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

Minimal resonances in annular non-Euclidean strips

Differential growth processes play a prominent role in shaping leaves and biological tissues. Using both analytical and numerical calculations, we consider the shapes of closed, elastic strips which have been subjected to an inhomogeneous pattern of swelling. The stretching and bending energies of a closed strip are frustrated by compatibility constraints between the curvatures and metric of the strip. To analyze this frustration, we study the class of "conical" closed strips with a prescribed metric tensor on their center line. The resulting strip shapes can be classified according to their number of wrinkles and the prescribed pattern of swelling. We use this class of strips as a variational ansatz to obtain the minimal energy shapes of closed strips and find excellent agreement with the results of a numerical bead-spring model. Within this class of strips, we derive a condition under which a strip can have vanishing mean curvature along the center line.Comment: 14 pages, 13 figures. Published version. Updated references and added 2 figure

Magnetovac Cylinder to Magnetovac Torus

A method for mapping known cylindrical magnetovac solutions to solutions in torus coordinates is developed. Identification of the cylinder ends changes topology from R1 x S1 to S1 x S1. An analytic Einstein-Maxwell solution for a toroidal magnetic field in tori is presented. The toroidal interior is matched to an asymptotically flat vacuum exterior, connected by an Israel boundary layer.Comment: to appear in Class. Quant. Gra

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

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

Rubisco catalytic properties of wild and domesticated relatives provide scope for improving wheat photosynthesis

Rubisco is a major target for improving crop photosynthesis and yield, yet natural diversity in catalytic properties of this enzyme is poorly understood. Rubisco from 25 genotypes of the Triticeae tribe, including wild relatives of bread wheat (Triticum aestivum), were surveyed to identify superior enzymes for improving photosynthesis in this crop. In vitro Rubisco carboxylation velocity (V c), Michaelis–Menten constants for CO2 (K c) and O2 (K o) and specificity factor (S c/o) were measured at 25 and 35 °C. V c and K c correlated positively, while V c and S c/o were inversely related. Rubisco large subunit genes (rbcL) were sequenced, and predicted corresponding amino acid differences analysed in relation to the corresponding catalytic properties. The effect of replacing native wheat Rubisco with counterparts from closely related species was analysed by modelling the response of photosynthesis to varying CO2 concentrations. The model predicted that two Rubisco enzymes would increase photosynthetic performance at 25 °C while only one of these also increased photosynthesis at 35 °C. Thus, under otherwise identical conditions, catalytic variation in the Rubiscos analysed is predicted to improve photosynthetic rates at physiological CO2 concentrations. Naturally occurring Rubiscos with superior properties amongst the Triticeae tribe can be exploited to improve wheat photosynthesis and crop productivity

Aharonov-Bohm-like effect for light propagating in nematics with disclinations

Using a geometric approach for the propagation of light in anisotropic media, we investigate what effect the director field of disclinations may have on the polarization state of light. Parallel transport around the defect, of the spinor describing the polarization, indicates the acquisition of a topological phase, in analogy with the Aharonov-Bohm effect.Comment: 6 pages, to appear in Europhysics Letter