On the Deformation of a Hyperelastic Tube Due to Steady Viscous Flow Within

In this chapter, we analyze the steady-state microscale fluid--structure interaction (FSI) between a generalized Newtonian fluid and a hyperelastic tube. Physiological flows, especially in hemodynamics, serve as primary examples of such FSI phenomena. The small scale of the physical system renders the flow field, under the power-law rheological model, amenable to a closed-form solution using the lubrication approximation. On the other hand, negligible shear stresses on the walls of a long vessel allow the structure to be treated as a pressure vessel. The constitutive equation for the microtube is prescribed via the strain energy functional for an incompressible, isotropic Mooney--Rivlin material. We employ both the thin- and thick-walled formulations of the pressure vessel theory, and derive the static relation between the pressure load and the deformation of the structure. We harness the latter to determine the flow rate--pressure drop relationship for non-Newtonian flow in thin- and thick-walled soft hyperelastic microtubes. Through illustrative examples, we discuss how a hyperelastic tube supports the same pressure load as a linearly elastic tube with smaller deformation, thus requiring a higher pressure drop across itself to maintain a fixed flow rate.Comment: 19 pages, 3 figures, Springer book class; v2: minor revisions, final form of invited contribution to the Springer volume entitled "Dynamical Processes in Generalized Continua and Structures" (in honour of Academician D.I. Indeitsev), eds. H. Altenbach, A. Belyaev, V. A. Eremeyev, A. Krivtsov and A. V. Porubo

Strange Attractors in Dissipative Nambu Mechanics : Classical and Quantum Aspects

We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in $R^{3}$ phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems such as the much studied Lorenz and R\"{o}ssler Strange attractors, as well as the more recent constructions of Chen and Leipnik-Newton. The rotational, volume preserving part of the flow preserves in time a family of two intersecting surfaces, the so called {\em Nambu Hamiltonians}. They foliate the entire phase space and are, in turn, deformed in time by Dissipation which represents their irrotational part of the flow. It is given by the gradient of a scalar function and is responsible for the emergence of the Strange Attractors. Based on our recent work on Quantum Nambu Mechanics, we provide an explicit quantization of the Lorenz attractor through the introduction of Non-commutative phase space coordinates as Hermitian $N \times N$ matrices in $R^{3}$. They satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction it violates the quantum commutation relations. We demonstrate that the Heisenberg-Nambu evolution equations for the Quantum Lorenz system give rise to an attracting ellipsoid in the $3 N^{2}$ dimensional phase space.Comment: 35 pages, 4 figures, LaTe

Design of Experiments for Screening

The aim of this paper is to review methods of designing screening experiments, ranging from designs originally developed for physical experiments to those especially tailored to experiments on numerical models. The strengths and weaknesses of the various designs for screening variables in numerical models are discussed. First, classes of factorial designs for experiments to estimate main effects and interactions through a linear statistical model are described, specifically regular and nonregular fractional factorial designs, supersaturated designs and systematic fractional replicate designs. Generic issues of aliasing, bias and cancellation of factorial effects are discussed. Second, group screening experiments are considered including factorial group screening and sequential bifurcation. Third, random sampling plans are discussed including Latin hypercube sampling and sampling plans to estimate elementary effects. Fourth, a variety of modelling methods commonly employed with screening designs are briefly described. Finally, a novel study demonstrates six screening methods on two frequently-used exemplars, and their performances are compared

Aesthetic response to color combinations: preference, harmony, and similarity

Previous studies of preference for and harmony of color combinations have produced confusing results. For example, some claim that harmony increases with hue similarity, whereas others claim that it decreases. We argue that such confusions are resolved by distinguishing among three types of judgments about color pairs: (1) preference for the pair as a whole, (2) harmony of the pair as a whole, and (3) preference for its figural color when viewed against its colored background. Empirical support for this distinction shows that pair preference and harmony both increase as hue similarity increases, but preference relies more strongly on component color preference and lightness contrast. Although pairs with highly contrastive hues are generally judged to be neither preferable nor harmonious, figural color preference ratings increase as hue contrast with the background increases. The present results thus refine and clarify some of the best-known and most contentious claims of color theorists

Polarized secretion of Leukemia Inhibitory Factor

<p>Abstract</p> <p>Background</p> <p>The direction of cytokine secretion from polarized cells determines the cytokine's cellular targets. Leukemia inhibitory factor (LIF) belongs to the interleukin-6 (IL-6) family of cytokines and signals through LIFR/gp130. Three factors which may regulate the direction of LIF secretion were studied: the site of stimulation, signal peptides, and expression levels. Stimulation with IL-1β is known to promote IL-6 secretion from the stimulated membrane (apical or basolateral) in the human intestinal epithelial cell line Caco-2. Since LIF is related to IL-6, LIF secretion was also tested in Caco-2 following IL-1β stimulation. Signal peptides may influence the trafficking of LIF. Two isoforms of murine LIF, LIF-M and LIF-D, encode different signal peptides which have been associated with different locations of the mature protein in fibroblasts. To determine the effect of the signal peptides on LIF secretion, secretion levels were compared in Madin-Darby canine kidney (MDCK) clones which expressed murine LIF-M or LIF-D or human LIF under the control of an inducible promoter. Low and high levels of LIF expression were also compared since saturation of the apical or basolateral route would reveal specific transporters for LIF.</p> <p>Results</p> <p>When Caco-2 was grown on permeable supports, LIF was secreted constitutively with around 40% secreted into the apical chamber. Stimulation with IL-1β increased LIF production. After treating the apical surface with IL-1β, the percentage secreted apically remained similar to the untreated, whereas, when the cells were stimulated at the basolateral surface only 20% was secreted apically. In MDCK cells, an endogenous LIF-like protein was detected entirely in the apical compartment. The two mLIF isoforms showed no difference in their secretion patterns in MDCK. Interestingly, about 70% of murine and human LIF was secreted apically from MDCK over a 400-fold range of expression levels within clones and a 200,000-fold range across clones.</p> <p>Conclusion</p> <p>The site of stimulation affected the polarity of LIF secretion, while, signal peptides and expression levels did not. Exogenous LIF is transported in MDCK without readily saturated steps.</p

An industry consensus study on an HPLC fluorescence method for the determination of (±)-catechin and (±)-epicatechin in cocoa and chocolate products

<p>Abstract</p> <p>Background</p> <p>This manuscript describes the results of an HPLC study for the determination of the flavan-3-ol monomers, (±)-catechin and (±)-epicatechin, in cocoa and plain dark and milk chocolate products. The study was performed under the auspices of the National Confectioners Association (NCA) and involved the analysis of a series of samples by laboratories of five member companies using a common method.</p> <p>Methodology</p> <p>The method reported in this paper uses reversed phase HPLC with fluorescence detection to analyze (±)-epicatechin and (±)-catechin extracted with an acidic solvent from defatted cocoa and chocolate. In addition to a variety of cocoa and chocolate products, the sample set included a blind duplicate used to assess method reproducibility. All data were subjected to statistical analysis with outliers eliminated from the data set.</p> <p>Results</p> <p>The percent coefficient of variation (%CV) of the sample set ranged from approximately 7 to 15%.</p> <p>Conclusions</p> <p>Further experimental details are described in the body of the manuscript and the results indicate the method is suitable for the determination of (±)-catechin and (±)-epicatechin in cocoa and chocolate products and represents the first collaborative study of this HPLC method for these compounds in these matrices.</p