Critical Thickness Ratio for Buckled and Wrinkled Fruits and Vegetables

Fruits and vegetables are usually composed of exocarp and sarcocarp and they take a variety of shapes when they are ripe. Buckled and wrinkled fruits and vegetables are often observed. This work aims at establishing the geometrical constraint for buckled and wrinkled shapes based on a mechanical model. The mismatch of expansion rate between the exocarp and sarcocarp can produce a compressive stress on the exocarp. We model a fruit/vegetable with exocarp and sarcocarp as a hyperelastic layer-substrate structure subjected to uniaxial compression. The derived bifurcation condition contains both geometrical and material constants. However, a careful analysis on this condition leads to the finding of a critical thickness ratio which separates the buckling and wrinkling modes, and remarkably, which is independent of the material stiffnesses. More specifically, it is found that if the thickness ratio is smaller than this critical value a fruit/vegetable should be in a buckling mode (under a sufficient stress); if a fruit/vegetable in a wrinkled shape the thickness ratio is always larger than this critical value. To verify the theoretical prediction, we consider four types of buckled fruits/vegetables and four types of wrinkled fruits/vegetables with three samples in each type. The geometrical parameters for the 24 samples are measured and it is found that indeed all the data fall into the theoretically predicted buckling or wrinkling domains. Some practical applications based on this critical thickness ratio are briefly discussed.Comment: 11 pages 9 figures 2 table

Effect of synthetic and bovine milk conjugated linoleic acid (CLA) on immune function : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Nutrition Science at Massey University

CLA is a collective name for a mixture of positional and geometrical isomers of linoleic acid (c-9, c-12-octadecadioenic acid) which possess conjugated double bonds. CLA occurs in a variety of foods, but is present at higher concentrations in products from ruminants. Milk fat is the richest natural source of CLA. The objective of this research was to examine the immunomodulatory properties of CLA (both synthetic and natural CLA derived from bovine milk fat). Two experiments were conducted at the Milk and Health Research Centre, Massey University, Palmerston North, New Zealand. The aim of the first experiment was to investigate the dose effect of different concentrations of synthetic CLA (Tonalin) on immune function. Mice were fed either skim milk powder based diet or the same diet supplemented with 0.1, 0.25, 0.5, 1.0 or 2.0% synthetic CLA (Tonalin) by weight. Animals were immunised orally with a mixture of polio vaccine in sodium bicarbonate (25μl) and subcutaneously with Fluvax and Tetanus toxoid vaccine on days 7 and 21. After 4 weeks feeding, mice were euthanased by isoflurane overdose. Various immune parameters were measured and the results showed that synthetic CLA (Tonalin) enhanced a range of immune functions. Synthetic CLA stimulated PHA induced T lymphocyte proliferation at 0.25, 0.5 and 1.0% as compared with the control group (p < 0.05). Synthetic CLA enhanced macrophage phagocytosis in a dose dependent manner. Synthetic CLA enhanced antibody responses (mucosal and systemic) to vaccines (polio vaccine, Fluvax and Tetanus toxoid). Natural killer cell activity was significantly enhanced in mice fed 0.25 and 0.5% CLA. In general, 0.25% CLA was regarded as the best CLA level which achieved optimal immunoregulating effects. The aim of the second experiment was to examine the effect of natural CLA derived from milk fat on immune responses in mice. Mice were fed a skim milk powder (SMP) based diet. The control diet was skim milk powder only, without any CLA or milk fat supplementation. The dietary treatments were: ordinary milk fat, fractionated milk fat (1st stage), 0.2% synthetic CLA (Tonalin) and CLA enriched milk fat. Animals were fed these diets for 28 days. Mice were immunised orally with a mixture of polio vaccine/ovalbumin/cholera toxin in sodium bicarbonate on days 7, 14 and 21 and subcutaneously with Fluvax and ADT (Diptheria and Tetanus toxoid vaccine) on days 7 and 21. Natural CLA was found to stimulate PHA and Con A induced T lymphocyte blastogenesis. Supplementation with natural CLA also led to increased antibody responses to vaccines and increased CD25+ populations in peripheral blood in mice. Natural CLA also enhanced macrophage phagocytosis. Synthetic CLA enhanced a range of immune functions which is consistent with the results in the first experiment. It is noted that although the CLA content is low in milk fat, the natural CLA derived from milk fat expressed potent effects in enhancing the growth of immune cells and promoting a range of immune functions in mice. Key words: conjugated linoleic acid (CLA), lymphocyte, macrophage, immunity, milk fa

Twisted Topological Graph Algebras

We define the notion of a twisted topological graph algebra associated to a topological graph and a $1$-cocycle on its edge set. We prove a stronger version of a Vasselli's result. We expand Katsura's results to study twisted topological graph algebras. We prove a version of the Cuntz-Krieger uniqueness theorem, describe the gauge-invariant ideal structure. We find that a twisted topological graph algebra is simple if and only if the corresponding untwisted one is simple.Comment: 27 page