Effective scraping in a scraped surface heat exchanger: some fluid flow analysis

An outline of mathematical models that have been used to understand the behaviour of scraped surface heat exchangers is presented. In particular the problem of the wear of the blades is considered. A simple model, exploiting known behaviour of viscous flow in corners and in wedges, and accounting for the forces on the blade is derived and solutions generated. The results shows initial rapid wear but that the wear rate goes to zero

Hypoglycemia in patient with type 2 diabetes treated with insulin: it can happen

There are many misconceptions about the prevalence and effects of hypoglycemia in people with type 2 diabetes (T2D), including hypoglycemia does not occur or does not have adverse consequences in T2D. This narrative review aims to help dispel these myths. Around 25% of people with T2D taking insulin for >5 years were found to have severe hypoglycemic events, which is comparable to the severe hypoglycemia rate in adults with type 1 diabetes (T1D) diagnosed within 5 years. The total number of hypoglycemic events among insulin-treated T2D, including severe hypoglycemia, is as high or higher than among those with T1D. Recent evidence suggests serious consequences of hypoglycemia may, in some respects, be greater in individuals with T2D, particularly regarding effects on the cardiovascular system. Hypoglycemia is generally patient-reported. Issues with hypoglycemia unawareness, limited glucose testing, limited recall, lack of event logging and fear of failure or shaming limits the number of hypoglycemic episodes reported by people with diabetes. Barriers to healthcare provider inquiry and reporting include lack of knowledge regarding the problem’s magnitude, competing priorities during patient visits, lack of incentives to report and limitations to documentation systems for adequate reporting. All people with diabetes should be encouraged to discuss their experiences with hypoglycemia without judgment or shame. Glucose targets, testing schedules (blood glucose or continuous glucose monitoring) and treatment plans should be reviewed often and individualized to the minimize risk of hypoglycemia. Finally, people with T2D on insulin should always be encouraged to have oral glucose and rescue medication immediately available

Percutaneous angioplasty for infrainguinal graft-related stenoses

Objective:To assess the success of percutaneous transluminal angioplasty (PTA) in treating infrainguinal graft-related stenoses.Design:Retrospective analysis of stenoses undergoing PTA over 6 years.Materials:Fifty-seven stenoses in 42 grafts.Methods:Site, length and type of stenoses recorded. Follow-up till discharge, graft occlusion or death.Results:PTA was successful in 48/57 stenoses in 36 grafts (G), with a poor result in seven. Further PTA was required in seven stenoses (7 G). One graft occluded at PTA and one stenosis was inaccessible. Overall graft (G) patency (median 13 months) was 82% (1 year patency 84%). Of 48 successful PTAs (37 G), 36 remained patent (28 G), eight (4 G) occluded and four were lost to follow-up (4 G). Fourteen of thirty-six stenoses which remained patent required further intervention (seven PTA, six jump grafts, one vein patch). The four occlusions were associated with small veins (two), multiple stenoses (one) and a PTFE graft which occluded 10 days following PTA. Of the seven PTAs with a poor angiographic result, five remained patent, three after further intervention.Conclusion:PTA is the best treatment for localised stenoses. Stenoses >2 cm or multiple (three or more) stenoses are best treated surgically. Follow-up is essential, as 20% require further intervention

Indestructibility of Vopenka's Principle

We show that Vopenka's Principle and Vopenka cardinals are indestructible under reverse Easton forcing iterations of increasingly directed-closed partial orders, without the need for any preparatory forcing. As a consequence, we are able to prove the relative consistency of these large cardinal axioms with a variety of statements known to be independent of ZFC, such as the generalised continuum hypothesis, the existence of a definable well-order of the universe, and the existence of morasses at many cardinals.Comment: 15 pages, submitted to Israel Journal of Mathematic

Directed assembly of optically bound matter

We present a study of optically bound matter formation in a counter-propagating evanescent field, exploiting total internal reflection on a prism surface. Small ensembles of silica microspheres are assembled in a controlled manner using optical tweezers. The structures and dynamics of the resulting optically bound chains are interpreted using a simulation implementing generalized Lorentz-Mie theory. In particular, we observe enhancement of the scattering force along the propagation direction of the optically bound colloidal chains leading to a microscopic analogue of a driven pendulum which, at least superficially, resembles Newton’s cradle

Two Stage Auctions II: Common-Value Strategies and the Winner's Curse

game theory ; supply ; economic models ; economic equilibrium

Fair Division by Point Allocation

economic theory

Two Stage Auctions I: Private-Value Strategies

game theory ; economic equilibrium ; information

An Envy-Free Cake Division Algorithm

mathematics

Fair Division Pareto-Optimality Versus Strategic Robustness

economic theory