A uniformly valid far field asymptotic expansion of the green function for two-dimensional propagation above a homogeneous impedance plane

A generalized asymptotic expansion in the far field for the problem of cylindrical wave reflection at a homogeneous impedance plane is derived. The expansion is shown to be uniformly valid over all angles of incidence and values of surface impedance, including the limiting cases of zero and infinite impedance. The technique used is a rigorous application of the modified steepest descent method of Ot

The correlation of ULF waves and auroral intensity before, during and after substorm expansion phase onset

We present case studies of the evolution of magnetic wave amplitudes and auroral intensity through the late growth phase and the expansion phase of the substorm cycle. We present strong evidence that substorm-related auroral enhancements are clearly and demonstrably linked to ULF wave amplitudes observed at the same location. In most cases, we find that the highest correlations are observed when the magnetometer time series is advanced in time, indicating that the ULF wave amplitudes start to grow before measured auroral intensities, though interestingly this is not always the case. Further we discuss the four possible reasons that may be able to explain both the timing and the high correlations between these two phenomena, including: a simple coincidence, an artifact of instrumental effects, the response of the ionosphere to magnetic waves and auroral particle precipitation, and finally that ULF waves and auroral particle precipitation are physically linked. We discount coincidence and instrumental effects since in the studies presented here they are unlikely or in general will contribute negligible effects, and we find that the ionospheric response to waves and precipitation can explain some, but not all of the results contained within this paper. Specifically, ionospheric response to substorm waves and auroral precipitation cannot explain that the result that previous studies have shown, that onset of ULF wave activity and the onset of auroral particle precipitation occur at the same time and in the same location. This leaves the possibility that ULF waves and auroral particles are physically linked.

Comprehensive ground-based and in situ observations of substorm expansion phase onset

In this paper, we present comprehensive ground-based and space-based in situ geosynchronous observations of a substorm expansion phase onset on 1 October 2005. The Double Star TC-2 and GOES-12 spacecraft were both located within the substorm current wedge during the substorm expansion phase onset, which occurred over the Canadian sector. We find that an onset of ULF waves in space was observed after onset on the ground by extending the AWESOME timing algorithm into space. Furthermore, a population of low-energy field-aligned electrons was detected by the TC-2 PEACE instrument contemporaneous with the ULF waves in space. These electrons appear to be associated with an enhancement of field-aligned Poynting flux into the ionosphere which is large enough to power visible auroral displays. The observations are most consistent with a near-Earth initiation of substorm expansion phase onset, such as the Near-Geosynchronous Onset (NGO) substorm scenario. A lack of data from further downtail, however, means other mechanisms cannot be ruled out.

Wavelet-based ULF wave diagnosis of substorm expansion phase onset

Using a discrete wavelet transform with a Meyer wavelet basis, we present a new quantitative algorithm for determining the onset time of Pi1 and Pi2 ULF waves in the nightside ionosphere with ∼20- to 40-s resolution at substorm expansion phase onset. We validate the algorithm by comparing both the ULF wave onset time and location to the optical onset determined by the Imager for Magnetopause-to-Aurora Global Exploration (IMAGE)–Far Ultraviolet Imager (FUV) instrument. In each of the six events analyzed, five substorm onsets and one pseudobreakup, the ULF onset is observed prior to the global optical onset observed by IMAGE at a station closely conjugate to the optical onset. The observed ULF onset times expand both latitudinally and longitudinally away from an epicenter of ULF wave power in the ionosphere. We further discuss the utility of the algorithm for diagnosing pseudobreakups and the relationship of the ULF onset epicenter to the meridians of elements of the substorm current wedge. The importance of the technique for establishing the causal sequence of events at substorm onset, especially in support of the multisatellite Time History of Events and Macroscale Interactions During Substorms (THEMIS) mission, is also described.

Timing and localization of ionospheric signatures associated with substorm expansion phase onset

In this paper, we present case studies of the optical and magnetic signatures of the characteristics of the first minute of substorm expansion phase onset observed in the ionosphere. We find that for two isolated substorms, the onset of magnetic pulsations in the 24–96 s period wavelet band are colocated in time and space with the formation and development of small-scale optical undulations along the most equatorward preexisting auroral arc prior to auroral breakup. These undulations undergo an inverse spatial cascade into vortices prior to the release of the westward traveling surge. We also present a case study of a multiple activation substorm, whereby discrete onsets of ULF wave power above a predetermined quiet time threshold are shown to be associated with specific optical intensifications and brightenings. Moreover, in the multiple activation substorm event, we show that neither the formation of the small-scale undulations nor the formation of similar structures along a north–south aligned arc is sufficient to produce auroral breakup associated with expansion phase onset. It is only ∼10 min after these two disparate activation regions initiate that auroral breakup and the subsequent formation of a westward traveling surge occur. We discuss the implications of these results in terms of the triggering mechanisms likely to be occurring during these specific events.

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

Effects of target expansion on selection performance in older computer users

Point and click interactions using a mouse are an integral part of computer use for current desktop systems. Compared with younger users though, older adults experience greater difficulties performing cursor positioning tasks, and this can present limitations to using a computer easily and effectively. Target expansion is a technique for improving pointing performance, where the target dynamically grows as the cursor approaches. This has the advantage that targets conserve screen real estate in their unexpanded state, yet can still provide the benefits of a larger area to click on. This paper presents two studies of target expansion with older and younger participants, involving multidirectional point-select tasks with a computer mouse. Study 1 compares static versus expanding targets, and Study 2 compares static targets with three alternative techniques for expansion. Results show that expansion can improve times by up to 14%, and reduce error rates by up to 50%. Additionally, expanding targets are beneficial even when the expansion happens late in the movement, i.e. after the cursor has reached the expanded target area or even after it has reached the original target area. Participants’ subjective feedback on the target expansion are generally favorable, and this lends further support for the technique.

Late Pleistocene climate change and the global expansion of anatomically modern humans

The extent to which past climate change has dictated the pattern and timing of the out-of-Africa expansion by anatomically modern humans is currently unclear [Stewart JR, Stringer CB (2012) Science 335:1317–1321]. In particular, the incompleteness of the fossil record makes it difficult to quantify the effect of climate. Here, we take a different approach to this problem; rather than relying on the appearance of fossils or archaeological evidence to determine arrival times in different parts of the world, we use patterns of genetic variation in modern human populations to determine the plausibility of past demographic parameters. We develop a spatially explicit model of the expansion of anatomically modern humans and use climate reconstructions over the past 120 ky based on the Hadley Centre global climate model HadCM3 to quantify the possible effects of climate on human demography. The combinations of demographic parameters compatible with the current genetic makeup of worldwide populations indicate a clear effect of climate on past population densities. Our estimates of this effect, based on population genetics, capture the observed relationship between current climate and population density in modern hunter–gatherers worldwide, providing supporting evidence for the realism of our approach. Furthermore, although we did not use any archaeological and anthropological data to inform the model, the arrival times in different continents predicted by our model are also broadly consistent with the fossil and archaeological records. Our framework provides the most accurate spatiotemporal reconstruction of human demographic history available at present and will allow for a greater integration of genetic and archaeological evidence.

The impact of added cultural distance and cultural diversity on international expansion patterns: a Penrosian perspective

International strategy research has identified a variety of multinational enterprise (MNE) expansion patterns. Some MNEs appear to expand internationally at a stable rate, whereas others expand rapidly in one period and then tend to experience slower growth. The latter pattern suggests the occurrence of the Penrose effect. We identified two determinants of these diverging patterns. First, we propose that high levels of added cultural distance (reflecting expansion into new local contexts) during one period, may negatively affect further international expansion because of dynamic adjustment costs. Second, we suggest that managing a network of subsidiaries operating in a set of local contexts with high cultural diversity, increases environmental and internal governance complexity. Extant cultural diversity of the local contexts where the MNE is active in a first period may therefore discourage adding further cultural distance. We test the hypothesized relationships using a panel of 91 German companies.

A self-similar expansion model for use in solar wind transient propogation studies

Since the advent of wide-angle imaging of the inner heliosphere, a plethora of techniques have been developed to investigate the three-dimensional structure and kinematics of solar wind transients, such as coronal mass ejections, from their signatures in single- and multi-spacecraft imaging observations. These techniques, which range from the highly complex and computationally intensive to methods based on simple curve fitting, all have their inherent advantages and limitations. In the analysis of single-spacecraft imaging observations, much use has been made of the fixed φ fitting (FPF) and harmonic mean fitting (HMF) techniques, in which the solar wind transient is considered to be a radially propagating point source (fixed φ, FP, model) and a radially expanding circle anchored at Sun centre (harmonic mean, HM, model), respectively. Initially, we compare the radial speeds and propagation directions derived from application of the FPF and HMF techniques to a large set of STEREO/Heliospheric Imager (HI) observations. As the geometries on which these two techniques are founded constitute extreme descriptions of solar wind transients in terms of their extent along the line of sight, we describe a single-spacecraft fitting technique based on a more generalized model for which the FP and HM geometries form the limiting cases. In addition to providing estimates of a transient’s speed and propagation direction, the self-similar expansion fitting (SSEF) technique provides, in theory, the capability to estimate the transient’s angular extent in the plane orthogonal to the field of view. Using the HI observations, and also by performing a Monte Carlo simulation, we assess the potential of the SSEF technique.

Local and average structure in zinc cyanide: towards an understanding of the atomistic origin of negative thermal expansion

Neutron diffraction at 11.4 and 295 K and solid-state 67Zn NMR are used to determine both the local and average structures in the disordered, negative thermal expansion (NTE) material, Zn(CN)2. Solid-state NMR not only confirms that there is head-to-tail disorder of the C≡N groups present in the solid, but yields information about the relative abundances of the different Zn(CN)4-n(NC)n tetrahedral species, which do not follow a simple binomial distribution. The Zn(CN)4 and Zn(NC)4 species occur with much lower probabilities than are predicted by binomial theory, supporting the conclusion that they are of higher energy than the other local arrangements. The lowest energy arrangement is Zn(CN)2(NC)2. The use of total neutron diffraction at 11.4 K, with analysis of both the Bragg diffraction and the derived total correlation function, yields the first experimental determination of the individual Zn−N and Zn−C bond lengths as 1.969(2) and 2.030(2) Å, respectively. The very small difference in bond lengths, of ~0.06 Å, means that it is impossible to obtain these bond lengths using Bragg diffraction in isolation. Total neutron diffraction also provides information on both the average and local atomic displacements responsible for NTE in Zn(CN)2. The principal motions giving rise to NTE are shown to be those in which the carbon and nitrogen atoms within individual Zn−C≡N−Zn linkages are displaced to the same side of the Zn···Zn axis. Displacements of the carbon and nitrogen atoms to opposite sides of the Zn···Zn axis, suggested previously in X-ray studies as being responsible for NTE behavior, in fact make negligible contribution at temperatures up to 295 K.

The significance of occupancy steadiness in residential consumer response to Time of Use pricing: Evidence from a stochastic adjustment model

The recent roll-out of smart metering technologies in several developed countries has intensified research on the impacts of Time-of-Use (TOU) pricing on consumption. This paper analyses a TOU dataset from the Province of Trento in Northern Italy using a stochastic adjustment model. Findings highlight the non-steadiness of the relationship between consumption and TOU price. Weather and active occupancy can partly explain future consumption in relation to price.

The stochastic component in choice and regression to the mean

In this article, we illustrate experimentally an important consequence of the stochastic component in choice behaviour which has not been acknowledged so far. Namely, its potential to produce ‘regression to the mean’ (RTM) effects. We employ a novel approach to individual choice under risk, based on repeated multiple-lottery choices (i.e. choices among many lotteries), to show how the high degree of stochastic variability present in individual decisions can distort crucially certain results through RTM effects. We demonstrate the point in the context of a social comparison experiment.

Automated determination of auroral breakup during the substorm expansion phase using all sky imager data

This technique paper describes a novel method for quantitatively and routinely identifying auroral breakup following substorm onset using the Time History of Events and Macroscale Interactions During Substorms (THEMIS) all-sky imagers (ASIs). Substorm onset is characterised by a brightening of the aurora that is followed by auroral poleward expansion and auroral breakup. This breakup can be identified by a sharp increase in the auroral intensity i(t) and the time derivative of auroral intensity i'(t). Utilising both i(t) and i'(t) we have developed an algorithm for identifying the time interval and spatial location of auroral breakup during the substorm expansion phase within the field of view of ASI data based solely on quantifiable characteristics of the optical auroral emissions. We compare the time interval determined by the algorithm to independently identified auroral onset times from three previously published studies. In each case the time interval determined by the algorithm is within error of the onset independently identified by the prior studies. We further show the utility of the algorithm by comparing the breakup intervals determined using the automated algorithm to an independent list of substorm onset times. We demonstrate that up to 50% of the breakup intervals characterised by the algorithm are within the uncertainty of the times identified in the independent list. The quantitative description and routine identification of an interval of auroral brightening during the substorm expansion phase provides a foundation for unbiased statistical analysis of the aurora to probe the physics of the auroral substorm as a new scientific tool for aiding the identification of the processes leading to auroral substorm onset.