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At least 37 records · Page 2

Statistical mechanics of light elements at high pressure. IV - A model free energy for the metallic phase

A large quantity of data on the thermodynamic properties of hydrogen-helium metallic liquids have been obtained in extended computer calculations in which a Monte Carlo code essentially identical to that described by Hubbard (1972) was used. A model free energy for metallic hydrogen with a relatively small mass fraction of helium is discussed, taking into account the definition of variables, a procedure for choosing the free energy, values for the fitting parameters, and the evaluation of the entropy constants. Possibilities concerning a use of the obtained data in studies of the interiors of the outer planets are briefly considered.

Dewitt, H. E.↗

Downfolding Complex Materials Problems Onto Model Hamiltonians for Quantum Computers

Simulating the properties of quantum materials is expected to be one of the exciting applications for quantum computers and where we hope to see advantages over classical hardware. The complexity of ab initio Hamiltonians describing the physics of application-relevant materials places them beyond the realm of possibility for solution on near-term hardware with a limited number of qubits. Various Hamiltonian approximations, including Hamiltonian downfolding, offers a possibility towards simulating complex materials on near-term hardware. This is accomplished by approximating the relevant physics of a given material through their representation by simpler model Hamiltonians, such as the Hubbard Hamiltonian or extensions of it. Here we employ a well-defined first-principles methodology for deriving downfolded multi-band extended Hubbard Hamiltonians of materials, capturing strong electronic correlation and electron-phonon coupling, based on the formalism of Wannier functions and the calculation of the screened Coulomb interaction. We demonstrate for a variety of systems that quantum simulation of these downfolded Hamiltonians reproduces key properties, thus establishing downfolding as a promising route to achieve near-term simulation of application-relevant systems on quantum hardware.

Antonios Markos Alvertis↗

Downfolding complex materials problems onto model Hamiltonians for quantum computers

Simulating the properties of quantum materials is expected to be one of the exciting applications for quantum computers and where we hope to see advantages over classical hardware. The complexity of ab initio Hamiltonians describing the physics of application-relevant materials places them beyond the realm of possibility for solution on near-term hardware with a limited number of qubits. Various Hamiltonian approximations, including Hamiltonian downfolding, offers a possibility towards simulating complex materials on near-term hardware. This is accomplished by approximating the relevant physics of a given material through their representation by simpler model Hamiltonians, such as the Hubbard Hamiltonian or extensions of it. Here we employ a well-defined first-principles methodology for deriving downfolded multi-band extended Hubbard Hamiltonians of materials, capturing strong electronic correlation and electron-phonon coupling, based on the formalism of Wannier functions and the calculation of the screened Coulomb interaction. We demonstrate for a variety of systems that quantum simulation of these downfolded Hamiltonians reproduces key properties, thus establishing downfolding as a promising route to achieve near-term simulation of application-relevant systems on quantum hardware.

Antonios M. Alvertis↗

Petrogenesis in a modestly endowed moon

Four lines of recent evidence show that the moon is more modestly endowed in refractory elements and heat sources than previously thought. However, even this reduced endowment is adequate for the genesis of known lunar rock types. The thickness and nature of the initially molten zone and the structure of the crust and the lithosphere produced from it are the major uncertainties in models of lunar petrogenesis.

Hubbard, N. J.↗

Regional chemical variations in lunar basaltic lavas

The higher Al2O3 concentrations in mare soils at Apollo landing sites, relative to mare basalts, have generally been attributed to the presence of 20-30% of terra material in the mare surface regolith. This viewpoint is shown to be erroneous when entire maria are studied; the amount of terra material in typical mare surface regoliths is only about 5%, or less. The bulk of the mare soils are the comminuted remains of aluminous mare basalt flows. On a regional scale, the sample and orbital data for maria define prominent chemical variations that are well beyond those expected from simple igneous processes and therefore indicate that gradations in one or more of the major parameters of planetary differentiation caused these variations. The increasingly abundant evidence for regional variations in the chemical compositions of lunar basalts requires that regional petrogenetic provinces must be considered in models of lunar evolution.

Hubbard, N.↗

Statistical mechanics of light elements at high pressure. V Three-dimensional Thomas-Fermi-Dirac theory

A numerical technique for solving the Thomas-Fermi-Dirac (TED) equation in three dimensions, for an array of ions obeying periodic boundary conditions, is presented. The technique is then used to calculate deviations from ideal mixing for an alloy of hydrogen and helium at zero temperature and high presures. Results are compared with alternative models which apply perturbation theory to calculation of the electron distribution, based upon the assumption of weak response of the electron gas to the ions. The TFD theory, which permits strong electron response, always predicts smaller deviations from ideal mixing than would be predicted by perturbation theory. The results indicate that predicted phase separation curves for hydrogen-helium alloys under conditions prevailing in the metallic zones of Jupiter and Saturn are very model dependent.

Macfarlane, J. J.↗

Oblateness, radius, and mean stratospheric temperature of Neptune from the 1985 August 20 occultation

The oblateness and equatorial radius of Neptune at the 1-microbar pressure level, together with the position angle of the projected spin axis, are the goals of a general oblate atmosphere model for Neptune employing a data ensemble obtained from the occultation of a bright IR star that provided accurate measurements of the limb position at these and several other stations. The observed reduction in central flash intensity is explained by a 150-135 K temperature decrease as pressure rises from 1 to 400 microbar. Attention is given to the implications of these oblateness results for models of the Neptune interior.

Hubbard, W. B.↗

Results for Titan's atmosphere from its occultation of 28 Sagittarii

The occultation of the bright K giant star 28 Sgr by Titan was observed from three stations in the Mediterranean area, and the resulting data set is examined here. Average mesospheric temperatures of about 180 K are derived, with evidence for lateral and vertical atmospheric inhomogeneities on scales ranging from about 10-1000 km. The results are consistent with published models of Titan's atmosphere.

Hubbard, W. B.↗

Origin of high-Ti lunar ultramafic glasses

A series of high pressure melting experiments were performed on a synthetic analog of the Apollo 14 Black Glass. At 15 kb and 1400 C, olivine is the liquidus phase. At 25 kb and 1450 C, orthopyroxene and Cr-spinel crystallize. A multiple saturation point with olivine + orthopyroxene + spinel on the liquidus occurs at 20 kb and 1440 C. It was proposed that the high-Ti ultramafic glass evolved from a low-Ti Green Glass generated deep in the lunar interior that assimilated shallow-level, late stage cumulates of magma ocean differentiation. Heat for assimilation is provided by superheat of the low-Ti magma and melts high-Ca pyroxene and ilmenite cumulates at a depth of 100 km. This model is a variant of that proposed by Hubbard and Minear and rejected by Ringwood and Kesson.

Wagner, T. P.↗

Fuzzy Modeling and Parallel Distributed Compensation for Aircraft Flight Control from Simulated Flight Data

A method is described that combines fuzzy system identification techniques with Parallel Distributed Compensation (PDC) to develop nonlinear control methods for aircraft using minimal a priori knowledge, as part of NASA’s Learn-to-Fly initiative. A fuzzy model was generated with simulated flight data, and consisted of a weighted average of multiple linear time invariant state-space cells having parameters estimated using the equation-error approach and a least-squares estimator. A compensator was designed for each subsystem using Linear Matrix Inequalities (LMI) to guarantee closed-loop stability and performance requirements. This approach is demonstrated using simulated flight data to automatically develop a fuzzy model and design control laws for a simplified longitudinal approximation of the F-16 nonlinear flight dynamics simulation. Results include a comparison of flight data with the estimated fuzzy models and simulations that illustrate the feasibility and utility of the combined fuzzy modeling and control approach.

Weinstein, Rose↗

Thermodynamics of a solar mixture of molecular hydrogen and helium at high pressure

The thermodynamic properties of a model molecular hydrogen and helium mixture are calculated in the strongly interacting region of 0.005 to 0.3 per cu cm for a range of temperatures that are of interest for the envelopes of the Jovian planets. Computed adiabats fit the gravity data and boundary conditions from model atmospheres of Jupiter.

Slattery, W. L.↗

Interior structure of Uranus

Critical measurements relative to interior structure which can be made during a spacecraft mission to Uranus are discussed. Models of atmospheric composition, possible magnetic moment, and gravitational harmonics are described, and it is shown that high quality imaging of the atmospheric rotation and determination of the possible magnetic field rotation will facilitate construction of an accurate model of the interior structure of the planet.

Hubbard, W. B.↗

The Helmholtz resonance behavior of single and multiple rooms

The results of exploratory measurements of the noise fields inside rooms which are excited to resonance either acoustically or mechanically are presented. The data illustrate the nature and extent of the sound pressure level enhancements in single rooms and also how multiple rooms may resonate by means of either acoustic or mechanical coupling. Sound pressure level enhancements of about 5 dB were measured during resonance of rooms having flexible walls. For such conditions the sound pressure levels in the room were essentially uniform and in phase. Variability of up to 20 dB was measured in a room hallway complex having significant acoustic interactions. Resonant frequency prediction methods which work well at model scale, give only fair results for rooms.

Hubbard, H. H.↗

Intrinsic luminosities of the Jovian planets

Available data and theories on the size and nature of interior power sources in the four Jovian planets are reviewed. These four planets are Jupiter, Saturn, Uranus and Neptune. Various models, ranging from simple cooling to gravitational layering to radioactivity, are discussed. The evidence and interpretations presented in the discussion seem to indicate that (1) all four Jovian planets were once more luminous and are presently cooling to a state of equilibrium with sunlight; and (2) the thermal evolution of the Jovian planets is predominantly controlled by their photospheres and does not depend on interior conductivity. Both conclusions are consistent with either the simple adiabatic cooling model or with more complicated gravitational unmixing models of the type discussed by Stevenson and Salpeter (1977).

Hubbard, W. B.↗

Thermodynamics of dense molecular hydrogen-helium mixtures at high pressure

Effective intermolecular pair potentials derived from liquid hydrogen and helium shock wave experiments are presently used in Monte Carlo simulations of mixtures of hydrogen and helium, at densities of up to 1.2 g/cu cm. The model interaction Helmholtz free energy derived accurately reproduces both the Monte Carlo calculation results and the experimental data obtained for densities of up to about 0.6 g/cu cm. An equation of state is derived from the free energy expression that could be useful in interior models of such Jovian planets as Saturn.

Marley, Mark S.↗