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At least 829 records · Page 46

Behavior of Hydrogarnet‐Type Defects in Hydrous Stishovite at Various Temperatures and Pressures

Abstract Dense polymorphs of silica have been demonstrated experimentally to incorporate from 1.5 wt% to as much as 11.6 wt% H 2 O as OH groups, with implications for the hydrogen budgets of Earth and other planets. This OH is thought to enter the SiO 2 structure via a charge‐balanced substitution in which silicon vacancies (V Si ) are compensated by protonating four of the surrounding six oxygen atoms, often referred to as a hydrogarnet‐type defect. There are many possible configurations for this defect structure in dense silica, but the nature of these configurations and whether they can be distinguished experimentally is unknown. We present here density functional theory calculations that systematically assess the possible configurations of a hydrogarnet‐type defect in stishovite (rutile‐type SiO 2 ), with direct comparisons to experimental vibrational spectroscopy data. We predict that stishovite synthesized at 450 K and 10 GPa quenched to room temperature is dominated by a single defect type with tetrahedral geometry. This leads to OH stretching modes (2,500–3,000 cm −1 ) and SiOH bending modes (∼1,400–1,450 cm −1 ) largely consistent with experimentally observed modes. One remaining issue is that our calculations produce results compatible with experimental data on H to D exchange, but do not explain why a considerable fraction of the 1,420 cm −1 mode shifts by only 40 cm −1 in deuterated samples. At elevated pressures and temperatures, we find that a second square planar defect configuration also becomes favorable, leading to modes that should allow differentiation from the tetrahedral configuration.

Geochemistry & Geophysics↗

The three-dimensional boundary layer on a rotating helical blade

The laminar boundary layer on a twisted helical blade is considered. The blade geometry is the same as that proposed by Horlock and Wordsworth (1965). However, the blade is twisted about the leading edge in the manner described by Miyake and Fujita (1974). The flow may be considered to be the analog, in a rotating reference frame, of the flat-plate boundary layer in a stationary frame. It is shown that a coordinate system which is orthogonal in the blade surface may be developed. With the appropriate scaling of the dependent variables a solution for the boundary layer flow is readily obtained. The systems of ordinary differential equations for the stream function of the primary flow and the cross-flow are solved numerically.

Morris, P. J.↗

Covariance and the hierarchy of frame bundles

This is an essay on the general concept of covariance, and its connection with the structure of the nested set of higher frame bundles over a differentiable manifold. Examples of covariant geometric objects include not only linear tensor fields, densities and forms, but affinity fields, sectors and sector forms, higher order frame fields, etc., often having nonlinear transformation rules and Lie derivatives. The intrinsic, or invariant, sets of forms that arise on frame bundles satisfy the graded Cartan-Maurer structure equations of an infinite Lie algebra. Reduction of these gives invariant structure equations for Lie pseudogroups, and for G-structures of various orders. Some new results are introduced for prolongation of structure equations, and for treatment of Riemannian geometry with higher-order moving frames. The use of invariant form equations for nonlinear field physics is implicitly advocated.

Estabrook, Frank B.↗

Relative tracking of multiple spacecraft by interferometry

An analysis is conducted of earth-based radiometric tracking of one spacecraft relative to an angularly nearby second spacecraft. Two cases are studied: relative positioning between a lander and a rover on the surface of Mars and relative tracking between a Mars lander and a Mars orbiter. All spacecraft signals are simultaneously received in the same beamwidth of an earth tracking antenna. Differential interferometric measurement errors are predicted. Errors which scale with angular separation between sources and errors which scale with temporal separation between measurement epochs are reduced virtually to zero. System thermal noise and systematic phase shifts introduced by receiver electronics typically dominate the error budget. Solar plasma delays become dominant for signal paths which pass close to the sun. Precise line-of-sight range measurements, differenced between stations, are also considered. Meter-level accuracy is obtained for lander/rover relative position by combining interferometric and precise range measurements. Either data type alone, for geometries where earth is not near zero declination as seen from Mars and Mars is not near zero declination as seen from earth, can provide accuracy at the 10-100-m level.

Border, James S.↗

Magnus force induced magnetic diode effect in skyrmion systems

We show that skyrmions can exhibit a “magnetic diode effect,” where there is a nonreciprocal response in the transport when the magnetic field is reversed. This effect can be achieved for skyrmions moving in channels with a sawtooth potential on one side and a reversed sawtooth potential on the other side. We consider the cases of both spin-transfer torque (STT) and spin–orbit torque (SOT). When the magnetic field is held fixed, the velocity response of the skyrmion is the same for current applied in either direction for both torques, so there is no current diode effect. When the magnetic field is reversed, under STT driving the velocity of the skyrmion reverses and its absolute value changes. Under SOT driving, the velocity remains in the same direction but drops to a much lower value, resulting in negative differential conductivity. For a fixed current, we find a nonreciprocal skyrmion velocity as a function of the applied field’s sign, in analogy to the velocity–current curves observed in the usual diode effect. The nonreciprocity is generated by the Magnus force, which causes skyrmions to interact preferentially with one side of the channel. Since the channel sides have opposite asymmetry, a positive magnetic field can cause the skyrmion to interact with the “hard” asymmetry side of the channel, while a negative magnetic field causes the skyrmion to interact with the “easy” asymmetry side. This geometry could be used to create new kinds of magnetic-field-induced diode effects that can be harnessed in new types of skyrmion-based devices.

36 MATERIALS SCIENCE↗

The PENELOPE Physics Models and Transport Mechanics. Implementation into Geant4

A translation of the PENELOPE physics subroutines to C++, designed as an extension of the GEANT4 toolkit, is presented. The Fortran code system PENELOPE performs Monte Carlo simulation of coupled electron-photon transport in arbitrary materials for a wide energy range, nominally from 50 eV up to 1 GeV. PENELOPE implements the most reliable interaction models that are currently available, limited only by the required generality of the code. In addition, the transport of electrons and positrons is simulated by means of an elaborate class II scheme in which hard interactions (involving deflection angles or energy transfers larger than pre-defined cutoffs) are simulated from the associated restricted differential cross sections. After a brief description of the interaction models adopted for photons and electrons/positrons, we describe the details of the class-II algorithm used for tracking electrons and positrons. The C++ classes are adapted to the specific code structure of GEANT4. They provide a complete description of the interactions and transport mechanics of electrons/positrons and photons in arbitrary materials, which can be activated from the G4ProcessManager to produce simulation results equivalent to those from the original PENELOPE programs. The combined code, named PENG4, benefits from the multi-threading capabilities and advanced geometry and statistical tools of GEANT4.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The prediction of the noise of supersonic propellers in time domain - New theoretical results

In this paper, a new formula for the prediction of the noise of supersonic propellers is derived in the time domain which is superior to the previous formulations in several respects. The governing equation is based on the Ffowcs Williams-Hawkings (FW-H) equation with the thickness source term replaced by an equivalent loading source term derived by Isom (1975). Using some results of generalized function theory and simple four-dimensional space-time geometry, the formal solution of the governing equation is manipulated to a form requiring only the knowledge of blade surface pressure data and geometry. The final form of the main result of this paper consists of some surface and line integrals. The surface integrals depend on the surface pressure, time rate of change of surface pressure, and surface pressure gradient. These integrals also involve blade surface curvatures. The line integrals which depend on local surface pressure are along the trailing edge, the shock traces on the blade, and the perimeter of the airfoil section at the inner radius of the blade. The new formulation is for the full blade surface and does not involve any numerical observer time differentiation. The method of implementation on a computer for numerical work is also discussed.

Farassat, F.↗

Finite Element Analysis of a Deployable Space Structure

The dynamic characteristics of the Solar Array Flight Experiment (SAFE) structure during deployment and retraction are investigated. The SAFE structure consists of a deployable mast with an attached solar blanket designed with accordion type folds to permit packaging in a small volume. The planar form of the blanket geometry during deployment is maintained by a blanket tension/guidewire system. Structurally, the mast is modeled as an Euler beam column with inplane and out of plane bending and finite torsional stiffness. For out of plane motion, the blanket is modeled as a distributed mass uniformly supported by the three guidewires. For inplane motion the blanket displacements are assumed to vary linearly from the mast base to the mast tip. The mathematical model uses a virtual work formulation, required because the axial loading on the mast is nonconservative, combined with assumed beam modes to derive the differential equations of motion. Consideration of the time dependent boundary conditions results in an infinite set of ODE with time dependent coefficients. Finally, correlation of mast tip accelerations to mast base bending moments for specified modal motions are indicated.

Weeks, G. E.↗

Computational attributes of the integral form of the equation of transfer

Difficulties can arise in radiative and neutron transport calculations when a highly anisotropic scattering phase function is present. In the presence of anisotropy, currently used numerical solutions are based on the integro-differential form of the linearized Boltzmann transport equation. This paper, departs from classical thought and presents an alternative numerical approach based on application of the integral form of the transport equation. Use of the integral formalism facilitates the following steps: a reduction in dimensionality of the system prior to discretization, the use of symbolic manipulation to augment the computational procedure, and the direct determination of key physical quantities which are derivable through the various Legendre moments of the intensity. The approach is developed in the context of radiative heat transfer in a plane-parallel geometry, and results are presented and compared with existing benchmark solutions. Encouraging results are presented to illustrate the potential of the integral formalism for computation. The integral formalism appears to possess several computational attributes which are well-suited to radiative and neutron transport calculations.

Frankel, J. I.↗

Progress on Inverse Estimation Technique of Non-Linear Pitch Damping Coefficient Curves Using Free-Flight CFD Generated Trajectories

Characterization of entry vehicle pitch damping coefficient curves is crucial to ensure appropriate re-entry and overall mission success. The pitch damping coefficient (C_(m_q )+C_(m_α ̇ )) is used to encapsulate the oscillatory growth or decay of a body during a trajectory. The inverse estimation technique utilizes an existing Free-Flight CFD (FF-CFD) dataset and wraps a reconstruction algorithm in an optimizer. The reconstruction integrates the planar equations of motion derived by Schoenenberger, Queen [1] using Python’s scipy.integrate.solve_ivp. The optimizer’s objective function is the normalized 𝐿2 residual of the angle of attack peaks between the reconstructed trajectory and the original data produced with FF-CFD. Inclusion of the peak times in this residual calculation allows for simultaneous optimization of the pitch moment coefficient, C_(m_α ). This residual equation is shown below in Eq. 1. The optimizer scipy.optimize.minimize was used with the gradient-based Powell method for the analysis presented, however the differential evolution method was investigated as means of comparison, and was found to produce marginally lower residual values with prohibitively longer run times. Further, the pitch damping curve is found by fitting a cubic interpolation function to a set of (α, (C_(m_q )+C_(m_α ̇ ))) control points, where the α points are held constant and the (C_(m_q )+C_(m_α ̇ )) values are the optimized parameters. The pitch moment curve uses a linear interpolation between the minimum and maximum α in the dataset. FF-CFD generated trajectories using the Dragonfly capsule geometry with the Genesis ballistic range model parameters were simulated and used for this analysis. These FF-CFD trajectories simulate planar motion, as restricted by the reconstructing the equations of motion, of three different cases: 1-DoF (free-to-pitch), 2-DoF (free-to-pitch and heave), and 3-DoF (free-to-pitch, heave, and decelerate). Pitch damping coefficient curves generated using this inverse estimation curve technique with FF-CFD 1-DoF Dragonfly data are found in Fig. 1. Preliminary results reconstructing ballistic range shots using these FF-CFD derived predictions of the pitch damping curve (Fig. 1) are shown in Fig. 2. It should be noted that the ballistic range shot used a Genesis model whereas the FF-CFD data used a Dragonfly geometry, however these geometries are similar.

entry↗

Unwinding the amplituhedron in binary

We present new, fundamentally combinatorial and topological characterizations of the amplituhedron. Upon projecting external data through the amplituhedron, the resulting configuration of points has a specified (and maximal) generalized “winding number”. Equivalently, the amplituhedron can be fully described in binary: canonical projections of the geometry down to one dimension have a specified (and maximal) number of “sign flips” of the projected data. The locality and unitarity of scattering amplitudes are easily derived as elementary consequences of this binary code. Minimal winding defines a natural “dual” of the amplituhedron. This picture gives us an avatar of the amplituhedron purely in the configuration space of points in vector space (momentum-twistor space in the physics), a new interpretation of the canonical amplituhedron form, and a direct bosonic understanding of the scattering super-amplitude in planar N = 4 SYM as a differential form on the space of physical kinematical data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

High-energy Gamma Rays from the Milky Way: Three-dimensional Spatial Models for the Cosmic-Ray and Radiation Field Densities in the Interstellar Medium

High-energy γ -rays of interstellar origin are produced by the interaction of cosmic-ray (CR) particles with the diffuse gas and radiation fields in the Galaxy. The main features of this emission are well understood and are reproduced by existing CR propagation models employing 2D galactocentric cylindrically symmetrical geometry. However, the high-quality data from instruments like the Fermi Large Area Telescope reveal significant deviations from the model predictions on few to tens of degrees scales, indicating the need to include the details of the Galactic spiral structure and thus requiring 3D spatial modeling. In this paper, the high-energy interstellar emissions from the Galaxy are calculated using the new release of the GALPROP code employing 3D spatial models for the CR source and interstellar radiation field (ISRF) densities. Three models for the spatial distribution of CR sources are used that are differentiated by their relative proportion of input luminosity attributed to the smooth disk or spiral arms. Two ISRF models are developed based on stellar and dust spatial density distributions taken from the literature that reproduce local near- to far-infrared observations. The interstellar emission models that include arms and bulges for the CR source and ISRF densities provide plausible physical interpretations for features found in the residual maps from high-energy γ -ray data analysis. The 3D models for CR and ISRF densities provide a more realistic basis that can be used for the interpretation of the nonthermal interstellar emissions from the Galaxy.

79 ASTRONOMY AND ASTROPHYSICS↗

Aerodynamic Shape Sensitivity Analysis and Design Optimization of Complex Configurations Using Unstructured Grids

A three-dimensional unstructured grid approach to aerodynamic shape sensitivity analysis and design optimization has been developed and is extended to model geometrically complex configurations. The advantage of unstructured grids (when compared with a structured-grid approach) is their inherent ability to discretize irregularly shaped domains with greater efficiency and less effort. Hence, this approach is ideally suited for geometrically complex configurations of practical interest. In this work the nonlinear Euler equations are solved using an upwind, cell-centered, finite-volume scheme. The discrete, linearized systems which result from this scheme are solved iteratively by a preconditioned conjugate-gradient-like algorithm known as GMRES for the two-dimensional geometry and a Gauss-Seidel algorithm for the three-dimensional; similar procedures are used to solve the accompanying linear aerodynamic sensitivity equations in incremental iterative form. As shown, this particular form of the sensitivity equation makes large-scale gradient-based aerodynamic optimization possible by taking advantage of memory efficient methods to construct exact Jacobian matrix-vector products. Simple parameterization techniques are utilized for demonstrative purposes. Once the surface has been deformed, the unstructured grid is adapted by considering the mesh as a system of interconnected springs. Grid sensitivities are obtained by differentiating the surface parameterization and the grid adaptation algorithms with ADIFOR (which is an advanced automatic-differentiation software tool). To demonstrate the ability of this procedure to analyze and design complex configurations of practical interest, the sensitivity analysis and shape optimization has been performed for a two-dimensional high-lift multielement airfoil and for a three-dimensional Boeing 747-200 aircraft.

Taylor, Arthur C., III↗

Formation of the Conducting Filament in TaO x -Resistive Switching Devices by Thermal-Gradient-Induced Cation Accumulation

Here, the distribution of tantalum and oxygen ions in electroformed and/or switched TaO x -based resistive switching devices has been assessed by high-angle annular dark-field microscopy, X-ray energy-dispersive spectroscopy, and electron energy-loss spectroscopy. The experiments have been performed in the plan-view geometry on the cross-bar devices producing elemental distribution maps in the direction perpendicular to the electric field. The maps revealed an accumulation of +20% Ta in the inner part of the filament with a 3.5% Ta-depleted ring around it. The diameter of the entire structure was approximately 100 nm. The distribution of oxygen was uniform with changes, if any, below the detection limit of 5%. We interpret the elemental segregation as due to diffusion driven by the temperature gradient, which in turn is induced by the spontaneous current constriction associated with the negative differential resistance-type I–V characteristics of the as-fabricated metal/oxide/metal structures. A finite-element model was used to evaluate the distribution of temperature in the devices and correlated with the elemental maps. In addition, a fine-scale (~5 nm) intensity contrast was observed within the filament and interpreted as due phase separation of the functional oxide in the two-phase composition region. Understanding the temperature-gradient-induced phenomena is central to the engineering of oxide memory cells.

36 MATERIALS SCIENCE↗

Slow manifold reduction as a systematic tool for revealing the geometry of phase space

Many non-dissipative reduced plasma models can be derived from more fundamental non-dissipative models by restricting to an approximate invariant manifold. I present a general systematic procedure for finding the Hamiltonian formulation of a plasma model that can be derived in this manner. Several illustrative examples are considered in detail.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Tip-based proximity ferroelectric switching and piezoelectric response in wurtzite multilayers

Proximity ferroelectricity is a paradigm for inducing ferroelectricity when a nonferroelectric polar material (such as Al⁢ N), which is unswitchable with an external field below the dielectric breakdown field, becomes a practically switchable ferroelectric in direct contact with a thin switchable ferroelectric layer (such as Al 1−𝑥 ⁢Sc 𝑥 ⁢N). Here, we develop a Landau-Ginzburg-Devonshire approach to study the proximity effect of local piezoelectric response and polarization reversal in wurtzite ferroelectric multilayers under a sharp electrically biased tip. Using finite-element modeling, we analyze the probe-induced nucleation of nanodomains, the features of local polarization hysteresis loops and coercive fields in the Al 1−𝑥 ⁢Sc 𝑥 ⁢N/Al⁢ N bilayers and three-layers. Similar to the wurtzite multilayers sandwiched between two parallel electrodes, the regimes of “proximity switching” (when all layers collectively switch) and the regime of “proximity suppression” (when they collectively do not switch) are the only two possible regimes in the probe-electrode geometry. However, the parameters and asymmetry of the local piezoresponse and polarization hysteresis loops depend significantly on the sequence of the layers with respect to the probe. The physical mechanism of proximity ferroelectricity in the local probe geometry is a depolarizing electric field determined by the polarization of the layers and their relative thickness. The field, whose direction is opposite to the polarization vector in the layer(s) with the larger spontaneous polarization (such as Al⁢ N), renormalizes the double-well ferroelectric potential to lower the steepness of the switching barrier in the “otherwise unswitchable” polar layers. Tip-based control of domains in otherwise nonferroelectric layers using proximity ferroelectricity can provide nanoscale control of domain reversal in memory, actuation, sensing, and optical applications. The ability of the tip-induced proximity switching to differentially switch multilayers, based on the order of the layers, provides a powerful tool for selective domain engineering.

36 MATERIALS SCIENCE↗

Expansion of epicyclic gear dynamic analysis program

The multiple mesh/single stage dynamics program is a gear tooth analysis program which determines detailed geometry, dynamic loads, stresses, and surface damage factors. The program can analyze a variety of both epicyclic and single mesh systems with spur or helical gear teeth including internal, external, and buttress tooth forms. The modifications refine the options for the flexible carrier and flexible ring gear rim and adds three options: a floating Sun gear option; a natural frequency option; and a finite element compliance formulation for helical gear teeth. The option for a floating Sun incorporates two additional degrees of freedom at the Sun center. The natural frequency option evaluates the frequencies of planetary, star, or differential systems as well as the effect of additional springs at the Sun center and those due to a flexible carrier and/or ring gear rim. The helical tooth pair finite element calculated compliance is obtained from an automated element breakup of the helical teeth and then is used with the basic gear dynamic solution and stress postprocessing routines. The flexible carrier or ring gear rim option for planetary and star spur gear systems allows the output torque per carrier and ring gear rim segment to vary based on the dynamic response of the entire system, while the total output torque remains constant.

Boyd, Linda Smith↗

Is the Oort A-value a universal growth rate limit for accretion disk shear instabilities?

A weak-field local MHD instability that is of importance to accretion disks is examined. The maximum growth rate of the instability is found to be not only independent of the magnetic field strength but independent of field geometry as well. In particular, all Keplerian disks are unstable in the presence of any weak poloidal field, with the ratio of the maximum growth rate to disk angular velocity given by 3/4. The maximum growth rate of any weak field configuration that is not purely toroidal is given by the local Oort A-value of the disk. The behavior is studied by using a form of the dynamical Hill equations. It is conjectured that the Oort A-value is an upper bound to the growth rate of any instability feeding upon the free energy of differential rotation.

Balbus, Steven A.↗