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Detection of global predicates: Techniques and their limitations (1998)

Chase, Craig M. ; Garg, Vijay K.

Springer

Distributed computing 11 (1998), S. 191-201

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ISSN: 1432-0452

Keywords: Key words:Distributed debugging – Predicate detection – Unstable predicates

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science

Notes: Summary. We show that the problem of predicate detection in distributed systems is NP-complete. In the past, efficient algorithms have been developed for special classes of predicates such as stable predicates, observer independent predicates, and conjunctive predicates. We introduce a class of predicates, semi-linear predicates, which properly contains all of the above classes. We first discuss stable, observer independent and semi-linear classes of predicates and their relationships with each other. We also study closure properties of these classes with respect to conjunction and disjunction. Finally, we discuss algorithms for detection of predicates in these classes. We provide a non-deterministic detection algorithm for each class of predicate. We show that each class can be equivalently characterized by the degree of non-determinism present in the algorithm. Stable predicates are defined as those that can be detected by an algorithm with the most non-determinism. All other classes can be derived by appropriately constraining the non-determinism in this algorithm.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s004460050049

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Entrance flow in elliptical ducts (1993)

Velusamy, K. ; Garg, Vijay K.

Chichester : Wiley-Blackwell

International Journal for Numerical Methods in Fluids 17 (1993), S. 1079-1096

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ISSN: 0271-2091

Keywords: Entrance flow ; Elliptical duct ; Engineering ; Engineering General

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

Notes: A control volume-based solution of the complete set of Navier-Stokes equations for the laminar, three dimensional developing flow in elliptical cross-section ducts is described. Numerical results for velocity and pressure development, pressure defect and entrance lengths are presented for a wide range of aspect ratios from 0·1 to 0·999. The present results match very well with earlier numerical solutions for developing flow in a circular duct and the fully developed flow in elliptical ducts. A comparison with earlier numerical and experimental data for developing flow in elliptical ducts is also satisfactory for pressure development but not so good for the velocity profiles. The relative growth rate of boundary layer thickness along the major axis is slower than that along the minor axis which is contrary to the assumption used in earlier numerical analyses. The present results show no transverse recirculation contrary to the speculation based on earlier experimental data. The ratio of entry length in an elliptical duct to that in a circular duct with radius equal to the semi-major axis of the elliptical duct is nearly equal to the aspect ratio of the duct. In conformity with the previous work, the present results find the total pressure defect to be independent of the aspect ratio, with a value of 1·234.

Additional Material: 13 Ill.