Lyapunov Instability for a hard-disk fluid in equilibrium and nonequilibrium thermostated by deterministic scattering

We compute the full Lyapunov spectra for a hard-disk fluid under temperature gradient and shear. The system is thermalized by deterministic and time-reversible scattering at the boundary. This thermostating mechanism allows for energy fluctuations around a mean value which is reflected by only two vanishing Lyapunov exponents in equilibrium and nonequilibrium. The Lyapunov exponents are calculated with a recently developed formalism for systems with elastic hard collisions. In a nonequilibrium steady state the average phase space volume is contracted onto a fractal attractor leading to a negative sum of Lyapunov exponents. Since the system is driven inhomogeneously we do not expect the conjugate pairing rule to hold which is confirmed numerically.Comment: 13 pages (revtex) with 8 figures (encapsulated postscript

Rotating raster generator

A rotating raster generator is provided which enables display of a television raster at any arbitrary roll angle. The generator includes four integrator circuits each of which receives a first voltage input corresponding to the sine or cosine of the desired roll angle and a second input comprising conventional horizontal or vertical sync pulses. The integrator circuits each comprise an operational amplifier and a capacitor connected for producing a ramp output having a rate of change proportional to the roll angle input, an electronic switch responsive to the sync input for resetting the integrator, and a summer that adds the ramp output of the integrator to the roll angle input so as to provide a zero-centered deflection control voltage

The geoid spectrum from altimetry

Satellite altimetry information from the world's major oceans was analyzed to arrive at a geoid power spectrum. Using the equivalent of about 7 revolutions of data (mostly from GEOS-3) the power spectrum of the sea surface generally follows the expected values from Kaula's rule applied to the geoid. Analysis of overlapping altimetry arcs (and oceanographic data) shows that the surface spectrum is dominated by the geoid to about 500 cycles (40 km half wavelength) but that sea state departures are significant starting at about 250 cycles (80 km). Estimates of geopotential variances from a derived (smooth) geoid spectrum show significantly less power than Kaula's rule to about 60 cycles, but somewhat more from there to about 400 cycles. At less than 40 km half wavelength, the total power in the marine geoid may be negligible

Effect of resonance-oblateness coupling on a satellite orbit

Second order effects of the coupling between geopotential resonance and oblateness on a satellite orbit are calculated. Results show that: (1) these effects arise from the interaction of resonance with the secular changes of the orbit's node, perigee, and mean anomaly; (2) they have the same period and phase as first order resonance perturbations; and (3) their amplitudes are proportional to the square of the period and dominate the first order effects as the orbit becomes commensurate. A striking example of this coupling is seen in the 18 day resonance variation of the node of the orbit of the first earth resources technology satellite. Analysis of this one arc second (31m) variation yielded a strong 14th order constraint to the geopotential for odd degree terms. This constraint is poorly predicted by current models

The 13th order resonance from Navy tracking on a diademe 2 fragment

A strong constraint on 13th order (odd degree) terms in the geopotential has been derived from Navy tracking on a DIADEME 2 fragment (1967-14F). This object (perigee height: 580 km, orbit inclination: 38.9 deg) is presently decaying slowly through perfect commensurability with these terms. The resonance forces will increase its inclination by 0.02 deg when the passage is complete by late 1974. The constraint (lumped harmonics), derived by adjustment of a pair of harmonic coefficients to the Navy inclination data (principally) is: 10 to the 9th power (14.8 + or - 0.8, 48.3 + or - 0.7) = 0.023(C,S)13,13 -0.172(C,S)15,13 0.505(C,S)17,13 - 0.884(C,S)19,13 + (C,S)21,13 0.673(C,S)23,13 0.099(C,S)25,13 0.295(C,S)27,13 -0.279(C,S)29,13 0.018(C,S)31,13 + There should be a significant contribution to this result from terms as high as 29th degree. But current geopotential solutions (for 13th order terms) to this degree are about 20% in error when judged by this independent data

The geopotential at synchronous-orbit altitudes

The earth's gravity potential at synchronous orbit satellite altitudes is studied by analyzing the small effects of the resonant harmonic of gravity in tracking data from eight satellites during 21 distinct drift-free arcs. Results show: (1) absolute accuracy of second degree resonant geopotential coefficients better than three percent and coefficients through fourth degree better than 15 percent; (2) positions of equilibrium points for geostationary satellites better than 1/2 degree; and (3) accuracy in predicting orbits for 24-hour satellites better than 1 degree for periods greater than 2 years

Transition metal oxides using quantum Monte Carlo

The transition metal-oxygen bond appears prominently throughout chemistry and solid-state physics. Many materials, from biomolecules to ferroelectrics to the components of supernova remnants contain this bond in some form. Many of these materials' properties strongly depend on fine details of the TM-O bond and intricate correlation effects, which make accurate calculations of their properties very challenging. We present quantum Monte Carlo, an explicitly correlated class of methods, to improve the accuracy of electronic structure calculations over more traditional methods like density functional theory. We find that unlike s-p type bonding, the amount of hybridization of the d-p bond in TM-O materials is strongly dependant on electronic correlation.Comment: 20 pages, 4 figures, to appear as a topical review in J. Physics: Condensed Matte

Propagation of flexural and membrane waves with fluid loaded NASTRAN plate and shell elements

Modeling of flexural and membrane type waves existing in various submerged (or in vacuo) plate and/or shell finite element models that are excited with steady state type harmonic loadings proportioned to e(i omega t) is discussed. Only thin walled plates and shells are treated wherein rotary inertia and shear correction factors are not included. More specifically, the issue of determining the shell or plate mesh size needed to represent the spatial distribution of the plate or shell response is of prime importance towards successfully representing the solution to the problem at hand. To this end, a procedure is presented for establishing guide lines for determining the mesh size based on a simple test model that can be used for a variety of plate and shell configurations such as, cylindrical shells with water loading, cylindrical shells in vacuo, plates with water loading, and plates in vacuo. The procedure for doing these four cases is given, with specific numerical examples present only for the cylindrical shell case