Unified Field Theoretical Models from Generalized Affine Geometries III

In this work the underlying structure of new type of Unified Field Theoretical model introduced in by the authors is elucidated and analyzed from the geometrical and group theoretical point of view. Our goal is to take advantage of the geometrical and topological properties of this theory in order to determine the minimal group structure of the resultant spacetime manifold able to support a fermionic structure. From this fact, the relation between antisymmetric torsion and Dirac structure of the spacetime is determined and important physical consequences enumerated. In the case of spacetime with torsion the real meaning of the spin-frame alignment is find and the question of the minimal coupling is discussed based in the important cases of tratorial, totally antisymmetric and general torsion fields.     

A conserved karyotype of Sternopygus macrurus (Sternopygidae, Gymnotiformes) in the Amazon region: differences from other hydrographic basins suggest cryptic speciation

We studied the karyotypes of 35 Sternopygus macrurus fishes of four localities from rivers of the Eastern Amazon basin. In these four places the karyotypes have 2n = 46 chromosomes, NF = 92, where 30 are metacentric (M) and 16 submetacentric (SM). The constitutive heterochromatin (CH) is found in the centromeric region of most chromosomes and in the pericentromeric region of pairs 5, 17 and 19. Pair 1 has a large and not common heterochromatic block in the short arm, useful as a marker for this species if not found in other Sternopygus taxa. The NOR is located in the distal region of the short arm of pair 1, showing a size heteromorphism in some specimens. The CMA₃ and DAPI fluorochrome bandings and the fluorescent in situ hybridization (FISH), using pantelomeric human probes techniques are described for the first time for this species. DAPI has banding coincident with the C-banded regions, which suggests that the CH is AT base-pair-rich. CMA₃ banding is coincident with the NOR, meaning that this region is GC base-pair-rich. The FISH showed that the probes hybridized only with the telomeric regions, without any sign of interstitial telomeric regions. The karyotype of the samples from different places in the Amazon basin is quite conserved, probably because of the gene flow among the populations. The karyotype differences among the Sternopygus macrurus from the Amazon basin and the São Francisco and Paraná rivers suggest that these taxa may be different species.     

Thermodynamics based on the principle of least abbreviated action: Entropy production in a network of coupled oscillators

We present some novel thermodynamic ideas based on the Maupertuis principle. By considering Hamiltonians written in terms of appropriate action-angle variables we show that thermal states can be characterized by the action variables and by their evolution in time when the system is nonintegrable. We propose dynamical definitions for the equilibrium temperature and entropy as well as an expression for the nonequilibrium entropy valid for isolated systems with many degrees of freedom. This entropy is shown to increase in the relaxation to equilibrium of macroscopic systems with short-range interactions, which constitutes a dynamical justification of the Second Law of Thermodynamics. Several examples are worked out to show that this formalism yields the right microcanonical (equilibrium) quantities. The relevance of this approach to nonequilibrium situations is illustrated with an application to a network of coupled oscillators (Kuramoto model). We provide an expression for the entropy production in this system finding that its positive value is directly related to dissipation at the steady state in attaining order through synchronization.     

Diffusion in a one-dimensional gas of hard point particles

We simulate the classical diffusion of a particle of massM in an infinite one-dimensional system of hard point particles of massm in equilibrium. Each computer run corresponds to about 10⁸ collisions of the diffusive particle. We find that (t) 1/t fort large enough, and a crossover from an M m regime where=2 to=3 forM=m. The diffusion constant has a sharp maximum atM=m. We study moments x(t)² and x(t)⁴, and examine the behavior ofq ² (t)=x(t)⁴/3x(t)²². We find thatq(t)1 (consistent with a normal distribution) in theM limit (for all timest) and in the t limit for allM. On sabbatical leave from IVIC-Instituto Venezolano de Investigaciones Cientificas.     

Gas‐phase elimination kinetics of selected aliphatic α,β‐unsaturated aldehydes catalyzed by hydrogen chloride

The gas‐phase elimination of 2‐methyl‐2‐propenal catalyzed by HCl yields propene and CO gas, while E‐2‐pentenal with the same catalyst gives butene and CO gas. The kinetics determinations were carried out in a static system with the reaction vessels deactivated with allyl bromide and the presence of the free radical inhibitor toluene. Temperature and pressure ranges were 350.0–410.0 °C and 34–76 Torr. The elimination reactions are homogeneous and unimolecular, and follow a first‐order rate law. The rate coefficients for the reactions are expressible by the following Arrhenius equations: Data from the kinetic and thermodynamic parameters of these catalyzed elimination reactions implies a mechanism of a concerted five‐membered cyclic transition state structure for the formation of the corresponding olefin and carbon monoxide. Copyright © 2015 John Wiley & Sons, Ltd.     

Exact solution of a coagulation equation with a product kernel in the multicomponent case

In this paper, we obtain the general solution for the continuous Smoluchowski equation in the multicomponent case with a product kernel as a series expansion. The solution of the problem involves the Laplace transform in several dimensions. We obtain a nonlinear partial differential equation (PDE) of the advective kind generalizing the one previously given by other authors for the mono-component case.As in its relative mono-component case, gelation is produced at some point, the conditions for its occurrence being the same as those for the mono-component case, though substituting a sum of derivatives by a derivative in the Laplace transform field. We demonstrate that for a multicomponent particle size distribution (PSD) of multiplicative form, it is sufficient for one of the marginal PSDs to generate instantaneous gelation for the occurrence of instantaneous gelation in the multicomponent PSD.The general solution is applied to several specific cases, a discrete case that recovers a previously known solution, and another two continuous cases which can be used to check numerical methods designed to directly solve the Smoluchowski equation in more general cases.We have compared the solutions for the multicomponent PSD for constant, additive and product kernels and we conjecture about the relation existing between the functional forms for the solutions both in the mono-component and the multicomponent case.Finally, we have analysed the shape of the solutions for multicomponent PSD for constant, additive and product kernels for very small masses of components, obtaining a qualitatively different behaviour for the product kernel. This has effects in the mixing state of the sol phase as time passes.     

Measurement of geometric phase for mixed states using single photon interferometry

Geometric phase may enable inherently fault-tolerant quantum computation. However, due to potential decoherence effects, it is important to understand how such phases arise for mixed input states. We report the first experiment to measure mixed-state geometric phases in optics, using a Mach-Zehnder interferometer, and polarization mixed states that are produced in two different ways: decohering pure states with birefringent elements; and producing a nonmaximally entangled state of two photons and tracing over one of them, a form of remote state preparation.     

The hydrogen atom as a projection of an homogeneous space

The Kustaanheimo-Stiefel transformation as applied to the nonrelativistic hydrogen atom provides one of the rare examples of a free particle moving on a four-dimensional homogeneous space.