On the validity of tidal turbine array configurations obtained from steady-state adjoint optimisation

Extracting the optimal amount of power from an array of tidal turbines requires an intricate understanding of tidal dynamics and the effects of turbine placement on the local and regional scale flow. Numerical models have contributed significantly towards this understanding, and more recently, adjoint-based modelling has been employed to optimise the positioning of the turbines in an array in an automated way and improve on simple, regular man-made configurations. Adjoint-based optimisation of high-resolution and ideally 3D transient models is generally a very computationally expensive problem. As a result, existing work on the adjoint optimisation of tidal turbine placement has been mostly limited to steady-state simulations in which very high, non-physical values of the background viscosity are required to ensure that a steady-state solution exists. However, such compromises may affect the reliability of the modelled turbines, their wakes and interactions, and thus bring into question the validity of the computed optimal turbine positions. This work considers a suite of idealised simulations of flow past tidal turbine arrays in a 2D channel. It compares four regular array configurations, detailed by Divett et al. (2013), with the configuration found through adjoint optimisation in a steady-state, high-viscosity setup. The optimised configuration produces considerably more power. The same configurations are then used to produce a suite of transient simulations that do not use constant high-viscosity, and instead use large eddy simulation (LES) to parameterise the resulting turbulent structures. It is shown that the LES simulations produce less power than that predicted by the constant high-viscosity runs. Nevertheless, they still follow the same trends in the power curve throughout time, with optimised layouts continuing to perform significantly better than simplified configuration

Efficient unstructured mesh generation for marine renewable energy applications

Renewable energy is the cornerstone of preventing dangerous climate change whilst maintaining a robust energy supply. Tidal energy will arguably play a critical role in the renewable energy portfolio as it is both predictable and reliable, and can be put in place across the globe. However, installation may impact the local and regional ecology via changes in tidal dynamics, sediment transport pathways or bathymetric changes. In order to mitigate these effects, tidal energy devices need to be modelled in order to predict hydrodynamic changes. Robust mesh generation is a fundamental component required for developing simulations with high accuracy. However, mesh generation for coastal domains can be an elaborate procedure. Here, we describe an approach combining mesh generators with Geographical Information Systems. We demonstrate robustness and efficiency by constructing a mesh with which to examine the potential environmental impact of a tidal turbine farm installation in the Orkney Islands. The mesh is then used with two well-validated ocean models, to compare their flow predictions with and without a turbine array. The results demonstrate that it is possible to create an easy-to-use tool to generate high-quality meshes for combined coastal engineering, here tidal turbines, and coastal ocean simulations

Experimental Designs and the 'Emotion Stimulus Critique': Hidden Problems and Potential Solutions in the Study of Emotion.

Emotional experience is increasingly being measured using experimental tasks, but the stimuli used are often only proxies for the emotion being studied. Stimuli are intended to evoke a distinct emotional experience, but certain designs fail to adequately control for the actual experience in question. In this methodological paper, we review designs used in clinical psychology aimed at measuring emotion and develop the argument of the 'emotion stimulus critique'. Designs of neuroimaging studies on emotion in this context are given preference. We argue that studies often concentrate on standardization of the stimulus material (i.e. words, images, and movies) for eliciting an emotional experience, whereas standardization of the actual participant's experience is seldom performed. Our proposal discusses the use of standardized stimuli in experimental designs and contrasts this with the necessity of controlling for a participant's unique emotional response. We highlight the importance of each participant's 'inner metric', i.e. the individual's experiential anchor, which needs to be taken into account when examining the emotional correlates of psychiatric disorders or psychotherapeutic change. Implications of the emotion stimulus critique for research are discussed within the context of psychology, particularly clinical psychology and psychotherapy

Future Challenges in Psychotherapy Research for Personality Disorders.

Individuals with personality disorders are frequently seen in mental health settings. Their symptoms typically reflect a high level of suffering and burden of disease, with potentially harmful societal consequences, including costs related to absenteeism at work, high use of health services, ineffective or harmful parenting, substance use, suicidal and non-suicidal self-harming behavior, and aggressiveness with legal consequences. Psychotherapy is currently the first-line treatment for patients with personality disorders, but the study of psychotherapy in the domain of personality disorders faces specific challenges. Challenges include knowing what works for whom, identifying which putative mechanisms of change explain therapeutic effects, and including the social interaction context of patients with a personality disorder. By following a dimensional approach, psychotherapy research on personality disorders may serve as a model for the development and study of innovative psychotherapeutic interventions. We recommend developing the following: (a) an evidence base to make treatment decisions based on individual features; (b) a data-driven approach to predictors, moderators, and mechanisms of change in psychotherapy; (c) methods for studying the interaction between social context and psychotherapy

ADM formulation of the General Relativity

Se realiza el estudio del formalismo ADM para la Teoría de la Relatividad General mediante el método de las foliaciones en las superficies de Cauchy. Se presenta explícitamente el desarrollo matemático que conduce, finalmente, a la formulación hamiltoniana de la Relatividad General.The study of the ADM formalism for the General Relativity Theory through the foliation methods on the Cauchy surfacesis is realized. The mathematical development that leads to the Hamiltonian formulation of General Relativity is presented explicitly

Post-subduction tectonics induced by extension from a lithospheric drip

Acknowledgements S.P. acknowledges support from the Natural Environmental Research Council (NERC) Grant NE/R013500/1 and from the European Union’s Horizon 2020 Research and Innovation Program under Marie Skłodowska-Curie Grant Agreement 790203. We thank the TanDEM-X Science Communication Team (German Aerospace Center (DLR) e.V.) for providing TanDEM topographic data. We thank the NERC Geophysical Equipment Facility for loan 1038. Numerical simulations were undertaken on the NCI National Facility in Canberra, Australia, which is supported by the Australian Commonwealth Government. A.G. was funded by an Independent Research Fellowship from the Royal Astronomical Society.Peer reviewedPostprin

The trade-off between tidal-turbine array yield and impact on flow: A multi-objective optimisation problem

Abstract This paper introduces a new approach for investigating trade-offs between different societal objectives in the design of tidal-turbine arrays. This method is demonstrated through the trade-off between the yield of an array, and the extent to which that array alters the flow. This is posed as a multi-objective optimisation problem, and the problem is investigated using the array layout optimisation tool OpenTidalFarm. Motivated by environmental concerns, OpenTidalFarm is adapted to not only maximise array yield but also to minimise the effect of the array upon the hydrodynamics of the region, specifically the flow velocity. A linear scalarisation of the multi-objective optimisation problem is solved for a series of different weightings of the two conflicting objectives. Two idealised test scenarios are evaluated and in each case a set of Pareto solutions is found. These arrays are assessed for the power they generate and the severity of change they cause in the flow velocity. These analyses allow for the identification of trade-offs between these two objectives, while the methods proposed can similarly be applied to the two key societal objectives of energy production and conservation, thus providing information that could be valuable to stakeholders and policymakers when making decisions on array design

Diffusion of electrons in random magnetic fields,

Diffusion of electrons in a two-dimensional system in static random magnetic fields is studied by solving the time-dependent Schr\"{o}dinger equation numerically. The asymptotic behaviors of the second moment of the wave packets and the temporal auto-correlation function in such systems are investigated. It is shown that, in the region away from the band edge, the growth of the variance of the wave packets turns out to be diffusive, whereas the exponents for the power-law decay of the temporal auto- correlation function suggest a kind of fractal structure in the energy spectrum and in the wave functions. The present results are consistent with the interpretation that the states away from the band edge region are critical.Comment: 22 pages (8 figures will be mailed if requested), LaTeX, to appear in Phys. Rev.

Corrections to Einstein's relation for Brownian motion in a tilted periodic potential

In this paper we revisit the problem of Brownian motion in a tilted periodic potential. We use homogenization theory to derive general formulas for the effective velocity and the effective diffusion tensor that are valid for arbitrary tilts. Furthermore, we obtain power series expansions for the velocity and the diffusion coefficient as functions of the external forcing. Thus, we provide systematic corrections to Einstein's formula and to linear response theory. Our theoretical results are supported by extensive numerical simulations. For our numerical experiments we use a novel spectral numerical method that leads to a very efficient and accurate calculation of the effective velocity and the effective diffusion tensor.Comment: 29 pages, 7 figures, submitted to the Journal of Statistical Physic

Expansion of Vortex Cores by Strong Electronic Correlation in La2−x_{2-x}Srx_xCuO4_4 at Low Magnetic Induction

The vortex core radius \rv, defined as the peak position of the supercurrent around the vortex, has been determined by muon spin rotation measurements in the mixed state of \lscox for $x=0.13$, 0.15, and 0.19. At lower doping (x=0.13 and 0.15), \rv(T) increases with decreasing temperature T, which is opposite to the behavior predicted by the conventional theory. Moreover, \rv(T\to0) is significantly larger than the Ginsburg-Landau coherence length determined by the upper critical field, and shows a clear tendency to decrease with increasing the doping x. These features can be qualitatively reproduced in a microscopic model involving antiferromagnetic electronic correlations.Comment: 6 pages, 4 figures, to be published in Phys. Rev.