Efficient algorithms for single-axis attitude estimation

The computationally efficient algorithms determine attitude from the measurement of art lengths and dihedral angles. The dependence of these algorithms on the solution of trigonometric equations was reduced. Both single time and batch estimators are presented along with the covariance analysis of each algorithm

Spin-axis attitude estimation and magnetometer bias determination for the AMPTE mission

Algorithms were developed for magnetometer biases and spin axis attitude calculation. Numerical examples of the performance of the algorithm are given

Particle Filtering for Sequential Spacecraft Attitude Estimation

A new spacecraft attitude estimation approach using particle filtering is derived. Based on sequential Monte Carlo simulation, the particle filter approximately represents the prob-ability distribution of the state vector with random samples. The filter formulation is based on the star camera measurements using a gyro-based or attitude dynamics-based model for attitude propagation. Modified Rodrigues parameters are used for attitude parametriza-tion when the sample mean and covariance of the attitude are computed. The ambiguity problem associated with the modified Rodrigues parameters in the mean and covariance computation is addressed as well. By using the uniform attitude probability distribution as the initial attitude distribution and using a gradually decreasing measurement variance in the computation of the importance weights, the particle filter based attitude estimator possesses global convergence properties. Simulation results indicate that the particular particle filter, known as bootstrap filter, with as many as 2000 particles is able to converge from arbitrary initial attitude error and initial gyro bias errors as large as 4500 degrees per hour per axis. I

Short period attractors and non-ergodic behavior in the deterministic fixed energy sandpile model

We study the asymptotic behaviour of the Bak, Tang, Wiesenfeld sandpile automata as a closed system with fixed energy. We explore the full range of energies characterizing the active phase. The model exhibits strong non-ergodic features by settling into limit-cycles whose period depends on the energy and initial conditions. The asymptotic activity $\rho_a$ (topplings density) shows, as a function of energy density $\zeta$, a devil's staircase behaviour defining a symmetric energy interval-set over which also the period lengths remain constant. The properties of $\zeta$-$\rho_a$ phase diagram can be traced back to the basic symmetries underlying the model's dynamics.Comment: EPL-style, 7 pages, 3 eps figures, revised versio

On the Applicability of Weak-Coupling Results in High Density QCD

Quark matter at asymptotically high baryon chemical potential is in a color superconducting state characterized by a gap Delta. We demonstrate that although present weak-coupling calculations of Delta are formally correct for mu -> Infinity, the contributions which have to this point been neglected are large enough that present results can only be trusted for mu >> mu_c ~ 10^8 MeV. We make this argument by using the gauge dependence of the present calculation as a diagnostic tool. It is known that the present calculation yields a gauge invariant result for mu -> Infinity; we show, however, that the gauge dependence of this result only begins to decrease for mu > mu_c, and conclude that the result can certainly not be trusted for mu < mu_c. In an appendix, we set up the calculation of the influence of the Meissner effect on the magnitude of the gap. This contribution to Delta is, however, much smaller than the neglected contributions whose absence we detect via the resulting gauge dependence.Comment: 21 pages, 3 figures, uses LaTeX2e and ReVTeX, updated figures, made minor text change

Spontaneous symmetry breaking in strong-coupling lattice QCD at high density

We determine the patterns of spontaneous symmetry breaking in strong-coupling lattice QCD in a fixed background baryon density. We employ a next-nearest-neighbor fermion formulation that possesses the SU(N_f)xSU(N_f) chiral symmetry of the continuum theory. We find that the global symmetry of the ground state varies with N_f and with the background baryon density. In all cases the condensate breaks the discrete rotational symmetry of the lattice as well as part of the chiral symmetry group.Comment: 10 pages, RevTeX 4; added discussion of accidental degeneracy of vacuum after Eq. (35

Crystalline ground state in chiral Gross-Neveu and Cooper pair models at finite densities

We study the possibility of spatially non-uniform ground state in (1+1)-dimensional models with quartic fermi interactions at finite fermion densities by introducing chemical potential \mu. We examine the chiral Gross-Neveu model and the Cooper pair model as toy models of the chiral symmetry breaking and the difermion pair condensates which are presumed to exist in QCD. We confirm in the chiral Gross-Neveu model that the ground state has a crystalline structure in which the chiral condensate oscillates in space with wave number 2\mu. Whereas in the Cooper pair model we find that the vacuum structure is spatially uniform. Some discussions are given to explain this difference.Comment: 18 pages, REVTeX, 3 eps figure

Phases of QCD at High Baryon Density

We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss how the quark masses and chemical potentials determine the structure of the superfluid quark phase. We comment on the possibility of kaon condensation at very high baryon density and study the competition between superfluid, density wave, and chiral crystal phases at intermediate density.Comment: 15 pages. To appear in the proceedings of the ECT Workshop on Neutron Star Interiors, Trento, Italy, June 200

A chiral crystal in cold QCD matter at intermediate densities?

The analogue of Overhauser (particle-hole) pairing in electronic systems (spin-density waves with non-zero total momentum $Q$) is analyzed in finite-density QCD for 3 colors and 2 flavors, and compared to the color-superconducting BCS ground state (particle-particle pairing, $Q$=0). The calculations are based on effective nonperturbative four-fermion interactions acting in both the scalar diquark as well as the scalar-isoscalar quark-hole ('$\sigma$') channel. Within the Nambu-Gorkov formalism we set up the coupled channel problem including multiple chiral density wave formation, and evaluate the resulting gaps and free energies. Employing medium-modified instanton-induced 't Hooft interactions, as applicable around $\mu_q\simeq 0.4$ GeV (or 4 times nuclear saturation density), we find the 'chiral crystal phase' to be competitive with the color superconductor.Comment: 14 pages ReVTeX, including 11 ps-/eps-figure

Superdense Matter

We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss the use of weak coupling methods. We study the phase structure as a function of the number of flavors and their masses. We also introduce effective theories that describe low energy excitations at high baryon density. Finally, we study the possibility of kaon condensation at very large baryon density.Comment: 13 pages, talk at ICPAQGP, Jaipur, India, Nov. 26-30, 2001; to appear in the proceeding