Journal Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

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Martijn J Schuemie, Patrick B Ryan, George Hripcsak, David Madigan, Marc A Suchard
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 376; doi:10.1098/rsta.2017.0356

Abstract:Concerns over reproducibility in science extend to research using existing healthcare data; many observational studies investigating the same topic produce conflicting results, even when using the same data. To address this problem, we propose a paradigm shift. The current paradigm centres on generating one estimate at a time using a unique study design with unknown reliability and publishing (or not) one estimate at a time. The new paradigm advocates for high-throughput observational studies using consistent and standardized methods, allowing evaluation, calibration and unbiased dissemination to generate a more reliable and complete evidence base. We demonstrate this new paradigm by comparing all depression treatments for a set of outcomes, producing 17 718 hazard ratios, each using methodology on par with current best practice. We furthermore include control hypotheses to evaluate and calibrate our evidence generation process. Results show good transitivity and consistency between databases, and agree with four out of the five findings from clinical trials. The distribution of effect size estimates reported in the literature reveals an absence of small or null effects, with a sharp cut-off at p = 0.05. No such phenomena were observed in our results, suggesting more complete and more reliable evidence.This article is part of a discussion meeting issue 'The growing ubiquity of algorithms in society: implications, impacts and innovations'.
Olga Trichtchenko, Emilian I. Părău, Jean-Marc Vanden-Broeck, Paul Milewski
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 376; doi:10.1098/rsta.2017.0345

Abstract:The focus of this work is on three-dimensional nonlinear flexural–gravity waves, propagating at the interface between a fluid and an ice sheet. The ice sheet is modelled using the special Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypothesis, presented in (Plotnikov & Toland. 2011 Phil. Trans. R. Soc. A 369, 2942–2956 (doi:10.1098/rsta.2011.0104)). The fluid is assumed inviscid and incompressible, and the flow irrotational. A numerical method based on boundary integral equation techniques is used to compute solitary waves and forced waves to Euler's equations.
F. T. Smith
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 376; doi:10.1098/rsta.2017.0348

Abstract:Slowly varying shear flow is considered over one or more flexible three-dimensional patches in a surface inside a boundary layer. At certain shear values, resonances emerge in which the effects on flow and patch shape are enlarged by an order of magnitude. Fast evolution then occurs: this leads to fully nonlinear unsteady interaction, after some delay, combining with finite-time break-ups to form a distinct path into transition.
Andrew F. Roberts, Elizabeth C. Hunke, Richard Allard, David A. Bailey, Anthony P. Craig, Jean-François Lemieux, Matthew D. Turner
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 376; doi:10.1098/rsta.2017.0344

Abstract:A new collaborative organization for sea-ice model development, the CICE Consortium, has devised quality control procedures to maintain the integrity of its numerical codes' physical representations, enabling broad participation from the scientific community in the Consortium's open software development environment. Using output from five coupled and uncoupled configurations of the Los Alamos Sea Ice Model, CICE, we formulate quality control methods that exploit common statistical properties of sea-ice thickness, and test for significant changes in model results in a computationally efficient manner. New additions and changes to CICE are graded into four categories, ranging from bit-for-bit amendments to significant, answer-changing upgrades. These modifications are assessed using criteria that account for the high level of autocorrelation in sea-ice time series, along with a quadratic skill metric that searches for hemispheric changes in model answers across an array of different CICE configurations. These metrics also provide objective guidance for assessing new physical representations and code functionality.
Sahil Agarwal, John S. Wettlaufer
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 376; doi:10.1098/rsta.2017.0332

Abstract:The fluctuation statistics of the observed sea-ice extent during the satellite era are compared with model output from CMIP5 models using a multifractal time series method. The two robust features of the observations are that on annual to biannual time scales the ice extent exhibits white noise structure, and there is a decadal scale trend associated with the decay of the ice cover. It is shown that (i) there is a large inter-model variability in the time scales extracted from the models, (ii) none of the models exhibits the decadal time scales found in the satellite observations, (iii) five of the 21 models examined exhibit the observed white noise structure, and (iv) the multi-model ensemble mean exhibits neither the observed white noise structure nor the observed decadal trend. It is proposed that the observed fluctuation statistics produced by this method serve as an appropriate test bed for modelling studies.
Erland M. Schulson
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 376; doi:10.1098/rsta.2017.0336

Abstract:Static and kinetic friction play a fundamental role in sea-ice mechanics. The coefficient of static friction increases with hold time under normal load and is modelled in terms of creep and fracture of asperities in contact. The coefficient of kinetic friction exhibits velocity strengthening at lower speeds and velocity weakening at intermediate speeds. Strengthening is modelled in terms of asperity creep and hardness; weakening is modelled in terms of a progressive increase in the true area of contact wetted by meltwater produced through frictional heating. The concept is introduced of contact size distribution in which the smallest contacts melt first, leading to the onset of weakening; the largest melt last, leading to a third regime of kinetic friction and again to strengthening where hydrodynamics governs. Neither the static nor the kinetic coefficient is significantly affected by the presence of sea water. The paper closes with a few implications for sea-ice mechanics. The paper is based largely upon a critical review of the literature, but includes a more quantitative, physics-based analysis of velocity strengthening and a new analysis of velocity weakening that incorporates parameters that describe the (proposed) fractal character of the sliding interface.
Vernon A. Squire
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 376; doi:10.1098/rsta.2017.0342

Abstract:Because of their capacity to alter floe size distribution and concentration and consequently to influence atmosphere-ocean fluxes, there is a compelling justification and demand to include waves in ice/ocean models and earth system models. Similarly, global wave forecasting models like WAVEWATCH III® need better parametrizations to capture the effects of a sea ice cover such as the marginal ice zone on incoming wave energy. Most parametrizations of wave propagation in sea ice assume without question that the frequency-dependent attenuation which is observed to occur with distance x travelled is exponential, i.e. A = A0 e−αx. This is the solution of the simple first-order linear ordinary differential equation dA/dx = − αA, which follows from an Airy wave mode ansatz . Yet, in point of fact, it now appears that exponential decay may not be observed consistently and a more general equation of the type dA/dx = − αAn is proposed to allow for a broader range of attenuation behaviours should this be necessary to fit data.
J. P. Dempsey, D. M. Cole, S. Wang
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 376; doi:10.1098/rsta.2017.0346

Abstract:The break-up of sea ice in the Arctic and Antarctic has been studied during three field trips in the spring of 1993 at Resolute, NWT, and the fall of 2001 and 2004 on McMurdo Sound via in situ cyclic loading and fracture experiments. In this paper, the back-calculated fracture information necessary to the specification of an accurate viscoelastic fictitious (cohesive) crack model is presented. In particular, the changing shape of the stress separation curve with varying conditions and loading scenarios is revealed.
P. I. Plotnikov, J. F. Toland
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 376; doi:10.1098/rsta.2017.0343

Abstract:This paper outlines a mathematical approach to steady periodic waves which propagate with constant velocity and without change of form on the surface of a three-dimensional expanse of fluid which is at rest at infinite depth and moving irrotationally under gravity, bounded above by a frictionless elastic sheet. The elastic sheet is supposed to have gravitational potential energy, bending energy proportional to the square integral of its mean curvature (its Willmore functional), and stretching energy determined by the position of its particles relative to a reference configuration. The equations and boundary conditions governing the wave shape are derived by formulating the problem, in the language of geometry of surfaces, as one for critical points of a natural Lagrangian, and a proof of the existence of solutions is sketched.
Frank Smith, Alexander Korobkin, Emilian Parau, Daniel Feltham, Vernon Squire
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 376; doi:10.1098/rsta.2018.0157

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