On insertion-deletion systems over relational words

We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation between their labels. We define the operations of insertion and deletion on relational words generalizing corresponding operations on strings. We prove that the transitive and reflexive closure of these operations has a decidable membership problem for the case of short insertion-deletion rules (of size two/three and three/two). At the same time, we show that in the general case such systems can produce a coding of any recursively enumerable language leading to undecidabilty of reachability questions.Comment: 24 pages, 8 figure

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

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

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

Age determination of the HR8799 planetary system using asteroseismology

Discovery of the first planetary system by direct imaging around HR8799 has made the age determination of the host star a very important task. This determination is the key to derive accurate masses of the planets and to study the dynamical stability of the system. The age of this star has been estimated using different procedures. In this work we show that some of these procedures have problems and large uncertainties, and the real age of this star is still unknown, needing more observational constraints. Therefore, we have developed a comprehensive modeling of HR8799, and taking advantage of its gamma Doradus-type pulsations, we have estimated the age of the star using asteroseismology. The accuracy in the age determination depends on the rotation velocity of the star, and therefore an accurate value of the inclination angle is required to solve the problem. Nevertheless, we find that the age estimate for this star previously published in the literature ([30,160] Myr) is unlikely, and a more accurate value might be closer to the Gyr. This determination has deep implications on the value of the mass of the objects orbiting HR8799. An age around $\approx$ 1 Gyr implies that these objects are brown dwarfs.Comment: 5 pages, 3 figures, accepted in MNRAS Letter

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

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 $\alpha + ^{40}$Ca and $\alpha + ^{16}$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

Vassiliev Invariants for Links from Chern-Simons Perturbation Theory

The general structure of the perturbative expansion of the vacuum expectation value of a product of Wilson-loop operators is analyzed in the context of Chern-Simons gauge theory. Wilson loops are opened into Wilson lines in order to unravel the algebraic structure encoded in the group factors of the perturbative series expansion. In the process a factorization theorem is proved for Wilson lines. Wilson lines are then closed back into Wilson loops and new link invariants of finite type are defined. Integral expressions for these invariants are presented for the first three primitive ones of lower degree in the case of two-component links. In addition, explicit numerical results are obtained for all two-component links of no more than six crossings up to degree four.Comment: 44 pages, LaTex, epsf.sty, 15 figure

The cold origin of the warm dust around epsilon Eridani

Context: The K2V star eps Eri hosts one known inner planet, an outer Kuiper belt analog, and an inner disk of warm dust. Spitzer/IRS measurements indicate that the warm dust is present at distances as close as a few AU from the star. Its origin is puzzling, since an "asteroid belt" that could produce this dust would be unstable because of the known inner planet. Aims: Here we test the hypothesis that the observed warm dust is generated by collisions in the outer belt and is transported inward by Poynting-Robertson (P-R) drag and strong stellar winds. Methods: We simulated a steady-state distribution of dust particles outside 10AU with a collisional code and in the inner region (r<10AU) with single-particle numerical integrations. By assuming homogeneous spherical dust grains composed of water ice and silicate, we calculated the thermal emission of the dust and compared it with observations. We investigated two different orbital configurations for the inner planet inferred from RV measurements, one with a highly eccentric orbit of e=0.7 and another one with a moderate one of e=0.25. We also produced a simulation without a planet. Results: Our models can reproduce the shape and magnitude of the observed SED from mid-IR to sub-mm wavelengths, as well as the Spitzer/MIPS radial brightness profiles. The best-fit dust composition includes both ice and silicates. The results are similar for the two possible planetary orbits and without a planet. Conclusions: The observed warm dust in the system can indeed stem from the outer belt and be transported inward by P-R and stellar wind drag. The inner planet has little effect on the distribution of dust, so that the planetary orbit could not be constrained. Reasonable agreement between the model and observations can only be achieved by relaxing the assumption of purely silicate dust and assuming a mixture of silicate and ice in comparable amounts.Comment: 9 pages, 9 figures, abstract abridge

The Architectural Design Rules of Solar Systems based on the New Perspective

On the basis of the Lunar Laser Ranging Data released by NASA on the Silver Jubilee Celebration of Man Landing on Moon on 21st July 1969-1994, theoretical formulation of Earth-Moon tidal interaction was carried out and Planetary Satellite Dynamics was established. It was found that this mathematical analysis could as well be applied to Star and Planets system and since every star could potentially contain an extra-solar system, hence we have a large ensemble of exoplanets to test our new perspective on the birth and evolution of solar systems. Till date 403 exoplanets have been discovered in 390 extra-solar systems. I have taken 12 single planet systems, 4 Brown Dwarf - Star systems and 2 Brown Dwarf pairs. Following architectural design rules are corroborated through this study of exoplanets. All planets are born at inner Clarke Orbit what we refer to as inner geo-synchronous orbit in case of Earth-Moon System. By any perturbative force such as cosmic particles or radiation pressure, the planet gets tipped long of aG1 or short of aG1. Here aG1 is inner Clarke Orbit. The exoplanet can either be launched on death spiral as CLOSE HOT JUPITERS or can be launched on an expanding spiral path as the planets in our Solar System are. It was also found that if the exo-planet are significant fraction of the host star then those exo-planets rapidly migrate from aG1 to aG2 and have very short Time Constant of Evolution as Brown Dwarfs have. This vindicates our basic premise that planets are always born at inner Clarke Orbit. This study vindicates the design rules which had been postulated at 35th COSPAR Scientific Assembly in 2004 at Paris, France, under the title ,New Perspective on the Birth & Evolution of Solar Systems.Comment: This paper has been reported to Earth,Moon and Planets Journal as MOON-S-09-0007