Semilinear problems for the fractional laplacian with a singular nonlinearity

The aim of this paper is to study the solvability of the problem (-Δ)s u = F(x,u) := λ f(x)/uγ + Mup in ω u > 0 in ω, u = 0 in RN \ ω, where Ω is a bounded smooth domain of RN, N > 2s, M ε {0, 1}, 0 0, λ > 0, p > 1 and f is a nonnegative function. We distinguish two cases: - For M = 0, we prove the existence of a solution for every γ > 0 and λ > 0. A1 - For M = 1, we consider f ≡ 1 and we find a threshold ∧ such that there exists a solution for every 0 ∧Work partially supported by project MTM2013-40846-P MINECO. The third author is also supported for the grant BES-2011-044216 associated to MTM2010-1812

Data-driven model reduction-based nonlinear MPC for large-scale distributed parameter systems

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordModel predictive control (MPC) has been effectively applied in process industries since the 1990s. Models in the form of closed equation sets are normally needed for MPC, but it is often difficult to obtain such formulations for large nonlinear systems. To extend nonlinear MPC (NMPC) application to nonlinear distributed parameter systems (DPS) with unknown dynamics, a data-driven model reduction-based approach is followed. The proper orthogonal decomposition (POD) method is first applied off-line to compute a set of basis functions. Then a series of artificial neural networks (ANNs) are trained to effectively compute POD time coefficients. NMPC, using sequential quadratic programming is then applied. The novelty of our methodology lies in the application of POD's highly efficient linear decomposition for the consequent conversion of any distributed multi-dimensional space-state model to a reduced 1-dimensional model, dependent only on time, which can be handled effectively as a black-box through ANNs. Hence we construct a paradigm, which allows the application of NMPC to complex nonlinear high-dimensional systems, even input/output systems, handled by black-box solvers, with significant computational efficiency. This paradigm combines elements of gain scheduling, NMPC, model reduction and ANN for effective control of nonlinear DPS. The stabilization/destabilization of a tubular reactor with recycle is used as an illustrative example to demonstrate the efficiency of our methodology. Case studies with inequality constraints are also presented.The authors would like to acknowledge the financial support of the EC FP6 Project: CONNECT [COOP-2006-31638] and the EC FP7 project CAFE [KBBE-212754]

MatLab Toolbox for the numerical solution of linear Volterra integral equations arising in metastatic tumor growth models

This paper introduces VIE Toolbox composed by fourteen MatLab functions used for the numerical resolution of Volterra Integral Equations (VIEs) of the second kind on infinite intervals. An application to metastatic tumor growth models is also considered, assuming five different tumor growth laws, e.g. exponential, power-law, Gompertz, generalized logistic and von Bertalanffy-West laws, for lung and breast tumors data

Evaluation of the Iatrogenic Sciatic Nerve Injury following Double Pelvic Osteotomy Performed with Piezoelectric Cutting Tool in Dogs

(1) Background: The double pelvic osteotomy (DPO) is a prophylactic surgical procedure associated with 0.4% incidence of sciatic nerve injury. The piezoelectric cutting tool is a surgical device able to involve only mineralized tissue avoiding neurovascular tissue and other soft tissue. This study aimed to evaluate the sciatic nerve injury observed in dogs underwent iliac osteotomy performed using the piezoelectric cutting tool. (2) Methods: Dogs underwent DPO performed with piezoelectric cutting tool were included. Neurological assessment was performed 6 and 24 h after surgery and then repeated 12 days, 4 and 8 weeks after surgery. Temporary and or permanent sciatic nerve injury were recorded. (3) Results: 84 DPOs performed in fifty dogs were included. No temporary/permanent neurological disease associated with iatrogenic damage of the sciatic nerve were observed. (4) Conclusions: The iliac osteotomy performed with piezoelectric cutting tool was not associated to iatrogenic sciatic nerve injury

A compact array calibrator to study the feasibility of acoustic neutrino detection

[EN] Underwater acoustic detection of ultra-high-energy neutrinos was proposed already in 1950s: when a neutrino interacts with a nucleus in water, the resulting particle cascade produces a pressure pulse that has a bipolar temporal structure and propagates within a flat disk-like volume. A telescope that consists of thousands of acoustic sensors deployed in the deep sea can monitor hundreds of cubic kilometres of water looking for these signals and discriminating them from acoustic noise. To study the feasibility of the technique it is critical to have a calibrator able to mimic the neutrino signature that can be operated from a vessel. Due to the axial-symmetry of the signal, their very directive short bipolar shape and the constraints of operating at sea, the development of such a calibrator is very challenging. Once the possibility of using the acoustic parametric technique for this aim was validated with the first compact array calibrator prototype, in this paper we describe the new design for such a calibrator composed of an array of piezo ceramic tube transducers emitting in axial direction.We acknowledge the financial support of the Spanish Ministerio de Economía y Competitividad, Grants FPA2012-37528-C02-02, and Consolider MultiDark CSD2009-00064, of the Generalitat Valenciana, Grants ACOMP/2015/175 PrometeoII/2014/079 and of the European FEDER funds.Ardid Ramírez, M.; Camarena Femenia, F.; Felis-Enguix, I.; Herrero Debón, A.; Llorens Alvarez, CD.; Martínez Mora, JA.; Saldaña-Coscollar, M. (2016). A compact array calibrator to study the feasibility of acoustic neutrino detection. EPJ Web of Conferences. 116(03001):1-4. https://doi.org/10.1051/epjconf/201611603001S141160300

Indirect detection of Dark Matter with the ANTARES Neutrino Telescope

[EN] One of the main objectives of the ANTARES neutrino telescope is the search for neutrinos produced in self-annihilation of Dark Matter (DM) particles. The analysis for different sources of DM (Sun, Galactic Center, Earth, ...) or DM models (SUSY, Secluded) will be described and the results presented. The specific advantages of neutrino telescopes in general and of ANTARES in particular will be explained. As an example, the indirect search for DM towards the Sun performed by neutrino telescopes currently leads to more stringent limits on the spin-dependent WIMP-nucleon cross section with respect to existing direct detection experiments.We acknowledge the financial support of the Spanish Ministerio de Economía y Competitividad, Grants FPA2012-37528-C02-02, and Consolider MultiDark CSD2009-00064, of the Generalitat Valenciana, Grants ACOMP/2015/175 PrometeoII/2014/079 and of the European FEDER funds.Ardid Ramírez, M. (2016). Indirect detection of Dark Matter with the ANTARES Neutrino Telescope. EPJ Web of Conferences. 116:1-5. https://doi.org/10.1051/epjconf/201611604002S1511

All-sky Search for High-Energy Neutrinos from Gravitational Wave Event GW170104 with the ANTARES Neutrino Telescope

Advanced LIGO detected a significant gravitational wave signal (GW170104) originating from the coalescence of two black holes during the second observation run on January 4$^{\textrm{th}}$, 2017. An all-sky high-energy neutrino follow-up search has been made using data from the ANTARES neutrino telescope, including both upgoing and downgoing events in two separate analyses. No neutrino candidates were found within $\pm500$ s around the GW event time nor any time clustering of events over an extended time window of $\pm3$ months. The non-detection is used to constrain isotropic-equivalent high-energy neutrino emission from GW170104 to less than $\sim4\times 10^{54}$ erg for a $E^{-2}$ spectrum

The ANTARES Collaboration: Contributions to ICRC 2017 Part I: Neutrino astronomy (diffuse fluxes and point sources)

Papers on neutrino astronomy (diffuse fluxes and point sources, prepared for the 35th International Cosmic Ray Conference (ICRC 2017, Busan, South Korea) by the ANTARES Collaboratio