Fractional isoperimetric Noether's theorem in the Riemann-Liouville sense

We prove Noether-type theorems for fractional isoperimetric variational problems with Riemann-Liouville derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples, in the fractional context of the calculus of variations, are discussed.Comment: Submitted 12-Oct-2012; revised 05-Jan-2013; accepted 23-Jan-2013; for publication in Reports on Mathematical Physics. arXiv admin note: substantial text overlap with arXiv:1001.450

Upholding the unified model for Active Galactic Nuclei: VLT/FORS2 spectropolarimetry of Seyfert 2 galaxies

The origin of the unification model for Active Galactic Nuclei (AGN) was the detection of broad hydrogen recombination lines in the optical polarized spectrum of the Seyfert 2 galaxy (Sy2) NGC 1068. Since then, a search for the hidden broad-line region (HBLR) of nearby Sy2s started, but polarized broad lines have only been detected in ?30–40% of the nearby Sy2s observed to date. Here we present new VLT/FORS2 optical spectropolarimetry of a sample of 15 Sy2s, including Compton-thin and Compton-thick sources. The sample includes six galaxies without previously published spectropolarimetry, some of them normally treated as non-hidden BLR (NHBLR) objects in the literature, four classified as NHBLR, and five as HBLR based on previous data. We report ?4? detections of a HBLR in 11 of these galaxies (73% of the sample) and a tentative detection in NGC 5793, which is Compton-thick according to the analysis of X-ray data performed here. Our results confirm that at least some NHBLRs are misclassified, bringing previous publications reporting differences between HBLR and NHBLR objects into question. We detect broad H? and H? components in polarized light for 10 targets, and just broad H? for NGC 5793 and NGC 6300, with line widths ranging between 2100 and 9600 km s?1. High bolometric luminosities and low column densities are associated with higher polarization degrees, but not necessarily with the detection of the scattered broad components

Solar Intranetwork Magnetic Elements: bipolar flux appearance

The current study aims to quantify characteristic features of bipolar flux appearance of solar intranetwork (IN) magnetic elements. To attack such a problem, we use the Narrow-band Filter Imager (NFI) magnetograms from the Solar Optical Telescope (SOT) on board \emph{Hinode}; these data are from quiet and an enhanced network areas. Cluster emergence of mixed polarities and IN ephemeral regions (ERs) are the most conspicuous forms of bipolar flux appearance within the network. Each of the clusters is characterized by a few well-developed ERs that are partially or fully co-aligned in magnetic axis orientation. On average, the sampled IN ERs have total maximum unsigned flux of several 10^{17} Mx, separation of 3-4 arcsec, and a lifetime of 10-15 minutes. The smallest IN ERs have a maximum unsigned flux of several 10^{16} Mx, separations less than 1 arcsec, and lifetimes as short as 5 minutes. Most IN ERs exhibit a rotation of their magnetic axis of more than 10 degrees during flux emergence. Peculiar flux appearance, e.g., bipole shrinkage followed by growth or the reverse, is not unusual. A few examples show repeated shrinkage-growth or growth-shrinkage, like magnetic floats in the dynamic photosphere. The observed bipolar behavior seems to carry rich information on magneto-convection in the sub-photospheric layer.Comment: 26 pages, 14 figure

Spin glass transition in a magnetic field: a renormalization group study

We study the transition of short range Ising spin glasses in a magnetic field, within a general replica symmetric field theory, which contains three masses and eight cubic couplings, that is defined in terms of the fields representing the replicon, anomalous and longitudinal modes. We discuss the symmetry of the theory in the limit of replica number n to 0, and consider the regular case where the longitudinal and anomalous masses remain degenerate. The spin glass transitions in zero and non-zero field are analyzed in a common framework. The mean field treatment shows the usual results, that is a transition in zero field, where all the modes become critical, and a transition in non-zero field, at the de Almeida-Thouless (AT) line, with only the replicon mode critical. Renormalization group methods are used to study the critical behavior, to order epsilon = 6-d. In the general theory we find a stable fixed-point associated to the spin glass transition in zero field. This fixed-point becomes unstable in the presence of a small magnetic field, and we calculate crossover exponents, which we relate to zero-field critical exponents. In a finite magnetic field, we find no physical stable fixed-point to describe the AT transition, in agreement with previous results of other authors.Comment: 36 pages with 4 tables. To be published in Phys. Rev.

II Ciclo de Conferências : Conselho Técnico-Científico: temas atuais em investigação

A obra é constituída pelos resumos das comunicações apresentadas pelos docentes da Escola Superior Agrária do Instituto Politécnico de Castelo Branco e são referentes aos projetos de investigação nos quais estão envolvidos.O atual Conselho Técnico-Científico (CTC) da Escola Superior Agrária de Castelo Branco (ESACB) tomou posse em fevereiro de 2012, tendo decidido dar continuidade ao ciclo de conferências iniciado pelo CTC anterior. Os trabalhos de Investigação, Inovação e Experimentação que foram apresentados demonstram não só o dinamismo e a ligação com a comunidade, como também a preocupação na identificação e resolução de problemas, que acrescentem valor aos produtos e processos que se situam no âmbito das competências desta Escola. Sendo este um objetivo prioritário da missão do IPCB/ESA, a divulgação destas conferências permite chegar a um público mais alargado e abrir caminhos para a concretização de novos projetos, que contribuam de forma efetiva para o desenvolvimento e aumento da competitividade da região e do país

Replica Symmetry Breaking Instability in the 2D XY model in a random field

We study the 2D vortex-free XY model in a random field, a model for randomly pinned flux lines in a plane. We construct controlled RG recursion relations which allow for replica symmetry breaking (RSB). The fixed point previously found by Cardy and Ostlund in the glass phase $T<T_c$ is {\it unstable} to RSB. The susceptibility $\chi$ associated to infinitesimal RSB perturbation in the high-temperature phase is found to diverge as $\chi \propto (T-T_c)^{-\gamma}$ when $T \rightarrow T_c^{+}$. This provides analytical evidence that RSB occurs in finite dimensional models. The physical consequences for the glass phase are discussed.Comment: 8 pages, REVTeX, LPTENS-94/2

Stokes Diagnostis of 2D MHD-simulated Solar Magnetogranulation

We study the properties of solar magnetic fields on scales less than the spatial resolution of solar telescopes. A synthetic infrared spectropolarimetric diagnostics based on a 2D MHD simulation of magnetoconvection is used for this. We analyze two time sequences of snapshots that likely represent two regions of the network fields with their immediate surrounding on the solar surface with the unsigned magnetic flux density of 300 and 140 G. In the first region we find from probability density functions of the magnetic field strength that the most probable field strength at logtau_5=0 is equal to 250 G. Weak fields (B < 500 G) occupy about 70% of the surface, while stronger fields (B 1000 G) occupy only 9.7% of the surface. The magnetic flux is -28 G and its imbalance is -0.04. In the second region, these parameters are correspondingly equal to 150 G, 93.3 %, 0.3 %, -40 G, and -0.10. We estimate the distribution of line-of-sight velocities on the surface of log tau_5=-1. The mean velocity is equal to 0.4 km/s in the first simulated region. The averaged velocity in the granules is -1.2 km/s and in the intergranules is 2.5 km/s. In the second region, the corresponding values of the mean velocities are equal to 0, -1.8, 1.5 km/s. In addition we analyze the asymmetry of synthetic Stokes-V profiles of the Fe I 1564.8 nm line. The mean values of the amplitude and area asymmetry do not exceed 1%. The spatially smoothed amplitude asymmetry is increased to 10% while the area asymmetry is only slightly varied.Comment: 24 pages, 12 figure

Small-scale solar magnetic fields

As we resolve ever smaller structures in the solar atmosphere, it has become clear that magnetism is an important component of those small structures. Small-scale magnetism holds the key to many poorly understood facets of solar magnetism on all scales, such as the existence of a local dynamo, chromospheric heating, and flux emergence, to name a few. Here, we review our knowledge of small-scale photospheric fields, with particular emphasis on quiet-sun field, and discuss the implications of several results obtained recently using new instruments, as well as future prospects in this field of research.Comment: 43 pages, 18 figure