Calculus Made Easy

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Loss of solutions in shear banding fluids in shear banding fluids driven by second normal stress differences

Edge fracture occurs frequently in non-Newtonian fluids. A similar instability has often been reported at the free surface of fluids undergoing shear banding, and leads to expulsion of the sample. In this paper the distortion of the free surface of such a shear banding fluid is calculated by balancing the surface tension against the second normal stresses induced in the two shear bands, and simultaneously requiring a continuous and smooth meniscus. We show that wormlike micelles typically retain meniscus integrity when shear banding, but in some cases can lose integrity for a range of average applied shear rates during which one expects shear banding. This meniscus fracture would lead to ejection of the sample as the shear banding region is swept through. We further show that entangled polymer solutions are expected to display a propensity for fracture, because of their much larger second normal stresses. These calculations are consistent with available data in the literature. We also estimate the meniscus distortion of a three band configuration, as has been observed in some wormlike micellar solutions in a cone and plate geometry.Comment: 23 pages, to be published in Journal of Rheolog

Diffusion in a generalized Rubinstein-Duke model of electrophoresis with kinematic disorder

Using a generalized Rubinstein-Duke model we prove rigorously that kinematic disorder leaves the prediction of standard reptation theory for the scaling of the diffusion constant in the limit for long polymer chains $D \propto L^{-2}$ unaffected. Based on an analytical calculation as well as Monte Carlo simulations we predict kinematic disorder to affect the center of mass diffusion constant of an entangled polymer in the limit for long chains by the same factor as single particle diffusion in a random barrier model.Comment: 29 pages, 3 figures, submitted to PR

Extending the literature base of a theme of friendship in a first grade classroom

The process of instructional development was engaged in to extend the literature base of a theme in a reading program for grade one. The theme of friendship, a part of the established curriculum, was chosen for the project. Works from the different genres of literature were found to offer many perspectives and related expressive activities. Along with teacher-directed instruction, learning centers, sustaining and specific to the theme, were developed to provide children with opportunities to take charge of their learning. This extended theme will offer a print rich environment in which children can be energized to engage in the language processes. As a result, their personal-social and thinking-language abilities can be enhanced. Also, the overall goal of nurturing lifetime involvement in reading can be furthered

The Impact of Hypoxia on Neutrophil Degranulation and Consequences for the Host.

Neutrophils are key effector cells of innate immunity, rapidly recruited to defend the host against invading pathogens. Neutrophils may kill pathogens intracellularly, following phagocytosis, or extracellularly, by degranulation and the release of neutrophil extracellular traps; all of these microbicidal strategies require the deployment of cytotoxic proteins and proteases, packaged during neutrophil development within cytoplasmic granules. Neutrophils operate in infected and inflamed tissues, which can be profoundly hypoxic. Neutrophilic infiltration of hypoxic tissues characterises a myriad of acute and chronic infectious and inflammatory diseases, and as well as potentially protecting the host from pathogens, neutrophil granule products have been implicated in causing collateral tissue damage in these scenarios. This review discusses the evidence for the enhanced secretion of destructive neutrophil granule contents observed in hypoxic environments and the potential mechanisms for this heightened granule exocytosis, highlighting implications for the host. Understanding the dichotomy of the beneficial and detrimental consequences of neutrophil degranulation in hypoxic environments is crucial to inform potential neutrophil-directed therapeutics in order to limit persistent, excessive, or inappropriate inflammation

Leibniz, Acosmism, and Incompossibility

Leibniz claims that God acts in the best possible way, and that this includes creating exactly one world. But worlds are aggregates, and aggregates have a low degree of reality or metaphysical perfection, perhaps none at all. This is Leibniz’s tendency toward acosmism, or the view that there this no such thing as creation-as-a-whole. Many interpreters reconcile Leibniz’s acosmist tendency with the high value of worlds by proposing that God sums the value of each substance created, so that the best world is just the world with the most substances. I call this way of determining the value of a world the Additive Theory of Value (ATV), and argue that it leads to the current and insoluble form of the problem of incompossibility. To avoid the problem, I read “possible worlds” in “God chooses the best of all possible worlds” as referring to God’s ideas of worlds. These ideas, though built up from essences, are themselves unities and so well suited to be the value bearers that Leibniz’s theodicy requires. They have their own value, thanks to their unity, and that unity is not preserved when more essences are added

Targets for the MalI repressor at the divergent Escherichia coliK-12malX-malI promoters

Random mutagenesis has been used to identify the target DNA sites for the MalI repressor at the divergent Escherichia coli K-12 malX-malI promoters. The malX promoter is repressed by MalI binding to a DNA site located from position -24 to position -9, upstream of the malX promoter transcript start. The malI promoter is repressed by MalI binding from position +3 to position +18, downstream of the malI transcript start. MalI binding at the malI promoter target is not required for repression of the malX promoter. Similarly, MalI binding at the malX promoter target is not required for repression of the malI. Although the malX and malI promoters are regulated by a single DNA site for cyclic AMP receptor protein, they function independently and each is repressed by MalI binding to a different independent operator site

A systematic examination of preoperative surgery warm-up routines

Recent evidence indicates that a preoperative warm-up is a potentially useful tool in facilitating performance. But what factors drive such improvements and how should a warm-up be implemented?In order to address these issues, we adopted a two-pronged approach: (1) we conducted a systematic review of the literature to identify existing studies utilising preoperative simulation techniques; (2) we performed task analysis to identify the constituent parts of effective warm-ups. We identified five randomised control trials, four randomised cross-over trials and four case series. The majority of these studies reviewed surgical performance following preoperative simulation relative to performance without simulation.Four studies reported outcome measures in real patients and the remainder reported simulated outcome measures. All but one of the studies found that preoperative simulation improves operative outcomes-but this improvement was not found across all measured parameters. While the reviewed studies had a number of methodological issues, the global data indicate that preoperative simulation has substantial potential to improve surgical performance. Analysis of the task characteristics of successful interventions indicated that the majority of these studies employed warm-ups that focused on the visual motor elements of surgery. However, there was no theoretical or empirical basis to inform the design of the intervention in any of these studies.There is an urgent need for a more rigorous approach to the development of "warm-up" routines if the potential value of preoperative simulation is to be understood and realised. We propose that such interventions need to be grounded in theory and empirical evidence on human motor performance