On the quasi-Monte Carlo quadrature with Halton points for elliptic PDEs with log-normal diffusion

This article is dedicated to the computation of the moments of the solution to elliptic partial differential equations with random, log-normally distributed diffusion coefficients by the quasi-Monte Carlo method. Our main result is that the convergence rate of the quasi-Monte Carlo method based on the Halton sequence for the moment computation depends only linearly on the dimensionality of the stochastic input parameters. Especially, we attain this rather mild dependence on the stochastic dimensionality without any randomization of the quasi-Monte Carlo method under consideration. For the proof of the main result, we require related regularity estimates for the solution and its powers. These estimates are also provided here. Numerical experiments are given to validate the theoretical findings. This article is dedicated to the computation of the moments of the solution to elliptic partial differential equations with random, log-normally distributed diffusion coefficients by the quasi-Monte Carlo method. Our main result is that the convergence rate of the quasi-Monte Carlo method based on the Halton sequence for the moment computation depends only linearly on the dimensionality of the stochastic input parameters. Especially, we attain this rather mild dependence on the stochastic dimensionality without any randomization of the quasi-Monte Carlo method under consideration. For the proof of the main result, we require related regularity estimates for the solution and its powers. These estimates are also provided here. Numerical experiments are given to validate the theoretical findings

Multilevel Accelerated Quadrature for PDEs with Log-Normally Distributed Diffusion Coefficient

This article is dedicated to multilevel quadrature methods for the rapid solution of stochastic partial differential equations with a log-normally distributed diffusion coefficient. The key idea of such approaches is a sparse-grid approximation of the occurring product space between the stochastic and the spatial variable. We develop the mathematical theory and present error estimates for the computation of the solution's moments with focus on the mean and the variance. Especially, the present framework covers the multilevel Monte Carlo method and the multilevel quasi-Monte Carlo method as special cases. The theoretical findings are supplemented by numerical experiments. This article is dedicated to multilevel quadrature methods forthe rapid solution of stochastic partial differential equationswith a log-normally distributed diffusion coefficient. The key ideaof such approaches is a sparse-grid approximation of the occurring product space between the stochastic and the spatial variable. We develop the mathematical theory and present error estimates for the computation of the solution's moments with focus on the mean and the variance. Especially, the present framework covers the multilevel Monte Carlo method and the multilevel quasi-Monte Carlo method as special cases. The theoretical findings are supplemented by numerical experiments

Towards autonomous decision-making: A probabilistic model for learning multi-user preferences

Information systems have revolutionized the provisioning of decision-relevant information, and decision support tools have improved human decisions in many domains. Autonomous decision- making, on the other hand, remains hampered by systems’ inability to faithfully capture human preferences. We present a computational preference model that learns unobtrusively from lim- ited data by pooling observations across like-minded users. Our model quantifies the certainty of its own predictions as input to autonomous decision-making tasks, and it infers probabilistic segments based on user choices in the process. We evaluate our model on real-world preference data collected on a commercial crowdsourcing platform, and we find that it outperforms both individual and population-level estimates in terms of predictive accuracy and the informative- ness of its certainty estimates. Our work takes an important step toward systems that act autonomously on their users’ behalf

Analysis of the domain mapping method for elliptic diffusion problems on random domains

In this article, we provide a rigorous analysis of the solution to elliptic diffusion problems on random domains. In particular, based on the decay of the Karhunen-Lo`eve expansion of the domain perturbation field, we establish decay rates for the derivatives of the random solution that are independent of the stochastic dimension. For the implementation of a related approximation scheme, like quasi-Monte Carlo quadrature, stochastic collocation, etc., we propose parametric finite elements to compute the solution of the diffusion problem on each individual realization of the domain generated by the perturbation field. This simplifies the implementation and yields a non-intrusive approach. Having this machinery at hand, we can easily transfer it to stochastic interface problems. The theoretical findings are complemented by numerical examples for both, stochastic interface problems and boundary value problems on random domains. In this article, we provide a rigorous analysis of the solution to elliptic diffusion problems on random domains. In particular, based on the decay of the Karhunen-Loeve expansion of the domain perturbation field, we establish decay rates for the derivativesof the random solution that are independent of the stochastic dimension. For the implementation of a related approximation scheme, like quasi-Monte Carlo quadrature, stochastic collocation, etc., we propose parametric finite elements to compute the solution of the diffusion problem on each individual realization of the domain generated by the perturbation field. This simplifies the implementation and yields a non-intrusive approach. Having this machinery at hand, we can easily transfer it to stochastic interface problems. The theoretical findings are complemented by numerical examples for both, stochastic interface problems and boundary value problems on random domains

On Endogenous Fissility of Argillites within Carbonous Deposits Of Donbass

Based on direct numerical simulations of forced turbulence, shear turbulence, decaying turbulence, a turbulent channel flow as well as a Kolmogorov flow with Taylor-based Reynolds numbers Reλ between 69 and 295, the normalized probability density function of the length distribution P(l) of dissipation elements, the conditional mean scalar difference Δkl at the extreme points as well as the scaling of the two-point velocity difference along gradient trajectories Δun are studied. Using the field of the instantaneous turbulent kinetic energy k as a scalar, we find good agreement between the model equation for P(l) as proposed by Wang and Peters (2008 J. Fluid Mech. 608 113–38) and the results obtained in the different direct numerical simulation cases. This confirms the independence of the model solution from both the Reynolds number and the type of turbulent flow, so that it can be considered universally valid. In addition, we show a 2/3 scaling for the mean conditional scalar difference. In the second part of the paper, we examine the scaling of the conditional two-point velocity difference along gradient trajectories. In particular, we compare the linear s/τ scaling, where τ denotes an integral time scale and s the separation arclength along a gradient trajectory in the inertial range as derived by Wang (2009 Phys. Rev. E 79 046325) with the sa∞ scaling, where a∞ denotes the asymptotic value of the conditional mean strain rate of large dissipation elements

JOKARUS - Design of a compact optical iodine frequency reference for a sounding rocket mission

We present the design of a compact absolute optical frequency reference for space applications based on hyperfine transitions in molecular iodine with a targeted fractional frequency instability of better than $3\cdot 10^{-14}$. It is based on a micro-integrated extended cavity diode laser with integrated optical amplifier, fiber pigtailed second harmonic generation wave-guide modules, and a quasi-monolithic spectroscopy setup with operating electronics. The instrument described here is scheduled for launch end of 2017 aboard the TEXUS 54 sounding rocket as an important qualification step towards space application of iodine frequency references and related technologies. The payload will operate autonomously and its optical frequency will be compared to an optical frequency comb during its space flight

Towards a rheological classification of flow induced crystallization experiments of polymer melts

Departing from molecular based rheology and rubber theory, four different flow regimes are identified associated to (1) the equilibrium configuration of the chains, (2) orientation of the contour path, (3) stretching of the contour path, and (4) rotational isomerization and a deviation from the Gaussian configuration of the polymer chain under strong stretching conditions. The influence of the ordering of the polymer chains on the enhanced point nucleation, from which spherulites grow, and on fibrous nucleation, from which the shish-kebab structure develops, is discussed in terms of kinetic and thermodynamic processes. The transitions between the different flow regimes, and the associated physical processes governing the flow induced crystallization process, are defined by Deborah numbers based on the reptation and stretching time of the chain, respectively, as well as a critical chain stretch. An evaluation of flow induced crystallization experiments reported in the literature performed in shear, uniaxial and planar elongational flows quantitatively illustrates that the transition from an enhanced nucleation rate of spherulites towards the development of the shish-kebab structure correlates with the transition from the orientation of the chain segments to the rotational isomerization of the high molecular weight chains in the melt. For one particular case this correlation is quantified by coupling the wide angle X-ray diffraction and birefringence measurements of the crystallization process to numerical simulations of the chain stretch of the high molecular weight chains using the extended Pom-Pom model in a cross-slot flo

Root traits explain different foraging strategies between resprouting life histories

11 páginas, 5 figuras, 2 tablas.Drought and fire are prevalent disturbances in Mediterranean ecosystems. Plant species able to regrow after severe disturbances (i. e. resprouter life history) have higher allocation to roots and higher water potential during the dry season than coexisting non-resprouting species. However, seedlings of non-resprouters have a higher survival rate after summer drought. We predict that, to counteract their shallow-rooting systems and to maximize seedling survival, non-resprouters have root traits that confer higher efficiency in soil resource acquisition than resprouters. We tested this prediction in seedlings of less than 1.5 months old. We select 13 coexisting woody species (including both resprouters and non-resprouters), grew them in a common garden and measured the following root traits: length, surface, average diameter, root tissue density (RTD), specific root length (SRL), surface:volume ratio (SVR), specific tip density (STD), tip distribution in depth, internal links ratio (ILR), and degree of branching. These root traits were compared between the two resprouting life histories using both standard cross-species and phylogenetic-informed analysis. Non-resprouters showed higher SRL and longer, thinner and more branched laterals, especially in the upper soil layers. The external links (i. e. the most absorptive root region) were also more abundant, longer, thinner and with higher SVR for non-resprouters. The results were supported by the phylogenetic-informed analysis for the root traits most strongly related to soil resource acquisition (SRL, SVR and branching pattern). The seedling root structure of non-resprouters species allows them to more efficiently explore the upper soil layer, whereas seedling roots of resprouters will permit both carbon storage and deep soil penetration.We thank all the volunteers for their help in the common garden and laboratory tasks, especially H. Simo˜es, J. Bandeira, C. Pérez-Cervelló, S. Ribeiro and B. Moreira. The Banc de Llavors Forestals of Generalitat Valenciana provided the installations for the common garden experiment. This work has been financed by the Spanish projects SINREG (REN2003-07198-C02-02/GLO), PERSIST (CGL2006-07126/BOS), and GRACCIE (CONSOLIDER– Ingenio 2010 program; CSD200-00067). CEAM is supported by the Generalitat Valencia and Bancaixa; CIDE is supported by the Generalitat Valencia and the University of Valencia.Peer reviewe

"Getting Switzerland to move”: E valuation of a new "Sport for All” programme

Summary: Objectives: Even though sports participation in Switzerland appears to be quite elevated, recent research suggests that only about a third of the population are doing enough sports from a health perspective. Methods: Against this background several Swiss health insurance companies together with the Swiss Olympic Association have recently developed a novel approach to get people to start physical exercise: Under the label of > sport clubs offer training and information courses aimed at motivating and helping previously inactive people to take on regular exercise. Results: The paper presents results from an interdisciplinary evaluation of the first three years of the > campaign. Starting from an overview of the basic idea and features of the campaign it asks whether > has reached its self-declared goal of "getting Switzerland moving”. Available evidence on the social background of participants and their further activities shows that by systematically avoiding any reference to conventional notions of sport and by stressing the health and fun aspect instead, > has indeed managed to mobilise an important group with underaverage levels of activity (particularly middle-aged women). In addition, on average the level of physical exercise of participants appears to have increased. Yet, the number of participants is below the original target values and, contrary to the campaign's initial goal, participants are reluctant to leave the programme after one course to take up an independent activity or to join a club. Conclusions: The paper explores the achievements and problems of the campaign so far and offers an explanation of recent problems which can also serve as a basis for the implementation of similar programmes in other countrie