14,441 research outputs found
Emergence of order in selection-mutation dynamics
We characterize the time evolution of a d-dimensional probability
distribution by the value of its final entropy. If it is near the
maximally-possible value we call the evolution mixing, if it is near zero we
say it is purifying. The evolution is determined by the simplest non-linear
equation and contains a d times d matrix as input. Since we are not interested
in a particular evolution but in the general features of evolutions of this
type, we take the matrix elements as uniformly-distributed random numbers
between zero and some specified upper bound. Computer simulations show how the
final entropies are distributed over this field of random numbers. The result
is that the distribution crowds at the maximum entropy, if the upper bound is
unity. If we restrict the dynamical matrices to certain regions in matrix
space, for instance to diagonal or triangular matrices, then the entropy
distribution is maximal near zero, and the dynamics typically becomes
purifying.Comment: 8 pages, 8 figure
Thermal vortex dynamics in thin circular ferromagnetic nanodisks
The dynamics of gyrotropic vortex motion in a thin circular nanodisk of soft
ferromagnetic material is considered. The demagnetization field is calculated
using two-dimensional Green's functions for the thin film problem and fast
Fourier transforms. At zero temperature, the dynamics of the
Landau-Lifshitz-Gilbert equation is simulated using fourth order Runge-Kutta
integration. Pure vortex initial conditions at a desired position are obtained
with a Lagrange multipliers constraint. These methods give accurate estimates
of the vortex restoring force constant and gyrotropic frequency, showing
that the vortex core motion is described by the Thiele equation to very high
precision. At finite temperature, the second order Heun algorithm is applied to
the Langevin dynamical equation with thermal noise and damping. A spontaneous
gyrotropic motion takes place without the application of an external magnetic
field, driven only by thermal fluctuations. The statistics of the vortex radial
position and rotational velocity are described with Boltzmann distributions
determined by and by a vortex gyrotropic mass ,
respectively, where is the vortex gyrovector.Comment: 18 pages, 17 figure
Asymptotic boundary forms for tight Gabor frames and lattice localization domains
We consider Gabor localization operators defined by two
parameters, the generating function of a tight Gabor frame
, parametrized by the elements of a
given lattice , i.e. a discrete cocompact subgroup
of , and a lattice localization domain
with its boundary consisting of line segments connecting points of .
We find an explicit formula for the boundary form
, the normalized limit of the projection
functional
,
where are the eigenvalues of the localization
operators applied to dilated domains , is an
integer and is the area of the fundamental domain of the
lattice .Comment: 35 page
Coevolution of dynamical states and interactions in dynamic networks
We explore the coupled dynamics of the internal states of a set of
interacting elements and the network of interactions among them. Interactions
are modeled by a spatial game and the network of interaction links evolves
adapting to the outcome of the game. As an example we consider a model of
cooperation, where the adaptation is shown to facilitate the formation of a
hierarchical interaction network that sustains a highly cooperative stationary
state. The resulting network has the characteristics of a small world network
when a mechanism of local neighbor selection is introduced in the adaptive
network dynamics. The highly connected nodes in the hierarchical structure of
the network play a leading role in the stability of the network. Perturbations
acting on the state of these special nodes trigger global avalanches leading to
complete network reorganization.Comment: 4 pages, 5 figures, for related material visit
http:www.imedea.uib.es/physdept
The Penn State - Torun Centre for Astronomy Planet Search stars. II. Lithium abundance analysis of the Red Giant Clump sample
Using the sample of 348 stars from the PennState-Torun Centre for Astronomy
Planet Search, for which uniformly determined atmospheric parameters are
available, with chemical abundances and rotational velocities presented here,
we investigate various channels of Li enrichment in giants. Our work is based
on the HET/HRS spectra. The A(Li) was determined from the 670.8nm line, while
we use a more extended set of lines for alpha-elements abundances. In a series
of K-S tests, we compare Li-rich giants with other stars in the sample. We also
use available IR photometric and kinematical data in search for evidence of
mass-loss. We investigate properties of the most Li-abundant giants in more
detail by using multi-epoch precise radial velocities. We present Li and
alpha-elements abundances, as well as vsini for 348 stars. We detected Li in 92
stars, of which 82 are giants. 11 of them show significant Li abundance
A(Li)>1.4 and 7 of them are Li-overabundant objects, according to criterion of
A(Li)>1.5 and their location on HR diagram, including two giants with Li
abundances close to meteoritic level. For another 271 stars, upper limits of
A(Li) are presented. We show that Li-rich giants are among the most massive
stars from our sample and show larger than average effective temperatures. They
are indistinguishable from the complete sample in terms of their distribution
of luminosity, [Fe/H], vsini, and alpha-elements abundances. Our results do not
point out to one specific Li enrichment mechanism operating in our sample of
giants. On the contrary, in some cases, we cannot identify fingerprints of any
of known scenarios. We show, however, that the 4 most Li-rich giant in our
sample either have low-mass companions or have RV variations at the level of
~100 m/s, which strongly suggests that the presence of companions is an
important factor in the Li-enrichment processes in giants.Comment: Accepted for publication in A&A, 13 figures, 11 tables, 26 page
The Penn State - Toru\'n Centre for Astronomy Planet Search stars IV. Dwarfs and the complete sample
Our knowledge of the intrinsic parameters of exoplanets is as precise as our
determinations of their stellar hosts parameters. In the case of radial
velocity searches for planets, stellar masses appear to be crucial. But before
estimating stellar masses properly, detailed spectroscopic analysis is
essential. With this paper we conclude a general spectroscopic description of
the Pennsylvania-Torun Planet Search (PTPS) sample of stars. We aim at a
detailed description of basic parameters of stars representing the complete
PTPS sample. We present atmospheric and physical parameters for dwarf stars
observed within the PTPS along with updated physical parameters for the
remaining stars from this sample after the first Gaia data release. We used
high resolution (R=60 000) and high signal-to-noise-ratio (S/N=150-250) spectra
from the Hobby-Eberly Telescope and its High Resolution Spectrograph. Stellar
atmospheric parameters were determined through a strictly spectroscopic local
thermodynamic equilibrium analysis (LTE) of the equivalent widths of FeI and
FeII lines. Stellar masses, ages, and luminosities were estimated through a
Bayesian analysis of theoretical isochrones. We present , log ,
[Fe/H], micrturbulence velocities, absolute radial velocities, and rotational
velocities for 156 stars from the dwarf sample of PTPS. For most of these stars
these are the first determinations. We refine the definition of PTPS subsamples
of stars (giants, subgiants, and dwarfs) and update the luminosity classes for
all PTPS stars. Using available Gaia and Hipparcos parallaxes, we redetermine
the stellar parameters (masses, radii, luminosities, and ages) for 451 PTPS
stars. The complete PTPS sample of 885 stars is composed of 132 dwarfs, 238
subgiants, and 515 giants, of which the vast majority are of roughly solar
mass.Comment: 11 pages, 10 figures, Accepted for publication in Astronomy &
Astrophysic
Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices (The Extended Version)
We consider a product of an arbitrary number of independent rectangular
Gaussian random matrices. We derive the mean densities of its eigenvalues and
singular values in the thermodynamic limit, eventually verified numerically.
These densities are encoded in the form of the so called M-transforms, for
which polynomial equations are found. We exploit the methods of planar
diagrammatics, enhanced to the non-Hermitian case, and free random variables,
respectively; both are described in the appendices. As particular results of
these two main equations, we find the singular behavior of the spectral
densities near zero. Moreover, we propose a finite-size form of the spectral
density of the product close to the border of its eigenvalues' domain. Also,
led by the striking similarity between the two main equations, we put forward a
conjecture about a simple relationship between the eigenvalues and singular
values of any non-Hermitian random matrix whose spectrum exhibits rotational
symmetry around zero.Comment: 50 pages, 8 figures, to appear in the Proceedings of the 23rd Marian
Smoluchowski Symposium on Statistical Physics: "Random Matrices, Statistical
Physics and Information Theory," September 26-30, 2010, Krakow, Polan
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