Thermodynamic analysis of dilute ternary systems. 1. The Ag-Au-Sn system

Heats of solution of silver and gold in dilute silver-gold-tin alloys as function of alloy compositio

Structural changes in cartilage and collagen studied by high temperature Raman spectroscopy

Understanding the high temperature behavior of collagen and collagenous tissue is important for surgical procedures and biomaterials processing for the food, pharmaceutical, and cosmetics industries. One primary event for proteins is thermal denaturation that involves unfolding the polypeptide chains while maintaining the primary structure intact. Collagen in the extracellular matrix of cartilage and other connective tissue is a hierarchical material containing bundles of triple-helical fibers associated with water and proteoglycan components. Thermal analysis of dehydrated collagen indicates irreversible denaturation at high temperature between 135°C and 200°C, with another reversible event at ∼60-80°C for hydrated samples. We report high temperature Raman spectra for freeze-dried cartilage samples that show an increase in laser-excited fluorescence interpreted as conformational changes associated with denaturation above 140°C. Spectra for separated collagen and proteoglycan fractions extracted from cartilage indicate the changes are associated with collagen. The Raman data also show appearance of new features indicating peptide bond hydrolysis at high temperature implying that molecular H2O is retained within the freeze-dried tissue. This is confirmed by thermogravimetric analysis that show 5-7 wt% H2O remaining within freeze-dried cartilage that is released progressively upon heating up to 200°C. Spectra obtained after exposure to high temperature and re-hydration following recovery indicate that the capacity of the denatured collagen to re-absorb water is reduced. Our results are important for revealing the presence of bound H2O within the collagen component of connective tissue even after freeze-drying and its role in denaturation that is accompanied by or perhaps preceded by breakdown of the primary polypeptide structure

A Feynman integral via higher normal functions

We study the Feynman integral for the three-banana graph defined as the scalar two-point self-energy at three-loop order. The Feynman integral is evaluated for all identical internal masses in two space-time dimensions. Two calculations are given for the Feynman integral; one based on an interpretation of the integral as an inhomogeneous solution of a classical Picard-Fuchs differential equation, and the other using arithmetic algebraic geometry, motivic cohomology, and Eisenstein series. Both methods use the rather special fact that the Feynman integral is a family of regulator periods associated to a family of K3 surfaces. We show that the integral is given by a sum of elliptic trilogarithms evaluated at sixth roots of unity. This elliptic trilogarithm value is related to the regulator of a class in the motivic cohomology of the K3 family. We prove a conjecture by David Broadhurst that at a special kinematical point the Feynman integral is given by a critical value of the Hasse-Weil L-function of the K3 surface. This result is shown to be a particular case of Deligne's conjectures relating values of L-functions inside the critical strip to periods.Comment: Latex. 70 pages. 3 figures. v3: minor changes and clarifications. Version to appear in Compositio Mathematic

A Robust Numerical Method for Integration of Point-Vortex Trajectories in Two Dimensions

The venerable 2D point-vortex model plays an important role as a simplified version of many disparate physical systems, including superfluids, Bose-Einstein condensates, certain plasma configurations, and inviscid turbulence. This system is also a veritable mathematical playground, touching upon many different disciplines from topology to dynamic systems theory. Point-vortex dynamics are described by a relatively simple system of nonlinear ODEs which can easily be integrated numerically using an appropriate adaptive time stepping method. As the separation between a pair of vortices relative to all other inter-vortex length scales decreases, however, the computational time required diverges. Accuracy is usually the most discouraging casualty when trying to account for such vortex motion, though the varying energy of this ostensibly Hamiltonian system is a potentially more serious problem. We solve these problems by a series of coordinate transformations: We first transform to action-angle coordinates, which, to lowest order, treat the close pair as a single vortex amongst all others with an internal degree of freedom. We next, and most importantly, apply Lie transform perturbation theory to remove the higher-order correction terms in succession. The overall transformation drastically increases the numerical efficiency and ensures that the total energy remains constant to high accuracy.Comment: 21 pages, 4 figure

Acute effects of Hibiscus sabdariffa calyces on postprandial blood pressure, vascular function, blood lipids, biomarkers of insulin resistance and inflammation in humans

The acute impact of Hibiscus sabdariffa calyces (HSC) extract on postprandial vascular function and other cardiometabolic risk factors have not been studied previously. This study investigated the acute impact of HSC extract consumption on blood pressure (BP), vascular function and other cardiometabolic risk markers. Twenty-five men with 1% to 10% cardiovascular disease (CVD) risk (determined by QRISK 2) were randomised to consume either 250 mL of the aqueous extract of HSC or water with breakfast in a randomised, controlled, single-blinded, 2-meal cross-over study (ClinicalTrials.gov, NTC02165553) with a two weeks washout period between study days. BP was measured at baseline and hourly for 4 h. Flow mediated dilatation (FMD) of the branchial artery was measured at baseline, 2 and 4 h post intervention drink consumption. Acute consumption of aqueous extract of HSC caused a significant increase in % FMD ( < 0.001), a non-significant decrease in systolic BP (SBP) and diastolic BP (DBP); non-significant increase in urinary and plasma nitric oxide (NOx) and reduced response of serum glucose, plasma insulin, serum triacylglycerol and C-reactive protein (CRP) levels; significant ( = 0.026) improvement in the area under systemic antioxidant response curve (0 to 2 h); no significant changes in arterial stiffness following the acute consumption of the extract of HSC. Gallic acid, 4-O-methylgallic acid, 3-O-methylgallic acid and hippuric acid reached a maximum plasma concentration at 1 to 2 h post consumption of the extract of HSC. The extract of HSC improved postprandial vascular function and may be a useful dietary strategy to reduce endothelial dysfunction and CVD risk, although this requires confirmation

Quantitative infrared spectroscopy of minor constituents of the Earth's atmosphere

We obtain quantitative laboratory spectroscopic measurements of molecular constituents which are of importance in understanding the health of the Earth's atmosphere, and, in particular, emphasize those species which are important for understanding stratospheric kinetics or are used for long term monitoring of the stratosphere. Our measurements provide: (1) line and band intensity values which are needed to establish limits of detectability for as yet unobserved species and to quantify the abundance of those species which are observed; (2) line-positions, -half widths and pressure induced shifts are all needed for remote sensing techniques, and (3) data on the above basic molecular parameters at temperatures and pressures appropriate for the real atmosphere