1+3 Covariant Cosmic Microwave Background anisotropies II: The almost - Friedmann Lemaitre model

This is the second of a series of papers extending the 1+3 covariant and gauge invariant treatment of kinetic theory to an examination of Cosmic Microwave Background temperature anisotropies arising from inhomogeneities in the early universe. The first paper dealt with algebraic issues. Here we derive the mode form of the integrated Boltzmann equations, first, giving a covariant version of the standard derivation using the mode recursion relations, second, demonstrating the link to the multipole divergence equations and finally various analytic ways of solving the resulting equations are discussed. A general integral form of solution is obtained for the equations with Thomson scattering. The covariant Friedmann-Lemaitre multipole form of the transport equations are found using the covariant and gauge-invariant generalization of the Peebles and Yu expansion in Thompson scattering time. The dispersion relations and damping scale are then obtained from the covariant approach. The equations are integrated to give the covariant and gauge-invariant equivalent of the canonical scalar sourced anisotropies. We carry out a simple treatment of the matter dominated free-streaming projection, slow decoupling, and tight-coupling cases, with the aim both giving a unified transparent derivation of this range of results and clarifying the connection between the more usual approaches (for example that of Hu and Sugiyama) and the treatment for scalar perturbations (for example the treatment of Challinor and Lasenby).Comment: To appear in Annals of Physic

1+3 Covariant Cosmic Microwave Background anisotropies I: Algebraic relations for mode and multipole representations

This is the first of a series of papers extending a covariant and gauge invariant (CGI) treatment of kinetic theory in curved space-times to a treatment of Cosmic Background Radiation (CBR) temperature anisotropies arising from inhomogeneities in the early universe. This paper deals with algebraic issues, both generically and in the context of models linearised about RW geometries. The approach represents radiation anisotropies by PSTF tensors. The Angular correlation functions for the mode coefficients are found in terms of these quantities, following the Wilson-Silk approach, but derived and dealt with in CGI form. The covariant multipole and mode-expanded angular correlation functions are related to the usual treatments in the literature. The CGI mode expansion is related to the coordinate approach by linking the Legendre functions to the PSTF representation, using a covariant addition theorem for the tensors to generate the Legendre Polynomial recursion relation. This paper lays the foundation for further papers in the series, which use this formalism in a CGI approach to develop solutions of the Boltzmann and Liouville equations for the CBR before and after decoupling, thus providing a unified CGI derivation of the variety of approaches to CBR anisotropies in the current literature.Comment: Notational changes bringing our conventions further inline with the canonical treatment, some additional comments. 30 pages late

Gauge-ready formulation of the cosmological kinetic theory in generalized gravity theories

We present cosmological perturbations of kinetic components based on relativistic Boltzmann equations in the context of generalized gravity theories. Our general theory considers an arbitrary number of scalar fields generally coupled with the gravity, an arbitrary number of mutually interacting hydrodynamic fluids, and components described by the relativistic Boltzmann equations like massive/massless collisionless particles and the photon with the accompanying polarizations. We also include direct interactions among fluids and fields. The background FLRW model includes the general spatial curvature and the cosmological constant. We consider three different types of perturbations, and all the scalar-type perturbation equations are arranged in a gauge-ready form so that one can implement easily the convenient gauge conditions depending on the situation. In the numerical calculation of the Boltzmann equations we have implemented four different gauge conditions in a gauge-ready manner where two of them are new. By comparing solutions solved separately in different gauge conditions we can naturally check the numerical accuracy.Comment: 26 pages, 9 figures, revised thoroughly, to appear in Phys. Rev.

Effect of metallacarborane salt H[COSANE] doping on the performance properties of polybenzimidazole membranes for high temperature PEMFCs

[EN] In this paper, a series of composite proton exchange membranes comprising a cobaltacarborane protonated H[Co(C2B9H11)(2)] named (H[COSANE]) and polybenzimidazole (PBI) for a high temperature proton exchange membrane fuel cell (PEMFC) is reported, with the aim of enhancing the proton conductivity of PBI membranes doped with phosphoric acid. The effects of the anion [Co(C2B9H11)(2)] concentration in three different polymeric matrices based on the PBI structure, poly(2,2 '-(m-phenylene)-5,5 '-bibenzimidazole) (PBI-1), poly[2,2 '-(p-oxydiphenylene)-5,5 '-bibenzimidazole] (PBI-2) and poly(2,2 '-(p-hexafluoroisopropylidene)-5,5 '-bibenzimidazole) (PBI-3), have been investigated. The conductivity, diffusivity and mobility are greater in the composite membrane poly(2,2 '-(p-hexafluoroisopropylidene)-5,5 '-bibenzimidazole) containing fluorinated groups, reaching a maximum when the amount of H[COSANE] was 15%. In general, all the prepared membranes displayed excellent and tunable properties as conducting materials, with conductivities higher than 0.03 S cm(-1)above 140 degrees C. From an analysis of electrode polarization (EP) the proton diffusion coefficients and mobility have been calculated.This work was financially supported by the Ministerio de Economia y Competitividad (MINECO) under project ENE/2015-69203-R and by Consejo Nacional de Ciencia y Tecnologia (CONACyT) for the postdoctoral grant to J. O. The technical support of Servei de Microscpia Electrnica at Universitat Politecnica de Valencia and Servei Central d'Instrumentacio Cientifica at Universitat Jaume I is gratefully acknowledged. The authors thanks Prof. Santiago V. Luis (from Universitat Jaume I) and Dr Isabel Fuentes, Prof. Francesc Teixidor and Prof. Clara Vinas (from Instituto de Materiales de Barcelona, CSIC), for supplying the H[COSANE] compound.Olvera-Mancilla, J.; Escorihuela, J.; Alexandrova, L.; Andrio, A.; Garcia-Bernabe, A.; Del Castillo, LF.; Compañ Moreno, V. (2020). Effect of metallacarborane salt H[COSANE] doping on the performance properties of polybenzimidazole membranes for high temperature PEMFCs. Soft Matter. 16(32):7624-7635. https://doi.org/10.1039/d0sm00743aS762476351632https://earthsky.org/earth/atmospheric-co2-record-high-may-2019Steele, B. C. H., & Heinzel, A. (2001). Materials for fuel-cell technologies. Nature, 414(6861), 345-352. doi:10.1038/35104620CLEGHORN, S. (1997). Pem fuel cells for transportation and stationary power generation applications. International Journal of Hydrogen Energy, 22(12), 1137-1144. doi:10.1016/s0360-3199(97)00016-5Wang, Y., Chen, K. S., Mishler, J., Cho, S. C., & Adroher, X. C. (2011). 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Ionic Liquid-Based Electrolytes for Supercapacitor and Supercapattery

There is a strong desire to replace or complement aqueous and organic electrolytes by ionic liquids (ILs) in electrochemical energy storage (EES) devices to achieve high operating voltages and hence high energy capacity. ILs are regarded as the inherent and competitive electrolytes since they were introduced to the electrochemical research community because they can overcome many disadvantages of the conventional aqueous and organic electrolytes, such as narrow potential windows, volatility, and flammability. This paper reviews critically the recent literatures of IL-based electrolytes used in supercapacitor, supercapattery, and micro-supercapacitor. Supercapattery is a generic term for various hybrid devices combining the merits of rechargeable battery and supercapacitor and often shows capacitive behavior. Fundamentals of supercapattery are briefly explained with typical examples. Micro-supercapacitor falls in the same scope of supercapacitor and supercapattery and shares the same fundamental concerns besides topology or structure. The future of IL-based electrolytes for the capacitive EES devices are also prospected