We propose two methods for obtaining the position space of non-linear relativity, i.e. the dual of its usual momentum space formulation. In the first approach we require that plane waves still be solutions to free field theory. This is equivalent to postulating the invariance of the linear contraction between position and momentum spaces, and dictates a set of energy-dependent spacetime Lorentz transformations. In turn this leads to an energy dependent metric. The second, more problematic approach allows for the position space to acquire a non-linear representation of the Lorentz group independently of the chosen representation in momentum space. This requires a non-linear contraction between momentum and position spaces. We discuss a variety of physical implications of these approaches and show how they point to two rather distinct formulations of theories of gravity with an invariant energy and/or length scale.

The COBE-DMR 4-yr maps displayed a strong non-Gaussian signal in the 'interscale' components of the bispectrum: their observed values did not display the scatter expected from Gaussian maps. We re-examine this and other suggested non-Gaussian features in the light of WMAP. We find that they all disappear. Given that it was proved that COBE-DMR high noise levels and documented systematics could at most dilute the observed non-Gaussian features, we conclude that this data set must have contained non-negligible undocumented systematic errors. It turns out that the culprit is a combination of QuadCube pixelization and data collected during the 'eclipse season'.

We investigate the effect of foreground residuals in the WMAP (Wilkinson Microwave Anisotropy Probe) data by adding foreground contamination to Gaussian ensembles of cosmic microwave background (CMB) signal and noise maps. We evaluate a set of non‐Gaussian estimators on the contaminated ensembles to determine with what accuracy any residual in the data can be constrained using higher‐order statistics. We apply the estimators to the raw and cleaned Q‐, V‐ and W‐band first‐year maps. The foreground subtraction method applied to clean the data in Bennett et al. appears to have induced a correlation between the power spectra and normalized bispectra of the maps which is absent in Gaussian simulations. It also appears to increase the correlation between the Δℓ= 1 inter‐ℓ bispectrum of the cleaned maps and the foreground templates. In a number of cases the significance of the effect is above the 98 per cent confidence level.

We construct a multi-fidelity framework for statistical learning and global optimization that is capable of effectively synthesizing seakeeping predictions having two different levels of modeling fidelity, namely a strip theory and a boundary element method based on potential flow assumption. The objective of this work is to demonstrate that the multi-fidelity framework can be used efficiently to discover optimal small waterplane area twin hull shapes having superior seakeeping performance using a limited number of expensive high-fidelity simulations combined with a larger number of inexpensive low-fidelity simulations. Specifically, we employ multi-fidelity Gaussian process regression and Bayesian optimization to build probabilistic surrogate models and efficiently explore a 35-dimensional design space to optimize hull shapes that minimize wave-induced motions and accelerations, and satisfy specific requirements in terms of displacement and metacentric height. Our results demonstrate the superior characteristics of this optimization framework in constructing accurate surrogate models and identifying optimal designs with a significant reduction in the computational effort. 1. Introduction During the past decades, estimating the seaworthiness of a ship in the early design stages has become a primary concern for naval architects. Increased requirements in terms of comfort and ergonomics have steered the research in developing innovative hull forms, with the specific target of decreasing motions in waves. From a safety point of view, extreme accelerations can exert harmful dynamic loads (on the vessel, cargo, or equipment), slamming, or green water effects that can severely damage the structural integrity of the vessel or lead to stability losses. When ship behavior in waves becomes a quantity of interest in the hull-form optimization process, seakeeping performance needs to be predicted with numerical models able to combine high fidelity and high computational efficiency. Nowadays, ship motion predictions mainly rely on three families of numerical models, here sorted by increasing level of fidelity: 2-D strip theories, 3-D boundary element methods (BEM), both developed under the assumption of potential flow, and unsteady fully viscous nonlinear 3-D methods in which ship motions are simulated in six Degrees of Freedom (DOF) for incident regular or irregular waves (see Fig. 5). In this article, we introduce a probabilistic method for constructing surrogate models using multi-fidelity training datasets that allows to increase the accuracy of the model with significant savings in computational resources. For the purpose of demonstration of the multi-fidelity framework, the training datasets used in this article are composed of classical 2-D and 3-D potential flow predictions; for this reason, we will refer to 2-D strip theories as low-fidelity models and a more accurate 3-D BEM as high-fidelity models. In the present study, our goal is to demonstrate the ability of the multi-fidelity framework in efficiently discovering hull forms with superior seakeeping characteristics by using simplified prediction models. Although in the present study, we do not include any viscous effects, the methodology is general and can combine any type of high-fidelity simulations or experimental data with low-fidelity simulations, experimental data, or even empirical correlations.

The accurate prediction of motion in waves of a marine vehicle is essential to assess the maximum sea state vs. operational requirements. This is particularly true for small crafts, such as Autonomous Surface Vessels (ASV). Two different numerical methods to predict motions of a SWATH-ASV are considered: an inviscid strip theory initially developed at MIT for catamarans and then adapted for SWATHs and new a hybrid strip theory, based on the numerical solution of the radiation forces by an unsteady viscous, non-linear free surface flow solver. Motion predictions obtained by the viscous flow method are critically discussed against those obtained by potential flow strip theory. Effects of viscosity are analyzed by comparison of sectional added mass and damping calculated at different frequencies and for different sections, RAOs and motions response in irregular waves at zero speed. Some relevant conclusions can be drawn from this study: influence of viscosity is definitely non negligible for SWATH vessels like the one presented: amplitude of the pitch and heave motions predicted at the resonance frequency differ of 20% respectively and 50%; in this respect, the hybrid method with fully non-linear, viscous free surface calculation of the radiation forces turns out to be a very valuable tool to improve the accuracy of traditional strip theories, without the burden of long computational times requested by fully viscous time domain three dimensional simulations.

Efficient design of wave energy converters based on floating body motion heavily depends on the capacity of the designer to accurately predict the device's dynamics, which ultimately leads to the power extraction. We present a (quasi-nonlinear) time-domain hydromechanical dynamic model to simulate a particular type of pitch-resonant WEC which uses gyroscopes for power extraction. The dynamic model consists of a time-domain three-dimensional Rankine panel method coupled, during time integration, with a MATLAB algorithm that solves for the equations of the gyroscope and Power Take-Off (PTO). The former acts as a force block, calculating the forces due to the waves on the hull, which is then sent to the latter through TCP/IP, which couples the external dynamics and performs the time integration using a 4th-order Runge-Kutta method. The panel method, accounting for the gyroscope and PTO dynamics, is then used for the calculation of the optimal flywheel spin, PTO damping, and average power extracted, completing the basic design cycle of the WEC. The proposed numerical method framework is capable of considering virtually any type of nonlinear force (e.g., nonlinear wave loads) and it is applied and verified in the paper against the traditional frequency domain linear model. It proved to be a versatile tool to verify performance in resonant conditions.

The improvement of the seakeeping capabilities of Floating, Production, Storage and Offloading (FPSO) vessels increases safety and allows its operation on severe weather conditions. It also increases the fatigue life of the risers. Hence, any improvement on the FPSO motion is mostly welcome. Guimarães [1], following similar efforts by Silva [2], studied the reduction of pitch motions of FPSO vessels with the use of the OWCs (Oscillating Water Columns) passive system. However, both experimental and numerical results were inconclusive due to green water effects during experiments and panel issues with the panel code WAMIT [3], respectively. The objective of the present work is to report a series of new tests that prove the feasibility of an “L-shaped” moon pool concept and estimates and tests the ideal length of such concept that maximizes the restoring moment and minimizes pitch the most. The tests were conducted in the Laboratório de Ondas e Correntes (Laboratory of Waves and Currents) of the Federal University of Rio de Janeiro (COPPE/UFRJ).

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