Topological Properties from Einstein's Equations?

In this work we propose a new procedure for to extract global information of a space-time. We considered a space-time immersed in a higher dimensional space and we formulate the equations of Einstein through of the Frobenius conditions to immersion. Through of an algorithm and the implementation into algebraic computing system we calculate normal vectors from the immersion to find out the second fundamental form. We make a application for space-time with spherical symmetry and static. We solve the equations of Einstein to the vacuum and we obtain space-times with different topologies.Comment: 7 pages, accepted for publication in Int. J. Mod. Phys.

Embedding Versus Immersion in General Relativity

We briefly discuss the concepts of immersion and embedding of space-times in higher-dimensional spaces. We revisit the classical work by Kasner in which he constructs a model of immersion of the Schwarzschild exterior solution into a six-dimensional pseudo-Euclidean manifold. We show that, from a physical point of view, this model is not entirely satisfactory since the causal structure of the immersed space-time is not preserved by the immersion.Comment: 5 page

Active swarms on a sphere

Here we show that coupling to curvature has profound effects on collective motion in active systems, leading to patterns not observed in flat space. Biological examples of such active motion in curved environments are numerous: curvature and tissue folding are crucial during gastrulation, epithelial and endothelial cells move on constantly growing, curved crypts and vili in the gut, and the mammalian corneal epithelium grows in a steady-state vortex pattern. On the physics side, droplets coated with actively driven microtubule bundles show active nematic patterns. We study a model of self-propelled particles with polar alignment on a sphere. Hallmarks of these motion patterns are a polar vortex and a circulating band arising due to the incompatibility between spherical topology and uniform motion - a consequence of the hairy ball theorem. We present analytical results showing that frustration due to curvature leads to stable elastic distortions storing energy in the band.Comment: 5 pages, 4 figures plus Supporting Informatio

A Systematic and Thorough Search for Domains of the Scavenger Receptor Cysteine-Rich Group-B Family in the Human Genome

No abstract available

Riemannian Geometry of Noncommutative Surfaces

A Riemannian geometry of noncommutative n-dimensional surfaces is developed as a first step towards the construction of a consistent noncommutative gravitational theory. Historically, as well, Riemannian geometry was recognized to be the underlying structure of Einstein's theory of general relativity and led to further developments of the latter. The notions of metric and connections on such noncommutative surfaces are introduced and it is shown that the connections are metric-compatible, giving rise to the corresponding Riemann curvature. The latter also satisfies the noncommutative analogue of the first and second Bianchi identities. As examples, noncommutative analogues of the sphere, torus and hyperboloid are studied in detail. The problem of covariance under appropriately defined general coordinate transformations is also discussed and commented on as compared with other treatments.Comment: 28 pages, some clarifications, examples and references added, version to appear in J. Math. Phy

Statistical models of mixtures with a biaxial nematic phase

We consider a simple Maier-Saupe statistical model with the inclusion of disorder degrees of freedom to mimic the phase diagram of a mixture of rod-like and disc-like molecules. A quenched distribution of shapes leads to the existence of a stable biaxial nematic phase, in qualitative agreement with experimental findings for some ternary lyotropic liquid mixtures. An annealed distribution, however, which is more adequate to liquid mixtures, precludes the stability of this biaxial phase. We then use a two-temperature formalism, and assume a separation of relaxation times, to show that a partial degree of annealing is already sufficient to stabilize a biaxial nematic structure.Comment: 11 pages, 2 figure

A note on the computation of geometrically defined relative velocities

We discuss some aspects about the computation of kinematic, spectroscopic, Fermi and astrometric relative velocities that are geometrically defined in general relativity. Mainly, we state that kinematic and spectroscopic relative velocities only depend on the 4-velocities of the observer and the test particle, unlike Fermi and astrometric relative velocities, that also depend on the acceleration of the observer and the corresponding relative position of the test particle, but only at the event of observation and not around it, as it would be deduced, in principle, from the definition of these velocities. Finally, we propose an open problem in general relativity that consists on finding intrinsic expressions for Fermi and astrometric relative velocities avoiding terms that involve the evolution of the relative position of the test particle. For this purpose, the proofs given in this paper can serve as inspiration.Comment: 8 pages, 2 figure

Interface-mediated interactions: Entropic forces of curved membranes

Particles embedded in a fluctuating interface experience forces and torques mediated by the deformations and by the thermal fluctuations of the medium. Considering a system of two cylinders bound to a fluid membrane we show that the entropic contribution enhances the curvature-mediated repulsion between the two cylinders. This is contrary to the usual attractive Casimir force in the absence of curvature-mediated interactions. For a large distance between the cylinders, we retrieve the renormalization of the surface tension of a flat membrane due to thermal fluctuations.Comment: 11 pages, 5 figures; final version, as appeared in Phys. Rev.

Generalization of Linearized Gouy-Chapman-Stern Model of Electric Double Layer for Nanostructured and Porous Electrodes: Deterministic and Stochastic Morphology

We generalize linearized Gouy-Chapman-Stern theory of electric double layer for nanostructured and morphologically disordered electrodes. Equation for capacitance is obtained using linear Gouy-Chapman (GC) or Debye-$\rm{\ddot{u}}$ckel equation for potential near complex electrode/electrolyte interface. The effect of surface morphology of an electrode on electric double layer (EDL) is obtained using "multiple scattering formalism" in surface curvature. The result for capacitance is expressed in terms of the ratio of Gouy screening length and the local principal radii of curvature of surface. We also include a contribution of compact layer, which is significant in overall prediction of capacitance. Our general results are analyzed in details for two special morphologies of electrodes, i.e. "nanoporous membrane" and "forest of nanopillars". Variations of local shapes and global size variations due to residual randomness in morphology are accounted as curvature fluctuations over a reference shape element. Particularly, the theory shows that the presence of geometrical fluctuations in porous systems causes enhanced dependence of capacitance on mean pore sizes and suppresses the magnitude of capacitance. Theory emphasizes a strong influence of overall morphology and its disorder on capacitance. Finally, our predictions are in reasonable agreement with recent experimental measurements on supercapacitive mesoporous systems