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NASA NTRS1989

Equilibrium polymerization on the equivalent-neighbor lattice

The equilibrium polymerization problem is solved exactly on the equivalent-neighbor lattice. The Flory-Huggins (Flory, 1986) entropy of mixing is exact for this lattice. The discrete version of the n-vector model is verified when n approaches 0 is equivalent to the equal reactivity polymerization process in the whole parameter space, including the polymerized phase. The polymerization processes for polymers satisfying the Schulz (1939) distribution exhibit nonuniversal critical behavior. A close analogy is found between the polymerization problem of index the Schulz r and the Bose-Einstein ideal gas in d = -2r dimensions, with the critical polymerization corresponding to the Bose-Einstein condensation.

Kaufman, Miron↗

NASA NTRS1989

Interval polynomial positivity

It is shown that a univariate interval polynomial is globally positive if and only if two extreme polynomials are globally positive. It is shown that the global positivity property of a bivariate interval polynomial is completely determined by four extreme bivariate polynomials. The cardinality of the determining set for k-variate interval polynomials is 2k. One of many possible generalizations, where vertex implication for global positivity holds, is made by considering the parameter space to be the set dual of a boxed domain.

Bose, N. K.↗

NASA NTRS1989

Boundary implications for frequency response of interval FIR filters

It is shown that vertex implication results in parameter space apply to interval trigonometric polynomials, which characterize the frequency response of a finite impulse response (FIR) digital filter. A weak result and a strong result are given, and the conclusions are illustrated by examples.

Bose, N. K.↗

NASA NTRS1990

Vertex implications of stability for a class of delay-differential interval system

Although vertex implication in parameter space does not hold for stability of general delay-differential interval systems, it is shown that in an important special case when the characteristic equation of the system is describable by certain quasi-polynomials the vertex implication for stability does hold. It is also pointed out that vertex implication for stability does not hold in general for delay-differential systems with interval delay.

Kim, K. D.↗

NASA NTRS1990

A first-order Lyapunov robustness method for linear systems with uncertain parameters

A method for stability-robustness analysis based on a quadratic Liapunov function that varies linearly with uncertainty parameters is derived. Linear time-invariant systems with structured uncertainties are discussed. The Liapunov function is optimized numerically to maximize the robustness region in parameter space. Numerical results are given for four examples in which the first-order method is compared to previous Liapunov methods. While the zero-order method is slightly better than the first-order method for one example, the first-order method is clearly superior in the other three (more realistic) examples. The first-order method is especially superior for the active control of flexible structures, where robustness with respect to (1) unmodeled coupling between modeled modes and (2) unmodeled modes is important. For such applications, the first-order method is much better at detecting the increased robustness associated with increased separation between frequencies.

Leal, M. A.↗

NASA NTRS1990

Performance of a parallel code for the Euler equations on hypercube computers

The performance of hypercubes were evaluated on a computational fluid dynamics problem and the parallel environment issues were considered that must be addressed, such as algorithm changes, implementation choices, programming effort, and programming environment. The evaluation focuses on a widely used fluid dynamics code, FLO52, which solves the two dimensional steady Euler equations describing flow around the airfoil. The code development experience is described, including interacting with the operating system, utilizing the message-passing communication system, and code modifications necessary to increase parallel efficiency. Results from two hypercube parallel computers (a 16-node iPSC/2, and a 512-node NCUBE/ten) are discussed and compared. In addition, a mathematical model of the execution time was developed as a function of several machine and algorithm parameters. This model accurately predicts the actual run times obtained and is used to explore the performance of the code in interesting but yet physically realizable regions of the parameter space. Based on this model, predictions about future hypercubes are made.

Barszcz, Eric↗

NASA NTRS1990

Origin and dynamics of emission line clouds in cooling flow environments

The author suggests that since clouds are born co-moving in a turbulent intra-cluster medium (ICM), the allowed parameter space can now be opened up to a more acceptable range. Large-scale motions can be driven in the central parts of cooling flows by a number of mechanisms including the motion of the central and other galaxies, and the dissipation of advected, focussed rotational and magnetic energy. In addition to the velocity width paradox, two other paradoxes (Heckman et al. 1989) can be solved if the ICM is turbulent. Firstly, the heating source for the emission line regions has always been puzzling - line luminosities are extremely high for a given (optical or radio) galaxy luminosity compared to those in non-cooling flow galaxies, therefore a mechanism peculiar to cooling flows must be at work. However most, if not all, previously suggested heating mechanisms either fail to provide enough ionization or give the wrong line ratios, or both. The kinetic energy in the turbulence provides a natural energy source if it can be efficiently converted to cloud heat. Researchers suggest that this can be done via magneto-hydrodynamic waves through plasma slip. Secondly, while the x ray observations indicate extended mass deposition, the optical line emission is more centrally concentrated. Since many of the turbulence-inducing mechanisms are strongest in the central regions of the ICM, so is the method of heating. In other words material is dropping out everywhere but only being lit up in the center.

Loewenstein, Michael↗

NASA NTRS1990

MHD shocks in the ISM

Researchers survey shock solutions of a partially ionized gas with a magnetic field. The gas is modeled by interacting neutral, ion, electron and charged grain components. They employ a small neutral-ion chemical network to follow the dissociation and ionization of the major species. Cooling by molecular hydrogen (rotational, vibrational and dissociation), grains and dipole molecules is included. There are three basic types of solutions (C, C asterisk, and J) and some more complicated flows involving combinations of the basic types. The initial preshock conditions cover hydrogen nuclei densities of 1 less than n less than 10(exp 10) cm(-3) and shock velocities of 5 less than v(sub s) less than 60 km/s. The magnetic field is varied over 5 decades and the sensitivity of the results to grain parameters, UV and cosmic ray fluxes is ascertained. The parameter space is quite complicated, but there exist some simple divisions. When the initial ionization fraction is small (chi sub i less than 10(-5)), there is a sharp transition between fully C solutions at low velocity and strong J solutions at high velocity. When the initial ionization fraction is larger, C asterisk and/or very weak J shocks are present at low velocities in addition to the C solutions. The flow again changes to strong J shocks at high velocities. When the ionization fraction is large and the flow is only slightly greater than the bulk Alfven velocity, there is a complicated mixture of C, C asterisk and J solutions.

Chernoff, D. F.↗

NASA NTRS1991

Dibaryons in neutron stars

The effects are studied of H-dibaryons on the structure of neutron stars. It was found that H particles could be present in neutron stars for a wide range of dibaryon masses. The appearance of dibaryons softens the equations of state, lowers the maximum neutron star mass, and affects the transport properties of dense matter. The parameter space is constrained for dibaryons by requiring that a 1.44 solar mass neutron star be gravitationally stable.

Olinto, Angela V.↗

NASA NTRS1991

Solar neutrinos and the MSW effect for three-neutrino mixing

Researchers considered three-neutrino Mikheyev-Smirnov-Wolfenstein (MSW) mixing, assuming m sub 3 is much greater than m sub 2 is greater than m sub 1 as expected from theoretical consideration if neutrinos have mass. They calculated the corresponding mixing parameter space allowed by the Cl-37 and Kamiokande 2 experiments. They also calculated the expected depletion for the Ga-71 experiment. They explored a range of theoretical uncertainty due to possible astrophysical effects by varying the B-8 neutrino flux and redoing the MSW mixing calculation.

Shi, X.↗

NASA NTRS1991

Relaxation processes in a low-order three-dimensional magnetohydrodynamics model

The time asymptotic behavior of a Galerkin model of 3D magnetohydrodynamics (MHD) has been interpreted using the selective decay and dynamic alignment relaxation theories. A large number of simulations has been performed that scan a parameter space defined by the rugged ideal invariants, including energy, cross helicity, and magnetic helicity. It is concluded that time asymptotic state can be interpreted as a relaxation to minimum energy. A simple decay model, based on absolute equilibrium theory, is found to predict a mapping of initial onto time asymptotic states, and to accurately describe the long time behavior of the runs when magnetic helicity is present. Attention is also given to two processes, operating on time scales shorter than selective decay and dynamic alignment, in which the ratio of kinetic to magnetic energy relaxes to values 0(1). The faster of the two processes takes states initially dominant in magnetic energy to a state of near-equipartition between kinetic and magnetic energy through power law growth of kinetic energy. The other process takes states initially dominant in kinetic energy to the near-equipartitioned state through exponential growth of magnetic energy.

Stribling, Troy↗

NASA NTRS1991

The origin of the moon and the single impact hypothesis. IV

The smoothed-particle hydrodynamics method developed to simulate the conditions under which a major planetary collision may have led to the formation of the moon is presently used in 41 simulations exploring the relevant parameter space. Two possible scenarios emerge: one in which the moon is formed directly in the collision or only after dissipation and evolution of the disk. Attention is given to the Giant Blowoff hypothesis, in which not only the primitive atmosphere but large amounts of mantle material flow over the surface of the orbiting disk and blow off in the forward direction. Large amounts of angular momentum can also be lost.

Cameron, A. G. W.↗

NASA NTRS1991

Structured background grids for generation of unstructured grids by advancing front method

A new method of background grid construction is introduced for generation of unstructured tetrahedral grids using the advancing-front technique. Unlike the conventional triangular/tetrahedral background grids which are difficult to construct and usually inadequate in performance, the new method exploits the simplicity of uniform Cartesian meshes and provides grids of better quality. The approach is analogous to solving a steady-state heat conduction problem with discrete heat sources. The spacing parameters of grid points are distributed over the nodes of a Cartesian background grid by interpolating from a few prescribed sources and solving a Poisson equation. To increase the control over the grid point distribution, a directional clustering approach is used. The new method is convenient to use and provides better grid quality and flexibility. Sample results are presented to demonstrate the power of the method.

Pirzadeh, Shahyar↗

NASA NTRS1991

Light scattering by lunar-like particle size distributions

A fundamental input to models of light scattering from planetary regoliths is the mean phase function of the regolith particles. Using the known size distribution for typical lunar soils, the mean phase function and mean linear polarization for a regolith volume element of spherical particles of any composition were calculated from Mie theory. The two contour plots given here summarize the changes in the mean phase function and linear polarization with changes in the real part of the complex index of refraction, n - ik, for k equals 0.01, the visible wavelength 0.55 micrometers, and the particle size distribution of the typical mature lunar soil 72141. A second figure is a similar index-phase surface, except with k equals 0.1. The index-phase surfaces from this survey are a first order description of scattering by lunar-like regoliths of spherical particles of arbitrary composition. They form the basis of functions that span a large range of parameter-space.

Goguen, Jay D.↗

NASA NTRS1991

Cosmological constraints on pseudo-Nambu-Goldstone bosons

Particle physics models with pseudo-Nambu-Goldstone bosons (PNGBs) are characterized by two mass scales: a global spontaneous symmetry breaking scale, f, and a soft (explicit) symmetry breaking scale, Lambda. General model insensitive constraints were studied on this 2-D parameter space arising from the cosmological and astrophysical effects of PNGBs. In particular, constraints were studied arising from vacuum misalignment and thermal production of PNGBs, topological defects, and the cosmological effects of PNGB decay products, as well as astrophysical constraints from stellar PNGB emission. Bounds on the Peccei-Quinn axion scale, 10(exp 10) GeV approx. = or less than f sub pq approx. = or less than 10(exp 10) to 10(exp 12) GeV, emerge as a special case, where the soft breaking scale is fixed at Lambda sub QCD approx. = 100 MeV.

Frieman, Joshua A.↗

NASA NTRS1991

Boundary implications for frequency response of interval FIR and IIR filters

It is shown that vertex implication results in parameter space apply to interval trigonometric polynomials. Subsequently, it is shown that the frequency responses of both interval FIR and IIR filters are bounded by the frequency responses of certain extreme filters. The results apply directly in the evaluation of properties of designed filters, especially because it is more realistic to bound the filter coefficients from above and below instead of determining those with infinite precision because of finite arithmetic effects. Illustrative examples are provided to show how the extreme filters might be easily derived in any specific interval FIR or IIR filter design problem.

Bose, N. K.↗

NASA NTRS1992

Accretion disks in active galactic nuclei - Vertically averaged models

Simple models of accretion disks surrounding supermassive black holes in AGN are constructed. By considering several different opacity laws, it is shown that some conclusions arrived at by previous investigators are model-dependent. A simple technique for solving the full vertically averaged disk equations, taking into account both self-gravity and central object gravity and gas pressure and radiation pressure, is presented. The self-consistency of the standard non-self-gravitating, geometrically thin accretion disk models is discussed, and the findings of Lin and Shields (1986) that such models are valid only in a restricted parameter space are confirmed.

Cannizzo, John K.↗

NASA NTRS1992

Accretion disks in active galactic nuclei - Vertically explicit models

A region of the parameter space accessible to accretion disks in AGN is explored using vertically integrated models to describe the thin-disk structure. Particular attention is paid to the role of convection. From a comparison of strongly convective solutions with varying mixing lengths to solutions obtained using a recent theory of convection developed for accretion disks, it is argued that it may be appropriate to take the mixing length to be roughly one-third of a pressure scale height when applying standard mixing-length theory to disks. Scalings are presented for various critical points in the locus of steady-state solutions, and rough estimates of time scales for behavior associated with disk instability are provided.

Cannizzo, John K.↗