Coupled fluid-structure interaction analysis

A general-purpose fluid-structure interaction capability which can be used in analyzing internal acoustic problems in automobiles and aircraft has been formulated. This capability has become an important issue in the last few years because of the emphasis that has been placed on noise control in all vehicles. A variety of output features that are needed by the analyst in identifying the causes of the acoustic problems have been studied and implemented. The fluid (air) is modeled as an inviscid, irrotational fluid with pressure variables as the degrees of freedom. An acoustic absorber element and an acoustic barier element are also implemented.     

Exact solutions for the flow of a generalized Oldroyd-B fluid induced by a constantly accelerating plate between two side walls perpendicular to the plate

The unsteady flow of an incompressible generalized Oldroyd-B fluid induced by a constantly accelerating plate between two side walls perpendicular to the plate has been studied using Fourier sine and Laplace transforms. The obtained solutions for the velocity field and shear stresses, written in terms of the generalized G and R functions, are presented as sum of the similar Newtonian solutions and the corresponding non-Newtonian contributions. For α = β = 1 and λ_r → λ these solutions are going to the corresponding Newtonian solutions. Furthermore, the solutions for generalized Maxwell fluids as well as those for ordinary Oldroyd-B and Maxwell fluids, performing the same motion, are also obtained as limiting cases of our general solutions. In the absence of the side walls, namely when the distance between the two walls tends to infinity, the solutions corresponding to the motion over an infinite constantly accelerating plate are recovered. For λ_r → 0 and β → 1, these solutions reduce to the known solutions from the literature. Finally, the effect of the material parameters on the velocity profile is spotlighted by means of the graphical illustrations.     

Mechanochemical conversion of nano potassium hydrogen terephthalate to thallium analogue nanoblocks with strong hydrogen bonding and straight chain metalophillic interactions

Irreversible mechanochemical conversion of three‐dimensional K^I coordination polymer [K(μ₆‐HTA)]_n ( 1 ), [H₂TA = terephetalic acid], prepared by sonochemical procedure, to Tl^I analogue coordination polymer nanoblocks was studied. The structure of [Tl(μ₃‐HTA)]_n ( 2 ) is exactly the same as 1 and the Tl ion has distorted octahedral coordination. The carbonyl oxygen is coordinated to two different metal ions, while another oxygen atom is bonded to one metal and participates in a very strong hydrogen bond. Both compounds have secondary straight chain metallophilic interactions. In addition to the same structures of 1 and 2 , the same crystal data of them also approved that the chemistry of thallium(I) parallels that of the potassium(I) in many ways.     

A Model on the Mn^2＋ Luminescence Band Redshift with Mn（Ⅱ） Doping and Aggregation within CdS＇Mn Microwires ＊

We report the microphoto-luminescence band redshifts with individual and multi-Mn（Ⅱ） ion emissions within CdS microwires. The localized exciton magnetic polaxons （LEMPs） corresponding to the d-d optical transitions of Mn（Ⅱ） account for this shift. This LEMP emission from the double-, three- and four-Mn（Ⅱ） ions with ferromag- netic coupling after photoexeitation can happen in diluted magnetic semiconductors, except for the individual Mn（Ⅱ） doping. In addition, a simple spin-exchange polaronic model is established to account for these emission peaks well. Through this model, we can verify the local geometry of the Mn（Ⅱ） ions in CdS microwires.     

EP modular operators and their products

We study first EP modular operators on Hilbert C^?-modules and then we provide necessary and sufficient conditions for the product of two EP modular operators to be EP. These enable us to extend some results of Koliha (2000) [13] for an arbitrary C^?-algebra and the C^?-algebras of compact operators.     

Tautomery and acid-base properties of some azoderivatives of benzoylacetone

The structural, tautomeric and acid-base properties of the new 1-phenyl-2-(2-hydroxy-3-sulfo-5-chlorophenylhydrazo)butane-1,3-dione (H₂L¹), 1-phenyl-2-(2-hydroxy-3,5-disulfophenylhydrazo)butane-1,3-dione (H₂L²), 1-phenyl-2-(2-hydroxy-3-sulfo-5-nitrophenylhydrazo)butane-1,3-dione (H₂L³) and 1-phenyl-2-(2-hydroxy-4-nitrophenylhydrazo)butane-1,3-dione (H₂L⁴) were studied using IR, ¹H and ¹³C NMR spectroscopies and potentiometry. The study reveals that H₂L^1-4 and the known 1-phenyl-2-(2-hydroxyphenylhydrazo)butane-1,3-dione (H₂L⁵) exist in solution as a mixture of Z-enol-azo-II and hydrazo-III tautomeric forms and that an increase in the solvent polarity shifts the tautomeric balance to the enol-azo form. The thermodynamic parameters of the proton dissociation in H₂L^1-5 were determined showing that this process is unspontaneous, endothermic and entropically unfavorable.     

Simple infinite-dimensional quotients of the group C-algebras ofcertain discrete 6-dimensional nilpotent groups

We study here the simple infinite-dimensional quotients of the group C^*-algebras of two discrete6-dimensional nilpotent groups H_6,1 and H_6,2 as the higher-dimensional analogues of the irrational rotation algebras. P Milnes and S. Walters, jointly and individually, have studied the lower-dimensional cases in a series of papers, and also have started the study of some other 6-dimensional groups. For G = H_6,1 or H_6,2, we can determine the crossed product presentations for the simple quotients of C^* (G), and matrix representations for those arising from non-faithful representations of the groups. The isomorphism classifications of these quotients are obtained using K-theoretic tools, namely, the K-groups and the range of trace on K₀. This marks the first use of K-theory in the classification of quotients for 6-dimensional groups.     

Characterizing Interaction with Visual Mathematical Representations

This paper presents a characterization of computer-based interactions by which learners can explore and investigate visual mathematical representations (VMRs). VMRs (e.g., geometric structures, graphs, and diagrams) refer to graphical representations that visually encode properties and relationships of mathematical structures and concepts. Currently, most mathematical tools provide methods by which a learner can interact with these representations. Interaction, in such cases, mediates between the VMR and the thinking, reasoning, and intentions of the learner, and is often intended to support the cognitive tasks that the learner may want to perform on or with the representation. This paper brings together a diverse set of interaction techniques and categorizes and describes them according to their common characteristics, goals, intended benefits, and features. In this way, this paper aims to provide a preliminary framework to help designers of mathematical cognitive tools in their selection and analysis of different interaction techniques as well as to foster the design of more innovative interactive mathematical tools. An effort is made to demonstrate how the different interaction techniques developed in the context of other disciplines (e.g., information visualization) can support a diverse set of mathematical tasks and activities involving VMRs.     

Asymptotically covariantly constant spinor hair on black holes

It is demonstrated, in a straightforward approach, that a static black hole has no spinor hair if we assume that the fields vanish at infinity. We extend this to the case of asymptotically covariantly constant spinors (Witten spinors) which approach a constant value at spatial infinity. We show that with the dominant energy condition and in absence of external spinor sources, Witten spinors must vanish everywhere in the region exterior to a stationary black hole with an horizon in an asymptotically flat space-time.     

Application of microwave heating for the fast extraction of fat content from the poultry feeds

A rapid method has been developed to extract and quantitatively measure the total oil content in poultry feeds using a domestic microwave oven. The optimized extraction procedure involves the replicate (6×) extraction of 5 g of ground feed with 12 ml of hexane for 20 s in a 900 W oven. Each replicate involves the collection of the resulting miscella and its replacement with fresh solvent for re-extraction. The collected extracts were centrifuged and transferred to a vial. The solvent was evaporated to a constant weight and the residual lipid weighed. In comparison to conventional Soxhlet extraction method, lipid contents obtained using the optimized microwave procedure was not significantly different. However, FTIR analysis indicated that the microwave procedure was superior in minimizing the formation of free fatty acids (FFA) relative to the Soxhlet procedure if the temperature of the sample was kept within the range of 45–50 °C. This simple, sequential extraction procedure is rapid, highly efficient and provides a simple mean of quantitating the lipid content of poultry feed in less than 40 min without the need for specialized microwave oven.