Analytic solution of the algebraic equation associated to the Ricci tensor in extended Palatini gravity

In this work we discuss the exact solution to the algebraic equation associated to the Ricci tensor in the quadratic $f(R,Q)$ extension of Palatini gravity. We show that an exact solution always exists, and in the general case it can be found by a simple matrix diagonalization. Furthermore, the general implications of the solution are analysed in detail, including the generation of an effective cosmological constant, and the recovery of the $f(R)$ and $f(Q)$ theories as particular cases in their corresponding limit. In addition, it is proposed a power series expansion of the solution which is successfully applied to the case of the electromagnetic field. We show that this power series expansion may be useful to deal perturbatively with some problems in the context of Palatini gravity.Comment: arXiv admin note: text overlap with arXiv:1101.3864, arXiv:1306.6537, arXiv:1112.2223 by other author

κ(R,T)\kappa(R,T) gravity

In this note we explore a modified theory of gravitation that is not based on the least action principle, but on a natural generalization of the original Einstein's field equations. This approach leads to the non-covariant conservation of the stress-energy tensor, a feature shared with other Lagrangian theories of gravity such as the $f(R,T)$ case. We consider the cosmological implications of a pair of particular models within this theory, and we show that they have some interesting properties. In particular, for some of the studied models we find that the density is bounded from above, and cannot exceed a maximum value that depends on certain physical constants. In the last part of the work we compare the theory to the $f(R,T)$ case and show that they lead to different predictions for the motion of test particles.Comment: 9 pages, 1 figure. Typos corrected, two subsections adde

Addressing European ocean energy challenge:The dtoceanplus structured innovation tool for concept creation and selection

The whole energy system requires renewables that scale and produce reliable, valuable energy at an acceptable cost. The key to increasing the deployment of ocean energy is bringing down development and operating costs. This paper proposes a structured approach to innovation in ocean energy systems that would spur innovation and expand the market for ocean energy. This approach can be used by a wide range of stakeholders—including technology and project developers and investors—when considering creating or improving designs. The Structured Innovation design tool within the DTOceanPlus suite is one of a kind beyond the current state-of-the-art. It enables the adaptation and integration of systematic problem-solving tools based on quality function deployment (QFD), the theory of inventive thinking (TRIZ), and the failure modes and effects analysis (FMEA) methodologies for the ocean energy sector. In obtaining and assessing innovative concepts, the integration of TRIZ into QFD enables the designers to define the innovation problem, identifies trade-offs in the system, and, with TRIZ as a systematic inventive problem-solving methodology, generates potential design concepts for the contradicting requirements. Additionally, the FMEA is used to assess the technical risks associated with the proposed design concepts. The methodology is demonstrated using high-level functional requirements for a small array of ten tidal turbines to improve the devices layout and power cabling architecture. The Structured Innovation design tool output comprises critical functional requirements with the highest overall impact and the least organisational effort to implement, along with appropriate alternative solutions to conflicting requirements

Removing singular refractive indices with sculpted surfaces

Open Access JournalThe advent of Transformation Optics established the link between geometry and material properties, and has resulted in a degree of control over electromagnetic fields that was previously impossible. For waves confined to a surface it is known that there is a simpler, but related, geometrical equivalence between the surface shape and the refractive index, and here we demonstrate that conventional devices possessing a singularity - that is, the requirement of an infinite refractive index - can be realised for waves confined to an appropriately sculpted surface. In particular, we redesign three singular omnidirectional devices: the Eaton lens, the generalized Maxwell Fish-Eye, and the invisible sphere. Our designs perfectly reproduce the behaviour of these singular devices, and can be achieved with simple isotropic media of low refractive index contrast.Engineering and Physical Sciences Research Council (EPSRC

Canards, Folded Nodes, and Mixed-Mode Oscillations in Piecewise-Linear Slow-Fast Systems

Canard-induced phenomena have been extensively studied in the last three decades, from both the mathematical and the application viewpoints. Canards in slow-fast systems with (at least) two slow variables, especially near folded-node singularities, give an essential generating mechanism for mixed-mode oscillations (MMOs) in the framework of smooth multiple timescale systems. There is a wealth of literature on such slow-fast dynamical systems and many models displaying canard-induced MMOs, particularly in neuroscience. In parallel, since the late 1990s several papers have shown that the canard phenomenon can be faithfully reproduced with piecewise-linear (PWL) systems in two dimensions, although very few results are available in the three-dimensional case. The present paper aims to bridge this gap by analyzing canonical PWL systems that display folded singularities, primary and secondary canards, with a similar control of the maximal winding number as in the smooth case. We also show that the singular phase portraits are compatible in both frameworks. Finally, we show using an example how to construct a (linear) global return and obtain robust PWL MMOs