Propagation of nonstationary curved and stretched premixed flames with multistep reaction mechanisms

The propagation speed of a thin premixed flame disturbed by an unsteady fluid flow of a larger scale is considered. The flame may also have a general shape but the reaction zone is assumed to be thin compared to the flame thickness. Unlike in preceding publications, the presented asymptotic analysis is performed for a general multistep reaction mechanism and, at the same time, the flame front is curved by the fluid flow. The resulting equations define the propagation speed of disturbed flames in terms of the properties of undisturbed planar flames and the flame stretch. Special attention is paid to the near-equidiffusion limit. In this case, the flame propagation speed is shown to depend on the effective Zeldovich number Z(f) , and the flame stretch. Unlike the conventional Zeldovich number, the effective Zeldovich number is not necessarily linked directly to the activation energies of the reactions. Several examples of determining the effective Zeldovich number for reduced combustion mechanisms are given while, for realistic reactions, the effective Zeldovich number is determined from experiments. Another feature of the present approach is represented by the relatively simple asymptotic technique based on the adaptive generalized curvilinear system of coordinates attached to the flame (i.e., intrinsic disturbed flame equations [IDFE]).

A refinement calculus for logic programs

Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic programming language, including executable constructs such as sequential conjunction, disjunction, and existential quantification, as well as specification constructs such as general predicates, assumptions and universal quantification. A declarative semantics is defined for this wide-spectrum language based on executions. Executions are partial functions from states to states, where a state is represented as a set of bindings. The semantics is used to define the meaning of programs and specifications, including parameters and recursion. To complete the calculus, a notion of correctness-preserving refinement over programs in the wide-spectrum language is defined and refinement laws for developing programs are introduced. The refinement calculus is illustrated using example derivations and prototype tool support is discussed.

A formal model of real-time program compilation

Program compilation can be formally defined as a sequence of equivalence-preserving transformations, or refinements, from high-level language programs to assembler code, Recent models also incorporate timing properties, but the resulting formalisms are intimidatingly complex. Here we take advantage of a new, simple model of real-time refinement, based on predicate transformer semantics, to present a straightforward compilation formalism that incorporates real-time constraints. (C) 2002 Elsevier Science B.V. All rights reserved.

Branching processes and computational collapse of discretized unimodal mappings

In computer simulations of smooth dynamical systems, the original phase space is replaced by machine arithmetic, which is a finite set. The resulting spatially discretized dynamical systems do not inherit all functional properties of the original systems, such as surjectivity and existence of absolutely continuous invariant measures. This can lead to computational collapse to fixed points or short cycles. The paper studies loss of such properties in spatial discretizations of dynamical systems induced by unimodal mappings of the unit interval. The problem reduces to studying set-valued negative semitrajectories of the discretized system. As the grid is refined, the asymptotic behavior of the cardinality structure of the semitrajectories follows probabilistic laws corresponding to a branching process. The transition probabilities of this process are explicitly calculated. These results are illustrated by the example of the discretized logistic mapping.

Defining 'underwater cultural heritage'

The newly adopted United Nations Education, Scientific and Cultural Organization's Convention on the Protection of the Underwater Cultural Heritage provides the first universal protection regime for this value archaeological resource. A central difficulty in concluding this Convention was defining underwater cultural heritage. This article considers the development of the definition agreed upon and analyses its utility in providing for a pragmatic and effective protection regime.

Development of axon pathways in the zebrafish central nervous system

The zebrafish has a number of distinct advantages as an experimental model in developmental biology. For example, large numbers of embryos can be generated in each lay, development proceeds rapidly through a very precise temporal staging which exhibits minimal batch-to-batch variability, embryos are transparent and imaging of wholemounts negates the need for tedious histological preparation while preserving three-dimensional spatial relationships. The zebrafish nervous system is proving a convenient model for studies of axon guidance because of its small size and highly stereotypical trajectory of axons. Moreover, a simple scaffold of axon tracts and nerves is established early and provides a template for subsequent development. The ease with which this template can be visualized as well as the ability to spatially resolve individual pioneer axons enables the role of specific cell-cell and molecular interactions to be clearly deciphered. We describe here the morphology and development of the earliest axon pathways in the embryonic zebrafish central nervous system and highlight the major questions that remain to be addressed with regard to axon guidance.

Language choice of the Foochows in Sarawak, Malaysia

This paper investigates the factors affecting the language choices of the Chinese Foochows of Sarawak, focusing in particular on how the use of the Foochow dialect vis-a`-vis English and other languages might potentially result in a shift in language allegiance away from Foochow. In the context of Sarawak, the Foochows are a substantial, cohesive and homogeneous Chinese ethnic group with a distinctive language and ethnic identity. One would predict that they would engage in extensive language maintenance behaviour. Instead, Foochows living in non-Foochow dominant areas do not seem to have sufficient attachment to the language to transmit it to the next generation. Is this because the Foochows consider that accommodating to communicative norms is more important than preserving their native language as an inherent symbol of their ethnic identity? Or is it the result of the Foochows’ insecurity about the prestige of the dialect and the status of the Foochow people? These issues of accommodation and language allegiance are discussed, based on interview and questionnaire data from 11 Foochow participants. This data set is part of a larger study on the language use of different ethnic groups in multilingual organisational settings in Sarawak.

An international perspective on sunken state vessels as underwater cultural heritage

On 2 November 2001, the General Assembly of the United Nations Scientific, Economic and Cultural Organisation (UNESCO) adopted the convention on the Protection of the Underwater Cultural Heritage. Among the many complex issues addressed in the convention is the legal status of sunken state-owned vessels, including warships. Prior to the adoption of this convention, no conventional or customary international law existed with regards to the question of abandonment of state-owned vessels or the application of the principle of sovereign immunity to sunken state vessels. While difficulties between coastal states and maritime and former colonial powers resulted in a regime that does not comprehensively address the issues, the convention does provide some guidance in this regard and may provide a basis for further development.

Exact results for a tunnel-coupled pair of trapped Bose-Einstein condensates

A model describing coherent quantum tunnelling between two trapped Bose-Einstein condensates is discussed. It is not well known that the model admits an exact solution, obtained some time ago, with the energy spectrum derived through the algebraic Bethe ansatz. An asymptotic analysis of the Bethe ansatz equations leads us to explicit expressions for the energies of the ground and the first excited states in the limit of weak tunnelling and all energies for strong tunnelling. The results are used to extract the asymptotic limits of the quantum fluctuations of the boson number difference between the two Bose-Einstein condensates and to characterize the degree of coherence in the system.

Water table waves in an unconfined aquifer: Experiments and modeling

[1] Comprehensive measurements are presented of the piezometric head in an unconfined aquifer during steady, simple harmonic oscillations driven by a hydrostatic clear water reservoir through a vertical interface. The results are analyzed and used to test existing hydrostatic and nonhydrostatic, small-amplitude theories along with capillary fringe effects. As expected, the amplitude of the water table wave decays exponentially. However, the decay rates and phase lags indicate the influence of both vertical flow and capillary effects. The capillary effects are reconciled with observations of water table oscillations in a sand column with the same sand. The effects of vertical flows and the corresponding nonhydrostatic pressure are reasonably well described by small-amplitude theory for water table waves in finite depth aquifers. That includes the oscillation amplitudes being greater at the bottom than at the top and the phase lead of the bottom compared with the top. The main problems with respect to interpreting the measurements through existing theory relate to the complicated boundary condition at the interface between the driving head reservoir and the aquifer. That is, the small-amplitude, finite depth expansion solution, which matches a hydrostatic boundary condition between the bottom and the mean driving head level, is unrealistic with respect to the pressure variation above this level. Hence it cannot describe the finer details of the multiple mode behavior close to the driving head boundary. The mean water table height initially increases with distance from the forcing boundary but then decreases again, and its asymptotic value is considerably smaller than that previously predicted for finite depth aquifers without capillary effects. Just as the mean water table over-height is smaller than predicted by capillarity-free shallow aquifer models, so is the amplitude of the second harmonic. In fact, there is no indication of extra second harmonics ( in addition to that contained in the driving head) being generated at the interface or in the interior.