Measurements and computational analysis of heat transfer and flow in a simulated turbine blade internal cooling passage

Visual and quantitative information was obtained on heat transfer and flow in a branched-duct test section that had several significant features of an internal cooling passage of a turbine blade. The objective of this study was to generate a set of experimental data that could be used to validate computer codes for internal cooling systems. Surface heat transfer coefficients and entrance flow conditions were measured at entrance Reynolds numbers of 45,000, 335,000, and 726,000. The heat transfer data were obtained using an Inconel heater sheet attached to the surface and coated with liquid crystals. Visual and quantitative flow field results using particle image velocimetry were also obtained for a plane at mid channel height for a Reynolds number of 45,000. The flow was seeded with polystyrene particles and illuminated by a laser light sheet. Computational results were determined for the same configurations and at matching Reynolds numbers; these surface heat transfer coefficients and flow velocities were computed with a commercially available code. The experimental and computational results were compared. Although some general trends did agree, there were inconsistencies in the temperature patterns as well as in the numerical results. These inconsistencies strongly suggest the need for further computational studies on complicated geometries such as the one studied

Local chromatic number of quadrangulations of surfaces

The local chromatic number of a graph G, as introduced in [4], is the minimum integer k such that G admits a proper coloring (with an arbitrary number of colors) in which the neighborhood of each vertex uses less than k colors. In [17] a connection of the local chromatic number to topological properties of (a box complex of) the graph was established and in [18] it was shown that a topological condition implying the usual chromatic number being at least four has the stronger consequence that the local chromatic number is also at least four. As a consequence one obtains a generalization of the following theorem of Youngs [19]: If a quadrangulation of the projective plane is not bipartite it has chromatic number four. The generalization states that in this case the local chromatic number is also four. Both papers [1] and [13] generalize Youngs’ result to arbitrary non-orientable surfaces replacing the condition of the graph being not bipartite by a more technical condition of an odd quadrangulation. This paper investigates when these general results are true for the local chromatic number instead of the chromatic number. Surprisingly, we find out that (unlike in the case of the chromatic number) this depends on the genus of the surface. For the non-orientable surfaces of genus at most four, the local chromatic number of any odd quadrangulation is at least four, but this is not true for non-orientable surfaces of genus 5 or higher. We also prove that face subdivisions of odd quadrangulations and Fisk triangulations of arbitrary surfaces exhibit the same behavior for the local chromatic number as they do for the usual chromatic number

Quantification of complementarity in multi-qubit systems

Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation between classically incompatible properties, such as visibility of interference fringes and "which-way" information, but also between purely quantum mechanical properties, such as measures of entanglement. We discuss different complementarity relations for systems of 2-, 3-, or \textit{n} qubits. Using nuclear magnetic resonance techniques, we have experimentally verified some of these complementarity relations in a two-qubit system.Comment: 12 pages, 10 figures (A display error about the figures in the previous version

Prolonged exposure of cortical neurons to oligomeric amyloid-β impairs NMDA receptor function via NADPH oxidase-mediated ROS production: protective effect of green tea (–)-epigallocatechin-3-gallate

Excessive production of Aβ (amyloid β-peptide) has been shown to play an important role in the pathogenesis of AD (Alzheimer's disease). Although not yet well understood, aggregation of Aβ is known to cause toxicity to neurons. Our recent study demonstrated the ability for oligomeric Aβ to stimulate the production of ROS (reactive oxygen species) in neurons through an NMDA (N-methyl-d-aspartate)-dependent pathway. However, whether prolonged exposure of neurons to aggregated Aβ is associated with impairment of NMDA receptor function has not been extensively investigated. In the present study, we show that prolonged exposure of primary cortical neurons to Aβ oligomers caused mitochondrial dysfunction, an attenuation of NMDA receptor-mediated Ca2+ influx and inhibition of NMDA-induced AA (arachidonic acid) release. Mitochondrial dysfunction and the decrease in NMDA receptor activity due to oligomeric Aβ are associated with an increase in ROS production. Gp91ds-tat, a specific peptide inhibitor of NADPH oxidase, and Mn(III)-tetrakis(4-benzoic acid)-porphyrin chloride, an ROS scavenger, effectively abrogated Aβ-induced ROS production. Furthermore, Aβ-induced mitochondrial dysfunction, impairment of NMDA Ca2+ influx and ROS production were prevented by pre-treatment of neurons with EGCG [(−)-epigallocatechin-3-gallate], a major polyphenolic component of green tea. Taken together, these results support a role for NADPH oxidase-mediated ROS production in the cytotoxic effects of Aβ, and demonstrate the therapeutic potential of EGCG and other dietary polyphenols in delaying onset or retarding the progression of AD

Simplicial complex entropy.

We propose an entropy function for simplicial complices. Its value gives the expected cost of the optimal encoding of sequences of vertices of the complex, when any two vertices belonging to the same simplex are indistinguishable. We focus on the computational properties of the entropy function, showing that it can be computed efficiently. Several examples over complices consisting of hundreds of simplices show that the proposed entropy function can be used in the analysis of large sequences of simplicial complices that often appear in computational topology applications