Symplectic integrators for index one constraints

We show that symplectic Runge-Kutta methods provide effective symplectic integrators for Hamiltonian systems with index one constraints. These include the Hamiltonian description of variational problems subject to position and velocity constraints nondegenerate in the velocities, such as those arising in sub-Riemannian geometry and control theory.Comment: 13 pages, accepted in SIAM J Sci Compu

Geometric Integration of Hamiltonian Systems Perturbed by Rayleigh Damping

Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter $\epsilon$, and the schemes under study preserve the symplectic structure in the case $\epsilon=0$. In the case $0<\epsilon\ll 1$ the energy dissipation rate is shown to be asymptotically correct by backward error analysis. Theoretical results on monotone decrease of the modified Hamiltonian function for small enough step sizes are given. Further, an analysis proving near conservation of relative equilibria for small enough step sizes is conducted. Numerical examples, verifying the analyses, are given for a planar pendulum and an elastic 3--D pendulum. The results are superior in comparison with a conventional explicit Runge-Kutta method of the same order

Geometric Generalisations of SHAKE and RATTLE

A geometric analysis of the Shake and Rattle methods for constrained Hamiltonian problems is carried out. The study reveals the underlying differential geometric foundation of the two methods, and the exact relation between them. In addition, the geometric insight naturally generalises Shake and Rattle to allow for a strictly larger class of constrained Hamiltonian systems than in the classical setting. In order for Shake and Rattle to be well defined, two basic assumptions are needed. First, a nondegeneracy assumption, which is a condition on the Hamiltonian, i.e., on the dynamics of the system. Second, a coisotropy assumption, which is a condition on the geometry of the constrained phase space. Non-trivial examples of systems fulfilling, and failing to fulfill, these assumptions are given

Social origin, schooling and individual change in intelligence during childhood influence long-term mortality: a 68-year follow-up study

Background Intelligence at a single time-point has been linked to health outcomes. An individual's IQ increases with longer schooling, but the validity of such increase is unclear. In this study, we assess the hypothesis that individual change in the performance on IQ tests between ages 10 and 20 years is associated with mortality later in life

Middleborns disadvantaged? testing birth-order effects on fitness in pre-industrial finns

Parental investment is a limited resource for which offspring compete in order to increase their own survival and reproductive success. However, parents might be selected to influence the outcome of sibling competition through differential investment. While evidence for this is widespread in egg-laying species, whether or not this may also be the case in viviparous species is more difficult to determine. We use pre-industrial Finns as our model system and an equal investment model as our null hypothesis, which predicts that (all else being equal) middleborns should be disadvantaged through competition. We found no overall evidence to suggest that middleborns in a family are disadvantaged in terms of their survival, age at first reproduction or lifetime reproductive success. However, when considering birth-order only among same-sexed siblings, first-, middle-and lastborn sons significantly differed in the number of offspring they were able to rear to adulthood, although there was no similar effect among females. Middleborn sons appeared to produce significantly less offspring than first-or lastborn sons, but they did not significantly differ from lastborn sons in the number of offspring reared to adulthood. Our results thus show that taking sex differences into account is important when modelling birth-order effects. We found clear evidence of firstborn sons being advantaged over other sons in the family, and over firstborn daughters. Therefore, our results suggest that parents invest differentially in their offspring in order to both preferentially favour particular offspring or reduce offspring inequalities arising from sibling competition

Characteristics and trends in required home care by GPs in Austria: diseases and functional status of patients

BACKGROUND: Almost all societies carry responsibility towards patients who require continuous medical care at home. In many health systems the general practitioner cooperates with community based services of home care and coordinates all medical and non medical activities. In Austria the general practitioner together and in cooperation with relatives of the patient and professional organisations usually takes on this task by visiting his patients. This study was carried out to identify diseases that need home care and to describe the functional profile of home care patients in eastern Austria. METHODS: Cross sectional observational study with 17 GP practices participating during 2 study periods in 1997 and in 2004 in eastern Austria. Each GP identified patients requiring home care and assessed their underlying diseases and functional status by filling in a questionnaire personally after an encounter. Patients in nursing homes were excluded. Statistical tests used were t-tests, contingency tables, nonparametric Wilcoxon signed rank sum test and Fisher-combination test. RESULTS: Patients with degenerative diseases of the central nervous system (65%) caused by Alzheimer's disease and cerebrovascular occlusive disease and patients with degenerative diseases of the skeletal system (53%) were the largest groups among the 198 (1997) and 261 (2004) home care cases of the 11 (1997) and 13 (2004) practices. Malignant diseases in a terminal state constituted only 5% of the cases. More than two thirds of all cases were female with an average age of 80 years. Slightly more than 70% of the patients were at least partially mobile. CONCLUSION: Home care and home visits for patients with degenerative diseases of the central nervous and skeletal system are important elements of GP's work. Further research should therefore focus on effective methods of training and rehabilitation to better the mental and physical status of patients living in their private homes

Beetroot juice supplementation speeds O2 uptake kinetics and improves exercise tolerance during severe-intensity exercise initiated from an elevated metabolic rate

Recent research has suggested that dietary nitrate (NO3-) supplementation might alter the physiological responses to exercise via specific effects on type II muscle. Severe-intensity exercise initiated from an elevated metabolic rate would be expected to enhance the proportional activation of higher-order (type II) muscle fibers. The purpose of this study was therefore to test the hypothesis that, compared to placebo (PL), NO3--rich beetroot juice (BR) supplementation would speed the phase II o2 kinetics (τp) and enhance exercise tolerance during severe-intensity exercise initiated from a baseline of moderate-intensity exercise. Nine healthy, physically-active subjects were assigned in a randomized, double-blind, crossover design to receive BR (140 mL/day, containing ~8 mmol of NO3-) and PL (140 mL/day, containing ~0.003 mmol of NO3-) for 6 days. On days 4, 5 and 6 of the supplementation periods, subjects completed a double-step exercise protocol that included transitions from unloaded-to-moderate intensity exercise (U→M) followed immediately by moderate-to-severe-intensity exercise (M→S). Compared to PL, BR elevated resting plasma nitrite concentration (PL: 65 ± 32 vs. BR: 348 ± 170 nM, P0.05). During M→S exercise, the faster o2 kinetics coincided with faster NIRS-derived muscle [deoxyhemoglobin] kinetics (τ; PL: 20 ± 9 vs. BR: 10 ± 3 s, P<0.05) and a 22% greater time-to-task failure (PL: 521 ± 158 vs. BR: 635 ± 258 s, P<0.05). Dietary supplementation with NO3--rich BR juice speeds o2 kinetics and enhances exercise tolerance during severe-intensity exercise when initiated from an elevated metabolic rate

Electrodeposited Co93.2P6.8 nanowire arrays with core-shell microstructure and perpendicular magnetic anisotropy

We demonstrate the formation of an unusual core-shell microstructure in Co93.2P6.8 nanowires electrodeposited by alternating current (ac) in an alumina template. By means of transmission electron microscopy, it is shown that the coaxial-like nanowires contain amorphous and crystalline phases. Analysis of the magnetization data for Co-P alloy nanowires indicates that a ferromagnetic core is surrounded by a weakly ferromagnetic or non-magnetic phase, depending on the phosphor content. The nanowire arrays exhibit an easy axis of magnetization parallel to the wire axis. For this peculiar composition and structure, the coercivity values are 2380 ± 50 and 1260 ± 35 Oe, parallel and perpendicular to the plane directions of magnetization, respectively. This effect is attributed to the core-shell structure making the properties and applications of these nanowires similar to pure cobalt nanowires with an improved perpendicular anisotropy. <br/