Mixing enhancement in a multi-stream injection nozzle

We present quantitative analysis of image sequences of multi-stream injection nozzle flows with several different injection geometries in an experiment simulating mixing in a chemical oxygen-iodine laser. To visualize mixing, image sequences were acquired with planar laser-induced fluorescence (PLIF) in iodine that was injected into the main flow. The injection nozzle consisted of a slot, ejector, and injector block, with rows of ejector and injector holes along the slot length. The ejector flow exits in an underexpanded state so that upon expanding it forces the slot and injector flows together to enhance mixing. For this study, the diameter and geometry of ejector holes were varied to assess their effect on mixing. Two configurations of ejector holes were used, each with two different diameters for a total of four cases with data collected at downstream stations. We carry out a quantitative mixing analysis for these configurations, using two methods to quantify the mixing. The first method considers the statistics of the PLIF image intensity histograms, which are bimodal for poorly-mixed flows and have a single peak in well-mixed flows. The second method quantifies the properties of the mixing interface. Our analysis shows that two injection schemes significantly enhance mixing by stretching the mixing interface.     

Transcritical buckling of columns

Summary This paper treats new effects, such as transcritical bifurcation and extinction, exhibited by the solution branches of buckled states of nonlinearly elastic columns. The general models used are intimately related to the three-dimensional theory of nonlinear elasticity. These new effects are caused by the interaction of the nonlinearity of material response, the lack of symmetry in the cross-section, the nature of boundary conditions, and the nonuniformity of the rod. Although a variety of sophisticated analytic tools are used to treat local and global branching of solutions, the main emphasis is placed on the mechanics that underlies the form of the governing equations.Dedicated to Prof. Klaus Kirchgässner on the occasion of his sixtieth birthday     

Finite Left-Distributive Algebras and Embedding Algebras

We consider algebras with one binary operation · and one generator (monogenic) and satisfying the left distributive lawa·(b·c)=(a·b)·(a·c). One can define a sequence of finite left-distributive algebrasA_n, and then take a limit to get an infinite monogenic left-distributive algebraA_∞. Results of Laver and Steel assuming a strong large cardinal axiom imply thatA_∞is free; it is open whether the freeness ofA_∞can be proved without the large cardinal assumption, or even in Peano arithmetic. The main result of this paper is the equivalence of this problem with the existence of a certain algebra of increasing functions on natural numbers, called anembedding algebra. Using this and results of the first author, we conclude that the freeness ofA_∞is unprovable in primitive recursive arithmetic.     

Ancillary nitrile substituents as convenient IR spectroscopic reporters for self-assembly of mercapto- and isocyanoazulenes on Au(111)

Synthesis and self-assembly of structurally related mercapto- and isocyanoazulenes, including novel 2-mercapto-1,3-dicyanoazulene (4) and 2-isocyano-1,3-dicyanoazulene (5), are reported. Exposing 5 adsorbed on Au(111) to a solution of 4 displaces the isocyanoazulene monolayer with that of the mercaptoazulene as judged by ν(C≡N) signatures of these films.     

Nachweis und Bestimmung des Chroms

Ohne Zusammenfassung     

Ueber die Diffusion einiger Gase durch auf h?here Temperatur erhitztes Platin

Ohne Zusammenfassung     

A framework for characterizing students’ cognitive processes related to informal best fit lines

Informal best fit lines frequently appear in school curricula. Previous research collectively illustrates that the adjective informal does not translate to cognitive simplicity. Using existing literature, we create a hypothetical framework of cognitive processes associated with studying informal best fit lines. We refine the framework using data from a cycle of design-based research about building students’ understanding of covariation. The refined framework includes student thinking processes for signifying observations as data, signifying data with scatterplots, perceiving aggregates in scatterplots, perceiving trends in aggregates, signifying trends with straight lines, and using straight lines as estimation tools. We explain how students’ perceptions of aggregates can proceed from the inside-out as well as from the outside-in. We also demonstrate how the amounts of variation encountered at different points in time and the extent to which students perceive straight lines to be abbreviations of linear covariation are important considerations for teaching and research.