880 research outputs found
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
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
(topplings density) shows, as a function of energy density , a
devil's staircase behaviour defining a symmetric energy interval-set over which
also the period lengths remain constant. The properties of -
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
Attitude and Phase Synchronization of Formation Flying Spacecraft: Lagrangian Approach
This article presents a unified synchronization framework with application to precision formation flying spacecraft. Central to the proposed innovation, in applying synchroniza-
tion to both translational and rotational dynamics in the Lagrangian form, is the use of the distributed stability and performance analysis tool, called contraction analysis that yields exact nonlinear stability proofs. The proposed decentralized tracking control law synchronizes the attitude of an arbitrary number of spacecraft into a common time-varying trajectory with global exponential convergence. Moreover, a decentralized translational tracking control law based on phase synchronization is presented, thus enabling coupled translational and rotational maneuvers. While the translational dynamics can be adequately controlled by linear control laws, the proposed method permits highly nonlinear systems with nonlinearly coupled inertia matrices such as the attitude dynamics of space-craft whose large and rapid slew maneuvers justify the nonlinear control approach. The
proposed method integrates both the trajectory tracking and synchronization problems in a single control framework
Time-optimal synthesis of unitary transformations in coupled fast and slow qubit system
In this paper, we study time-optimal control problems related to system of
two coupled qubits where the time scales involved in performing unitary
transformations on each qubit are significantly different. In particular, we
address the case where unitary transformations produced by evolutions of the
coupling take much longer time as compared to the time required to produce
unitary transformations on the first qubit but much shorter time as compared to
the time to produce unitary transformations on the second qubit. We present a
canonical decomposition of SU(4) in terms of the subgroup SU(2)xSU(2)xU(1),
which is natural in understanding the time-optimal control problem of such a
coupled qubit system with significantly different time scales. A typical
setting involves dynamics of a coupled electron-nuclear spin system in pulsed
electron paramagnetic resonance experiments at high fields. Using the proposed
canonical decomposition, we give time-optimal control algorithms to synthesize
various unitary transformations of interest in coherent spectroscopy and
quantum information processing.Comment: 8 pages, 3 figure
Accurate computation of quaternions from rotation matrices
The final publication is available at link.springer.comThe main non-singular alternative to 3Ă3 proper orthogonal matrices, for representing rotations in R3, is quaternions. Thus, it is important to have reliable methods to pass from one representation to the other. While passing from a quaternion to the corresponding rotation matrix is given by Euler-Rodrigues formula, the other way round can be performed in many different ways. Although all of them are algebraically equivalent, their numerical behavior can be quite different. In 1978, Shepperd proposed a method for computing the quaternion corresponding to a rotation matrix which is considered the most reliable method to date. Shepperdâs method, thanks to a voting scheme between four possible solutions, always works far from formulation singularities. In this paper, we propose a new method which outperforms Shepperdâs method without increasing the computational cost.Peer ReviewedPostprint (author's final draft
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
Numerical investigations of apatite ^4He/^3He thermochronometry
Apatite ^4He/^3He thermochronometry has the potential to constrain cooling histories for individual samples provided that several presently untested assumptions are valid. Here we simulate the sensitivity of ^4He/^3He spectra to assumptions regarding geometric model, crystallographic anisotropy, broken grain terminations, parent nuclide zonation, and the accuracy of results obtained from analyses of aggregates of multiple crystals. We find that ^4He/^3He spectra obtained from a cylinder with isotropic diffusion are almost indistinguishable from those obtained from an equivalent sphere with an equivalent initial ^4He distribution. Under similar conditions anisotropic diffusion from the cylinder can greatly bias ^4He/^3He spectra, but only if diffusion is >10 times faster in the axial than the radial direction. Existing data argue against anisotropy of this magnitude. We find that analysis of apatites with broken terminations will also bias ^4He/^3He spectra, but not greatly so. In contrast, we find that zonation of a factor of 3 in parent nuclide concentration produces ^4He/^3He spectra that deviate substantially from the homogeneous model. When parent nuclides are highly concentrated near the grain rim and/or cooling is fast, the resulting ^4He/^3He spectra will be readily identified as aberrant. However, more subtle zonation, higher concentrations in the grain interior, or samples that have cooled slowly regardless of zonation style can yield ^4He/^3He spectra that look acceptable but will lead to inaccurate thermochronometric interpretation if parent homogeneity is assumed. Finally, we find that analysis of an aggregate of crystals with identical ^4He distributions can yield ^4He/^3He spectra (and diffusion Arrhenius arrays) that are very different from those that would be obtained on the individual crystals if even small variations in He diffusion exist among the grains. Overall, our observations suggest that modeling tools that assume spherical geometry and isotropic diffusion are appropriate for interpreting apatite ^4He/^3He spectra. However, it is essential to analyze only individual crystals and to assess the degree of parent nuclide zonation in those crystals
Phase Locking, Devil's Staircases, Farey Trees, and Arnold Tongues in Driven Vortex Lattices with Periodic Pinning
Using numerical simulations, we observe phase locking, Arnold tongues, and
Devil's staircases for vortex lattices driven at varying angles with respect to
an underlying superconducting periodic pinning array. This rich structure
should be observalble in transport measurments. The transverse curves
have a Devil's staircase structure, with plateaus occurring near the driving
angles along symmetry directions of the pinning array. Each of the plateaus
corresponds to a different dyanmical phase with a distinctive vortex structure
and flow pattern.Comment: accepted to Physical Review Letter
Unpaired and spin-singlet paired states of a two-dimensional electron gas in a perpendicular magnetic field
We present a variational study of both unpaired and spin-singlet paired
states induced in a two-dimensional electron gas at low density by a
perpendicular magnetic field. It is based on an improved circular-cell
approximation which leads to a number of closed analytical results. The
ground-state energy of the Wigner crystal containing a single electron per cell
in the lowest Landau level is obtained as a function of the filling factor
: the results are in good agreement with those of earlier approaches and
predict for the upper filling factor at which the
solid-liquid transition occurs. A novel localized state of spin-singlet
electron pairs is examined and found to be a competitor of the unpaired state
for filling factor . The corresponding phase boundary is quantitatively
displayed in the magnetic field-electron density plane.Comment: 19 pages, 8 figures, submitted to Phys. Rev. B on 7th April 2001. to
appear in Phys. Rev.
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
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