagram rescaled by a
factor q^{-1/2} converge to a prescribed shape. The character formula (known as
the Kerov polynomial) can be viewed as a power series, the terms of which
correspond to two-dimensional surfaces with prescribed genus and we compute
explicitly the first two terms, thus we prove a conjecture of Biane.Comment: version 2: change of title; the section on Gaussian fluctuations was
moved to a subsequent paper [Piotr Sniady: "Gaussian fluctuations of
characters of symmetric groups and of Young diagrams" math.CO/0501112
Asteroseismology for "\`{a} la carte" stellar age-dating and weighing: Age and mass of the CoRoT exoplanet host HD 52265
In the context of CoRoT, Kepler, Gaia, TESS, and PLATO, precise and accurate
stellar ages, masses and radii are of paramount importance. They are crucial to
constrain scenarii of planetary formation and evolution.We aim at quantifying
how detailed stellar modeling improves the accuracy and precision on age and
mass of individual stars. We adopt a multifaceted approach where we examine how
the number of observational constraints as well as the uncertainties on
observations and on model input physics impact the age-dating and weighing. We
modelled the exoplanet host-star HD52265, a MS, solar-like oscillator observed
by CoRoT. We considered different sets of observational constraints (HR data,
metallicity, seismic constraints). For each case, we determined the age, mass,
and properties of HD52265 inferred from models, and quantified the impact of
the models inputs. Our seismic analysis provides an age A=2.10-2.54 Gyr, a mass
M=1.14-1.32 Msun, and a radius R=1.30-1.34 Rsun, which corresponds to
uncertainties of 10, 7, and 1.5% respectively. Our seismic study provides
constraints on surface convection, through the mixing-length found to be 12-15%
smaller than the solar one. Because of helium-mass degeneracy, the initial He
abundance is determined modulo the mass. The seismic mass of the exoplanet is
found to be Mp sin i=1.17-1.26 MJup, much more precise than what can be derived
by HR diagram inversion. We demonstrate that asteroseismology allows to improve
the age accuracy compared to other methods. We emphasize that the knowledge of
the mean properties of oscillations -as the large frequency separation- is not
enough for deriving accurate ages. We need precise individual frequencies to
narrow the age scatter due to model uncertainties. This strengthen the case for
precise classical stellar parameters and frequencies as will be obtained by
Gaia and PLATO.Comment: 23 pages, 9 figures, Accepted for publication in Astronomy &
Astrophysics Corrected by the language editor, Table link to CD
Longitudinal and transverse noise in a moving Vortex Lattice
We have studied the longitudinal and the transverse velocity fluctuations of
a moving vortex lattice (VL) driven by a transport current. They exhibit both
the same broad spectrum and the same order of magnitude. These two components
are insensitive to the velocity and to a small bulk perturbation. This means
that no bulk averaging over the disorder and no VL crystallization are
observed. This is consistently explained referring to a previously proposed
noisy flow of surface current whose elementary fluctuator is measured
isotropic.Comment: accepted for publication in Phys Rev
On the interpretation of echelle diagrams for solar-like oscillations. Effect of centrifugal distortion
This work aims at determining the impact of slow to moderate rotation on the
regular patterns often present in solar-like oscillation spectra. We focus on
the well-known asteroseismic diagnostic echelle diagrams, examining how
rotation may modify the estimates of the large and small spacings, as well as
the identification of modes. We illustrate the work with a real case: the
solar-like star Bootis. The modeling takes into account rotation effects
on the equilibrium models through an effective gravity and on the oscillation
frequencies through both perturbative and non-perturbative calculations. We
compare the results of both type of calculations in the context of the regular
spacings (like the small spacings and the scaled small spacings) and echelle
diagrams. We show that for echelle diagrams the perturbative approach remains
valid for rotational velocities up to 40-50 km/s. We show that for the
rotational velocities measured in solar-like stars, theoretical oscillation
frequencies must be corrected up to the second-order in terms of rotation rate,
including near degeneracy effects. For rotational velocities of about 16 km/S
and higher, diagnostics on large spacings and on modal identification through
echelle diagrams can be significantly altered by the presence of the
components of the rotationally split modes. We found these effects to be
detectable in the observed frequency range. Analysis of the effects of rotation
on small spacings and scaled small spacings reveals that these can be of the
order of, or even larger than surface effects, typically turbulence,
microscopic diffusion, etc. Furthermore, we show that scaled spacings are
significantly affected by stellar distortion even for small stellar rotational
velocities (from 10-15 km/s) and therefore some care must be taken when using
them as indicators for probing deep stellar interiors.Comment: 10 pages,5 figures, accepted for publication in ApJ;
http://iopscience.iop.org/0004-637X/721/1/537
The thermoelectric working fluid: thermodynamics and transport
Thermoelectric devices are heat engines, which operate as generators or
refrigerators using the conduction electrons as a working fluid. The
thermoelectric heat-to-work conversion efficiency has always been typically
quite low, but much effort continues to be devoted to the design of new
materials boasting improved transport properties that would make them of the
electron crystal-phonon glass type of systems. On the other hand, there are
comparatively few studies where a proper thermodynamic treatment of the
electronic working fluid is proposed. The present article aims to contribute to
bridge this gap by addressing both the thermodynamic and transport properties
of the thermoelectric working fluid covering a variety of models, including
interacting systems.Comment: 15 pages, 2 figure
Effect of ionic radii on the Curie temperature in Ba1-x-ySrxCayTiO3 compounds
<p>A series of Ba<sub>1-x-y</sub>Sr<sub>x</sub>Ca<sub>y</sub>TiO<sub>3</sub> compounds were prepared with varying average ionic radii and cation disorder on A-site. All samples showed typical ferroelectric behavior. A simple empirical equation correlated Curie temperature, <em>T<sub>C</sub></em>, with the values of ionic radii of A-site cations. This correlation was related to the distortion of TiO<sub>6</sub> octahedra observed during neutron diffraction studies. The equation was used for the selection of compounds with predetermined values of <em>T<sub>C</sub></em>. The effects of A-site ionic radii on the temperatures of phase transitions in Ba<sub>1-x-y</sub>Sr<sub>x</sub>Ca<sub>y</sub>TiO<sub>3</sub> were discussed. </p
Generation of internal gravity waves by penetrative convection
The rich harvest of seismic observations over the past decade provides
evidence of angular momentum redistribution in stellar interiors that is not
reproduced by current evolution codes. In this context, transport by internal
gravity waves can play a role and could explain discrepancies between theory
and observations. The efficiency of the transport of angular momentum by waves
depends on their driving mechanism. While excitation by turbulence throughout
the convective zone has already been investigated, we know that penetrative
convection into the stably stratified radiative zone can also generate internal
gravity waves. Therefore, we aim at developing a semianalytical model to
estimate the generation of IGW by penetrative plumes below an upper convective
envelope. We derive the wave amplitude considering the pressure exerted by an
ensemble of plumes on the interface between the radiative and convective zones
as source term in the equation of momentum. We consider the effect of a thermal
transition from a convective gradient to a radiative one on the transmission of
the wave into the radiative zone. The plume-induced wave energy flux at the top
of the radiative zone is computed for a solar model and is compared to the
turbulence-induced one. We show that, for the solar case, penetrative
convection generates waves more efficiently than turbulence and that
plume-induced waves can modify the internal rotation rate on shorter time
scales. We also show that a smooth thermal transition significatively enhances
the wave transmission compared to the case of a steep transition. We conclude
that driving by penetrative convection must be taken into account as much as
turbulence-induced waves for the transport of internal angular momentum.Comment: Accepted for publication in A&A, 21 page
- …