Attitude determination and calibration using a recursive maximum likelihood-based adaptive Kalman filter

An adaptive Kalman filter design that utilizes recursive maximum likelihood parameter identification is discussed. At the center of this design is the Kalman filter itself, which has the responsibility for attitude determination. At the same time, the identification algorithm is continually identifying the system parameters. The approach is applicable to nonlinear, as well as linear systems. This adaptive Kalman filter design has much potential for real time implementation, especially considering the fast clock speeds, cache memory and internal RAM available today. The recursive maximum likelihood algorithm is discussed in detail, with special attention directed towards its unique matrix formulation. The procedure for using the algorithm is described along with comments on how this algorithm interacts with the Kalman filter

Attractive Hubbard Model on a Honeycomb Lattice

We study the attractive fermionic Hubbard model on a honeycomb lattice using determinantal quantum Monte Carlo simulations. By increasing the interaction strength U (relative to the hopping parameter t) at half-filling and zero temperature, the system undergoes a quantum phase transition at 5.0 < U_c/t < 5.1 from a semi-metal to a phase displaying simultaneously superfluid behavior and density order. Doping away from half-filling, and increasing the interaction strength at finite but low temperature T, the system always appears to be a superfluid exhibiting a crossover between a BCS and a molecular regime. These different regimes are analyzed by studying the spectral function. The formation of pairs and the emergence of phase coherence throughout the sample are studied as U is increased and T is lowered

Peculiar Features of the Interaction Potential between Hydrogen and Antihydrogen at Intermediate Separations

We evaluate the interaction potential between a hydrogen and an antihydrogen using the second-order perturbation theory within the framework of the four-body system in a separable two-body basis. We find that the H-Hbar interaction potential possesses the peculiar features of a shallow local minimum located around interatomic separations of r ~ 6 a.u. and a barrier rising at r~5 a.u. Additional theoretical and experimental investigations on the nature of these peculiar features will be of great interest.Comment: 13 pages, 6 figure

Critical dynamics of the k-core pruning process

We present the theory of the k-core pruning process (progressive removal of nodes with degree less than k) in uncorrelated random networks. We derive exact equations describing this process and the evolution of the network structure, and solve them numerically and, in the critical regime of the process, analytically. We show that the pruning process exhibits three different behaviors depending on whether the mean degree of the initial network is above, equal to, or below the threshold _c corresponding to the emergence of the giant k-core. We find that above the threshold the network relaxes exponentially to the k-core. The system manifests the phenomenon known as "critical slowing down", as the relaxation time diverges when tends to _c. At the threshold, the dynamics become critical characterized by a power-law relaxation (1/t^2). Below the threshold, a long-lasting transient process (a "plateau" stage) occurs. This transient process ends with a collapse in which the entire network disappears completely. The duration of the process diverges when tends to _c. We show that the critical dynamics of the pruning are determined by branching processes of spreading damage. Clusters of nodes of degree exactly k are the evolving substrate for these branching processes. Our theory completely describes this branching cascade of damage in uncorrelated networks by providing the time dependent distribution function of branching. These theoretical results are supported by our simulations of the $k$-core pruning in Erdos-Renyi graphs.Comment: 12 pages, 10 figure

Supersoft X-rays reveal a classical nova in the M 31 globular cluster Bol 126

[Abridged] Classical novae (CNe) represent the main class of supersoft X-ray sources (SSSs) in the central region of our neighbouring galaxy M 31. Only three confirmed novae and three SSSs have been discovered in globular clusters (GCs) of any galaxy so far, of which one nova and two SSSs (including the nova) were found in M 31 GCs. To study the SSS state of CNe we carried out a high-cadence X-ray monitoring of the M 31 central area with XMM-Newton and Chandra. We analysed X-ray and optical data of a new transient X-ray source in the M 31 GC Bol 126, discovered serendipitously in Swift observations. Our optical data set was based on regular M 31 monitoring programmes from five different small telescopes. Additionally, we made use of Pan-STARRS 1 data obtained during the PAndromeda survey. Our observations reveal that the X-ray source in Bol 126 is the third SSS in an M 31 GC and can be confirmed as the second CN in the M 31 GC system. This nova is named M31N 2010-10f. Its properties in the X-ray and optical regimes agree with a massive white dwarf (M_WD >~ 1.3 M_sun) in the binary system. Incorporating the data on previously found (suspected) novae in M 31 GCs we used our high-cadence X-ray monitoring observations to estimate a tentative nova rate in the M 31 GC system of 0.05 /yr/GC. An optical estimate, based on the recent 10.5-year WeCAPP survey, gives a lower nova rate, which is compatible with the X-ray rate on the 95% confidence level. There is growing evidence that the nova rate in GCs is higher than expected from primordial binary formation and under conditions as in the field. Dynamical binary formation and/or additional accretion from the intracluster medium are possible scenarios for an increased nova rate, but observational confirmation for this enhancement has been absent, so far. Regular X-ray monitoring observations of M 31 provide a promising strategy to find these novae.Comment: 14 pages, 6 figures, 3 tables; accepted by Astronomy and Astrophysic

Comparison of the extended linear sigma model and chiral perturbation theory

The pion-nucleon scattering amplitudes are calculated in tree approximation with the use of the extended linear sigma model (ELSM) as well as heavy baryon chiral perturbation theory (HB$\chi$PT), and the non-relativistic forms of the ELSM results are compared with those of HB$\chi$PT. We find that the amplitudes obtained in ELSM do not agree with those derived from the more fundamental effective approach, HB$\chi$PT.Comment: 7 page

Self-DUal SU(3) Chern-Simons Higgs Systems

We explore self-dual Chern-Simons Higgs systems with the local $SU(3)$ and global $U(1)$ symmetries where the matter field lies in the adjoint representation. We show that there are three degenerate vacua of different symmetries and study the unbroken symmetry and particle spectrum in each vacuum. We classify the self-dual configurations into three types and study their properties.Comment: Columbia Preprint CU-TP-635, 19 page