Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the $p$-version

Plane wave discontinuous Galerkin (PWDG) methods are a class of Trefftz-type methods for the spatial discretization of boundary value problems for the Helmholtz operator $-\Delta-\omega^2$, $\omega>0$. They include the so-called ultra weak variational formulation from [O. Cessenat and B. Després, SIAM J. Numer. Anal., 35 (1998), pp. 255–299]. This paper is concerned with the a priori convergence analysis of PWDG in the case of $p$-refinement, that is, the study of the asymptotic behavior of relevant error norms as the number of plane wave directions in the local trial spaces is increased. For convex domains in two space dimensions, we derive convergence rates, employing mesh skeleton-based norms, duality techniques from [P. Monk and D. Wang, Comput. Methods Appl. Mech. Engrg., 175 (1999), pp. 121–136], and plane wave approximation theory.

Frying of potato chips in a blend of canola oil and palm olein: changes in levels of individual fatty acids and tocols

The changes occurring in the levels of nutritionally relevant oil components were assessed during repeated frying of potato chips in a blend of palm olein and canola oil (1:1 w/w). The blend suffered minimal reductions in omega-3 and omega-6 polyunsaturated fatty acids. There was no significant difference between the fatty acid composition of the oil extracted from the product and that of the frying medium, in all three cases. The blend also contained a significant amount of tocols which add a nutritional value to the oil. The concentration of the tocols was satisfactorily retained over the period of oil usage, in contrast to the significant loses observed in the case of the individual oils. The blend also performed well when assessed by changes in total polar compounds, free fatty acids, p-anisidine value. When fried in used oil, the product oil content increased progressively with oil usage time. This study shows that blended frying oils can combine good stability and nutritional quality

Nano structures through self-assembly of protected hydrophobic amino acids: encapsulation of rhodamine B dye by proline-based nanovesicles

The development of novel molecules for the creation of nanometer structures with specific properties has been the current interest of this research. We have developed a set of molecules from hydrophobic omega- and alpha-amino acids by protecting the -NH(2) with Boc (t-butyloxycarbonyl) group and -CO(2)H with para-nitroanilide such as BocHN-Xx-CONH-(p-NO(2))center dot C(6)H(4), where Xx is gamma-aminobutyric acid (gamma-Abu), (L)-isoleucine, alpha-aminoisobutyric acid, proline, etc. These molecules generate various nanometer structures, such as nanofibrils, nanotubes and nanovesicles, in methanol/water through the self-assembly of bilayers in which the nitro benzene moieties are stacked in the middle and the Boc-protected amino acids parts are packed in the outer surface. The bilayers can be further stacked one over the other through hydrophobic interactions to form multilayer structure, which helps to generate different kinds of nanoscopic structures. The formation of the nanostructures has been facilitated through the participation of various noncovalent interactions, such as hydrophobic interactions, hydrogen bonding and aromatic p-stacking interactions. Fluorescence microscopy and UV studies reveal that the nanovesicles generated from pro-based molecule can encapsulate dye molecules which can be released by addition of acid (at pH 2). These single amino acid based molecules are both easy to synthesize and cost-effective and therefore offer novel scaffolds for the future design of nanoscale structures.

Non-ergodicity of inviscid two-dimensional flow on a beta-plane and on the surface of a rotating sphere

It is shown that, for a sufficiently large value of β, two-dimensional flow on a doubly-periodic beta-plane cannot be ergodic (phase-space filling) on the phase-space surface of constant energy and enstrophy. A corresponding result holds for flow on the surface of a rotating sphere, for a sufficiently rapid rotation rate Ω. This implies that the higher-order, non-quadratic invariants are exerting a significant influence on the statistical evolution of the flow. The proof relies on the existence of a finite-amplitude Liapunov stability theorem for zonally symmetric basic states with a non-vanishing absolute-vorticity gradient. When the domain size is much larger than the size of a typical eddy, then a sufficient condition for non-ergodicity is that the wave steepness ε < 1, where ε = 2[surd radical]2Z/βU in the planar case and $\epsilon = 2^{\frac{1}{4}} a^{\frac{5}{2}}Z^{\frac{7}{4}}/\Omega U^{\frac{5}{2}}$ in the spherical case, and where Z is the enstrophy, U the r.m.s. velocity, and a the radius of the sphere. This result may help to explain why numerical simulations of unforced beta-plane turbulence (in which ε decreases in time) seem to evolve into a non-ergodic regime at large scales.

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

Effects of phthalic acid esters on the liver and thyroid

The effects, over periods from 3 days to 9 months of administration, of diets containing di-2-ethylhexyl phthalate are very similar to those observed in rats administered diets containing hypolipidemic drugs such as clofibrate. Changes occur in a characteristic order commencing with alterations in the distribution of lipid within the liver, quickly followed by proliferation of hepatic peroxisomes and induction of the specialized P-450 isoenzyme(s) catalyzing omega oxidation of fatty acids. There follows a phase of mild liver damage indicated by induction of glucose-6-phosphatase activity and a loss of glycogen, eventually leading to the formation of enlarged lysosomes through autophagy and the accumulation of lipofuscin. Associated changes are found in the kidney and thyroid. The renal changes are limited to the proximal convoluted tubules and are generally similar to changes found in the liver. The effects on the thyroid are more marked. Although the levels of thyroxine in plasma fail to about half normal values, serum triiodothyronine remains close to normal values while the appearance of the thyroid varies, very marked hyperactivity being noted 7 days after commencement of treatment, this is less marked at 14 days, but even after 9 months treatment there is clear cut evidence for hyperactivity with colloid changes which indicate this has persisted for some time. Straight chain analogs of di-2-ethylhexyl phthalate, di-n-hexyl phthalate and di-n-oxtyl phthalate differ entirely in their short-term effects on the liver and kidney but have similar effects on the thyroid. The short-term in vivo hepatic effects of the three phthalate esters can be reproduced in hepatocytes in tissue culture. All three phthalate esters, as well as clofibrate, have early marked effects on the metabolism of fatty acids in isolated hepatocytes. The nature of these changes is such as to increase storage of lipid in the liver. A hypothesis is presented to explain the progress from these initial metabolic effects to the final formation of liver tumors.

Dairy fat: perceptions and realities.

Milk provides many key nutrients but the saturated and trans fatty acids in milk fat are associated with perceived negative effects on human health, especially cardiovascular disease. Recent epidemiological studies and dietary intervention trials challenge this perception, however; available evidence does not support the concept that consumption of saturated fats or dairy products adversely affects the risk of coronary heart disease (although replacing some saturated fats with mono or polyunsaturated fats is likely to provide benefit). Furthermore, the trans fats found in dairy products are consumed in very low amounts and do not appear to have the negative health effects associated with the consumption of industrial sources of trans fat. Milk fat is an excellent source of oleic acid that originates mainly by endogenous synthesis from stearic acid, but increasing the milk fat content of unsaturated fatty acids requires dietary formulations that bypass rumen biohydrogenation. Recent research indicates that long-chain omega-3 fatty acids and conjugated linoleic acids have potential beneficial effects in health maintenance and the prevention of chronic diseases. Enhancing the milk fat content of these fatty acids offers exciting possibilities, but educating consumers about inaccurate and inappropriate generalisations about fat remains the primary challenge. Finally, individuals do not simply consume milk-fat-derived fatty acids on their own, but rather as components in dairy foods which are highly complex and may contain many beneficial ingredients. Overall, dairy products are critical in providing many of the essential nutrients in the human diet. Nevertheless, dairy products vary in their nutrient composition, including fat, and this needs to be considered in the context of dietary recommendations and our need to consume a balanced diet.

Effect of cinnamon on gastric emptying, arterial stiffness, postprandial lipemia, glycemia, and appetite responses to high-fat breakfast

Abstract BACKGROUND: Cinnamon has been shown to delay gastric emptying of a high-carbohydrate meal and reduce postprandial glycemia in healthy adults. However, it is dietary fat which is implicated in the etiology and is associated with obesity, type 2 diabetes and cardiovascular disease. We aimed to determine the effect of 3 g cinnamon (Cinnamomum zeylanicum) on GE, postprandial lipemic and glycemic responses, oxidative stress, arterial stiffness, as well as appetite sensations and subsequent food intake following a high-fat meal. METHODS: A single-blind randomized crossover study assessed nine healthy, young subjects. GE rate of a high-fat meal supplemented with 3 g cinnamon or placebo was determined using the 13C octanoic acid breath test. Breath, blood samples and subjective appetite ratings were collected in the fasted and during the 360 min postprandial period, followed by an ad libitum buffet meal. Gastric emptying and 1-day fatty acid intake relationships were also examined. RESULTS: Cinnamon did not change gastric emptying parameters, postprandial triacylglycerol or glucose concentrations, oxidative stress, arterial function or appetite (p < 0.05). Strong relationships were evident (p < 0.05) between GE Thalf and 1-day palmitoleic acid (r = -0.78), eiconsenoic acid (r = -0.84) and total omega-3 intake (r = -0.72). The ingestion of 3 g cinnamon had no effect on GE, arterial stiffness and oxidative stress following a HF meal. CONCLUSIONS: 3 g cinnamon did not alter the postprandial response to a high-fat test meal. We find no evidence to support the use of 3 g cinnamon supplementation for the prevention or treatment of metabolic disease. Dietary fatty acid intake requires consideration in future gastrointestinal studies.

Increased dietary α-linolenic acid has sex-specific effects upon eicosapentaenoic acid status in humans: re-examination of data from a randomised, placebo-controlled, parallel study

Background: There is a metabolic pathway by which mammals can convert the omega-3 (n-3) essential fatty acid α-linolenic acid (ALA) into longer-chain n-3 polyunsaturated fatty acids (LC n-3 PUFA) including eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA). As far as we know there are currently no studies that have specifically examined sex differences in the LC n-3 PUFA response to increased dietary ALA intake in humans, although acute studies with isotope-labelled ALA identified that women have a significantly greater capacity to synthesise EPA and DHA from ALA compared to men. Findings: Available data from a placebo-controlled, randomised study were re-examined to identify whether there are sex differences in the LC n-3 PUFA response to increased dietary ALA intake in humans. There was a significant difference between sexes in the response to increased dietary ALA, with women having a significantly greater increase in the EPA content of plasma phospholipids (mean +2.0% of total fatty acids) after six months of an ALA-rich diet compared to men (mean +0.7%, P = 0.039). Age and BMI were identified as predictors of response to dietary ALA among women. Conclusions: Women show a greater increase in circulating EPA than men during increased dietary ALA consumption. Further understanding of individual variation in the response to dietary ALA could inform nutrition advice, with recommendations being specifically tailored according to habitual diet, sex, age and BMI.

Easterly wave disturbances over Northeast Brazil: an observational analysis

This paper aims to identify the circulation associated with Easterly Wave Disturbances (EWDs) that propagate toward the Eastern Northeast Brazil (ENEB) and their impact on the rainfall over ENEB during 2006 and 2007 rainy seasons (April–July). The EWDs identification and trajectory are analyzed using an automatic tracking technique (TracKH). The EWDs circulation patterns and their main features were obtained using the composite technique. To evaluate the TracKH efficiency, a validation was done by comparing the EWDs number tracked against observed cases obtained from an observational analysis. The mean characteristics of EWDs are 5.5-day period, propagation speed of ~9.5 m·s−1, and a 4500 km wavelength. A synoptic analysis shows that between days −2 d and 0 d, the low level winds presented cyclonic relative vorticity and convergence anomalies both in 2006 and 2007. The EWDs signals are strongest at low levels. The EWDs propagation is associated with relative humidity and precipitation positive anomalies and OLR and omega negative anomalies. The EWDs tracks are seen over all ENEB and their lysis occurs between the ENEB and marginally inside the continent. The tracking captured 71% of EWDs in all periods, indicating that an objective analysis is a promising method for EWDs detection.

Impact of US Brown Swiss genetics on milk quality from low-input herds in Switzerland: interactions with grazing intake and pasture type

This study investigated the effect of, and interactions between, contrasting crossbreed genetics (US Brown Swiss [BS] × Improved Braunvieh [BV] × Original Braunvieh [OB]) and feeding regimes (especially grazing intake and pasture type) on milk fatty acid (FA) profiles. Concentrations of total polyunsaturated FAs, total omega-3 FAs and trans palmitoleic, vaccenic, α-linolenic, eicosapentaenoic and docosapentaenoic acids were higher in cows with a low proportion of BS genetics. Highest concentrations of the nutritionally desirable FAs, trans palmitoleic, vaccenic and eicosapentaenoic acids were found for cows with a low proportion of BS genetics (0-24% and/or 25-49%) on high grazing intake (75-100% of dry matter intake) diets. Multivariate analysis indicated that the proportion of OB genetics is a positive driver for nutritionally desirable monounsaturated and polyunsaturated FAs while BS genetics proportion was positive driver for total and undesirable individual saturated FAs. Significant genetics × feeding regime interactions were also detected for a range of FAs.

Meat quality and health implications of organic and conventional beef production

Recommendation to reduce fat consumption from ruminant meat does not consider the contribution of nutritionally beneficial fatty acids in lean beef. Here we report effects of production system (organic vs conventional) and finishing season on meat and fat quality of sirloin steaks from retail outlets and simulated fatty acid intakes by consumers. There was little difference in meat quality (pH, shear force and colour), but the fat profiles varied considerably between production systems and season. Meat fat from organic and summer finished cattle contained higher concentrations of conjugated linoleic acid, its precursor vaccenic acid and individual omega-3 fatty acids and had a lower ratio of omega-6 to omega-3 fatty acids compared with non-organic and winter finished cattle respectively. The fat profile from summer finished organic beef aligns better to recommended dietary guideline including those for long chain omega-3 fatty acids compared with that from winter finished, non-organic steak.

Improving the fatty acid profile of winter milk from housed cows with contrasting feeding regimes by oilseed supplementation

Many studies show concentrations of nutritionally desirable fatty acids in bovine milk are lower when cows have no access to grazing, leading to seasonal fluctuations in milk quality if cows are housed for part of the year. This study investigated the potential to improve the fatty acid profiles of bovine milk by oilseed supplementation (rolled linseed and rapeseed) during a period of indoor feeding in both organic and conventional production systems. Both linseed and rapeseed increased the concentrations of total monounsaturated fatty acids, vaccenic acid, oleic acid and rumenic acid in milk, but decreased the concentration of the total and certain individual saturated fatty acids. Linseed resulted in greater changes than rapeseed, and also significantly increased the concentrations of α-linolenic acid, total polyunsaturated fatty acids and total omega-3 fatty acids. The response to oilseed supplementation, with respect to increasing concentrations of vaccenic acid and omega-3 fatty acids, appeared more efficient for organic compared with conventional diets.

Variation in nutritionally relevant components in retail Jersey and Guernsey whole milk

This study investigates the quality of retail milk labelled as Jersey & Guernsey (JG) when compared with milk without breed specifications (NS) and repeatability of differences over seasons and years. 16 different brands of milk (4 Jersey & Guernsey, 12 non specified breed) were sampled over 2 years on 4 occasions. JG milk was associated with both favourable traits for human health, such as the higher total protein, total casein, α-casein, β-casein, κ-casein and α-tocopherol contents, and unfavourable traits, such as the higher concentrations of saturated fat, C12:0, C14:0 and lower concentrations of monounsaturated fatty acids. In summer, JG milk had a higher omega-3:omega-6 ratio than had NS milk. Also, the relative increase in omega-3 fatty acids and α-tocopherol, from winter to summer, was greater in JG milk. The latter characteristic could be of use in breeding schemes and farming systems producing niche dairy products. Seasonality had a more marked impact on the fatty acid composition of JG milk than had NS milk, while the opposite was found for protein composition. Potential implication for the findings in human health, producers, industry and consumers are considered.

Effect of feeding intensity and milking system on nutritionally relevant milk components in dairy farming systems in the North East of England

There is increasing concern that the intensification of dairy production reduces the concentrations of nutritionally desirable compounds in milk. This study therefore compared important quality parameters (protein and fatty acid profiles; α-tocopherol and carotenoid concentrations) in milk from four dairy systems with contrasting production intensities (in terms of feeding regimens and milking systems). The concentrations of several nutritionally desirable compounds (β-lactoglobulin, omega-3 fatty acids, omega-3/omega-6 ratio, conjugated linoleic acid c9t11, and/or carotenoids) decreased with increasing feeding intensity (organic outdoor ≥ conventional outdoor ≥ conventional indoors). Milking system intensification (use of robotic milking parlors) had a more limited effect on milk composition, but increased mastitis incidence. Multivariate analyses indicated that differences in milk quality were mainly linked to contrasting feeding regimens and that milking system and breed choice also contributed to differences in milk composition between production systems.