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

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

Anomalous frequency scaling of acoustic phonon damping in freestanding nickel cavities fabricated via laser delamination

Single-shot picosecond (ps) laser-induced delamination allows for the direct generation of suspended membranes from a continuous metallic film, offering a promising platform for the control of ultrafast magnetization dynamics driven by acoustic waves. Using the picosecond-ultrasonics method, we demonstrate that long-lived low-frequency acoustic waves can be optically excited in the delaminated cavities. At the same time, higher-frequency modes above 60 GHz exhibit a surprisingly fast damping, following a scaling law incompatible with the expected attenuation mediated by phonon–phonon scattering. Comparing measurements between delaminated cavities and a benchmark nickel film in contact with the substrate, we link our findings to structural modifications of the nickel crystal induced by the delamination proces

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

‘‘Beet-ing’’ the Mountain: A Review of the Physiological and Performance Effects of Dietary Nitrate Supplementation at Simulated and Terrestrial Altitude

Exposure to altitude results in multiple physiological consequences. These include, but are not limited to, a reduced maximal oxygen consumption, drop in arterial oxygen saturation, and increase in muscle metabolic perturbations at a fixed sub-maximal work rate. Exercise capacity during fixed work rate or incremental exercise and time-trial performance are also impaired at altitude relative to sea-level. Recently, dietary nitrate (NO3-) supplementation has attracted considerable interest as a nutritional aid during altitude exposure. In this review, we summarise and critically evaluate the physiological and performance effects of dietary NO3- supplementation during exposure to simulated and terrestrial altitude. Previous investigations at simulated altitude indicate that NO3- supplementation may reduce the oxygen cost of exercise, elevate arterial and tissue oxygen saturation, improve muscle metabolic function, and enhance exercise capacity/ performance. Conversely, current evidence suggests that NO3- supplementation does not augment the training response at simulated altitude. Few studies have evaluated the effects of NO3- at terrestrial altitude. Current evidence indicates potential improvements in endothelial function at terrestrial altitude following NO3- supplementation. No effects of NO3- supplementation have been observed on oxygen consumption or arterial oxygen saturation at terrestrial altitude, although further research is warranted. Limitations of the present body of literature are discussed, and directions for future research are provided

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