ATM-CMG control system stability

Stability analyses and simulation data and results are presented for an initial Control Moment Gyroscope system proposed for the Apollo Telescope Mount cluster (later named Skylab) using momentum vector feedback. A compensation filtering technique is presented which significantly improved analytical and simulation performance of the system. This technique is quite similar to the complementary filtering technique and represents an early NASA application

Computation of three-dimensional nozzle-exhaust flow fields with the GIM code

A methodology is introduced for constructing numerical analogs of the partial differential equations of continuum mechanics. A general formulation is provided which permits classical finite element and many of the finite difference methods to be derived directly. The approach, termed the General Interpolants Method (GIM), can combined the best features of finite element and finite difference methods. A quasi-variational procedure is used to formulate the element equations, to introduce boundary conditions into the method and to provide a natural assembly sequence. A derivation is given in terms of general interpolation functions from this procedure. Example computations for transonic and supersonic flows in two and three dimensions are given to illustrate the utility of GIM. A three-dimensional nozzle-exhaust flow field is solved including interaction with the freestream and a coupled treatment of the shear layer. Potential applications of the GIM code to a variety of computational fluid dynamics problems is then discussed in terms of existing capability or by extension of the methodology

Effective Hamiltonian for fermions in an optical lattice across Feshbach resonance

We derive the Hamiltonian for cold fermionic atoms in an optical lattice across a broad Feshbach resonance, taking into account of both multiband occupations and neighboring-site collisions. Under typical configurations, the resulting Hamiltonian can be dramatically simplified to an effective single-band model, which describes a new type of resonance between the local dressed molecules and the valence bond states of fermionic atoms at neighboring sites. On different sides of such a resonance, the effective Hamiltonian is reduced to either a t-J model for the fermionic atoms or an XXZ model for the dressed molecules. The parameters in these models are experimentally tunable in the full range, which allows for observation of various phase transitions.Comment: 5 pages, 2 figure

Small Fermi energy, zero point fluctuations and nonadiabaticity in MgB2_2

Small Fermi energy effects are induced in MgB$_2$ by the low hole doping in the $\sigma$ bands which are characterized by a Fermi energy $E_{\rm F}^\sigma \sim 0.5$ eV. We show that, due to the particularly strong deformation potential relative to the $E_{2g}$ phonon mode, lattice fluctuations are reflected in strong fluctuations in the electronic band structure. Quantum fluctuations associated to the zero-point lattice motion are responsible for an uncertainty of the Fermi energy of the order of the Fermi energy itself, leading to the breakdown of the adiabatic principle underlying the Born-Oppenheimer approximation in MgB$_2$ even if $\omega_{\rm ph}/E_{\rm F} \sim 0.1-0.2$, where $\omega_{\rm ph}$ are the characteristic phonon frequencies. This amounts to a new nonadiabatic regime, which could be relevant to other unconventional superconductors.Comment: to appear on Physical Review

Modeling of residual spheres for subduction zone earthquakes: 1. Apparent slab penetration signatures in the NW Pacific caused by deep diffuse mantle anomalies

We have computed focal residual spheres for 145 subduction zone earthquakes along the northwest edge of the Pacific using regional and global mantle velocity models from tomographic inversions. The mantle models explain much of the observed residual sphere data and, to a certain extent, suggest the location of mantle velocity heterogeneities which are responsible for various residual sphere patterns. For most deep events considered, the fast slablike residual sphere anomalies are caused by diffuse heterogeneities, mainly of deep lower mantle and receiver mantle origin rather than by an extension of the slab. The region immediately below the deepest earthquakes, depths of 650–1500 km, has an effect usually smaller than or comparable to the effect of other regions of the mantle. Without a proper account of the teleseismic effect, attributing the long-wavelength anomalies of the residual sphere to near-source slab effects alone, or even primarily, is not valid. The fast bands in many observed residual spheres agree with seismicity trends. Once the deep mantle and receiver mantle effects are removed, these may give the approximate orientation, but not the depth extent, of near-source fast velocities. For most deep earthquakes under Japan the predominant fast band is subhorizontal rather than near vertical. This type feature would be overlooked in conventional residual sphere studies using only steeply diving rays and cosine weighting of the data

Three-dimensional multigrid algorithms for the flux-split Euler equations

The Full Approximation Scheme (FAS) multigrid method is applied to several implicit flux-split algorithms for solving the three-dimensional Euler equations in a body fitted coordinate system. Each of the splitting algorithms uses a variation of approximate factorization and is implemented in a finite volume formulation. The algorithms are all vectorizable with little or no scalar computation required. The flux vectors are split into upwind components using both the splittings of Steger-Warming and Van Leer. The stability and smoothing rate of each of the schemes are examined using a Fourier analysis of the complete system of equations. Results are presented for three-dimensional subsonic, transonic, and supersonic flows which demonstrate substantially improved convergence rates with the multigrid algorithm. The influence of using both a V-cycle and a W-cycle on the convergence is examined