ARE CROP YIELDS NORMALLY DISTRIBUTED?

This paper revisits the issue of crop yield distributions using improved model specifications, estimation and testing procedures that address the methodological concerns raised in recent literature that could have invalidated previous conclusions of yield non-normality. It shows beyond reasonable doubt that some crop yield distributions are non-normal, kurtotic and right or left skewed, depending on the circumstances. A procedure to jointly estimate non-normal farm- and aggregate-level yield distributions with similar means but different variances is illustrated, and the consequences of incorrectly assuming yield normality are explored.Yield non-normality, probability distribution function models, Corn Belt yields, West Texas dryland cotton yields, Crop Production/Industries,

Sputtering of Oxygen Ice by Low Energy Ions

Naturally occurring ices lie on both interstellar dust grains and on celestial objects, such as those in the outer solar system. These ices are continu- ously subjected to irradiation by ions from the solar wind and/or cosmic rays, which modify their surfaces. As a result, new molecular species may form which can be sputtered off into space or planetary atmospheres. We determined the experimental values of sputtering yields for irradiation of oxygen ice at 10 K by singly (He+, C+, N+, O+ and Ar+) and doubly (C2+, N2+ and O2+) charged ions with 4 keV kinetic energy. In these laboratory experiments, oxygen ice was deposited and irradiated by ions in an ultra high vacuum chamber at low temperature to simulate the environment of space. The number of molecules removed by sputtering was observed by measurement of the ice thickness using laser interferometry. Preliminary mass spectra were taken of sputtered species and of molecules formed in the ice by temperature programmed desorption (TPD). We find that the experimental sputtering yields increase approximately linearly with the projectile ion mass (or momentum squared) for all ions studied. No difference was found between the sputtering yield for singly and doubly charged ions of the same atom within the experimental uncertainty, as expected for a process dominated by momentum transfer. The experimental sputter yields are in good agreement with values calculated using a theoretical model except in the case of oxygen ions. Preliminary studies have shown molecular oxygen as the dominant species sputtered and TPD measurements indicate ozone formation.Comment: to be published in Surface Science (2015

Local dependence of ion temperature gradient on magnetic configuration, rotational shear and turbulent heat flux in MAST

Experimental data from the Mega Amp Spherical Tokamak (MAST) is used to show that the inverse gradient scale length of the ion temperature R/LTi (normalized to the major radius R) has its strongest local correlation with the rotational shear and the pitch angle of the magnetic field (or, equivalently, an inverse correlation with q/{\epsilon}, the safety factor/the inverse aspect ratio). Furthermore, R/LTi is found to be inversely correlated with the gyro-Bohm-normalized local turbulent heat flux estimated from the density fluctuation level measured using a 2D Beam Emission Spectroscopy (BES) diagnostic. These results can be explained in terms of the conjecture that the turbulent system adjusts to keep R/LTi close to a certain critical value (marginal for the excitation of turbulence) determined by local equilibrium parameters (although not necessarily by linear stability).Comment: 6 pages, 3 figures, submitted to PR

Transition to subcritical turbulence in a tokamak plasma

Tokamak turbulence, driven by the ion-temperature gradient and occurring in the presence of flow shear, is investigated by means of local, ion-scale, electrostatic gyrokinetic simulations (with both kinetic ions and electrons) of the conditions in the outer core of the Mega-Ampere Spherical Tokamak (MAST). A parameter scan in the local values of the ion-temperature gradient and flow shear is performed. It is demonstrated that the experimentally observed state is near the stability threshold and that this stability threshold is nonlinear: sheared turbulence is subcritical, i.e. the system is formally stable to small perturbations, but, given a large enough initial perturbation, it transitions to a turbulent state. A scenario for such a transition is proposed and supported by numerical results: close to threshold, the nonlinear saturated state and the associated anomalous heat transport are dominated by long-lived coherent structures, which drift across the domain, have finite amplitudes, but are not volume filling; as the system is taken away from the threshold into the more unstable regime, the number of these structures increases until they overlap and a more conventional chaotic state emerges. Whereas this appears to represent a new scenario for transition to turbulence in tokamak plasmas, it is reminiscent of the behaviour of other subcritically turbulent systems, e.g. pipe flows and Keplerian magnetorotational accretion flows.Comment: 16 pages, 5 figures, accepted to Journal of Plasma Physic

Resonance bifurcations from robust homoclinic cycles

We present two calculations for a class of robust homoclinic cycles with symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic stability given by Krupa and Melbourne are not optimal. Firstly, we compute optimal conditions for asymptotic stability using transition matrix techniques which make explicit use of the geometry of the group action. Secondly, through an explicit computation of the global parts of the Poincare map near the cycle we show that, generically, the resonance bifurcations from the cycles are supercritical: a unique branch of asymptotically stable period orbits emerges from the resonance bifurcation and exists for coefficient values where the cycle has lost stability. This calculation is the first to explicitly compute the criticality of a resonance bifurcation, and answers a conjecture of Field and Swift in a particular limiting case. Moreover, we are able to obtain an asymptotically-correct analytic expression for the period of the bifurcating orbit, with no adjustable parameters, which has not proved possible previously. We show that the asymptotic analysis compares very favourably with numerical results.Comment: 24 pages, 3 figures, submitted to Nonlinearit

Fast and accurate prediction of numerical relativity waveforms from binary black hole coalescences using surrogate models

Simulating a binary black hole (BBH) coalescence by solving Einstein's equations is computationally expensive, requiring days to months of supercomputing time. Using reduced order modeling techniques, we construct an accurate surrogate model, which is evaluated in a millisecond to a second, for numerical relativity (NR) waveforms from non-spinning BBH coalescences with mass ratios in $[1, 10]$ and durations corresponding to about $15$ orbits before merger. We assess the model's uncertainty and show that our modeling strategy predicts NR waveforms {\em not} used for the surrogate's training with errors nearly as small as the numerical error of the NR code. Our model includes all spherical-harmonic ${}_{-2}Y_{\ell m}$ waveform modes resolved by the NR code up to $\ell=8.$ We compare our surrogate model to Effective One Body waveforms from $50$-$300 M_\odot$ for advanced LIGO detectors and find that the surrogate is always more faithful (by at least an order of magnitude in most cases).Comment: Updated to published version, which includes a section comparing the surrogate and effective-one-body models. The surrogate is publicly available for download at http://www.black-holes.org/surrogates/ . 6 pages, 6 figure

Edgeworth expansions for slow-fast systems with finite time scale separation

We derive Edgeworth expansions that describe corrections to the Gaussian limiting behaviour of slow-fast systems. The Edgeworth expansion is achieved using a semi-group formalism for the transfer operator, where a Duhamel-Dyson series is used to asymptotically determine the corrections at any desired order of the time scale parameter ε. The corrections involve integrals over higher-order auto-correlation functions. We develop a diagrammatic representation of the series to control the combinatorial wealth of the asymptotic expansion in ε and provide explicit expressions for the first two orders. At a formal level, the expressions derived are valid in the case when the fast dynamics is stochastic as well as when the fast dynamics is entirely deterministic. We corroborate our analytical results with numerical simulations and show that our method provides an improvement on the classical homogenization limit which is restricted to the limit of infinite time scale separation

A Surrogate Model of Gravitational Waveforms from Numerical Relativity Simulations of Precessing Binary Black Hole Mergers

We present the first surrogate model for gravitational waveforms from the coalescence of precessing binary black holes. We call this surrogate model NRSur4d2s. Our methodology significantly extends recently introduced reduced-order and surrogate modeling techniques, and is capable of directly modeling numerical relativity waveforms without introducing phenomenological assumptions or approximations to general relativity. Motivated by GW150914, LIGO's first detection of gravitational waves from merging black holes, the model is built from a set of $276$ numerical relativity (NR) simulations with mass ratios $q \leq 2$, dimensionless spin magnitudes up to $0.8$, and the restriction that the initial spin of the smaller black hole lies along the axis of orbital angular momentum. It produces waveforms which begin $\sim 30$ gravitational wave cycles before merger and continue through ringdown, and which contain the effects of precession as well as all $\ell \in \{2, 3\}$ spin-weighted spherical-harmonic modes. We perform cross-validation studies to compare the model to NR waveforms \emph{not} used to build the model, and find a better agreement within the parameter range of the model than other, state-of-the-art precessing waveform models, with typical mismatches of $10^{-3}$. We also construct a frequency domain surrogate model (called NRSur4d2s_FDROM) which can be evaluated in $50\, \mathrm{ms}$ and is suitable for performing parameter estimation studies on gravitational wave detections similar to GW150914.Comment: 34 pages, 26 figure

Measuring public perceptions of sex offenders: reimagining the Community Attitudes Toward Sex Offenders (CATSO) scale

The Community Attitudes Toward Sex Offenders (CATSO) scale is an 18-item self-report questionnaire designed to measure respondents’ attitudes toward sex offenders. Its original factor structure has been questioned by a number of previous studies, and so this paper sought to reimagine the scale as an outcome measure, as opposed to a scale of attitudes. A face validity analysis produced a provisional three-factor structure underlying the CATSO: ‘punitiveness,’ ‘stereotype endorsement,’ and ‘risk perception.’ A sample of 400 British members of the public completed a modified version of the CATSO, the Attitudes Toward Sex Offenders scale, the General Punitiveness Scale, and the Rational-Experiential Inventory. A three-factor structure of a 22-item modified CATSO was supported using half of the sample, with factors being labeled ‘sentencing and management,’ ‘stereotype endorsement,’ and ‘risk perception.’ Confirmatory factor analysis on data from the other half of the sample endorsed the three-factor structure; however, two items were removed in order to improve ratings of model fit. This new 20-item ‘Perceptions of Sex Offenders scale’ has practical utility beyond the measurement of attitudes, and suggestions for its future use are provided

Ion-scale turbulence in MAST: anomalous transport, subcritical transitions, and comparison to BES measurements

We investigate the effect of varying the ion temperature gradient (ITG) and toroidal equilibrium scale sheared flow on ion-scale turbulence in the outer core of MAST by means of local gyrokinetic simulations. We show that nonlinear simulations reproduce the experimental ion heat flux and that the experimentally measured values of the ITG and the flow shear lie close to the turbulence threshold. We demonstrate that the system is subcritical in the presence of flow shear, i.e., the system is formally stable to small perturbations, but transitions to a turbulent state given a large enough initial perturbation. We propose that the transition to subcritical turbulence occurs via an intermediate state dominated by low number of coherent long-lived structures, close to threshold, which increase in number as the system is taken away from the threshold into the more strongly turbulent regime, until they fill the domain and a more conventional turbulence emerges. We show that the properties of turbulence are effectively functions of the distance to threshold, as quantified by the ion heat flux. We make quantitative comparisons of correlation lengths, times, and amplitudes between our simulations and experimental measurements using the MAST BES diagnostic. We find reasonable agreement of the correlation properties, most notably of the correlation time, for which significant discrepancies were found in previous numerical studies of MAST turbulence.Comment: 67 pages, 37 figures. Submitted to PPC