Formulation and performance of variational integrators for rotating bodies

Variational integrators are obtained for two mechanical systems whose configuration spaces are, respectively, the rotation group and the unit sphere. In the first case, an integration algorithm is presented for Euler’s equations of the free rigid body, following the ideas of Marsden et al. (Nonlinearity 12:1647–1662, 1999). In the second example, a variational time integrator is formulated for the rigid dumbbell. Both methods are formulated directly on their nonlinear configuration spaces, without using Lagrange multipliers. They are one-step, second order methods which show exact conservation of a discrete angular momentum which is identified in each case. Numerical examples illustrate their properties and compare them with existing integrators of the literature

Intentional weight loss in overweight and obese individuals and cognitive function: a systematic review and meta-analysis.

High adiposity in middle age is associated with higher dementia risk. The association between weight loss and cognitive function in older adults is still controversial. A meta-analysis was undertaken to estimate the effectiveness of intentional weight loss on cognitive function in overweight and obese adults. A structured strategy was used to search randomized and non-randomized studies reporting the effect of intentional and significant weight loss on cognitive function in overweight and obese subjects. Information on study design, age, nutritional status, weight-loss strategy, weight lost and cognitive testing was extracted. A random-effect meta-analysis was conducted to obtain summary effect estimates for memory and attention-executive domains. Twelve studies met inclusion criteria. Seven were randomized trials and the remaining five included a control group. A low-order significant effect was found for an improvement in cognitive performance with weight loss in memory (effect size 0.13, 95% CI 0.00-0.26, P=0.04) and attention/executive functioning (effect size 0.14, 95% CI 0.01-0.27, P<0.001). Studies were heterogeneous in study design, sample selection, weight-loss intervention and assessment of cognitive function. Weight loss appears to be associated with low-order improvements in executive/attention functioning and memory in obese but not in overweight individual

What drives interannual variation in tree ring oxygen isotopes in the Amazon?

Oxygen isotope ratios in tree rings (δ18OTR) from northern Bolivia record local precipitation δ18O and correlate strongly with Amazon basin-wide rainfall. While this is encouraging evidence that δ18OTR can be used for palaeoclimate reconstructions, it remains unclear whether variation in δ18OTR is truly driven by within-basin processes, thus recording Amazon climate directly, or if the isotope signal may already be imprinted on incoming vapour, perhaps reflecting a pan-tropical climate signal. We use atmospheric back-trajectories combined with satellite observations of precipitation, together with water vapour transport analysis to show that δ18OTR in Bolivia are indeed controlled by basin-intrinsic processes, with rainout over the basin the most important factor. Furthermore, interannual variation in basin-wide precipitation and atmospheric circulation are both shown to affect δ18OTR. These findings suggest δ18OTR can be reliably used to reconstruct Amazon precipitation, and have implications for the interpretation of other palaeoproxy records from the Amazon basin

A dynamical trichotomy for structured populations experiencing positive density-dependence in stochastic environments

Positive density-dependence occurs when individuals experience increased survivorship, growth, or reproduction with increased population densities. Mechanisms leading to these positive relationships include mate limitation, saturating predation risk, and cooperative breeding and foraging. Individuals within these populations may differ in age, size, or geographic location and thereby structure these populations. Here, I study structured population models accounting for positive density-dependence and environmental stochasticity i.e. random fluctuations in the demographic rates of the population. Under an accessibility assumption (roughly, stochastic fluctuations can lead to populations getting small and large), these models are shown to exhibit a dynamical trichotomy: (i) for all initial conditions, the population goes asymptotically extinct with probability one, (ii) for all positive initial conditions, the population persists and asymptotically exhibits unbounded growth, and (iii) for all positive initial conditions, there is a positive probability of asymptotic extinction and a complementary positive probability of unbounded growth. The main results are illustrated with applications to spatially structured populations with an Allee effect and age-structured populations experiencing mate limitation

Tackling Exascale Software Challenges in Molecular Dynamics Simulations with GROMACS

GROMACS is a widely used package for biomolecular simulation, and over the last two decades it has evolved from small-scale efficiency to advanced heterogeneous acceleration and multi-level parallelism targeting some of the largest supercomputers in the world. Here, we describe some of the ways we have been able to realize this through the use of parallelization on all levels, combined with a constant focus on absolute performance. Release 4.6 of GROMACS uses SIMD acceleration on a wide range of architectures, GPU offloading acceleration, and both OpenMP and MPI parallelism within and between nodes, respectively. The recent work on acceleration made it necessary to revisit the fundamental algorithms of molecular simulation, including the concept of neighborsearching, and we discuss the present and future challenges we see for exascale simulation - in particular a very fine-grained task parallelism. We also discuss the software management, code peer review and continuous integration testing required for a project of this complexity.Comment: EASC 2014 conference proceedin

On local linearization of control systems

We consider the problem of topological linearization of smooth (C infinity or real analytic) control systems, i.e. of their local equivalence to a linear controllable system via point-wise transformations on the state and the control (static feedback transformations) that are topological but not necessarily differentiable. We prove that local topological linearization implies local smooth linearization, at generic points. At arbitrary points, it implies local conjugation to a linear system via a homeomorphism that induces a smooth diffeomorphism on the state variables, and, except at "strongly" singular points, this homeomorphism can be chosen to be a smooth mapping (the inverse map needs not be smooth). Deciding whether the same is true at "strongly" singular points is tantamount to solve an intriguing open question in differential topology

Continuous, Semi-discrete, and Fully Discretized Navier-Stokes Equations

The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and temporal discretization. We analyse the semi-discrete equations -- a semi-explicit nonlinear DAE -- in terms of the strangeness index and quantify the numerical difficulties in the fully discrete schemes, that are induced by the strangeness of the system. By analyzing the Kronecker index of the difference-algebraic equations, that represent commonly and successfully used time stepping schemes for the Navier--Stokes equations, we show that those time-integration schemes factually remove the strangeness. The theoretical considerations are backed and illustrated by numerical examples.Comment: 28 pages, 2 figure, code available under DOI: 10.5281/zenodo.998909, https://doi.org/10.5281/zenodo.99890

Vaccination against Foot-and-mouth disease : do initial conditions affect its benefit?

When facing incursion of a major livestock infectious disease, the decision to implement a vaccination programme is made at the national level. To make this decision, governments must consider whether the benefits of vaccination are sufficient to outweigh potential additional costs, including further trade restrictions that may be imposed due to the implementation of vaccination. However, little consensus exists on the factors triggering its implementation on the field. This work explores the effect of several triggers in the implementation of a reactive vaccination-to-live policy when facing epidemics of foot-and-mouth disease. In particular, we tested whether changes in the location of the incursion and the delay of implementation would affect the epidemiological benefit of such a policy in the context of Scotland. To reach this goal, we used a spatial, premises-based model that has been extensively used to investigate the effectiveness of mitigation procedures in Great Britain. The results show that the decision to vaccinate, or not, is not straightforward and strongly depends on the underlying local structure of the population-at-risk. With regards to disease incursion preparedness, simply identifying areas of highest population density may not capture all complexities that may influence the spread of disease as well as the benefit of implementing vaccination. However, if a decision to vaccinate is made, we show that delaying its implementation in the field may markedly reduce its benefit. This work provides guidelines to support policy makers in their decision to implement, or not, a vaccination-to-live policy when facing epidemics of infectious livestock disease

An effective theory for jet propagation in dense QCD matter: jet broadening and medium-induced bremsstrahlung

Two effects, jet broadening and gluon bremsstrahlung induced by the propagation of a highly energetic quark in dense QCD matter, are reconsidered from effective theory point of view. We modify the standard Soft Collinear Effective Theory (SCET) Lagrangian to include Glauber modes, which are needed to implement the interactions between the medium and the collinear fields. We derive the Feynman rules for this Lagrangian and show that it is invariant under soft and collinear gauge transformations. We find that the newly constructed theory SCET$_{\rm G}$ recovers exactly the general result for the transverse momentum broadening of jets. In the limit where the radiated gluons are significantly less energetic than the parent quark, we obtain a jet energy-loss kernel identical to the one discussed in the reaction operator approach to parton propagation in matter. In the framework of SCET$_{\rm G}$ we present results for the fully-differential bremsstrahlung spectrum for both the incoherent and the Landau-Pomeranchunk-Migdal suppressed regimes beyond the soft-gluon approximation. Gauge invariance of the physics results is demonstrated explicitly by performing the calculations in both the light-cone and covariant $R_{\xi}$ gauges. We also show how the process-dependent medium-induced radiative corrections factorize from the jet production cross section on the example of the quark jets considered here.Comment: 52 pages, 15 pdf figures, as published in JHE

Electroweak Gauge-Boson Production at Small q_T: Infrared Safety from the Collinear Anomaly

Using methods from effective field theory, we develop a novel, systematic framework for the calculation of the cross sections for electroweak gauge-boson production at small and very small transverse momentum q_T, in which large logarithms of the scale ratio M_V/q_T are resummed to all orders. These cross sections receive logarithmically enhanced corrections from two sources: the running of the hard matching coefficient and the collinear factorization anomaly. The anomaly leads to the dynamical generation of a non-perturbative scale q_* ~ M_V e^{-const/\alpha_s(M_V)}, which protects the processes from receiving large long-distance hadronic contributions. Expanding the cross sections in either \alpha_s or q_T generates strongly divergent series, which must be resummed. As a by-product, we obtain an explicit non-perturbative expression for the intercept of the cross sections at q_T=0, including the normalization and first-order \alpha_s(q_*) correction. We perform a detailed numerical comparison of our predictions with the available data on the transverse-momentum distribution in Z-boson production at the Tevatron and LHC.Comment: 34 pages, 9 figure