The conservation equations for multicomponent gas mixtures in arbitrary coordinate systems

The conservation equations for multicomponent reacting gas mixtures are generally given only in Cartesian or orthogonal curvilinear coordinate systems. Actually, the conservation equations are easily expressed in an arbitrary coordinate system. We present the general equations in tensor notation and then indicate the simplifications which arise for orthogonal curvilinear coordinates

Introduction : themed section on care, values and the future of welfare

The papers in the themed section emerge from the work of the ESRC Research Group on Care, Values and the Future of Welfare (CAVA), based at the University of Leeds. CAVA was funded from 1999 to undertake a five-year programme of research into changes in parenting and partnering in Britain and their implications for future social policies. At the heart of CAVA's research is an investigation into the values that people attach to their parenting and partnering activities. We are interested in ‘what matters’ to people in their family lives and personal relationships, especially as they undergo change. This question lay at the centre of our core empirical projects, all of which were based on in-depth qualitative research. (An account of our methodology may be found in the Appendix to this Introduction). The projects focused on different aspects of change: motherhood, care and employment; kin relationships after divorce; care and commitments in transnational families; practices of care and intimacy amongst those who live without a co-resident partner; and collective values of care and support in self-help groups, voluntary organisations and trade unions. Each of these projects is represented in the following collection

Droplet combustion at reduced gravity

The current work involves theoretical analyses of the effects identified, experiments in the NASA Lewis drop towers performed in the middeck areas of the Space Shuttle. In addition, there is laboratory work associated with the design of the flight apparatus. Calculations have shown that some of the test-matrix data can be obtained in drop towers, and some are achievable only in the space experiments. The apparatus consists of a droplet dispensing device (syringes), a droplet positioning device (opposing, retractable, hollow needles), a droplet ignition device (two matched pairs of retractable spark electrodes), gas and liquid handling systems, a data acquisition system (mainly giving motion-picture records of the combustion in two orthogonal views, one with backlighting for droplet resolution), and associated electronics

The Theory of Steady, One-dimensional, Laminar Flame Propagation for One-step Chemical Reactions

The Theory of Steady, One-dimensional, Laminar Flame Propagation for One-step Chemical Reactions. The present status of the theory of one-dimensional, steady, laminar flame propagation for one-step chemical reactions is reviewed with particular emphasis on methods of solution and on the physical processes that dominate observable results

Chern-Simons Invariants of Closed Hyperbolic 3-Manifolds

The Chern-Simons invariants of irreducible U(n)- flat connections on compact hyperbolic 3-manifolds of the form {\Gamma}\H^3 are derived. The explicit formula for the Chern-Simons functional is given in terms of Selberg type zeta functions related to the twisted eta invariants of Atiyah-Patodi-Singer.Comment: 10 pages, 2 diagram

Effect of thermal expansion on the linear stability of planar premixed flames for a simple chain-branching model: The high activation energy asymptotic limit

The linear stability of freely propagating, adiabatic, planar premixed ames is investigated in the context of a simple chain-branching chemistry model consisting of a chain-branching reaction step and a completion reaction step. The role of chain-branching is governed by a crossover temperature. Hydrodynamic effects, induced by thermal expansion, are taken into account and the results compared and contrasted with those from a previous purely thermal-di�usive constant density linear stability study. It is shown that when thermal expansion is properly accounted for, a region of stable ames predicted by the constant density model disappears, and instead the ame is unstable to a long-wavelength cellular instability. For a pulsating mode, however, thermal expansion is shown to have only a weak e�ect on the critical fuel Lewis number required for instability. These e�ects of thermal expansion on the two-step chain-branching ame are shown to be qualitatively similar to those on the standard one-step reaction model. Indeed, as found by constant density studies, in the limit that the chain-branching crossover temperature tends to the adiabatic ame temperature, the two-step model can be described to leading order by the one-step model with a suitably de�ned e�ective activation energy

Quantum Algorithms for Finding Constant-sized Sub-hypergraphs

We develop a general framework to construct quantum algorithms that detect if a $3$-uniform hypergraph given as input contains a sub-hypergraph isomorphic to a prespecified constant-sized hypergraph. This framework is based on the concept of nested quantum walks recently proposed by Jeffery, Kothari and Magniez [SODA'13], and extends the methodology designed by Lee, Magniez and Santha [SODA'13] for similar problems over graphs. As applications, we obtain a quantum algorithm for finding a $4$-clique in a $3$-uniform hypergraph on $n$ vertices with query complexity $O(n^{1.883})$, and a quantum algorithm for determining if a ternary operator over a set of size $n$ is associative with query complexity $O(n^{2.113})$.Comment: 18 pages; v2: changed title, added more backgrounds to the introduction, added another applicatio