In this work we analyze the existence of solution to the fractional quasilinear problem, \begin{equation*} \left\{ \begin{array}{rcll} (-\Delta)^s u &= & |\nabla u|^{p}+ \l f & \text{ in }\Omega , u &=& 0 &\hbox{ in } \mathbb{R}^N\setminus\Omega, u&>&0 &\hbox{ in }\Omega, \end{array}% \right. \end{equation*}% where $\Omega \subset \ren$ is a bounded regular domain ($\mathcal{C}^2$ is sufficient), $s\in (\frac 12, 1)$, $1<p$ and $f$ is a measurable nonnegative function with suitable hypotheses. The analysis is done separately in three cases, subcritical, $1<p<2s$, critical, $p=2s$, and supercritical, $p>2s$.

Boumediene Abdellaoui Ireneo Peral

In this work, we are interested on the study of the Fujita exponent and the meaning of the blow-up for the Fractional Cauchy problem with the Hardy potential, namely, \begin{equation*} u_t+(-\Delta)^s u=\lambda\dfrac{u}{|x|^{2s}}+u^{p}\inn\ren,\\ u(x,0)=u_{0}(x)\inn\ren, \end{equation*} where $N> 2s$, $0<s<1$, $(-\Delta)^s$ is the fractional laplacian of order $2s$, $\l>0$, $u_0\ge 0$, and $1<p<p_{+}(s,\lambda)$, where $p_{+}(\lambda, s)$ is the critical existence power found in \cite{BMP} and \cite{AMPP}.

Boumediene Abdellaoui Ireneo Peral Ana Primo

The search for correlations between secondary cosmic ray detection rates and seismic effects has long been a subject of investigation motivated by the hope of identifying a new precursor type that could feed a global early warning system against earthquakes. Here we show for the first time that the average variation of the cosmic ray detection rates correlates with the global seismic activity to be observed with a time lag of approximately two weeks, and that the significance of the effect varies with a periodicity resembling the undecenal solar cycle, with a shift in phase of around three years, exceeding 6 sigma at local maxima. The precursor characteristics of the observed correlations point to a pioneer perspective of an early warning system against earthquakes.

P. Homola V. Marchenko A. Napolitano R. Damian R. Guzik D. Alvarez-Castillo S. Stuglik O. Ruimi O. Skorenok J. Zamora-Saa J. M. Vaquero T. Wibig M. Knap K. Dziadkowiec M. Karpiel O. Sushchov J. W. Mietelski K. Gorzkiewicz N. Zabari K. Almeida Cheminant B. Idźkowski T. Bulik G. Bhatta N. Budnev R. Kamiński M. V. Medvedev K. Kozak O. Bar Ł. Bibrzycki M. Bielewicz M. Frontczak P. Kovács B. Łozowski J. Miszczyk M. Niedźwiecki L. del Peral M. Piekarczyk M. D. Rodriguez Frias K. Rzecki K. Smelcerz T. Sośnicki J. Stasielak A. A. Tursunov

The current methods to determine the primary energy of ultra-high energy cosmic rays (UHECRs) are different when dealing with hadron or photon primaries. The current experiments combine two different techniques, an array of surface detectors and fluorescence telescopes. The latter allow an almost calorimetric measurement of the primary energy. Thus, hadron-initiated showers detected by both type of detectors are used to calibrate the energy estimator from the surface array (usually the interpolated signal at a certain distance from the shower core S(r0)) with the primary energy. On the other hand, this calibration is not feasible when searching for photon primaries since no high energy photon has been unambiguously detected so far. Therefore, pure Monte Carlo parametrizations are used instead. In this work, we present a new method to determine the primary energy of hadron-induced showers in a hybrid experiment based on a technique previously developed for photon primaries. It consists on a set of calibration curves that relate the surface energy estimator, S(r0), and the depth of maximum development of the shower, Xmax, obtained from the fluorescence telescopes. Then, the primary energy can be determined from pure surface information since S(r0) and the zenith angle of the incoming shower are only needed. Considering a mixed sample of ultra-high energy proton and iron primaries and taking into account the reconstruction uncertainties and shower to shower fluctuations, we demonstrate that the primary energy may be determined with a systematic uncertainty below 1% and resolution around 16% in the energy range from 10^{18.5} to 10^{19.6} eV. Several array geometries, the shape of the energy error distributions and the uncertainties due to the unknown composition of the primary flux have been analyzed as well.

G. Ros G. A. Medina-Tanco A. D. Supanitsky L. del Peral M. D. Rodríguez-Frías

In this paper we study a variational Neumann problem for the higher order $s$-fractional Laplacian, with $s>1$. In the process, we introduce some non-local Neumann boundary conditions that appear in a natural way from a Gauss-like integration formula.

B. Barrios L. Montoro I. Peral F. Soria

The aim goal of this paper is to treat the following problem \begin{equation*} \left\{ \begin{array}{rcll} u_t+(-\D^s_{p}) u &=&\dyle \l \dfrac{u^{p-1}}{|x|^{ps}} & \text{ in } \O_{T}=\Omega \times (0,T), \\ u&\ge & 0 & \text{ in }\ren \times (0,T), \\ u &=& 0 & \text{ in }(\ren\setminus\O) \times (0,T), \\ u(x,0)&=& u_0(x)& \mbox{ in }\O, \end{array}% \right. \end{equation*} where $\Omega$ is a bounded domain containing the origin, $$ (-\D^s_{p})\, u(x,t):=P.V\int_{\ren} \,\dfrac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{N+ps}} \,dy$$ with $1<p<N, s\in (0,1)$ and $f, u_0$ are non negative functions. The main goal of this work is to discuss the existence of solution according to the values of $p$ and $\l$.

Boumediene Abdellaoui Amhed Attar Rachid Bentifour ireneo Peral

The concept of the capacity of a compact set in $\mathbb R^n$ generalizes readily to noncompact Riemannian manifolds and, with more substantial work, to metric spaces (where multiple natural definitions of capacity are possible). Motivated by analytic and geometric considerations, and in particular Jauregui's definition of capacity-volume mass and Jauregui and Lee's results on the lower semicontinuity of the ADM mass and Huisken's isoperimetric mass, we investigate how the capacity functional behaves when the background spaces vary. Specifically, we allow the background spaces to consist of a sequence of local integral current spaces converging in the pointed Sormani--Wenger intrinsic flat sense. For the case of volume-preserving ($\mathcal{VF}$) convergence, we prove two theorems that demonstrate an upper semicontinuity phenomenon for the capacity: one version is for balls of a fixed radius centered about converging points; the other is for Lipschitz sublevel sets. Our approach is motivated by Portegies' investigation of the semicontinuity of eigenvalues under $\mathcal{VF}$ convergence. We include examples to show the semicontinuity may be strict, and that the volume-preserving hypothesis is necessary. Finally, there is a discussion on how capacity and our results may be used towards understanding the general relativistic total mass in non-smooth settings.

Jeffrey L. Jauregui Raquel Perales Jacobus W. Portegies

The Japanese Experiment Module (JEM) Extreme Universe Space Observatory (EUSO) will be launched and attached to the Japanese module of the International Space Station (ISS). Its aim is to observe UV photon tracks produced by ultra-high energy cosmic rays developing in the atmosphere and producing extensive air showers. The key element of the instrument is a very wide-field, very fast, large-lense telescope that can detect extreme energy particles with energy above $10^{19}$ eV. The Atmospheric Monitoring System (AMS), comprising, among others, the Infrared Camera (IRCAM), which is the Spanish contribution, plays a fundamental role in the understanding of the atmospheric conditions in the Field of View (FoV) of the telescope. It is used to detect the temperature of clouds and to obtain the cloud coverage and cloud top altitude during the observation period of the JEM-EUSO main instrument. SENER is responsible for the preliminary design of the Front End Electronics (FEE) of the Infrared Camera, based on an uncooled microbolometer, and the manufacturing and verification of the prototype model. This paper describes the flight design drivers and key factors to achieve the target features, namely, detector biasing with electrical noise better than $100 \mu$V from $1$ Hz to $10$ MHz, temperature control of the microbolometer, from $10^{\circ}$C to $40^{\circ}$C with stability better than $10$ mK over $4.8$ hours, low noise high bandwidth amplifier adaptation of the microbolometer output to differential input before analog to digital conversion, housekeeping generation, microbolometer control, and image accumulation for noise reduction.

Oscar Maroto Laura Díez-Merino Jordi Carbonell Albert Tomàs Marcos Reyes Enrique Joven Yolanda Martín J. A. Morales de los Ríos Luis Del Peral M. D. Rodríguez Frías

A drift-diffusion model of miniband transport in strongly coupled superlattices is derived from the single-miniband Boltzmann-Poisson transport equation with a BGK (Bhatnagar-Gross-Krook) collision term. We use a consistent Chapman-Enskog method to analyze the hyperbolic limit, at which collision and electric field terms dominate the other terms in the Boltzmann equation. The reduced equation is of the drift-diffusion type, but it includes additional terms, and diffusion and drift do not obey the Einstein relation except in the limit of high temperatures.

L. L. Bonilla R. Escobedo A. Perales

One of the instruments aboard the Sunrise III mission, the Tunable Magnetograph (TuMag), is a tunable imaging spectropolarimeter in visible wavelengths. It is designed to probe the vector magnetic field and the line-of-sight velocity of the photosphere and the lower chromosphere. The quasi-simultaneous observation of two spectral lines provides excellent diagnostic measurements of the magnetic and dynamic coupling in these layers. The key technologies employed for TuMag are an LCVR-based polarimeter and a solid, LiNbO3 Fabry-P\'erot etalon as a spectrometer. However, it also incorporates several innovative features, such as home-made high-sensitivity scientific cameras and a double filter wheel. TuMag can sequentially observe any two out of the three spectral lines of Fe I at 525.02 and 525.06 nm and of Mg I at 517.3 nm. Laboratory measurements have demonstrated outstanding performance, including a wavefront root-mean-square error better than {\lambda}/13 for image quality, a full-width-at-half-maximum of 8.7 pm for the filtergraph transmission profile, and polarimetric efficiencies > 0.54. Here we report on the concept, design, calibration, and integration phases of the instrument, as well as on the data reduction pipeline.

J. C. del Toro Iniesta D. Orozco Suárez A. Álvarez-Herrero E. Sanchis Kilders I. Pérez-Grande B. Ruiz Cobo L. R. Bellot Rubio M. Balaguer Jiménez A. C. López Jiménez D. Álvarez García J. L. Ramos Más J. P. Cobos Carrascosa P. Labrousse A. J. Moreno Mantas J. M. Morales-Fernández B. Aparicio del Moral A. Sánchez Gómez E. Bailón Martínez F. J. Bailén H. Strecker A. L. Siu-Tapia P. Santamarina Guerrero A. Moreno Vacas J. Atiénzar García A. J. Dorantes Monteagudo I. Bustamante A. Tobaruela A. Fernández-Medina A. Núñez Peral M. Cebollero D. Garranzo-García P. García Parejo A. Gonzalo Melchor A. Sánchez Rodríguez A. Campos-Jara H. Laguna M. Silva-López J. Blanco Rodríguez J. L. Gasent Blesa P. Rodríguez Martínez A. Ferreres D. Gilabert Palmer I. Torralbo J. Piqueras D. González-Bárcena A. J. Fernández D. Hernández Expósito E. Páez Mañá E. Magdaleno Castelló M. Rodríguez Valido Andreas Korpi-Lagg Achim Gandorfer Sami K. Solanki Thomas Berkefeld Pietro Bernasconi Alex Feller Yukio Katsukawa Tino L. Riethmüller H. N. Smitha Masahito Kubo Valentín Martínez Pillet Bianca Grauf Alexander Bell Michael Carpenter