Extended Graph Research Articles

Hamilton Paths in Graphs of Linear Extensions for Unions of Posets

This paper proves that if a poset Q has an even number of linear extensions and these extensions can be generated by adjacent transpositions, then linear extensions of union of poset Q and an arbitrary poset P can also be generated by adjacent transpositions. This result is then applied to posets P and Q, which are sums of disjoint chains.

A decoupled flexible‐relative co‐ordinate recursive approach for flexible multibody dynamics

AbstractAn extended kinematic graph concept and a variational‐vector calculus approach are employed to develop a new recursive formulation for the dynamic analysis of flexible multibody systems. The extended graph concept introduced defines frames and transformations between frames as nodes and edges, respectively, rather than the more traditional body and joint convention. Kinematic relationships between adjacent flexible bodies are derived, using joint relative co‐ordinates and a state vector notation that represents both translational and rotational components of velocity. Deformation kinematics are formulated in terms of modal co‐ordinates, under small deformation assumptions. Joint relative co‐ordinates are decoupled from deformation modal co‐ordinates in both kinematic relations and in the recursive dynamics algorithm, leading to a significant reduction in the dimension of matrices that must be inverted. Dynamic analysis of a flexible closed‐loop spatial robot is performed to illustrate the efficiency of the algorithm.

Burner geometry effects on combustion and NO(x) emission characteristics using a variable geometry swirl combustor

The effects of burner geometry on combustion efficiency and NO(x) emissions are investigated using an experimental stationary-type gas-turbine combustor. The previous configuration of the University of Maryland variable-geometry multiannular swirl burner (Gupta et al., 1977 and 1988), in which fuel and air are introduced at the center and outer annuli, respectively, is compared with a novel configuration in which a fuel-air mixture is introduced at the center. The results are presented in extensive graphs and discussed in detail. It is found that the new configuration can be adjusted to produce significantly lower NO(x) emissions while maintaining high combustion efficiency over wide range of burner loadings. 14 references.

Population studies in groups and clusters of galaxies. IV - Comparison of the luminosity functions and morphological-type distributions in seven nearby groups

Published observational data on the Leo, Dorado, NGC 1400, NGC 5044, Antlia, Fornax, and Virgo groups of galaxies are analyzed in terms of the luminosity functions and morphological types of their members. The data sets employed are characterized, and the results are presented in extensive tables and graphs and discussed in detail. While the fractions of early and late galaxies in the groups are similar, the ratio of dwarfs to giants (D/G) in the early galaxies varies monotonically with the richness of the cluster, leading to artificial flattening at the faint end of the total luminosity function in environments with low D/G. The luminosity function for dwarfs in all environments is found to have a slope of about -1.3.

Spectroscopy and multicolor photometry of the medium redshift southern cluster of galaxies A3639

Spectroscopic observations at 360-700 nm and photometric observations in the Gunn g, r, and i bands are reported for Abell 3639. Data obtained using the EFOSC with CCD detectors at the Cassegrain focus of the 3.6-m telescope at ESO during 1987 and 1988 are presented in extensive tables, graphs, and sample spectra and characterized in detail. Ten of 14 cluster-core galaxies studied are identified as cluster members, giving a mean redshift of 0.1496 + or - 0.0027 and a velocity dispersion of sigma = 538 + 212 or - 128 km/sec. No evidence of an extended envelope is found for the dominant galaxy. Investigation of the luminosity function of cluster galaxies down to M(r) = -18 in an area of radius about 500 kpc and elimination of background galaxies on the basis of their position in the color-color diagram gives a total of 105 galaxies in the sample. 28 refs.

A Case Study of Flexible Object Manipulation

This article describes a project undertaken to explore pro gramming physical operations on complex flexible objects. Uncertainty about the exact state of the object makes it im possible to precisely specify the actions to be performed at the time the program is written. Furthermore, the detailed conse quences of manipulations on flexible objects cannot be deter mined before the action is performed. Lacking precise specifi cations, the programmer must abstract the essential properties of objects and actions. In an effort to study manipulation offlexible objects, a system to tie knots in rope with a robot arm was developed. The system includes an extensible graph representation for knots, a vision system that binds the contour of a physical rope to an abstract description, and a knot-tying language based on parametric motion commands. Knots of modest complexity, such as a bowline or figure 8, can be tied in a va riety of ropes with minimal constraints on the initial configu ration of the rope. The work highlights the importance of software engineering principles and a good programming en vironment for robot program development.

Low‐Frequency Rotational Noise in Closed‐Test‐Section Wind Tunnels

The effects of closed-section wind-tunnel walls on the sound field radiated from a helicopter rotor are investigated by means of numerical simulations, summarizing the findings reported by Mosher (1986). The techniques used to model the rotor and the test section (including geometry, wall absorption, and measurement location) are outlined, and the results are presented in extensive tables and graphs. It is found that first-harmonic acoustic measurements obtained in a hard-walled wind tunnel twice as wide as the rotor diameter do not accurately represent the free-field rotational noise, that the relationship between the sound-pressure levels in the wind tunnel and in the free field is complex, that multiple near-field measurements are needed to characterize the direct acoustic field of the rotor, and that absorptive linings are of little value in enlarging the accurate-measurement zone.

Logic hypergraph grammars and context‐free hypergraph grammars

AbstractThis paper presents an extended graph grammar, called a logic hypergraph grammar (LHG), and discusses its capabilities and parsing method. This grammar generates hypergraphs by resolution in logic programming and is intended to be a basis for analyzing and recognizing general structures by logic programming. An LHG is called a context‐free hypergraph grammar (CFHG) if each production rule represents a replacement of a hyperedge by a subhypergraph. Several normal forms are presented for CFHG and for a hierarchy on subclasses of languages of CFHGs with respect to the maximum number of vertices in nonterminal hyperedges. Finally, a parsing method of LHG using Prolog is presented.

Recognition of a class of unimodular functions

For some pseudo-Boolean functions, the problem of maximization reduces to a linear programming problem with a totally unimodular matrix. Among those, we consider the subclass of functions which can be transformed into functions whose nonlinear terms have nonnegative coefficients. A polynomial-time recognition algorithm for such functions is described. The notion of extended graph of a function is introduced; we show that it is bipartite if the linear programming formulation of the optimization problem has a totally unimodular constraint matrix.

Flow induced vibration and noise by a pair of tandem cylinders due to buffeting

The generation of noise by vortex buffeting on a pair of cylinders in tandem in unsteady high-Reynolds-number flow is investigated analytically. The derivation of the governing equations is outlined, and numerical results for several initial vortex configurations are presented in extensive graphs and characterized in detail. Particular attention is given to the possibility of chaotic vortex motion, and it is shown that chaotic motion does not occur when there are three vortices but does appear when there are four.

A Correlation Of Viscosity And Molecular Weight

Abstract Data have been obtained for molecular weight as a function of oil viscosity for a range of crude oils and bitumen fractions from 2.85 mPa.s (cp) to 1.23 X 1012 mPa.s (cp) at 25 °C (77 °F). A correlation based on these data has been useful in some compositional numerical simulations as well as in other studies, especially when viscosiry and molecular weight data are not easily obtained. The values are listed in Table l, along with density values. Much of the data consists of measurements on the residuals left behind after gas distillation or fractionation of Peace River bitumen. In this latter work, nitrogen was bubbled through Peace River tar in a succession of increasing temperatures. After each temperature step, a sample of the residual tar was removed and its viscosity, density, and molecular weight (by vapour pressure osmometry with toluene) measured. For the higher molecular weight samples, because of the high viscosities, it was necessary to make measurements at temperatures higher than room temperature (25 °C, 77 °F). The resulting values were then plotted on the standard ASTM viscosity chart and the curves extrapolated to 25 °C (77 °F). The value of the additional data on very heavy residual fractions lies in providing some possible numerical values for viscosity of the non-volatile component present in some compositional numerical simulations. The data for complete crudes and residual fractions are plotted on the extended graph (Fig. 1), along with some data for pure compounds in the low molecular weight region (normal paraffins plus benzene and toluene)(1), as indicated in the figure. Because of the wide range of the data and the variable nature of the samples, a visual estimate of the best curve was drawn through the data points below the viscosity value of 18 300 mPa.s. Because viscosity data were obtained on the distilled fractions as well as the residuals, these values were plotted in Figure 1 for comparison. (One point is left off the plot. It appears anomalous when compared with other similar data.) On the molecular weight-viscosity plot, most of the distillate fractions fall slightly below the curve obtained for original oils and tar residues. (They correspond to a temperature about 1 °C lower, but this is not expected to be significant.) Possibly a greater fraction of polar molecules in the original crudes cause the latter to exhibit a higher molecular weight than the compounds removed by distillation. In extending the plot beyond the value of 18 300 mPa.s we were guided by the published relation of Dunstan and Thole(2,3) Equation (Available In Full Paper) where µ is viscosity, M is molecular weight, a is a general constant, and b is a constant characteristic of any given homologous series. In this case we used a least squares fit to a straight line beginning at the point at µ = 18 300 mPa.s (cp) and increasing.

Hierarchical design of delay-insensitive systems

A set of building blocks is presented for the hierarchical design of delay-insensitive systems. It consists of delay-insensitive (DI) building blocks and hybrid (non-DI) building blocks. An extended signal transition graph (STG) model is used for circuit specification and analysis. It permits the clear specification of delay-insensitive circuits, distinguishing between environment/module behaviour and DI/non-DI components. A hierarchical composition procedure is described for the composition of deterministic STG specifications. As an example, a circuit for distributed mutual exclusion is designed and implemented.

Accretion onto a moving black hole - A fully relativistic treatment

The effect of constant-rate motion through a uniform adiabatic medium on the steady-state accretion of matter onto a Schwarzschild black hole is investigated theoretically by means of numerical simulations. The derivation of the model is given in detail, and the results are presented in extensive graphs. The appearance of the flows and the accretion rates are found to be in good agreement with published data for the Newtonian regime and generally similar for the relativistic case. 28 references.

General purpose inference engine for canonical graph models

The design and implementation of a General Purpose Inference Engine for canonical graph models that is both flexible and efficient is addressed. Conventional inference techniques (e.g. forward chaining, backward chaining and mixed strategies) are described, and new modes of flexibility through the provision of inexact matching between data and assertions/rules are explained. In GPIE, scanning/searching of the rules in the rule base is restricted to a minimum during execution, but at the expense of compilation of the rule set prior to execution. The generality of the rule set is transparent to the inference engine, thereby permitting reasoning at various levels. This research demonstrates that a graph-based inference engine offering flexible control structures and inxact matching can complement intermediate notations, such as conceptual graphs, offering the expressive power of a rich knowledge representation formalism. The availability of an extendible graph processor for building appropriate canonical graph models presents the exciting prospect of a general purpose reasoning engine.

Detection of the dMe flare star YZ Canis Minoris simultaneously at 20 and 90 centimeter wavelengths

Aperture-synthesis observations of YZ CMi at 20 and 90 cm are reported. The data are presented in extensive graphs and contour maps and discussed in detail. From the 90-cm brightness temperature of about 1000 K it is inferred that the emission is coherent. 19 references.

Tidal dissipation, surface heat flow, and figure of viscoelastic models of Io

The deformation of Io, the tidal dissipation rate, and its interior spatial distribution are investigated by means of numerical simulations based on (1) a three-layer model (with dissipation in the mantle) or (2) a four-layer model (with dissipation in the asthenosphere). The mathematical derivation of the models is outlined; the selection of the input-parameter values is explained; the results are presented in extensive graphs and contour maps; and the constraints imposed on the models by observational data on the hot-spot distribution, tidal deformation, and gravity field are discussed in detail. It is found that both dissipation mechanisms may play a role on Io: model (2) is better able to explain the concentration of hot spots near the equator, while the presence of a large hot spot near the south pole (if confirmed by observations) would favor model (1).

Environmental effects on the dwarf elliptical galaxies in the Virgo cluster

Published observational data on 98 Virgo-cluster dwarf ellipticals are compiled and analyzed statistically, applying the Kolmogorov-Smirnov test to evaluate the significance of correlations between several photometric parameters and the environmental parameters (1) projected distance from the cluster center, (2) distance from the nearest bright galaxy, and (3) local number density. The results are presented in extensive graphs and discussed in detail, and it is shown that galaxy brightness and diameter are not correlated with (2) or (3), but well correlated with (1), both being greater within 5 deg of the center than beyond that distance. These findings are found to support theoretical models in which dwarf ellipticals either have progenitors with very similar characteristics or form by internally driven mass loss from more massive elliptical systems; models based on ram-pressure stripping or tidal interactions appear to be ruled out. 53 references.

Spectroscopy of V471 Tau. I - Review of basic properties

Spectroscopic observations of the eclipsing binary V471 Tau are reported and analyzed. Data obtained mainly in the red band at Mt. Wilson Observatory and KPNO during the period 1975-1983 are compiled in extensive tables and graphs, and the radial velocity of the K dwarf component is determined using a Griffin-mask technique. Results discussed include: (1) distance 44 + or - 6 pc, (consistent with membership in the Hyades), (2) apparent period variation consistent with a third component, (3) emissionlike features affecting the radial-velocity determination, (4) transient features consistent with the presence of flares, and (5) phase-coherent variation in H-alpha (attributed to the action of the white-dwarf Lyman continuum emission on the K dwarf). 70 references.

Interacting dimers on a sierpinski gasket

The different manners of embedding subgraphs of many disjoint edges in a parent graph arise in several different chemical and physical contexts. The problem of enumeration, or more generally of weighted summation, of such embeddings seems quite difficult to great quantitatively, at least for general extended graphs. The special extended parent graph treated here with the inclusion of interaction between dimers is that of a Sierpinski gasket with a fractal dimension of ln 3/ln 2. The manners of solution should extend to other fractal graphs with low ‘ramification degree’.

Temporal and spatial adaptive algorithm for reacting flows

A numerical integration scheme for quasi-one-dimensional unsteady flows with finite-rate chemistry is developed and demonstrated. The governing Euler and species-conservation equations are derived; the integration method and the spatial and temporal grid embedding techniques are explained; and results for sample problems involving stream-tube flow with one dissociating gas, shock-tube flow with one dissociating gas, and diverging-channel flow with multiple reactions are presented in extensive graphs and briefly characterized. Accuracy comparable to that of globally fine grid solutions is obtained with significant savings in CPU time.