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NASA NTRS1995

Tests of two convection theories for red giant and red supergiant envelopes

Two theories of stellar envelope convection are considered here in the context of red giants and red supergiants of intermediate to high mass: Boehm-Vitense's standard mixing-length theory (MLT) and Canuto & Mazzitelli's new theory incorporating the full spectrum of turbulence (FST). Both theories assume incompressible convection. Two formulations of the convective mixing length are also evaluated: l proportional to the local pressure scale height (H(sub P)) and l proportional to the distance from the upper boundary of the convection zone (z). Applications to test both theories are made by calculating stellar evolutionary sequences into the red zone (z). Applications to test both theories are made by calculating stellar evolutionary sequences into the red phase of core helium burning. Since the theoretically predicted effective temperatures for cool stars are known to be sensitive to the assigned value of the mixing length, this quantity has been individually calibrated for each evolutionary sequence. The calibration is done in a composite Hertzsprung-Russell diagram for the red giant and red supergiant members of well-observed Galactic open clusters. The MLT model requires the constant of proportionality for the convective mixing length to vary by a small but statistically significant amount with stellar mass, whereas the FST model succeeds in all cases with the mixing lenghth simply set equal to z. The structure of the deep stellar interior, however, remains very nearly unaffected by the choices of convection theory and mixing lenghth. Inside the convective envelope itself, a density inversion always occurs, but is somewhat smaller for the convectively more efficient MLT model. On physical grounds the FST model is preferable, and seems to alleviate the problem of finding the proper mixing length.

Stothers, Richard B.↗

NASA NTRS1992

Reformulating Non-Monotonic Theories for Inference and Updating

We aim to help build programs that do large-scale, expressive non-monotonic reasoning (NMR): especially, 'learning agents' that store, and revise, a body of conclusions while continually acquiring new, possibly defeasible, premise beliefs. Currently available procedures for forward inference and belief revision are exhaustive, and thus impractical: they compute the entire non-monotonic theory, then re-compute from scratch upon updating with new axioms. These methods are thus badly intractable. In most theories of interest, even backward reasoning is combinatoric (at least NP-hard). Here, we give theoretical results for prioritized circumscription that show how to reformulate default theories so as to make forward inference be selective, as well as concurrent; and to restrict belief revision to a part of the theory. We elaborate a detailed divide-and-conquer strategy. We develop concepts of structure in NM theories, by showing how to reformulate them in a particular fashion: to be conjunctively decomposed into a collection of smaller 'part' theories. We identify two well-behaved special cases that are easily recognized in terms of syntactic properties: disjoint appearances of predicates, and disjoint appearances of individuals (terms). As part of this, we also definitionally reformulate the global axioms, one by one, in addition to applying decomposition. We identify a broad class of prioritized default theories, generalizing default inheritance, for which our results especially bear fruit. For this asocially monadic class, decomposition permits reasoning to be localized to individuals (ground terms), and reduced to propositional. Our reformulation methods are implementable in polynomial time, and apply to several other NM formalisms beyond circumscription.

Grosof, Benjamin N.↗

NASA NTRS2001

A {1,2}-Order Plate Theory Accounting for Three-Dimensional Thermoelastic Deformations in Thick Composite and Sandwich Laminates

A {1,2}-order theory for laminated composite and sandwich plates is extended to include thermoelastic effects. The theory incorporates all three-dimensional strains and stresses. Mixed-field assumptions are introduced which include linear in-plane displacements, parabolic transverse displacement and shear strains, and a cubic distribution of the transverse normal stress. Least squares strain compatibility conditions and exact traction boundary conditions are enforced to yield higher polynomial degree distributions for the transverse shear strains and transverse normal stress through the plate thickness. The principle of virtual work is used to derive a 10th-order system of equilibrium equations and associated Poisson boundary conditions. The predictive capability of the theory is demonstrated using a closed-form analytic solution for a simply-supported rectangular plate subjected to a linearly varying temperature field across the thickness. Several thin and moderately thick laminated composite and sandwich plates are analyzed. Numerical comparisons are made with corresponding solutions of the first-order shear deformation theory and three-dimensional elasticity theory. These results, which closely approximate the three-dimensional elasticity solutions, demonstrate that through - the - thickness deformations even in relatively thin and, especially in thick. composite and sandwich laminates can be significant under severe thermal gradients. The {1,2}-order kinematic assumptions insure an overall accurate theory that is in general superior and, in some cases, equivalent to the first-order theory.

Tessler, A.↗

NASA NTRS1949

Lecture Series "Boundary Layer Theory". Part I - Laminar Flows: Laminar Flows - Part 1

In the lecture series starting today author want to give a survey of a field of aerodynamics which has for a number of years been attracting an ever growing interest. The subject is the theory of flows with friction, and, within that field, particularly the theory of friction layers, or boundary layers. A great many considerations of aerodynamics are based on the ideal fluid, that is the frictionless incompressibility and fluid. By neglect of compressibility and friction the extensive mathematical theory of the ideal fluid, (potential theory) has been made possible. Actual liquids and gases satisfy the condition of incomressibility rather well if the velocities are not extremely high or, more accurately, if they are small in comparison with sonic velocity. For air, for instance, the change in volume due to compressibility amounts to about 1 percent for a velocity of 60 meters per second. The hypothesis of absence of friction is not satisfied by any actual fluid; however, it is true that most technically important fluids, for instance air and water, have a very small friction coefficient and therefore behave in many cases almost like the ideal frictionless fluid. Many flow phenomena, in particular most cases of lift, can be treated satisfactorily, - that is, the calculations are in good agreement with the test results, -under the assumption of frictionless fluid. However, the calculations with frictionless flow show a very serious deficiency; namely, the fact, known as d'Alembert's paradox, that in frictionless flow each body has zero drag whereas in actual flow each body experiences a drag of greater or smaller magnitude. For a long time the theory has been unable to bridge this gap between the theory of frictionless flow and the experimental findings about actual flow. The cause of this fundamental discrepancy is the viscosity which is neglected in the theory of ideal fluid; however, in spite of its extraordinary smallness it is decisive for the course of the flow phenomena.

Schlichting, H.↗

NASA NTRS2005

The SMART Theory and Modeling Team: An Integrated Element of Mission Development and Science Analysis

When targeting physical understanding of space plasmas, our focus is gradually shifting away from discovery-type investigations to missions and studies that address our basic understanding of processes we know to be important. For these studies, theory and models provide physical predictions that need to be verified or falsified by empirical evidence. Within this paradigm, a tight integration between theory, modeling, and space flight mission design and execution is essential. NASA's Magnetospheric MultiScale (MMS) mission is a pathfinder in this new era of space research. The prime objective of MMS is to understand magnetic reconnection, arguably the most fundamental of plasma processes. In particular, MMS targets the microphysical processes, which permit magnetic reconnection to operate in the collisionless plasmas that permeate space and astrophysical systems. More specifically, MMS will provide closure to such elemental questions as how particles become demagnetized in the reconnection diffusion region, which effects determine the reconnection rate, and how reconnection is coupled to environmental conditions such as magnetic shear angles. Solutions to these problems have remained elusive in past and present spacecraft missions primarily due to instrumental limitations - yet they are fundamental to the large-scale dynamics of collisionless plasmas. Owing to the lack of measurements, most of our present knowledge of these processes is based on results from modern theory and modeling studies of the reconnection process. Proper design and execution of a mission targeting magnetic reconnection should include this knowledge and have to ensure that all relevant scales and effects can be resolved by mission measurements. The SMART mission has responded to this need through a tight integration between instrument and theory and modeling teams. Input from theory and modeling is fed into all aspects of science mission design, and theory and modeling activities are tailored to SMART needs during mission development and science analysis. In this presentation, we will present an overview of SMART theory and modeling team activities. In particular, we will provide examples of science objectives derived from state-of-the art models, and of recent research results that continue to be utilized in SMART mission development.

Hesse, Michael↗

NASA NTRS2018

Information Theory Applied to Decision Making Structures

Decision making structures, such as control boards, process information on many topics as they select options for the system and project. The decisions are based on the information known to the board members and presenters (subject matter experts) and shared at the board during discussion. This information flow through this process can be modelled using information theory. Information theory provides a mathematical basis to understand the flow of information through the decision making process and the information needed for a particular decision. Information theory also provides the mathematical relationships on which to base the optimal decision making structure for a specific system development and organizational structure. Since decision making bodies provide control for the system or project, control theory can be used to construct a decision making model. This provides a starting point for adding cognitive science models. Information processing by each individual board participant can be represented through cognitive processes which are integrated across the board participants through information theory relationship. The set theory view of information theory provides a structure in which to look at the relationships between the participants in a decision making structure.

Watson, Michael D.↗

NASA NTRS2018

Information Theory Applied to Decision Making Structures

Watson, Michael D.↗

NASA NTRS1994

Derivation and experimental verification of clock synchronization theory

The objective of this work is to validate mathematically derived clock synchronization theories and their associated algorithms through experiment. Two theories are considered, the Interactive Convergence Clock Synchronization Algorithm and the Mid-Point Algorithm. Special clock circuitry was designed and built so that several operating conditions and failure modes (including malicious failures) could be tested. Both theories are shown to predict conservative upper bounds (i.e., measured values of clock skew were always less than the theory prediction). Insight gained during experimentation led to alternative derivations of the theories. These new theories accurately predict the clock system's behavior. It is found that a 100% penalty is paid to tolerate worst case failures. It is also shown that under optimal conditions (with minimum error and no failures) the clock skew can be as much as 3 clock ticks. Clock skew grows to 6 clock ticks when failures are present. Finally, it is concluded that one cannot rely solely on test procedures or theoretical analysis to predict worst case conditions. conditions.

INTERACTIVE CONVERGENCE CLOCK↗

NASA NTRS2022

Migration Theory in Climate Mobility Research

The purpose of this article is to explore how migration theory is invoked in empirical studies of climate-related migration, and to provide suggestions for engagement with theory in the emerging field of climate mobility. Theory is critical for understanding processes we observe in social-ecological systems because it points to a specific locus of attention for research, shapes research questions, guides quantitative model development, influences what researchers find, and ultimately informs policies and programs. Research into climate mobility has grown out of early studies on environmental migration, and has often developed in isolation from broader theoretical developments in the migration research community. As such, there is a risk that the work may be inadequately informed by the rich corpus of theory that has contributed to our understanding of who migrates; why they migrate; the types of mobility they employ; what sustains migration streams; and why they choose certain destinations over others. On the other hand, there are ways in which climate and broader environment migration research is enriching the conceptual frameworks being employed to understand migration, particularly forced migration. This paper draws on a review of 75 empirical studies and modeling efforts conducted by researchers from a diversity of disciplines, covering various regions, and using a variety of data sources and methods to assess how they used theory in their research. The goal is to suggest ways forward for engagement with migration theory in this large and growing research domain.

migration theory↗

NASA NTRS1974

Modified Brans-Dicke gravitational theory with nonzero divergence of the energy-momentum tensor

The Brans-Dicke theory of gravitation is modified by assuming that the divergence of the energy-momentum tensor is proportional to the covariant derivative of the scalar curvature. No ad hoc additions to the usual Brans-Dicke field equations are required as in Rastall's modification of the Einstein theory or as in the steady-state theories, of which this is a natural possibility. Three parameters emerge from the theory - namely, the unnormalized gravitational constant, the usual Brans-Dicke parameter, and the proportionality constant. In the post-Newtonian approximation, these parameters can be fixed by experiment. However, there exists a certain choice of the parameters for which the theory reduces to an Einstein theory with constant scalar curvature.

Smalley, L. L.↗

NASA NTRS1974

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.↗

NASA NTRS1975

Hybrid theory and calculation of e-N2 scattering

A theory of electron-molecule scattering was developed which was a synthesis of close coupling and adiabatic-nuclei theories. The theory is shown to be a close coupling theory with respect to vibrational degrees of freedom but is a adiabatic-nuclei theory with respect to rotation. It can be applied to any number of partial waves required, and the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations and not on experiment can be given as to which partial waves and energy domains require the various approximations. The theory allows all cross sections (i.e., pure rotational, vibrational, simultaneous vibration-rotation, differential and total) to be calculated. Explicit formulae for all the cross sections are presented.

Chandra, N.↗

NASA NTRS1976

A high order theory for uniform and laminated plates

A theory of plate deformation is derived which accounts for the effects of transverse shear deformation, transverse normal strain, and a nonlinear distribution of the in-plane displacements with respect to the thickness coordinate. The theory is compared with lower order plate theories through application to a particular problem involving a plate acted upon by a sinusoidal surface pressure. Comparison is also made with exact elasticity solution of this problem. It is found that when the ratio of the characteristic length of the load pattern to the plate thickness is of the order of unity, lower order theories are inadequate and the present high order theory is required to give meaningful results. Results are given for the bending of symmetric cross-ply and angle-ply laminates. Comparison with exact elasticity solutions indicates that the present plate theory is sufficiently accurate for predicting the behavior of thick laminates.

Lo, K. H.↗

NASA NTRS1976

Theory of a cylindrical probe in a collisionless magnetoplasma

A theory is presented for a cylindrical electrostatic probe in a collisionless plasma in the case where the probe axis is inclined at an angle to a uniform magnetic field. The theory is applicable to electron collection, and under more restrictive conditions, to ion collection. For a probe at space potential, the theory is exact in the limit where probe radius is much less than Debye length. At attracting probe potentials, the theory yields an upper bound and an adiabatic limit for current collection. At repelling probe potentials, it provides a lower bound. The theory is valid if the ratios of probe radius to Debye length and probe radius to mean gyroradius are not simultaneously large enough to produce extrema in the probe sheath potential. The numerical current calculations are based on the approximation that particle orbits are helices near the probe, together with the use of kinetic theory to relate velocity distributions near the probe to those far from it. Probe characteristics are presented for inclination angles from 0 to 90 deg and for probe-radius mean-gyroradius ratios from 0.1 to infinity. For an angle of 0 deg, the end-effect current is calculated separately.

Laframboise, J. G.↗

NASA NTRS1977

Gravitational radiation from binary systems in alternative metric theories of gravity - Dipole radiation and the binary pulsar

The generation of gravitational radiation in several currently viable metric theories of gravitation (Brans-Dicke, Rosen, Ni, and Lightman-Lee) is analyzed, and it is shown that these theories predict the emission of dipole gravitational radiation from systems containing gravitationally bound objects. In the binary system PSR 1913 + 16, this radiation results in a secular change in the orbital period of the system with a nominal magnitude of 3 parts in 100,000 per year. The size of the effect is proportional to the reduced mass of the system, to the square of the difference in (self-gravitational energy)/(mass) between the two components of the system, and to a parameter, xi, whose value varies from theory to theory. In general relativity xi equals 0, in Rosen's (1973) theory xi equals -20/3, and in Ni's (1973) theory xi equals -400/3. The current upper limit on such a secular period change is one part in 1 million per year. It is shown that further observations of the binary system that tighten this limit and that establish the masses of the components and the identity of the companion may provide a crucial test of otherwise viable alternatives to general relativity.

Will, C. M.↗

NASA NTRS1977

Evaluation of the Tensor Polynomial and Hoffman strength theories for composite materials

The Hoffman theory and the Tensor Polynomial (Tsai-Wu) theory with the stress interaction term set equal to zero have been found to be preferred alternatives to the general Tensor Polynomial theory for predicting strength of filamentary composite laminae. These theories were used to predict failure of off-axis boron/epoxy and E-glass/epoxy test specimens and gave excellent agreement with available experimental results. A numerical experiment was also performed to estimate the errors for ten different composite systems under six different loadings. The maximum error in predicted failure loads among all cases was below 10 percent. These results suggest that the Hoffman failure theory and the Tensor Polynomial theory with the stress interaction term equal to zero can predict failure of practical filamentary composite materials under general biaxial loading with sufficient accuracy for engineering applications.

Narayanaswami, R.↗

NASA NTRS1978

A comparison of three classical analytical theories for the motion of artificial satellites

Motivated by the heavy reliance upon the analytic orbit theory in orbit determination operations at the Goddard Space Flight Center (GSFC), a comparison study is performed for three classical analytical theories of artificial satellite motion about an oblate earth. The three analytical theories are: (1) Brouwer, (2) a modified Brouwer, i.e., Brouwer-Lyddane and Cohen, and (3) Vinti. Comparison results for each theory are produced for a number of representative satellites of current or past interest which proved amenable to analytic theory application. The uniformity of these results has significant implications for current and future mission operations and planning activities. Subsidiary topics arising from the results of this study which relate to the optimum usage of the individual theories are also discussed

Gordon, R. A.↗

NASA NTRS1979

Application of supersonic linear theory and hypersonic impact methods to three nonslender hypersonic airplane concepts at Mach numbers from 1.10 to 2.86

Aerodynamic predictions from supersonic linear theory and hypersonic impact theory were compared with experimental data for three hypersonic research airplane concepts over a Mach number range from 1.10 to 2.86. The linear theory gave good lift prediction and fair to good pitching-moment prediction over the Mach number (M) range. The tangent-cone theory predictions were good for lift and fair to good for pitching moment for M more than or equal to 2.0. The combined tangent-cone theory predictions were good for lift and fair to good for pitching moment for M more than or equal to 2.0. The combined tangent-cone/tangent-wedge method gave the least accurate prediction of lift and pitching moment. The zero-lift drag was overestimated, especially for M less than 2.0. The linear theory drag prediction was generally poor, with areas of good agreement only for M less than or equal to 1.2. For M more than or equal to 2.), the tangent-cone method predicted the zero-lift drag most accurately.

Pittman, J. L.↗