The Nonconvergence of h-Refinement in Prolate Elements

Prolate elements are a “plug-compatible” modification of spectral elements in which Legendre polynomials are replaced by prolate spheroidal wave functions of order zero. Prolate functions contain a“bandwidth parameter” $c \ge 0 $ c ≥ 0 whose value is crucial to numerical performance; the prolate functions reduce to Legendre polynomials for $c\,=\,0$ c = 0 . We show that the optimal bandwidth parameter $c$ c not only depends on the number of prolate modes per element $N$ N , but also on the element widths $h$ h . We prove that prolate elements lack $h$ h -convergence for fixed $c$ c in the sense that the error does not go to zero as the element size $h$ h is made smaller and smaller. Furthermore, the theoretical predictions that Chebyshev and Legendre polynomials require $\pi $ π degrees of freedom per wavelength to resolve sinusoidal functions while prolate series need only 2 degrees of freedom per wavelength are asymptotic limits as $N \rightarrow \infty $ N → ∞ ; we investigate the rather different behavior when $N \sim O(4-10)$ N ～ O ( 4 ? 10 ) as appropriate for spectral elements and prolate elements. On the other hand, our investigations show that there are certain combinations of $N,\,h$ N , h and $c>0$ c > 0 where a prolate basis clearly outperforms the Legendre polynomial approximation.     

Dartmouth Medical School bicentennial

To investigate the regulation of cell-to-cell coupling in myocardial ischaemia, the three-dimensional expression of connexin43 (Cx43) during experimental ischaemia was examined using a confocal laser scanning microscope. After induction of myocardial infarction in rats, serial optical sections were obtained from the left ventricular myocardium at various times (3 h to 60 days after ligation). The expression of Cx43 was detected immunohistochemically with FITC-labelled anti-rat Cx43 antibody. Fluorescent dots of Cx43 remained along the intercalated disc and decreased in number around the infarct up to 12 h after ligation. Cx43-expression disappeared completely within 48 h after ligation. After day 4, and especially on days 8 and 15 after ligation, the edges of the cardiomyocytes bordering the infarcted area manifested numerous sarcoplasmic tentacles that reacted positively to anti-desmin antibody. Distinct expression of Cx43 was observed extensively on the tentacles, although no cardiomyocytes remained viable around them. By day 60 after ligation, atypical expression of Cx43 had disappeared. These findings suggest that ischaemia induces temporally abnormal expression of Cx43, which might be responsible for abnormal conduction around the infarct.     

Effect of taro (Colocasia esculenta) flour addition on the functional and alveographic properties of wheat flour and dough

BACKGROUND: Taro is a plant widely produced in tropical areas for its underground corms. Taro corms are highly perishable owing to their high moisture content. In order to limit post‐harvest losses and improve the production and consumption, production and utilization of taro flour have been envisaged. In connection with this, the incorporation of taro flour into wheat‐based products has been reported to increase their keeping quality. Before consideration is given to taro flour as a substitute for wheat in bread manufacture, it is necessary to characterize the functionality of the composite flour and dough. The present study investigated the physicochemical and alveographic properties of wheat–taro composite flour. RESULTS: Three varieties of taro flour (WCN, RIN and KWN) were incorporated into wheat flour in proportions of 10%, 20% and 30% (w/w) and the water absorption capacity (WAC), retrogradation index (RI), foam capacity (FC) and other functional properties were measured. In addition, characteristics of dough rupture pressure (P), extensibility (L), elasticity index (Ie) and strength (W) of flour made from the different composites were measured using an alveograph. The results showed that WAC significantly increased from 132% (wheat flour) to 156% (30% composite flour), while RI significantly decreased from 38% to a mean value of 22%. Principal component analysis revealed that WAC and P formed a group of variables negatively correlated with a second group made of RI, FC, W, Ie and L. CONCLUSION: Incorporating taro flour up to a level of 10% had no significant effect on the functional and alveographic properties of the flours. This suggested that in order to guarantee the quality of bread made from wheat–taro composite the level of taro addition should not exceed 10%. Copyright © 2007 Society of Chemical Industry