Acoustics in 2D Spaces of Constant Curvature

[EN] In this work, we will consider a locally homogeneous and isotropic (2+1)D spacetime of Robertson-Walker type and therefore with underlying de Sitter space.M. M. T. wishes to thank the Spanish Ministerio de Economía y Competitividad and the European Regional Development Fund (ERDF) for financial support under grant TIN2014-59294-PTung, MM.; Gambi, JM.; María Luisa García del Pino (2016). Acoustics in 2D Spaces of Constant Curvature. Springer. 483-489. https://doi.org/10.1007/978-3-319-63082-3_75S483489Beals, R., Szmigielski, J.: Meijer G-functions: a gentle introduction. Not. Am. Math. Soc. 60(7), 866–872 (2013)Chen, H.Y., Chan, C.T.: Acoustic cloaking and transformation acoustics. J. Phys. D 43(11), 113001 (2010)Choquet-Bruhat, Y., Damour, T.: Introduction to General Relativity, Black Holes, and Cosmology. Oxford University Press, Oxford (2015)Cummer, S.A.: Transformation acoustics. In: Craster, V.R., Guenneau, S. (eds.) Acoustic Metamaterials: Negative Refraction, Imaging, Lensing and Cloaking, pp. 197–218. Springer Netherlands, Dordrecht (2013)Cummer, S.A., Schurig, D.: One path to acoustic cloaking. New J. Phys. 9(3), 45–52 (2007)Islam, J.N.: An Introduction to Mathematical Cosmology. Cambridge University Press, Cambridge (2001)Kalnins, E.G.: Separation of Variables for Riemannian Spaces of Constant Curvature. Pitman Monographs and Surveys in Pure and Applied Mathematics. Longman Scientific & Technical, New York (1986)Kuchowicz, B.: Conformally flat space-time of spherical symmetry in isotropic coordinates. Int. J. Theor. Phys. 7(4), 259–262 (1973)Lanczos, C.: The Variational Principles of Mechanics. Dover Publications, New York (1970)Mechel, F.P.: Formulas of Acoustics. Springer, Berlin (2002)Norris, A.N.: Acoustic metafluids. J. Acoust. Soc. Am. 125(2), 839–849 (2009)Redkov, V.M., Ovsiyuk, E.M.: Quantum mechanics in spaces of constant curvature. In: Contemporary Fundamental Physics. Nova Science, New York (2012)Rosenberg, S.: The Laplacian on a Riemannian Manifold: An Introduction to Analysis on Manifolds. London Mathematical Society Student Text, vol. 31. Cambridge University Press, Cambridge (1997)Tung, M.M.: A fundamental Lagrangian approach to transformation acoustics and spherical spacetime cloaking. Europhys. Lett. 98, 34002–34006 (2012)Tung, M.M., Peinado, J.: A covariant spacetime approach to transformation acoustics. In: Fontes, M., Günther, M., Marheineke, N. (eds.) Progress in Industrial Mathematics at ECMI 2012. Mathematics in Industry, vol. 19. Springer, Berlin (2014)Tung, M.M., Weinmüller, E.B.: Gravitational frequency shifts in transformation acoustics. Europhys. Lett. 101, 54006–54011 (2013)Tung, M.M., Gambi, J.M., García del Pino, M.L.: Maxwell’s fish-eye in (2+1)D spacetime acoustics. In: Russo, G.R., Capasso, V., Nicosia, G., Romano, V. (eds.) Progress in Industrial Mathematics at ECMI 2014. Mathematics in Industry, vol. 22. Springer, Berlin (2016)Visser, M., Barceló, C., Liberati, S.: Analogue models of and for gravity. Gen. Rel. Grav. 34, 1719–1734 (2002)Wolf, J.A.: Spaces of Constant Curvature. American Mathematical Society, Providence, Rhode Island (2011

From Newton's Laws to the Wheeler-DeWitt Equation

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Number of Information and its Relation to the Cosmological Constant Resulting from Landauer’s Principle

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Bianchi Type I Magnetofluid Cosmological Models with Variable Cosmological Constant Revisited

The behaviour of magnetic field in anisotropic Bianchi type I cosmological model for bulk viscous distribution is investigated. The distribution consists of an electrically neutral viscous fluid with an infinite electrical conductivity. It is assumed that the component $\sigma^{1}_{1}$ of shear tensor $\sigma^{j}_{i}$ is proportional to expansion ($\theta$) and the coefficient of bulk viscosity is assumed to be a power function of mass density. Some physical and geometrical aspects of the models are also discussed in presence and also in absence of the magnetic field.Comment: 13 page

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