Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants

We present two new adaptive quadrature routines. Both routines differ from previously published algorithms in many aspects, most significantly in how they represent the integrand, how they treat non-numerical values of the integrand, how they deal with improper divergent integrals and how they estimate the integration error. The main focus of these improvements is to increase the reliability of the algorithms without significantly impacting their efficiency. Both algorithms are implemented in Matlab and tested using both the "families" suggested by Lyness and Kaganove and the battery test used by Gander and Gautschi and Kahaner. They are shown to be more reliable, albeit in some cases less efficient, than other commonly-used adaptive integrators.Comment: 32 pages, submitted to ACM Transactions on Mathematical Softwar

Point Contact Spectroscopy of Superconducting Gap Anisotropy in Nickel Borocarbide Compound LuNi2B2C

Point contacts are used to investigate the anisotropy of the superconducting energy gap in LuNi2B2C in the ab plane and along the c axis. It is shown that the experimental curves should be described assuming that the superconducting gap is non-uniformly distributed over the Fermi surface. The largest and the smallest gaps have been estimated by two-gap fitting models. It is found that the largest contribution to the point-contact conductivity in the c direction is made by a smaller gap and, in the ab plane by a larger gap. The deviation from the one-gap BCS model is pronounced in the temperature dependence of the gap in both directions. The temperature range, where the deviation occurs, is for the c direction approximately 1.5 times more than in the ab plane. The \Gamma parameter, allowing quantitatively estimate the gap anisotropy by one-gap fitting, in c direction is also about 1.5 times greater than in the ab plane. Since it is impossible to describe satisfactorily such gap distribution either by the one- or two-gap models, a continuous, dual-maxima model of gap distribution over the Fermi surface should be used to describe superconductivity in this material.Comment: 10 pages, 14 Figs, accepted in PR

Relaxation rates and collision integrals for Bose-Einstein condensates

Near equilibrium, the rate of relaxation to equilibrium and the transport properties of excitations (bogolons) in a dilute Bose-Einstein condensate (BEC) are determined by three collision integrals, $\mathcal{G}^{12}$, $\mathcal{G}^{22}$, and $\mathcal{G}^{31}$. All three collision integrals conserve momentum and energy during bogolon collisions, but only $\mathcal{G}^{22}$ conserves bogolon number. Previous works have considered the contribution of only two collision integrals, $\mathcal{G}^{22}$ and $\mathcal{G}^{12}$. In this work, we show that the third collision integral $\mathcal{G}^{31}$ makes a significant contribution to the bogolon number relaxation rate and needs to be retained when computing relaxation properties of the BEC. We provide values of relaxation rates in a form that can be applied to a variety of dilute Bose-Einstein condensates.Comment: 18 pages, 4 figures, accepted by Journal of Low Temperature Physics 7/201

Thermoluminescence of zircon: a kinetic model

The mineral zircon, ZrSiO4, belongs to a class of promising materials for geochronometry by means of thermoluminescence (TL) dating. The development of a reliable and reproducible method for TL dating with zircon requires detailed knowledge of the processes taking place during exposure to ionizing radiation, long-term storage, annealing at moderate temperatures and heating at a constant rate (TL measurements). To understand these processes one needs a kinetic model of TL. This paper is devoted to the construction of such amodel. The goal is to study the qualitative behaviour of the system and to determine the parameters and processes controlling TL phenomena of zircon. The model considers the following processes: (i) Filling of electron and hole traps at the excitation stage as a function of the dose rate and the dose for both (low dose rate) natural and (high dose rate) laboratory irradiation. (ii) Time dependence of TL fading in samples irradiated under laboratory conditions. (iii) Short time annealing at a given temperature. (iv) Heating of the irradiated sample to simulate TL experiments both after laboratory and natural irradiation. The input parameters of the model, such as the types and concentrations of the TL centres and the energy distributions of the hole and electron traps, were obtained by analysing the experimental data on fading of the TL-emission spectra of samples from different geological locations. Electron paramagnetic resonance (EPR) data were used to establish the nature of the TL centres. Glow curves and 3D TL emission spectra are simulated and compared with the experimental data on time-dependent TL fading. The saturation and annealing behaviour of filled trap concentrations has been considered in the framework of the proposed kinetic model and comparedwith the EPR data associated with the rare-earth ions Tb3+ and Dy3+, which play a crucial role as hole traps and recombination centres. Inaddition, the behaviour of some of the SiOmn− centres has been compared with simulation results.

Critical Casimir forces and adsorption profiles in the presence of a chemically structured substrate

Motivated by recent experiments with confined binary liquid mixtures near demixing, we study the universal critical properties of a system, which belongs to the Ising universality class, in the film geometry. We employ periodic boundary conditions in the two lateral directions and fixed boundary conditions on the two confining surfaces, such that one of them has a spatially homogeneous adsorption preference while the other one exhibits a laterally alternating adsorption preference, resembling locally a single chemical step. By means of Monte Carlo simulations of an improved Hamiltonian, so that the leading scaling corrections are suppressed, numerical integration, and finite-size scaling analysis we determine the critical Casimir force and its universal scaling function for various values of the aspect ratio of the film. In the limit of a vanishing aspect ratio the critical Casimir force of this system reduces to the mean value of the critical Casimir force for laterally homogeneous ++ and +- boundary conditions, corresponding to the surface spins on the two surfaces being fixed to equal and opposite values, respectively. We show that the universal scaling function of the critical Casimir force for small but finite aspect ratios displays a linear dependence on the aspect ratio which is solely due to the presence of the lateral inhomogeneity. We also analyze the order-parameter profiles at criticality and their universal scaling function which allows us to probe theoretical predictions and to compare with experimental data.Comment: revised version, section 5.2 expanded; 53 pages, 12 figures, iopart clas

Ancient numerical daemons of conceptual hydrological modeling 2. Impact of time stepping schemes on model analysis and prediction

Despite the widespread use of conceptual hydrological models in environmental research and operations, they remain frequently implemented using numerically unreliable methods. This paper considers the impact of the time stepping scheme on model analysis (sensitivity analysis, parameter optimization, and Markov chain Monte Carlo-based uncertainty estimation) and prediction. It builds on the companion paper (Clark and Kavetski, 2010), which focused on numerical accuracy, fidelity, and computational efficiency. Empirical and theoretical analysis of eight distinct time stepping schemes for six different hydrological models in 13 diverse basins demonstrates several critical conclusions. (1) Unreliable time stepping schemes, in particular, fixed-step explicit methods, suffer from troublesome numerical artifacts that severely deform the objective function of the model. These deformations are not rare isolated instances but can arise in any model structure, in any catchment, and under common hydroclimatic conditions. (2) Sensitivity analysis can be severely contaminated by numerical errors, often to the extent that it becomes dominated by the sensitivity of truncation errors rather than the model equations. (3) Robust time stepping schemes generally produce "better behaved" objective functions, free of spurious local optima, and with sufficient numerical continuity to permit parameter optimization using efficient quasi Newton methods. When implemented within a multistart framework, modern Newton-type optimizers are robust even when started far from the optima and provide valuable diagnostic insights not directly available from evolutionary global optimizers. (4) Unreliable time stepping schemes lead to inconsistent and biased inferences of the model parameters and internal states. (5) Even when interactions between hydrological parameters and numerical errors provide "the right result for the wrong reason" and the calibrated model performance appears adequate, unreliable time stepping schemes make the model unnecessarily fragile in predictive mode, undermining validation assessments and operational use. Erroneous or misleading conclusions of model analysis and prediction arising from numerical artifacts in hydrological models are intolerable, especially given that robust numerics are accepted as mainstream in other areas of science and engineering. We hope that the vivid empirical findings will encourage the conceptual hydrological community to close its Pandora's box of numerical problems, paving the way for more meaningful model application and interpretation. Copyright 2010 by the American Geophysical Union.Dmitri Kavetski and Martyn P. Clar

A Uniform Search for Secondary Eclipses of Hot Jupiters in Kepler Q2 Lightcurves

We present the results of searching the Kepler Q2 public dataset for the secondary eclipses of 76 hot Jupiter planet candidates from the list of 1,235 candidates published by Borucki et al. (2011). This search has been performed by modeling both the Kepler PDC light curves and new light curves produced via our own photometric pipeline. We derive new stellar and planetary parameters for each system with robust errors. We find 16 systems with 1-2 sigma, 14 systems with 2-3 sigma, and 6 systems with >3 sigma confidence level secondary eclipse detections in at least one light curve. We find that the majority of detected planet candidates emit more light than expected due to thermal blackbody emission in the optical Kepler bandpass, and present a trend of increasing excess emission with decreasing maximum effective planetary temperature. We explore modeling biases, significant planetary albedos, non-LTE or other thermal emission, significant internal energy generation, and exoplanet mis-identification as possible causes of both the excess emission and its correlation with expected planetary temperature. Although we find no single cause is able to explain all of the planet candidates, significant planetary albedos, with a general trend of increasing planetary albedos with decreasing atmospheric temperatures, is able to explain most of the systems. We estimate an 11% false positive rate in the current Kepler planet candidate sample of hot Jupiters. We also establish robust upper limits on the eclipse depth for all systems, and find that a significant fraction of these systems have very low albedos, significantly augmenting and extending the sample of albedo determinations to planets as cool as 1200 K. Finally, we note that continued observations with Kepler, and improved techniques for the removal of systematic noise in the Kepler data, are needed to better characterize these systems.Comment: 33 pages, 9 figures, 3 tables. Submitted to the Astronomical Journal 9/13/2011. Accepted 12/4/201

Segregation, mobility and encounters in Jerusalem: The role of public transport infrastructure in connecting the ‘divided city’

This paper assesses ways in which urban segregation is shaped and transformed by Jerusalem’s public transport network, enhancing mobility and potential group encounters. We suggest that segregation should be understood as an issue of mobility and co-presence in public space, rather than the static residential-based segregation that continues to be a central focus of debate in urban studies. We explore public transport infrastructures, considering how their implementation reflects the variety of ways that transport can have impact: segmenting populations, linking populations and/or creating spaces for interaction or conflict between the city’s Jewish Israeli and Arab Palestinian populations. Space syntax network analysis suggests that in the case of Jerusalem, access to public transport is multi-dimensional: as well as providing access to resources, it shapes opportunities for spatial mobility that may either overcome or reinforce area-based housing segregation. We discuss these opportunities in the light of Jerusalem’s on-going ethno-national division in an increasingly fractured urban reality