41 research outputs found
Renormalization Group Flow of the Two-Dimensional Hierarchical Coulomb Gas
We consider a quasilinear parabolic differential equation associated with the
renormalization group transformation of the two-dimensional hierarchical
Coulomb system in the limit as the size of the block L goes to 1. We show that
the initial value problem is well defined in a suitable function space and the
solution converges, as t goes to infinity, to one of the countably infinite
equilibrium solutions. The nontrivial equilibrium solution bifurcates from the
trivial one. These solutions are fully described and we provide a complete
analysis of their local and global stability for all values of inverse
temperature. Gallavotti and Nicolo's conjecture on infinite sequence of
``phases transitions'' is also addressed. Our results rule out an intermediate
phase between the plasma and the Kosterlitz-Thouless phases, at least in the
hierarchical model we consider.Comment: 34pages,2figures, to appear in CM
Quasi-Random Discrete Ordinates Method for Transport Problems
The quasi-random discrete ordinates method (QRDOM) is here proposed for the
approximation of transport problems. Its central idea is to explore a quasi
Monte Carlo integration within the classical source iteration technique. It
preserves the main characteristics of the discrete ordinates method, but it has
the advantage of providing mitigated ray effect solutions. The QRDOM is
discussed in details for applications to one-group transport problems with
isotropic scattering in rectangular domains. The method is tested against
benchmark problems for which DOM solutions are known to suffer from the ray
effects. The numerical experiments indicate that the QRDOM provides accurate
results and it demands less discrete ordinates per source iteration when
compared against the classical DOM.Comment: 14 pages, 6 figure
Quasi-Random Discrete Ordinates Method to Radiative Transfer Equation with Linear Anisotropic Scattering
The quasi-random discrete ordinates method (QRDOM) is here proposed for the
approximation of transport problems. Its central idea is to explore a quasi
Monte Carlo integration within the classical source iteration technique. It
preserves the main characteristics of the discrete ordinates method, but it has
the advantage of providing mitigated ray effect solutions. The QRDOM is
discussed in details for applications to one-group transport problems with
isotropic scattering in rectangular domains. The method is tested against
benchmark problems for which DOM solutions are known to suffer from the ray
effects. The numerical experiments indicate that the QRDOM provides accurate
results and it demands less discrete ordinates per source iteration when
compared against the classical DOM.Comment: 15 pages, 5 figure
The first ALMA survey of protoplanetary discs at 3 mm: demographics of grain growth in the Lupus region
We present the first ALMA survey of protoplanetary discs at 3 mm, targeting
36 young stellar objects in the Lupus star-forming region with deep
observations (sensitivity 20-50 microJy/beam) at ~0.35" resolution (~50 au).
Building on previous ALMA surveys at 0.89 and 1.3 mm that observed the complete
sample of Class II discs in Lupus at a comparable resolution, we aim to assess
the level of grain growth in the relatively young Lupus region. We measure 3 mm
integrated fluxes, from which we derive disc-averaged 1-3 mm spectral indices.
We find that the mean spectral index of the observed Lupus discs is
, in all cases , with a tendency for larger spectral indices in the brightest discs
and in transition discs. Furthermore, we find that the distribution of spectral
indices in Lupus discs is statistically indistinguishable from that of the
Taurus and Ophiuchus star-forming regions. Assuming the emission is optically
thin, the low values measured for most discs
can be interpreted with the presence of grains larger than 1 mm. The
observations of the faint discs in the sample can be explained without invoking
the presence of large grains, namely through a mixture of optically thin and
optically thick emission from small grains. However, the bright (and typically
large) discs do inescapably require the presence of millimeter-sized grains in
order to have realistic masses. Based on a disc mass argument, our results
challenge previous claims that the presence of optically thick sub-structures
may be a universal explanation for the empirical millimeter size-luminosity
correlation observed at 0.89 mm.Comment: MNRAS Accepted; 12 pages, 5 figures, 2 tables. Machine-readable
tables available at https://zenodo.org/record/475628
Noise parametric identification and whitening for LIGO 40-meter interferometer data
We report the analysis we made on data taken by Caltech 40-meter prototype
interferometer to identify the noise power spectral density and to whiten the
sequence of noise. We concentrate our study on data taken in November 1994, in
particular we analyzed two frames of data: the 18nov94.2.frame and the
19nov94.2.frame.
We show that it is possible to whiten these data, to a good degree of
whiteness, using a high order whitening filter. Moreover we can choose to
whiten only restricted band of frequencies around the region we are interested
in, obtaining a higher level of whiteness.Comment: 11 pages, 15 figures, accepted for publication by Physical Review
Ringed Structures of the HD 163296 Protoplanetary Disk Revealed by ALMA
We present Atacama Large Millimeter and Submillimeter Array observations of the protoplanetary disk around the Herbig Ae star HD 163296 that trace the spatial distribution of millimeter-sized particles and cold molecular gas on spatial scales as small as 25 astronomical units (A.U.). The image of the disk recorded in the 1.3 mm continuum emission reveals three dark concentric rings that indicate the presence of dust depleted gaps at about 60, 100, and 160 A.U. from the central star. The maps of the ^(12)CO, ^(13)CO, and C^(18)O J=2−1 emission do not show such structures but reveal a change in the slope of the radial intensity profile across the positions of the dark rings in the continuum image. By comparing the observations with theoretical models for the disk emission, we find that the density of CO molecules is reduced inside the middle and outer dust gaps. However, in the inner ring there is no evidence of CO depletion. From the measurements of the dust and gas densities, we deduce that the gas-to-dust ratio varies across the disk and, in particular, it increases by at least a factor 5 within the inner dust gap compared to adjacent regions of the disk. The depletion of both dust and gas suggests that the middle and outer rings could be due to the gravitational torque exerted by two Saturn-mass planets orbiting at 100 and 160 A.U. from the star. On the other hand, the inner dust gap could result from dust accumulation at the edge of a magnetorotational instability dead zone, or from dust opacity variations at the edge of the CO frost line. Observations of the dust emission at higher angular resolution and of molecules that probe dense gas are required to establish more precisely the origins of the dark rings observed in the HD 163296 disk
Hierarchical Spherical Model from a Geometric Point of View
A continuous version of the hierarchical spherical model at dimension d=4 is
investigated. Two limit distribution of the block spin variable X^{\gamma},
normalized with exponents \gamma =d+2 and \gamma =d at and above the critical
temperature, are established. These results are proven by solving certain
evolution equations corresponding to the renormalization group (RG)
transformation of the O(N) hierarchical spin model of block size L^{d} in the
limit L to 1 and N to \infty . Starting far away from the stationary Gaussian
fixed point the trajectories of these dynamical system pass through two
different regimes with distinguishable crossover behavior. An interpretation of
this trajectories is given by the geometric theory of functions which describe
precisely the motion of the Lee--Yang zeroes. The large-- limit of RG
transformation with L^{d} fixed equal to 2, at the criticality, has recently
been investigated in both weak and strong (coupling) regimes by Watanabe
\cite{W}. Although our analysis deals only with N=\infty case, it complements
various aspects of that work.Comment: 27 pages, 6 figures, submitted to Journ. Stat. Phy