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At least 73 records · Page 4

The organic surface of 5145 Pholus: Constraints set by scattering theory

No known body in the Solar System has a spectrum redder than that of object 5145 Pholus. We use Hapke scattering theory and optical constants measured in this laboratory to examine the ability of mixtures of a number of organic solids and ices to reproduce the observed spectrum and phase variation. The primary materials considered are poly-HCN, kerogen, Murchison organic extract, Titan tholin, ice tholin, and water ice. In a computer grid search of over 10 million models, we find an intraparticle mixture of 15% Titan tholin, 10% poly-HCN, and 75% water ice with 10-micrometers particles to provide an excellent fit. Replacing water ice with ammonia ice improves the fits significantly while using a pure hydrocarbon tholin, Tholin alpha, instead of Titan tholin makes only modest improvements. All acceptable fits require Titan tholin or some comparable material to provide the steep slope in the visible, and poly-HCN or some comparable material to provide strong absorption in the near-infrared. A pure Titan tholin surface with 16-micrometers particles, as well as all acceptable Pholus models, fit the present spectrophotometric data for the transplutonian object 1992 QB(sub 1). The feasibility of gas-phase chemistry to generate material like Titan tholin on such small objects is examined. An irradiated transient atmosphere arising from sublimating ices may generate at most a few centimeters of tholin over the lifetime of the Solar System, but this is insignificant compared to the expected lag deposit of primordial contaminants left behind by the sublimating ice. Irradiation of subsurface N2/CH4 or NH3/CH4 ice by cosmic rays may generate approximately 20 cm of tholin in the upper 10 m of regolith in the same time scale but the identity of this tholin to its gas-phase equivalent has not been demonstrated.

Wilson, Peter D.↗

Dynamical basis sets for algebraic variational calculations in quantum-mechanical scattering theory

New basis sets are proposed for linear algebraic variational calculations of transition amplitudes in quantum-mechanical scattering problems. These basis sets are hybrids of those that yield the Kohn variational principle (KVP) and those that yield the generalized Newton variational principle (GNVP) when substituted in Schlessinger's stationary expression for the T operator. Trial calculations show that efficiencies almost as great as that of the GNVP and much greater than the KVP can be obtained, even for basis sets with the majority of the members independent of energy.

Sun, Yan↗

Analytical satellite theories based on a new set of canonical elements

A new analytical satellite theory is presented. Instead of the 6 classical elements of Delaunay, a set of 8 canonical elements is used. Whereas the time is the independent variable in classical theory, the true anomaly is the independent variable in the new theory. The new approach has four features: (1) The amount of formulas in the solution is reduced considerably. (2) The first order results are almost as accurate as second order results in classical theory. (3) The theory is easier to understand from a didactical point of view. (4) The problems connected with the inaccuracy of the mean motion that are typical for classical satellite theory are no longer present. The new elements are applied to analytical solutions of the zonal oblateness problem and to the problem of the 24 hour satellite.

Scheifele, G.↗

Eigenfunction methods in magnetospheric radial-diffusion theory

Complete sets of orthonormal basis functions constructed according to a generalization of the quantum-mechanical WKB approximation can be used to generate a nearly-diagonal matrix representation of the radial-transport operator for ring-current ions in the presence of radial diffusion and charge exchange. The resulting eigenfunctions (constructed by weighting the basis functions in proportion to the respective components of the eigenvectors of the matrix representation) and eigenvalues provide a spatial and temporal description of the evolving phase-space density during and following a magnetospheric disturbance (e.g., a magnetic storm). A linear superposition of the basis functions can also be used to eliminate any discrepancy between the steady-state solution of the transport equation and the appropriate WKB approximation of this steady-state solution.

Schulz, Michael↗

Fuzzy sets, rough sets, and modeling evidence: Theory and Application. A Dempster-Shafer based approach to compromise decision making with multiattributes applied to product selection

The Dempster-Shafer theory of evidence is applied to a multiattribute decision making problem whereby the decision maker (DM) must compromise with available alternatives, none of which exactly satisfies his ideal. The decision mechanism is constrained by the uncertainty inherent in the determination of the relative importance of each attribute element and the classification of existing alternatives. The classification of alternatives is addressed through expert evaluation of the degree to which each element is contained in each available alternative. The relative importance of each attribute element is determined through pairwise comparisons of the elements by the decision maker and implementation of a ratio scale quantification method. Then the 'belief' and 'plausibility' that an alternative will satisfy the decision maker's ideal are calculated and combined to rank order the available alternatives. Application to the problem of selecting computer software is given.

Dekorvin, Andre↗

Exploring Diverse Data Sets and Developing New Theories and Ideas With Project Integration Architecture

The development of new ideas is the essence of scientific research. This is frequently done by developing models of physical processes and comparing model predictions with results from experiments. With models becoming ever more complex and data acquisition systems becoming more powerful, the researcher is burdened with wading through data ranging in volume up to a level of many terabytes and beyond. These data often come from multiple, heterogeneous sources and usually the methods for searching through it are at or near the manual level. In addition, current documentation methods are generally limited to researchers pen-and-paper style notebooks. Researchers may want to form constraint-based queries on a body of existing knowledge that is, itself, distributed over many different machines and environments and from the results of such queries then spawn additional queries, simulations, and data analyses in order to discover new insights into the problem being investigated. Currently, researchers are restricted to working within the boundaries of tools that are inefficient at probing current and legacy data to extend the knowledge of the problem at hand and reveal innovative and efficient solutions. A framework called the Project Integration Architecture is discussed that can address these desired functionalities.

Benyo, Theresa L.↗

Scale setting of SU⁡(𝑁) Yang–Mills theory, topology and large-𝑁 volume independence

We set the scale of SU⁡(𝑁) Yang-Mills theories for 𝑁 =3, 5, 8 and in the large-𝑁 limit via gradient flow, as a first step towards the computation of the large-𝑁 Λ-parameter using step scaling. We adopt twisted boundary conditions to achieve large-𝑁 volume reduction and the Parallel Tempering on Boundary Conditions algorithm to tame topological freezing. This setup allows accurate determinations of the gradient-flow scales down to lattice spacings as fine as ∼0.025 fm for all the explored values of 𝑁, a regime that has never been reached with ergodic algorithms. Moreover, we are able to precisely estimate the finite-size systematics related to topological freezing, and to show the suppression of finite-volume effects expected by virtue of large-𝑁 twisted volume reduction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Functions of relaxed controls

Mathematical control theory problems involving solutions of certain partial differential equations, nonadditive set functions, or other functionals - approximation and existence theorems

FUNCTIONAL ANALYSIS↗

Pilot-Induced Oscillations and Human Dynamic Behavior

This is an in-depth survey and study of pilot-induced oscillations (PIO's) as interactions between human pilot and vehicle dynamics; it includes a broad and comprehensive theory of PIO's. A historical perspective provides examples of the diversity of PIO's in terms of control axes and oscillation frequencies. The constituents involved in PIO phenomena, including effective aircraft dynamics, human pilot dynamic behavior patterns, and triggering precursor events, are examined in detail as the structural elements interacting to produce severe pilot-induced oscillations. The great diversity of human pilot response patterns, excessive lags and/or inappropriate gain in effective aircraft dynamics, and transitions in either the human or effective aircraft dynamics are among the key sources implicated as factors in severe PIO's. The great variety of interactions which may result in severe PIO's is illustrated by examples drawn from famous PIO's. These are generalized under a pilot-behavior-theory-based set of categories proposed as a classification scheme pertinent to a theory of PIO's. Finally, a series of interim prescriptions to avoid PIO is provided.

McRuer, Duane T.↗

A non-linear dynamic lumped-parameter model of a rectangular plate.

A lumped-parameter model of a rectangular plate is developed by assuming fundamental mode solutions and using Hamilton's Principle and the Euler equations to set up the differential equation of motion for the system. The plate theory used may be described as the dynamic analogue of the von Karman large-deflection theory. Four sets of symmetrical boundary conditions are considered with the restriction of uniform pressure dynamic loads. The model takes the form of a mass on a cubic-hardening spring with each term defined by algebraic expressions of the plate parameters. The results for some specific problems are compared with two previous solutions. This method is less accurate but simpler to develop and apply.

Bayles, D. J.↗

Life analysis of helical gear sets using Lundberg-Palmgren theory

A mathematical model is developed for surface fatigue life of helical gears. The expected fatigue life of a pinion, gear, or gear set may be calculated from the model. An equation for the dynamic capacity of a gear set was also derived. Dynamic capacity is the transmitted tangential load which gives a 90 percent probability of survival of the gear set for one million pinion revolutions. The equations, when simplified by setting the helix angle to zero, reduce to the results which were previously developed for spur gears. A sample calculation is given which illustrates the use of the new fatigue life model.

Coy, J. J.↗

Constraint-Free Theories of Gravitation

Lovelock actions (more precisely, extended Gauss-Bonnet forms) when varied as Cartan forms on subspaces of higher dimensional flat Riemannian manifolds, generate well set, causal exterior differential systems. In particular, the Einstein- Hilbert action 4-form, varied on a 4 dimensional subspace of E(sub 10) yields a well set generalized theory of gravity having no constraints. Rcci-flat solutions are selected by initial conditions on a bounding 3-space.

Estabrook, Frank B.↗