On the forced matching numbers of bipartite graphs

Let G be a graph that admits a perfect matching. A forcing set for a perfect matching M of G is a subset S of M, such that S is contained in no other perfect matching of G. This notion has arisen in the study of finding resonance structures of a given molecule in chemistry. Similar concepts have been studied for block designs and graph colorings under the name defining set, and for Latin squares under the name critical set. There is some study of forcing sets of hexagonal systems in the context of chemistry, but only a few other classes of graphs have been considered. For the hypercubes Q(n), it turns out to be a very interesting notion which includes many challenging problems. In this paper we study the computational complexity of finding the forcing number of graphs, and we give some results on the possible values of forcing number for different matchings of the hypercube Q(n). Also we show an application to critical sets in back circulant Latin rectangles. (C) 2003 Elsevier B.V. All rights reserved.

Atoll lagoon flushing forced by waves

Water level and current measurements from two virtually enclosed South Pacific atolls, Manihiki and Rakahanga, support a new lagoon flushing mechanism which is driven by waves and modulated by the ocean tide for virtually enclosed atolls. This is evident because the lagoon water level remains above the ocean at all tidal phases (i.e., ruling out tidal flushing) and because the average lagoon water level rises significantly during periods with large waves. Hence, we develop a model by which the lagoons are flushed by waves pumping of ocean water into the lagoon and gravity draining water from the lagoon over the reef rim. That is, the waves on the exposed side push water into the lagoon during most of the tidal cycle while water leaves the lagoon on the protected side for most of the tidal cycle. This wave-driven through flow flushing is shown to be more efficient than alternating tidal flushing with respect to water renewal. Improved water quality should therefore be sought through enhancement of the natural wave pumping rather than by blasting deep channels which would change the system to an alternating tide-driven one.

Effect of thermal acclimation on female resistance to forced matings in the eastern mosquitofish

All copulations in the eastern mosquitofish, Gambusia holbrooki, are coercive-and-achieved by force. Female G. holbrooki never appear to cooperate with males, but vigorously resist matings at all times. We examined the role of females within a sexually coercive mating system by investigating the ability of female G. holbrooki to resist forced copulations after acclimation to 16 degrees C and 32 degrees C for 4-5 weeks. We also examined burst swimming performance of female G. holbrooki after acclimation, as this trait is likely to underlie a female's ability to resist forced matings. We predicted that if female G. holbrooki indiscriminately resist matings from all males, acclimation would enhance female resistance at their acclimation temperature. However, we found that it did not. We also predicted that if females are able to influence the outcome of mating interactions, acclimation to an optimal thermal environment may induce females to reduce resistance. In support of this prediction, females acclimated at 32 degrees C were able to modify their resistance behaviour between exposure to 16 degrees C and 32 degrees C. The rate of copulations experienced by 32 inverted perpendicular C-acclimated females was 2.5 times greater at 32 degrees C than at 16 degrees C. In addition, acclimation at 32 degrees C significantly enhanced burst swimming performance at 32 degrees C but no effect of acclimation was observed at 16 degrees C. Our results suggest that female G. holbrooki are able to play a greater role in determining the outcome of sexual coercive mating interactions than previously thought. (c) 2006 The Association for the Shidy of Animal Behavioor. Published by Elsevier Ltd. All rights reserved.

Entropy generation for microscale forced convection: effects of different thermal boundary conditions, velocity slip, temperature jump, viscous dissipation, and duct geometry

This work presents closed form solutions for fully developed temperature distribution and entropy generation due to forced convection in microelectromechanical systems (MEMS) in the Slip-flow regime, for which the Knudsen number lies within the range 0.001