88 research outputs found
The universal functorial equivariant Lefschetz invariant
We introduce the universal functorial equivariant Lefschetz invariant for
endomorphisms of finite proper G-CW-complexes, where G is a discrete group. We
use K_0 of the category of "phi-endomorphisms of finitely generated free
RPi(G,X)-modules". We derive results about fixed points of equivariant
endomorphisms of cocompact proper smooth G-manifolds.Comment: 33 pages; shortened version of the author's PhD thesis, supervised by
Wolfgang Lueck, Westfaelische Wilhelms-Universitaet Muenster, 200
VLT/NACO astrometry of the HR8799 planetary system. L'-band observations of the three outer planets
HR8799 is so far the only directly imaged multiple exoplanet system. The
orbital configuration would, if better known, provide valuable insight into the
formation and dynamical evolution of wide-orbit planetary systems. We present
L'-band observations of the HR8799 system obtained with NACO at VLT, adding to
the astrometric monitoring of the planets HR8799b, c and d. We investigate how
well the two simple cases of (i) a circular orbit and (ii) a face-on orbit fit
the astrometric data for HR8799d over a total time baseline of ~2 years. The
results indicate that the orbit of HR8799d is inclined with respect to our line
of sight, and suggest that the orbit is slightly eccentric or non-coplanar with
the outer planets and debris disk.Comment: 5 pages, 4 figures, 1 table, accepted for publication in A\&A.
Updated version includes minor changes made in the proof
Thermodynamics and Topology of Disordered Systems: Statistics of the Random Knot Diagrams on Finite Lattice
The statistical properties of random lattice knots, the topology of which is
determined by the algebraic topological Jones-Kauffman invariants was studied
by analytical and numerical methods. The Kauffman polynomial invariant of a
random knot diagram was represented by a partition function of the Potts model
with a random configuration of ferro- and antiferromagnetic bonds, which
allowed the probability distribution of the random dense knots on a flat square
lattice over topological classes to be studied. A topological class is
characterized by the highest power of the Kauffman polynomial invariant and
interpreted as the free energy of a q-component Potts spin system for
q->infinity. It is shown that the highest power of the Kauffman invariant is
correlated with the minimum energy of the corresponding Potts spin system. The
probability of the lattice knot distribution over topological classes was
studied by the method of transfer matrices, depending on the type of local
junctions and the size of the flat knot diagram. The obtained results are
compared to the probability distribution of the minimum energy of a Potts
system with random ferro- and antiferromagnetic bonds.Comment: 37 pages, latex-revtex (new version: misprints removed, references
added
Barrier and internal wave contributions to the quantum probability density and flux in light heavy-ion elastic scattering
We investigate the properties of the optical model wave function for light
heavy-ion systems where absorption is incomplete, such as Ca
and O around 30 MeV incident energy. Strong focusing effects
are predicted to occur well inside the nucleus, where the probability density
can reach values much higher than that of the incident wave. This focusing is
shown to be correlated with the presence at back angles of a strong enhancement
in the elastic cross section, the so-called ALAS (anomalous large angle
scattering) phenomenon; this is substantiated by calculations of the quantum
probability flux and of classical trajectories. To clarify this mechanism, we
decompose the scattering wave function and the associated probability flux into
their barrier and internal wave contributions within a fully quantal
calculation. Finally, a calculation of the divergence of the quantum flux shows
that when absorption is incomplete, the focal region gives a sizeable
contribution to nonelastic processes.Comment: 16 pages, 15 figures. RevTeX file. To appear in Phys. Rev. C. The
figures are only available via anonynous FTP on
ftp://umhsp02.umh.ac.be/pub/ftp_pnt/figscat
Debris disc candidates in systems with transiting planets
Debris discs are known to exist around many planet-host stars, but no debris
dust has been found so far in systems with transiting planets. Using publicly
available catalogues, we searched for infrared excesses in such systems. In the
recently published Wide-Field Infrared Survey Explorer (WISE) catalogue, we
found 52 stars with transiting planets. Two systems with one transiting "hot
Jupiter" each, TrES-2 and XO-5, exhibit small excesses both at 12 and 22
microns at a > 3 sigma level. Provided that one or both of these detections are
real, the frequency of warm excesses in systems with transiting planets of 2-4
% is comparable to that around solar-type stars probed at similar wavelengths
with Spitzer's MIPS and IRS instruments. Modelling suggests that the observed
excesses would stem from dust rings with radii of several AU. The inferred
amount of dust is close to the maximum expected theoretically from a
collisional cascade in asteroid belt analogues. If confirmed, the presence of
debris discs in systems with transiting planets may put important constraints
onto formation and migration scenarios of hot Jupiters.Comment: Accepted for publication in MNRAS Letter
Knot Theory: from Fox 3-colorings of links to Yang-Baxter homology and Khovanov homology
This paper is an extended account of my "Introductory Plenary talk at Knots
in Hellas 2016" conference We start from the short introduction to Knot Theory
from the historical perspective, starting from Heraclas text (the first century
AD), mentioning R.Llull (1232-1315), A.Kircher (1602-1680), Leibniz idea of
Geometria Situs (1679), and J.B.Listing (student of Gauss) work of 1847. We
spend some space on Ralph H. Fox (1913-1973) elementary introduction to diagram
colorings (1956). In the second section we describe how Fox work was
generalized to distributive colorings (racks and quandles) and eventually in
the work of Jones and Turaev to link invariants via Yang-Baxter operators, here
the importance of statistical mechanics to topology will be mentioned. Finally
we describe recent developments which started with Mikhail Khovanov work on
categorification of the Jones polynomial. By analogy to Khovanov homology we
build homology of distributive structures (including homology of Fox colorings)
and generalize it to homology of Yang-Baxter operators. We speculate, with
supporting evidence, on co-cycle invariants of knots coming from Yang-Baxter
homology. Here the work of Fenn-Rourke-Sanderson (geometric realization of
pre-cubic sets of link diagrams) and Carter-Kamada-Saito (co-cycle invariants
of links) will be discussed and expanded.
Dedicated to Lou Kauffman for his 70th birthday.Comment: 35 pages, 31 figures, for Knots in Hellas II Proceedings, Springer,
part of the series Proceedings in Mathematics & Statistics (PROMS
Quantum Holonomy in Three-dimensional General Covariant Field Theory and Link Invariant
We consider quantum holonomy of some three-dimensional general covariant
non-Abelian field theory in Landau gauge and confirm a previous result
partially proven. We show that quantum holonomy retains metric independence
after explicit gauge fixing and hence possesses the topological property of a
link invariant. We examine the generalized quantum holonomy defined on a
multi-component link and discuss its relation to a polynomial for the link.Comment: RevTex, 12 pages. The metric independence of path integral measure is
justified and the case of multi-component link is discussed in detail. To be
published in Physical Review
On the relation between the connection and the loop representation of quantum gravity
Using Penrose binor calculus for () tensor expressions, a
graphical method for the connection representation of Euclidean Quantum Gravity
(real connection) is constructed. It is explicitly shown that: {\it (i)} the
recently proposed scalar product in the loop-representation coincide with the
Ashtekar-Lewandoski cylindrical measure in the space of connections; {\it (ii)}
it is possible to establish a correspondence between the operators in the
connection representation and those in the loop representation. The
construction is based on embedded spin network, the Penrose graphical method of
calculus, and the existence of a generalized measure on the space of
connections modulo gauge transformations.Comment: 19 pages, ioplppt.sty and epsfig.st
A possible architecture of the planetary system HR 8799
HR8799 is a nearby A-type star with a debris disk and three planetary
candidates recently imaged directly. We undertake a coherent analysis of
various portions of observational data on all known components of the system.
The goal is to elucidate the architecture and evolutionary status of the
system. We try to further constrain the age and orientation of the system,
orbits and masses of the companions, as well as the location of dust. From the
high luminosity of debris dust and dynamical constraints, we argue for a rather
young system's age of <50Myr. The system must be seen nearly, but not exactly,
pole-on. Our analysis of the stellar rotational velocity yields an inclination
of 13-30deg, whereas i>20deg is needed for the system to be dynamically stable,
which suggests a probable inclination range of 20-30deg. The spectral energy
distribution is naturally reproduced with two dust rings associated with two
planetesimal belts. The inner "asteroid belt" is located at ~10AU inside the
orbit of the innermost companion and a "Kuiper belt" at >100AU is just exterior
to the orbit of the outermost companion. The dust masses in the inner and outer
ring are estimated to be ~1E-05 and 4E-02 M_earth, respectively. We show that
all three planetary candidates may be stable in the mass range suggested in the
discovery paper by Marois et al. 2008 (between 5 and 13 Jupiter masses), but
only for some of all possible orientations. Stable orbits imply a double
(4:2:1) mean-motion resonance between all three companions. We finally show
that in the cases where the companions themselves are orbitally stable, the
dust-producing planetesimal belts are also stable against planetary
perturbations.Comment: 12 pages, 14 figures, 4 tables, accepted to be published in Astronomy
& Astrophysics (May 20, 2009
LBT observations of the HR 8799 planetary system: First detection of HR8799e in H band
We have performed H and Ks band observations of the planetary system around
HR 8799 using the new AO system at the Large Binocular Telescope and the PISCES
Camera. The excellent instrument performance (Strehl ratios up to 80% in H
band) enabled detection the inner planet HR8799e in the H band for the first
time. The H and Ks magnitudes of HR8799e are similar to those of planets c and
d, with planet e slightly brighter. Therefore, HR8799e is likely slightly more
massive than c and d. We also explored possible orbital configurations and
their orbital stability. We confirm that the orbits of planets b, c and e are
consistent with being circular and coplanar; planet d should have either an
orbital eccentricity of about 0.1 or be non-coplanar with respect to b and c.
Planet e can not be in circular and coplanar orbit in a 4:2:1 mean motion
resonances with c and d, while coplanar and circular orbits are allowed for a
5:2 resonance. The analysis of dynamical stability shows that the system is
highly unstable or chaotic when planetary masses of about 5 MJup for b and 7
MJup for the other planets are adopted. Significant regions of dynamical
stability for timescales of tens of Myr are found when adopting planetary
masses of about 3.5, 5, 5, and 5 Mjup for HR 8799 b, c, d, and e respectively.
These masses are below the current estimates based on the stellar age (30 Myr)
and theoretical models of substellar objects.Comment: 13 pages, 10 figures, A&A, accepte
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