104 research outputs found
A nonlinear deformed su(2) algebra with a two-colour quasitriangular Hopf structure
Nonlinear deformations of the enveloping algebra of su(2), involving two
arbitrary functions of J_0 and generalizing the Witten algebra, were introduced
some time ago by Delbecq and Quesne. In the present paper, the problem of
endowing some of them with a Hopf algebraic structure is addressed by studying
in detail a specific example, referred to as . This algebra is
shown to possess two series of (N+1)-dimensional unitary irreducible
representations, where N=0, 1, 2, .... To allow the coupling of any two such
representations, a generalization of the standard Hopf axioms is proposed by
proceeding in two steps. In the first one, a variant and extension of the
deforming functional technique is introduced: variant because a map between two
deformed algebras, su_q(2) and , is considered instead of a
map between a Lie algebra and a deformed one, and extension because use is made
of a two-valued functional, whose inverse is singular. As a result, the Hopf
structure of su_q(2) is carried over to , thereby endowing the
latter with a double Hopf structure. In the second step, the definition of the
coproduct, counit, antipode, and R-matrix is extended so that the double Hopf
algebra is enlarged into a new algebraic structure. The latter is referred to
as a two-colour quasitriangular Hopf algebra because the corresponding R-matrix
is a solution of the coloured Yang-Baxter equation, where the `colour'
parameters take two discrete values associated with the two series of
finite-dimensional representations.Comment: 28 pages, LaTeX, no figures, to be published in J. Math. Phy
The X-ray Cluster Dipole
We estimate the dipole of the whole sky X-ray flux-limited sample of
Abell/ACO clusters (XBACs) and compare it to the optical Abell/ACO cluster
dipole. The X-ray cluster dipole is well aligned () with the
CMB dipole, while it follows closely the radial profile of its optical cluster
counterpart although its amplitude is per cent lower. In view of
the fact that the the XBACs sample is not affected by the volume incompleteness
and the projection effects that are known to exist at some level in the optical
parent Abell/ACO cluster catalogue, our present results confirm the previous
optical cluster dipole analysis that there are significant contributions to the
Local Group motion from large distances (Mpc). In order to
assess the expected contribution to the X-ray cluster dipole from a purely
X-ray selected sample we compare the dipoles of the XBACs and the Brightest
Cluster Sample (Ebeling et al. 1997a) in their overlap region. The resulting
dipoles are in mutual good aggreement with an indication that the XBACs sample
slightly underestimates the full X-ray dipole (by per cent) while the
Virgo cluster contributes about 10 - 15 per cent to the overall X-ray cluster
dipole. Using linear perturbation theory to relate the X-ray cluster dipole to
the Local group peculiar velocity we estimate the density parameter to be
.Comment: 16 pages, latex, + 4 ps figures, submitted to Ap
Static kinematics for an antagonistically actuated robot based on a beam-mechanics-based model
Soft robotic structures might play a major role in
the 4th industrial revolution. Researchers have successfully
demonstrated advantages of soft robotics over traditional
robots made of rigid links and joints in several application
areas including manufacturing, healthcare and surgical
interventions. However, soft robots have limited ability to exert
higher forces when it comes to interaction with the
environment, hence, change their stiffness on demand over a
wide range. One stiffness mechanism embodies tendon-driven
and pneumatic air actuation in an antagonistic way achieving
variable stiffness values. In this paper, we apply a beammechanics-based
model to this type of soft stiffness controllable
robot. This mathematical model takes into account the various
stiffness levels of the soft robotic manipulator as well as
interaction forces with the environment at the tip of the
manipulator. The analytical model is implemented into a
robotic actuation system made of motorised linear rails with
load cells (obtaining applied forces to the tendons) and a
pressure regulator. Here, we present and analyse the
performance and limitations of our model
The structural and scaling properties of nearby galaxy clusters: I - The universal mass profile
We present the integrated mass profiles for a sample of ten nearby (z<=0.15),
relaxed galaxy clusters, covering a temperature range of [2-9]keV, observed
with XMM-Newton. The mass profiles were derived from the observed gas density
and temperature profiles under the hypothesis of spherical symmetry and
hydrostatic equilibrium. All ten mass profiles are well described by an
NFW-type profile over the radial range from 0.01 to 0.5 R_200, where R_200 is
the radius corresponding to a density contrast of 200 with respect to the
critical density at the cluster redshift. A King model is inconsistent with
these data. The derived concentration parameters and total masses are in the
range c_200=4-6 and M_200=1.2 10^14-1.2 10^15 Msol, respectively. Our
qualitative and quantitative study of the mass profile shape shows, for the
first time, direct and clear observational evidence for the universality of the
total mass distribution in clusters. The mass profiles scaled in units of R_200
and M_200 nearly coincide, with a dispersion of less than 15% at 0.1 R_200. The
c_200--M_200 relation is consistent with the predictions of numerical
simulations for a LCDM cosmology, taking into account the measurement errors
and expected intrinsic scatter. Our results provide further strong evidence in
favour of the Cold Dark Matter cosmological scenario and show that the dark
matter collapse is well understood at least down to the cluster scale.Comment: 8 pages, 5 figures. Accepted for publication in A&
Nonlinear deformed su(2) algebras involving two deforming functions
The most common nonlinear deformations of the su(2) Lie algebra, introduced
by Polychronakos and Ro\v cek, involve a single arbitrary function of J_0 and
include the quantum algebra su_q(2) as a special case. In the present
contribution, less common nonlinear deformations of su(2), introduced by
Delbecq and Quesne and involving two deforming functions of J_0, are reviewed.
Such algebras include Witten's quadratic deformation of su(2) as a special
case. Contrary to the former deformations, for which the spectrum of J_0 is
linear as for su(2), the latter give rise to exponential spectra, a property
that has aroused much interest in connection with some physical problems.
Another interesting algebra of this type, denoted by , has two
series of (N+1)-dimensional unitary irreducible representations, where N=0, 1,
2, .... To allow the coupling of any two such representations, a generalization
of the standard Hopf axioms is proposed. The resulting algebraic structure,
referred to as a two-colour quasitriangular Hopf algebra, is described.Comment: 8 pages, LaTeX, no figures, submitted to Proc. 5th Int. Coll.
``Quantum Groups and Integrable Systems'', Prague, 20-22 June 1996 (to be
published in Czech. J. Phys.
Historical Mammal Extinction on Christmas Island (Indian Ocean) Correlates with Introduced Infectious Disease
It is now widely accepted that novel infectious disease can be a leading cause of serious population decline and even outright extinction in some invertebrate and vertebrate groups (e.g., amphibians). In the case of mammals, however, there are still no well-corroborated instances of such diseases having caused or significantly contributed to the complete collapse of species. A case in point is the extinction of the endemic Christmas Island rat (Rattus macleari): although it has been argued that its disappearance ca. AD 1900 may have been partly or wholly caused by a pathogenic trypanosome carried by fleas hosted on recently-introduced black rats (Rattus rattus), no decisive evidence for this scenario has ever been adduced. Using ancient DNA methods on samples from museum specimens of these rodents collected during the extinction window (AD 1888–1908), we were able to resolve unambiguously sequence evidence of murid trypanosomes in both endemic and invasive rats. Importantly, endemic rats collected prior to the introduction of black rats were devoid of trypanosome signal. Hybridization between endemic and black rats was also previously hypothesized, but we found no evidence of this in examined specimens, and conclude that hybridization cannot account for the disappearance of the endemic species. This is the first molecular evidence for a pathogen emerging in a naïve mammal species immediately prior to its final collapse
Galaxy Distances in the Nearby Universe: Corrections For Peculiar Motions
By correcting the redshift--dependent distances for peculiar motions through
a number of peculiar velocity field models, we recover the true distances of a
wide, all-sky sample of nearby galaxies (~ 6400 galaxies with velocities
cz<5500 km/s), which is complete up to the blue magnitude B=14 mag. Relying on
catalogs of galaxy groups, we treat ~2700 objects as members of galaxy groups
and the remaining objects as field galaxies.
We model the peculiar velocity field using: i) a cluster dipole
reconstruction scheme; ii) a multi--attractor model fitted to the Mark II and
Mark III catalogs of galaxy peculiar velocities. According to Mark III data the
Great Attractor has a smaller influence on local dynamics than previously
believed, whereas the Perseus-Pisces and Shapley superclusters acquire a
specific dynamical role. Remarkably, the Shapley structure, which is found to
account for nearly half the peculiar motion of the Local Group, is placed by
Mark III data closer to the zone of avoidance with respect to its optical
position.
Our multi--attractor model based on Mark III data favors a cosmological
density parameter Omega ~ 0.5 (irrespective of a biasing factor of order
unity). Differences among distance estimates are less pronounced in the ~ 2000
- 4000 km/s distance range than at larger or smaller distances. In the last
regions these differences have a serious impact on the 3D maps of the galaxy
distribution and on the local galaxy density --- on small scales.Comment: 24 pages including (9 eps figures and 7 tables). Figures 1,2,3,4 are
available only upon request. Accepted by Ap
Superclusters of galaxies from the 2dF redshift survey. II. Comparison with simulations
We investigate properties of superclusters of galaxies found on the basis of
the 2dF Galaxy Redshift Survey, and compare them with properties of
superclusters from the Millennium Simulation. We study the dependence of
various characteristics of superclusters on their distance from the observer,
on their total luminosity, and on their multiplicity. The multiplicity is
defined by the number of Density Field (DF) clusters in superclusters. Using
the multiplicity we divide superclusters into four richness classes: poor,
medium, rich and extremely rich. We show that superclusters are asymmetrical
and have multi-branching filamentary structure, with the degree of asymmetry
and filamentarity being higher for the more luminous and richer superclusters.
The comparison of real superclusters with Millennium superclusters shows that
most properties of simulated superclusters agree very well with real data, the
main differences being in the luminosity and multiplicity distributions.Comment: 15 pages, 13 Figures, submitted for Astronomy and Astrophysic
The richest superclusters. I. Morphology
We study the morphology of the richest superclusters from the catalogues of
superclusters of galaxies in the 2dF Galaxy Redshift Survey and compare the
morphology of real superclusters with model superclusters in the Millennium
Simulation. We use Minkowski functionals and shapefinders to quantify the
morphology of superclusters: their sizes, shapes, and clumpiness. We generate
empirical models of simple geometry to understand which morphologies correspond
to the supercluster shapefinders. We show that rich superclusters have
elongated, filamentary shapes with high-density clumps in their core regions.
The clumpiness of superclusters is determined using the fourth Minkowski
functional . In the - shapefinder plane the morphology of
superclusters is described by a curve which is characteristic to
multi-branching filaments. We also find that the differences between the fourth
Minkowski functional for the bright and faint galaxies in observed
superclusters are larger than in simulated superclusters.Comment: 14 pages, 8 figures, submitted to Astronomy and Astrophysic
The Apparent and Intrinsic Shape of the APM Galaxy Clusters
We estimate the distribution of intrinsic shapes of APM galaxy clusters from
the distribution of their apparent shapes. We measure the projected cluster
ellipticities using two alternative methods. The first method is based on
moments of the discrete galaxy distribution while the second is based on
moments of the smoothed galaxy distribution. We study the performance of both
methods using Monte Carlo cluster simulations covering the range of APM cluster
distances and including a random distribution of background galaxies. We find
that the first method suffers from severe systematic biases, whereas the second
is more reliable. After excluding clusters dominated by substructure and
quantifying the systematic biases in our estimated shape parameters, we recover
a corrected distribution of projected ellipticities. We use the non-parametric
kernel method to estimate the smooth apparent ellipticity distribution, and
numerically invert a set of integral equations to recover the corresponding
distribution of intrinsic ellipticities under the assumption that the clusters
are either oblate or prolate spheroids. The prolate spheroidal model fits the
APM cluster data best.Comment: 8 pages, including 7 figures, accepted for publication in MNRA
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