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NASA NTRS1988

Bounds on exotic-particle interactions from SN 1987A

The observation of a neutrino pulse from the supernova SN 1987A constrains the production of light exotic particles in the protoneutron star. A new bound on the axion decay constant is derived, f(a) of greater than about 10 to the 10th GeV. If right-handed (RH) neutrinos exist, 'RH Fermi constant' is G(RH) of less than about 10 exp-4 G(F), two orders of magnitude below laboratory bounds. The Dirac mass of hv sub m can be constrained below laboratory limits. The Dirac mass of the mu-neutrino can be constrained below laboratory limits.

Raffelt, Georg↗

NASA NTRS1989

Confidence set inference with a prior quadratic bound

In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z=(z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y (sup 0) = (y (sub 1) (sup 0), ..., y (sub D (sup 0)), using full or partial knowledge of the statistical distribution of the random errors in y (sup 0). The data space Y containing y(sup 0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x, Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. Confidence set inference is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface.

Backus, George E.↗

NASA NTRS1989

Bounds on current collection from the far field by plasma clouds in the ionosphere

Plasma clouds can enhance the collection of current to a charged body in the ionosphere in two ways. The first is by providing a large collection area for ionospheric electrons to be collected. The second is by ionization of neutral gas in the vicinity of the plasma cloud. The collection of electrons across a magnetic field is examined, and it is shown that the effective collection area is limited to the region of the cloud where the magnetic field effects are overwhelmed by the electric field effects from the charged body. Upper and lower bounds are obtained for the radius of the core region where the electric field influence dominates. From these, upper and lower bounds are obtained for the current collection.

Hastings, D. E.↗

NASA NTRS1989

Motivating the sure bounds

Motivation is provided for a theorem that provides upper and lower bounds for the reliability of reconfigurable digital control systems. The reliability goals for these systems are too high to be established by natural life testing, which means the probability of system failure must be computed from mathematical models that capture the essential elements of fault occurence and system fault recovery. The upper and lower bound theorem shows that system recovery can be adequately described by its first two moments, provided component failure rate is low and system recovery is fast. This result greatly simplifies both the fault injection experiments that study system recovery and the numerical computations that estimate the probability of system failure from a mathematical model.

White, Allan L.↗

NASA NTRS1989

Uncertainty bounds using sector theory

An approach based on sector-stability theory can furnish a description of the uncertainty associated with the frequency response of a model, given sector-bounds on the individual parameters of the model. The application of the sector-based approach to the formulation of useful uncertainty descriptions for linear, time-invariant multivariable systems is presently explored, and the approach is applied to two generic forms of parameter uncertainty in order to investigate its advantages and limitations. The results obtained show that sector-uncertainty bounds can be used to evaluate the impact of parameter uncertainties on the frequency response of the design model.

Waszak, Martin R.↗

NASA NTRS1989

Perturbation guidance for aerocruise with bounded control

A perturbation guidance algorithm is developed for the constant-altitude portion of the orbital-plane change maneuver, called aerocruise. It is obtained by solving a linear-quadratic regulator problem in terms of the perturbed state and control variables. The regulator problem with hard control-variable constraints is then studied. For the two-control-variable case, the simulation results show that the bounded-control algorithm gives better performance than that obtained using a limiter for the case where control variables exceed the bounds.

Hull, David G.↗

NASA NTRS1990

The mechanism of high-T(sub c) superconductivity due to bound hole mediators: Relationship to ferroelectricity

The mediation by bound holes creating Cooper pairing in high T(sub c) superconductors has its origin in charge transfer excitations on the multivalence cation (virtual excitions) and in bound excitions or polarizations associated with the oxygen 2p electrons. These phenomena are produced and/or enhanced by a high internal electric field which is itself created by virtue of the unique crystal structures and polyhedral building blocks of high T(sub c) materials. The polarizations which can create oxygen holes (in addition to excitions) may be due to simply the internal electric field or to polaronic and electron-deficient bond behavior. This gives rise to two energy-dependent oxygen bands near the Fermi level. The magnitude and direction of the internal electric fields were calculated for Y1Ba2Cu3O(7-delta) (1-2-3) and show strong z-direction fields at the Cu(2), O2, and O3 sites and an even stronger -z direction field at the O4 site. The field calculations also show why electrical conductivity in the 1-2-3 material is essentially in the base plane of the CuO5 pyramid (the CuO2 plane).

Vezzoli, G. C.↗

NASA NTRS1990

Shock-layer bounds for a singularly perturbed equation

The size of the shock-layer governed by a conservation law is studied. The conservation law is a parabolic reaction-convection-diffusion equation with a small parameter multiplying the diffusion term and convex flux. Rigorous upper and lower bounding functions for the solution of the conservation law are established based on maximum-principle arguments. The bounding functions demonstrate that the size of the shock-layer is proportional to the parameter multiplying the diffusion term.

Scroggs, Jeffrey S.↗

NASA NTRS1989

Bounds on effectiveness of software reuse

In an earlier work, the author developed a communication channel analogy model of the software development process, which established a quantifiable, parametric upper bound on human productivity in terms of information put into the process and yield of product output by the process. This paper extends this work to focus on factors of that bound associated with software reuse. Specifically, it is shown, that under policies of heavy reuse, human productivity associated with the language advantage grows at best logarithmically in the size of the reuse base.

Tausworthe, Robert C.↗

NASA NTRS1989

Computer simulation of Alfven resonance in a cylindrical, axially bounded flux tube

The resonant absorption of Alfven waves in an axially bounded cylindrical flux tube is investigated in a dissipative MHD simulation. It is found that in an axially bounded flux tube, in contrast to an infinite periodic model, the resonant frequency is nearly independent of the poloidal component of the magnetic field. This is a consequence of the 'ballooning' structure of the resonant Alfven waves. The scaling with resistivity and viscosity of the width of the resonance layer, the dissipation rate, and the time for steady state absorption to occur, are all in agreement with theory.

Strauss, H. R.↗

NASA NTRS1990

Invariant criteria for bound states, degree of ionization, and plasma phase transition

Basis invariant characterizations of bound states and bound fraction of a partially ionized hydrogen plasma are given in terms of properties of the spectrum of eigenvalues and eigenfunctions of the equilibrium quantum statistical one-proton-one-electron reduced density matrix. It is suggested that these can be used to place theories of a proposed plasma-ionization phase transition on a firm foundation. This general approach may be relevant to cosmological questions such as the quark deconfinement-confinement transition.

Girardeau, M. D.↗

NASA NTRS1990

Time optimal feedback control of discrete systems with bounded inputs

Deadbeat control theory gives a feedback solution to the time optimal control of discrete time systems. Experience has shown the results to be impractical because they ignore bounds on the actuator strength. This paper develops two algorithms for generating time optimal control in feedback form for discrete systems with bounded controls. The results are also applicable for generating recovery regions and the set of reachable states. For multiple control problems a method of generating sublayers is developed which decreases off-line and on-line computational effort. Two algorithms are presented with somewhat different computational and storage requirements. The algorithms are practical within certain dimension constraints, and are natural for implementation with parallel processing.

Chen, Xin↗

NASA NTRS1990

Bounds on halo-particle interactions from interstellar calorimetry

It is shown that the existence of neutral interstellar clouds constrains the interaction of any particulate dark-matter candidate with atomic hydrogen to be quite small. Even for a halo particle of mass 1 PeV (10 to the 6 GeV), it is shown that the cross section with hydrogen must be smaller than the typical atomic cross section that is expected for a positively charged particle bound to an electron. The argument presented is that if the clouds are in equilibrium, then the rate at which energy is deposited by collisions with dark-matter particles must be smaller than the rate at which the cloud can cool. This argument is used to constrain the interaction cross section of dark matter with hydrogen. Remarks are made on the general viability of charged dark matter. Comments are also made on a bound which derives from the dynamical stability of the halo.

Chivukula, Sekhar R.↗

NASA NTRS1990

Bounded energy states in homogeneous turbulent shear flow: An alternative view

The equilibrium structure of homogeneous turbulent shear flow is investigated from a theoretical standpoint. Existing turbulence models, in apparent agreement with physical and numerical experiments, predict an unbounded exponential time growth of the turbulent kinetic energy and dissipation rate; only the anisotropy tensor and turbulent time scale reach a structural equilibrium. It is shown that if vortex stretching is accounted for in the dissipation rate transport equation, then there can exist equilibrium solutions, with bounded energy states, where the turbulence production is balanced by its dissipation. Illustrative calculations are present for a k-epsilon model modified to account for vortex stretching. The calculations indicate an initial exponential time growth of the turbulent kinetic energy and dissipation rate for elapsed times that are as large as those considered in any of the previously conducted physical or numerical experiments on homogeneous shear flow. However, vortex stretching eventually takes over and forces a production-equals-dissipation equilibrium with bounded energy states. The validity of this result is further supported by an independent theoretical argument. It is concluded that the generally accepted structural equilibrium for homogeneous shear flow with unbounded component energies is in need of re-examination.

Bernard, Peter S.↗

NASA NTRS1991

Model reduction by trimming for a class of semi-Markov reliability models and the corresponding error bound

Semi-Markov processes have proved to be an effective and convenient tool to construct models of systems that achieve reliability by redundancy and reconfiguration. These models are able to depict complex system architectures and to capture the dynamics of fault arrival and system recovery. A disadvantage of this approach is that the models can be extremely large, which poses both a model and a computational problem. Techniques are needed to reduce the model size. Because these systems are used in critical applications where failure can be expensive, there must be an analytically derived bound for the error produced by the model reduction technique. A model reduction technique called trimming is presented that can be applied to a popular class of systems. Automatic model generation programs were written to help the reliability analyst produce models of complex systems. This method, trimming, is easy to implement and the error bound easy to compute. Hence, the method lends itself to inclusion in an automatic model generator.

White, Allan L.↗

NASA NTRS1990

Kinetic balance and variational bounds failure in the solution of the Dirac equation in a finite Gaussian basis set

The paper investigates bounds failure in calculations using Gaussian basis sets for the solution of the one-electron Dirac equation for the 2p1/2 state of Hg(79+). It is shown that bounds failure indicates inadequacies in the basis set, both in terms of the exponent range and the number of functions. It is also shown that overrepresentation of the small component space may lead to unphysical results. It is concluded that it is important to use matched large and small component basis sets with an adequate size and exponent range.

Dyall, Kenneth G.↗

NASA NTRS1992

Entropy-Based Bounds On Redundancies Of Huffman Codes

Report presents extension of theory of redundancy of binary prefix code of Huffman type which includes derivation of variety of bounds expressed in terms of entropy of source and size of alphabet. Recent developments yielded bounds on redundancy of Huffman code in terms of probabilities of various components in source alphabet. In practice, redundancies of optimal prefix codes often closer to 0 than to 1.

Smyth, Padhraic J.↗

NASA NTRS1991

Upper bound SEU rate for devices in an isotropic or nonisotropic flux

A method for constructing upper bound estimates for device single event upset (SEU) rates is presented. A directional Heinrich flux, as a function of direction, must be known. A computer code, included, converts the directional Heinrich flux into an 'effective flux'. The effective flux provides a simple way to estimate upper bound SEU rates for devices with a known normal incident cross section versus LET curve.

Edmonds, Larry D.↗