Post-Newtonian metric for a general class of scalar-tensor gravitational theories and observational consequences
Space-time Riemann metric for scalar-tensor gravitational theories with arbitrary omega parameter
Nordtvedt, K., Jr.↗
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Results for “SCALARS”
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Scalar-tensor theory in canonical form. II - Exact solutions for a static spherically symmetric charged mass distribution
Static spherically symmetric charged mass distribution exact solutions derived for electrons in scalar tensor theory of gravity by Hamilton-Jacobi method
Toton, E. T.↗
Dispersion methods and the two-nucleon interaction in charged scalar theory
Charged scalar static model, using dispersion theory to include two-meson effects in two nucleons binding energy at zero separation
Scarfone, L. M.↗
Optimal control theory for non-scalar-valued performance criteria
The theory of optimal control for nonscalar-valued performance criteria is discussed. In the space, where the performance criterion attains its value, the relations better than, worse than, not better than, and not worse than are defined by a partial order relation. The notion of optimality splits up into superiority and non-inferiority, because worse than is not the complement of better than, in general. A superior solution is better than every other solution. A noninferior solution is not worse than any other solution. Noninferior solutions have been investigated particularly for vector-valued performance criteria. Superior solutions for non-scalar-valued performance criteria attaining their values in abstract partially ordered spaces are emphasized. The main result is the infimum principle which constitutes necessary conditions for a control to be a superior solution to an optimal control problem.
Gerring, H. P.↗
Error enhancement in geomagnetic models derived from scalar data
Models of the main geomagnetic field are generally represented by a scalar potential gamma expanded in a finite number of spherical harmonics. Very accurate observations of F were used, but indications exist that the accuracy of models derived from them is considerably lower. One problem is that F does not always characterize gamma uniquely. It is not clear whether such ambiguity can be encountered in deriving gamma from F in geomagnetic surveys, but there exists a connection, due to the fact that the counterexamples of Backus are related to the dipole field, while the geomagnetic field is dominated by its dipole component. If the models are recovered with a finite error (i.e. they cannot completely fit the data and consequently have a small spurious component), this connection allows the error in certain sequences of harmonic terms in gamma to be enhanced without unduly large effects on the fit of F to the model.
Stern, D. P.↗
Application of the scalar and vector potentials to the aerodynamics of jets
The applicability of a method based on the Stokes potentials (vector and scalar potentials) to computations associated with the aerodynamics of jets was examined. The aerodynamic field near the nozzle could be represented and that the influence of a nonuniform velocity profile at the nozzle exit plane could be determined. Also computations were made for an axisymmetric jet exhausting into a quiescient atmosphere. The velocity at the axis of the jet, and the location of the half-velocity points along the jet yield accurate aerodynamic field computations. Inconsistencies among the different theoretical characterizations of jet flowfields are shown.
Russell, H. L.↗
Error enhancement in geomagnetic models derived from scalar data
An investigation conducted by Backus (1970) regarding the possible existence of two harmonic functions of certain characteristics in three-dimensional space is considered. The derivation of a model of the main geomagnetic field from scalar data is discussed along with a numerical simulation study. It is found that experimental discrepancies between vector field observations and the predictions of the model may have a mathematical origin, related to the work of Backus.
Stern, D. P.↗
Lognormality of gradients of advected scalars
The gradient of an advected scalar in turbulent flow is treated in a coordinate system moving with a fluid particle. This Lagrangian coordinate system is chosen to be rotating such that the gradient vector lies along the 1-axis at all times; the final results are independent of this particular coordinate system. In the absence of diffusion, the magnitude of the gradient at the position of the fluid particle is shown to be a lognormal random process. The action of diffusion is to reduce the probability density for the largest values of the gradient.
Hill, R. J.↗
Magsat scalar anomalies and major tectonic boundaries in Asia
The distribution of Magsat scalar anomalies is compared with locations of major tectonic boundaries in Asia. Foldbelts separate large-scale positive and negative anomalies inside and outside the Siberian Platform, and sediment-filled aulacogens within the Platform separate the anomalies into two parts which overlie the Anabar and Aldan Shields. Tectonic boundaries appear to exercise some control over the extent and distribution of the satellite-observed crustal anomalies.
Frey, H.↗
MAGSAT scalar anomalies
To facilitate processing large data arrays, elements of spherical Earth analysis programs NVERTSM, SMFLD, NVERTG and GLFD were implemented and tested on the LARS IBM 4341 computer. Currently, the problem of inverting 2 deg MAGSAT scalar anomalies for the region (80 W, 60 E) longitude and (40 S, 70 N) latitude is being implemented on the LARS-computer for quantitative comparison with free air gravity anomaly, geothermal and tectonic data. Gravity and MAGSAT anomalies from a subset of this region (30 W, 60 E), (40 S, 70 N) were already processed for a paper on satellite magnetic anomalies of Africa and Europe.
Braile, L. W.↗
The large-time behavior of the scalar, genuinely nonlinear Lax-Friedrichs scheme
The Lax-Friedrichs scheme, approximating the scalar, genuinely nonlinear conservation law u sub t + f sub x (u) = 0 where f(u) is, say, strictly convex double dot f dot a sub asterisk 0 is studied. The divided differences of the numerical solution at time t do not exceed 2 (t dot a sub asterisk) to the -1. This one-sided Lipschitz boundedness is in complete agreement with the corresponding estimate one has in the differential case; in particular, it is independent of the initial amplitude in sharp contrast to liner problems. It guarantees the entropy compactness of the scheme in this case, as well as providing a quantitive insight into the large-time behavior of the numerical computation.
Tadmor, E.↗
On the convergence of difference approximations to scalar conservation laws
A unified treatment of explicit in time, two level, second order resolution, total variation diminishing, approximations to scalar conservation laws are presented. The schemes are assumed only to have conservation form and incremental form. A modified flux and a viscosity coefficient are introduced and results in terms of the latter are obtained. The existence of a cell entropy inequality is discussed and such an equality for all entropies is shown to imply that the scheme is an E scheme on monotone (actually more general) data, hence at most only first order accurate in general. Convergence for total variation diminishing-second order resolution schemes approximating convex or concave conservation laws is shown by enforcing a single discrete entropy inequality.
Osher, S.↗
MAGSAT scalar anomaly map of South America
A scalar magnetic anomaly map was prepared for South America and adjacent marine areas directly from original MAGSAT orbits. The preparation of the map poses special problems, notably in the separation of external field and crustal anomalies, and in the reduction of data to a common altitude. External fields are manifested in a long-wavelength ring current effect, a medium-wavelength equatorial electrojet, and short-wavelength noise. The noise is reduced by selecting profiles from quiet periods, and since the electrojet is confined primarily to dusk profiles, its effect is minimized by drawing the data set from dawn profiles only. The ring current is corrected through the use of the standard ring current equation, augmented by further filtering with a Butterworth bandpass filter. Under the assumption that the time-variant ring current is best removed when a replication of redundant profiles is achieved, a test set of 25 groups of 3 nearly coincident orbits per group is set up for filtering with a range of long-wavelength cutoffs to determine which cutoff best replicates the residual profiles. Altitude differences are then normalized by an inversion of the profile data onto a grid of equivalent point dipoles, and recalculated at an altitude of 350 km. The resulting map, when compared to the 2 deg averaged map, shows more coherent anomalies, with notable differences in the region affected by the electrojet.
Ridgway, J. R.↗
The large-time behavior of the scalar, genuinely nonlinear Lax-Friedrichs scheme
The Lax-Friedrichs scheme, approximating the scalar, genuinely nonlinear conservation law u sub t + f sub x (u) = O where f(u) is, say, strictly double dot f dot a sub asterisk O is studied. The divided differences of the numerical solution at time t do not exceed 2 (t dot a sub asterisk) to the -1. This one-sided Lipschitz boundedness is in complete agreement with the corresponding estimate one has in the differential case; in particular, it is independent of the initial amplitude in sharp contrast to linear problems. It guarantees the entropy compactness of the scheme in this case, as well as providing a quantitative insight into the large-time behavior of the numerical computation.
Tadmor, E.↗
Multigrid techniques for the solution of the passive scalar advection-diffusion equation
The solution of elliptic passive scalar advection-diffusion equations is required in the analysis of many turbulent flow and convective heat transfer problems. The accuracy of the solution may be affected by the presence of regions containing large gradients of the dependent variables. The multigrid concept of local grid refinement is a method for improving the accuracy of the calculations in these problems. In combination with the multilevel acceleration techniques, an accurate and efficient computational procedure is developed. In addition, a robust implementation of the QUICK finite-difference scheme is described. Calculations of a test problem are presented to quantitatively demonstrate the advantages of the multilevel-multigrid method.
Phillips, R. E.↗
The discrete one-sided Lipschitz condition for convex scalar conservation laws
Physical solutions to convex scalar conservation laws satisfy a one-sided Lipschitz condition (OSLC) that enforces both the entropy condition and their variation boundedness. Consistency with this condition is therefore desirable for a numerical scheme and was proved for both the Godunov and the Lax-Friedrichs scheme--also, in a weakened version, for the Roe scheme, all of them being only first order accurate. A new, fully second order scheme is introduced here, which is consistent with the OSLC. The modified equation is considered and shows interesting features. Another second order scheme is then considered and numerical results are discussed.
Brenier, Yann↗
Modeling scalar flux and the energy and dissipation equations
Closure models derived from the Two-Scale Direct-Interaction Approximation were compared with data from direct simulations of turbulence. Attention was restricted to anisotropic scalar diffusion models, models for the energy dissipation equation, and models for energy diffusion.
Yoshizawa, A.↗
Pressure gradient alignment with strain rate and scalar gradient in simulated Navier-Stokes turbulence
In a simulated turbulent shear flow the pressure gradient caused by velocity fluctuations alone has increased probability for alignment with the most compressive strain direction, which is similar to passive scalar-gradient behavior. The pressure-gradient component depending on the mean shear indicates no correlation with the strain directions.
Ashurst, Wm. T.↗