On the behavior of clamped plates under large compression

We determine the asymptotic behavior of eigenvalues of clamped plates under large compression by relating this problem to eigenvalues of the Laplacian with Robin boundary conditions. Using the method of fundamental solutions, we then carry out a numerical study of the extremal domains for the first eigenvalue, from which we see that these depend on the value of the compression, and start developing a boundary structure as this parameter is increased. The corresponding number of nodal domains of the first eigenfunction of the extremal domain also increases with the compression.This work was partially supported by the Funda ̧c ̃ao para a Ciˆencia e a Tecnologia(Portugal) through the program “Investigador FCT” with reference IF/00177/2013 and the projectExtremal spectral quantities and related problems(PTDC/MAT-CAL/4334/2014).info:eu-repo/semantics/publishedVersio

Nonextensivity in the solar magnetic activity during the increasing phase of solar Cycle 23

In this paper we analyze the behavior of the daily Sunspot Number from the Sunspot Index Data Center (SIDC), the mean Magnetic Field strength from the National Solar Observatory/Kitt Peak (NSO/KP) and Total Solar Irradiance means from Virgo/SoHO, in the context of the $q$--Triplet which emerges within nonextensive statistical mechanics. Distributions for the mean solar Magnetic Field show two different behaviors, with a $q$--Gaussian for scales of 1 to 16 days and a Gaussian for scales longer than 32 days. The latter corresponds to an equilibrium state. Distributions for Total Solar Irradiance also show two different behaviors (approximately Gaussian) for scales of 128 days and longer, consistent with statistical equilibrium and $q$--Gaussian for scales $<$ 128 days. Distributions for the Sunspot Number show a $q$--Gaussian independent of timescales, consistent with a nonequilibrium state. The values obtained ("$q$--Triplet"$\equiv$$\{$$q$$_{stat}$,$q$$_{sen}$,$q$$_{rel}$$\}$) demonstrate that the Gaussian or $q$--Gaussian behavior of the aforementioned data depends significantly on timescales. These results point to strong multifractal behavior of the dataset analyzed, with the multifractal level decreasing from Sunspot Number to Total Solar Irradiance. In addition, we found a numerically satisfied dual relation between $q_{stat}$ and $q_{sen}$.Comment: 6 pages, 4 figure

A nonextensive insight to the stellar initial mass function

the present paper, we propose that the stellar initial mass distributions as known as IMF are best fitted by $q$-Weibulls that emerge within nonextensive statistical mechanics. As a result, we show that the Salpeter's slope of $\sim$2.35 is replaced when a $q$-Weibull distribution is used. Our results point out that the nonextensive entropic index $q$ represents a new approach for understanding the process of the star-forming and evolution of massive stars.Comment: 5 pages, 2 figures, Accepted to EP

Strong evidences for a nonextensive behavior of the rotation period in Open Clusters

Time-dependent nonextensivity in a stellar astrophysical scenario combines nonextensive entropic indices $q_{K}$ derived from the modified Kawaler's parametrization, and $q$, obtained from rotational velocity distribution. These $q$'s are related through a heuristic single relation given by $q\approx q_{0}(1-\Delta t/q_{K})$, where $t$ is the cluster age. In a nonextensive scenario, these indices are quantities that measure the degree of nonextensivity present in the system. Recent studies reveal that the index $q$ is correlated to the formation rate of high-energy tails present in the distribution of rotation velocity. On the other hand, the index $q_{K}$ is determined by the stellar rotation-age relationship. This depends on the magnetic field configuration through the expression $q_{K}=1+4aN/3$, where $a$ and $N$ denote the saturation level of the star magnetic field and its topology, respectively. In the present study, we show that the connection $q-q_{K}$ is also consistent with 548 rotation period data for single main-sequence stars in 11 Open Clusters aged less than 1 Gyr. The value of $q_{K}\sim$ 2.5 from our unsaturated model shows that the mean magnetic field topology of these stars is slightly more complex than a purely radial field. Our results also suggest that stellar rotational braking behavior affects the degree of anti-correlation between $q$ and cluster age $t$. Finally, we suggest that stellar magnetic braking can be scaled by the entropic index $q$.Comment: 6 pages and 2 figures, accepted to EPL on October 17, 201

The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics

We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of non-uniformly hyperbolic dynamical systems is compound Poisson. The returns to small balls around a fixed point in the phase space correspond to the occurrence of rare events, or exceedances of high thresholds, so that there is a connection between the laws of Return Times Statistics and Extreme Value Laws. The fact that the fixed point in the phase space is a repelling periodic point implies that there is a tendency for the exceedances to appear in clusters whose average sizes is given by the Extremal Index, which depends on the expansion of the system at the periodic point. We recall that for generic points, the exceedances, in the limit, are singular and occur at Poisson times. However, around periodic points, the picture is different: the respective point processes of exceedances converge to a compound Poisson process, so instead of single exceedances, we have entire clusters of exceedances occurring at Poisson times with a geometric distribution ruling its multiplicity. The systems to which our results apply include: general piecewise expanding maps of the interval (Rychlik maps), maps with indifferent fixed points (Manneville-Pomeau maps) and Benedicks-Carleson quadratic maps.Comment: To appear in Communications in Mathematical Physic

Outflows in the Narrow Line Region of Bright Seyfert Galaxies - I: GMOS-IFU Data

We present two-dimensional maps of emission-line fluxes and kinematics, as well as of the stellar kinematics of the central few kpc of five bright nearby Seyfert galaxies -- Mrk\,6, Mrk\,79, Mrk\,348, Mrk\,607 and Mrk\,1058 -- obtained from observations with the Gemini Multi-Object Spectrograph (GMOS) Integral Field Unit (IFU) on the Gemini North Telescope. The data cover the inner 3\farcs5$\times$5\farcs0 -- corresponding to physical scales in the range 0.6$\times$0.9 to 1.5$\times$2.2\,kpc$^2$ -- at a spatial resolution ranging from 110 to 280 pc with a spectral coverage of 4300 -- 7100\,\AA\ and velocity resolution of $\approx$ 90\,km\,s$^{-1}$. The gas excitation is Seyfert like everywhere but show excitation, but show excitation gradients that are correlated with the gas kinematics, reddening and/or the gas density. The gas kinematics show in all cases two components: a rotation one similar to that observed in the stellar velocity field, and an outflow component. In the case of Mrk607, the gas is counter-rotating relative to the stars. Enhanced gas velocity dispersion is observed in association to the outflows according to two patterns: at the locations of the highest outflow velocities along the ionization axis or perpendicularly to it in a strip centered at the nucleus that we attribute to an equatorial outflow. Bipolar outflows are observed in Mrk\,348 and Mrk\,79, while in Mrk\,1058 only the blueshifted part is clearly observed, while in the cases of Mrk\,6 and Mrk\,607 the geometry of the outflow needs further constraints from modeling to be presented in a forthcoming study, where the mass flow rate and powers will also be obtained.Comment: 20 pages, accepted by MNRA