Contractions, deformations and curvature

The role of curvature in relation with Lie algebra contractions of the pseudo-ortogonal algebras so(p,q) is fully described by considering some associated symmetrical homogeneous spaces of constant curvature within a Cayley-Klein framework. We show that a given Lie algebra contraction can be interpreted geometrically as the zero-curvature limit of some underlying homogeneous space with constant curvature. In particular, we study in detail the contraction process for the three classical Riemannian spaces (spherical, Euclidean, hyperbolic), three non-relativistic (Newtonian) spacetimes and three relativistic ((anti-)de Sitter and Minkowskian) spacetimes. Next, from a different perspective, we make use of quantum deformations of Lie algebras in order to construct a family of spaces of non-constant curvature that can be interpreted as deformations of the above nine spaces. In this framework, the quantum deformation parameter is identified as the parameter that controls the curvature of such "quantum" spaces.Comment: 17 pages. Based on the talk given in the Oberwolfach workshop: Deformations and Contractions in Mathematics and Physics (Germany, january 2006) organized by M. de Montigny, A. Fialowski, S. Novikov and M. Schlichenmaie

Controlling shot noise in double-barrier magnetic tunnel junctions

We demonstrate that shot noise in Fe/MgO/Fe/MgO/Fe double-barrier magnetic tunnel junctions is determined by the relative magnetic configuration of the junction and also by the asymmetry of the barriers. The proposed theoretical model, based on sequential tunneling through the system and including spin relaxation, successfully accounts for the experimental observations for bias voltages below 0.5V, where the influence of quantum well states is negligible. A weak enhancement of conductance and shot noise, observed at some voltages (especially above 0.5V), indicates the formation of quantum well states in the middle magnetic layer. The observed results open up new perspectives for a reliable magnetic control of the most fundamental noise in spintronic structures.Comment: 8 pages, 4 figure

Faecal Transplantation, Pro- and Prebiotics in Parkinson's Disease; Hope or Hype?

Faecal microbiome transplantation (FMT) is an attractive technique, because the administration is relatively simple and in general has a mild adverse effect pattern. Moreover, FMT consists of a broad mixture, which could be beneficial, because at this moment it is not known what type of changes in the microbiome are needed. However, except from a few cases no clinical data in Parkinson's disease (PD) is available yet. There is some indication that FMT might be beneficial in severe constipated PD patients, but the clinical data to support this are very scarce. So, actually there are no good data in the public domain to support FMT at this moment in PD patients. FMT at this moment is a black box with too many unanswered questions, also with respect to safety concerns. Only the administration of species of Lactobacillus and Bifidobacterium over a time period of four to twelve weeks has repeatedly proven to be effective in treating constipation in PD. Also, no solid clinical data are available about the possible effects of probiotic treatment on motor symptoms or progression of PD. Therefore, also probiotic treatments in PD should wait until better clinical data become available, in order to select the right target populations and to have good estimates of the clinical effects to be expected

The harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvature

The harmonic oscillator as a distinguished dynamical system can be defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane, and more generally on any configuration space with constant curvature and with a metric of any signature, either Riemannian (definite positive) or Lorentzian (indefinite). In this paper we study the main properties of these `curved' harmonic oscillators simultaneously on any such configuration space, using a Cayley-Klein (CK) type approach, with two free parameters \ki, \kii which altogether correspond to the possible values for curvature and signature type: the generic Riemannian and Lorentzian spaces of constant curvature (sphere ${\bf S}^2$, hyperbolic plane ${\bf H}^2$, AntiDeSitter sphere {\bf AdS}^{\unomasuno} and DeSitter sphere {\bf dS}^{\unomasuno}) appear in this family, with the Euclidean and Minkowski spaces as flat limits. We solve the equations of motion for the `curved' harmonic oscillator and obtain explicit expressions for the orbits by using three different methods: first by direct integration, second by obtaining the general CK version of the Binet's equation and third, as a consequence of its superintegrable character. The orbits are conics with centre at the potential origin in any CK space, thereby extending this well known Euclidean property to any constant curvature configuration space. The final part of the article, that has a more geometric character, presents those results of the theory of conics on spaces of constant curvature which are pertinent.Comment: 29 pages, 6 figure

Past climate changes facilitated homoploid speciation in three mountain spiny fescues (Festuca, Poaceae)

Apart from the overwhelming cases of allopolyploidization, the impact of speciation through homoploid hybridization is becoming more relevant than previously thought. Much less is known, however, about the impact of climate changes as a driven factor of speciation. To investigate these issues, we selected Festuca picoeuropeana, an hypothetical natural hybrid between the diploid species F. eskia and F. gautieri that occurs in two different mountain ranges (Cantabrian Mountains and Pyrenees) separated by more than 400 km. To unravel the outcomes of this mode of speciation and the impact of climate during speciation we used a multidisciplinary approach combining genome size and chromosome counts, data from an extensive nuclear genotypic analysis, plastid sequences and ecological niche models (ENM). Our results show that the same homoploid hybrid was originated independently in the two mountain ranges, being currently isolated from both parents and producing viable seeds. Parental species had the opportunity to contact as early as 21000 years ago although niche divergence occurs nowadays as result of a climate-driven shift. A high degree of niche divergence was observed between the hybrid and its parents and no recent introgression or backcrossed hybrids were detected, supporting the current presence of reproductive isolation barriers between these species

A new Doubly Special Relativity theory from a quantum Weyl-Poincare algebra

A mass-like quantum Weyl-Poincare algebra is proposed to describe, after the identification of the deformation parameter with the Planck length, a new relativistic theory with two observer-independent scales (or DSR theory). Deformed momentum representation, finite boost transformations, range of rapidity, energy and momentum, as well as position and velocity operators are explicitly studied and compared with those of previous DSR theories based on kappa-Poincare algebra. The main novelties of the DSR theory here presented are the new features of momentum saturation and a new type of deformed position operators.Comment: 13 pages, LaTeX; some references and figures added, and terminology is more precis

Evaluation of the transport properties of copper ions through a heterogeneous ion-exchange membrane in etidronic acid solutions by chronopotentiometry

[EN] The transport properties of copper chelates across an anion-exchange membrane were investigated by means of chronopotentiometry. Several solutions containing etidronic acid, copper sulfate and potassium chloride were evaluated. Tests were accomplished in a three-compartment reactor using a heterogeneous membrane containing quaternary ammonium functional groups. Results showed a strong relation between the amount of chelated anions and the limiting current density, the electrical resistance and the concentration polarization. An increase in the anionic equivalent charge of the solutions modified the three regions of the current-voltage curves. The acid medium was found to be less favorable because of the possibility of the formation of non-charged species in overlimiting regions. The presence of chloride anions increased the limiting current density, especially when the chloride concentration exceeded the etidronic acid concentration.Authors would like to thank the Institute for Technological Research (IPT), the Institute for Technological Research Foundation (FIPT), to the São Paulo Research Foundation (Fapesp - processes 2012/51871-9, 2014/21943-3 and 2014/13351-9) and the National Council for Scientific and Technological Development.Scarazzato, T.; Panossian, Z.; García Gabaldón, M.; Ortega Navarro, EM.; Tenório, J.; Pérez-Herranz, V.; Espinosa, D. (2017). Evaluation of the transport properties of copper ions through a heterogeneous ion-exchange membrane in etidronic acid solutions by chronopotentiometry. Journal of Membrane Science. 535:268-278. https://doi.org/10.1016/j.memsci.2017.04.048S26827853