More than 130 observation days of the horizontal and vertical extent of Saharan dust intrusions over Europe during the period May 2000 to December 2002 were studied by means of a coordinated lidar network in the frame of the European Aerosol Research Lidar Network (EARLINET). The number of dust events was greatest in late spring, summer, and early autumn periods, mainly in southern (S) and southeastern (SE) Europe. Multiple aerosol dust layers of variable thickness (300–7500 m) were observed. The center of mass of these layers was located in altitudes between 850 and 8000 m. However, the mean thickness of the dust layer typically stayed around 1500–3400 m and the corresponding mean center of mass ranged from 2500 to 6000 m. In exceptional cases, dust aerosols reached northwestern (NW), northern (N), or northeastern (NE) Europe, penetrating the geographical area located between 4°W–28°E (longitude) and 38°N–58°N (latitude). Mean aerosol optical depths (AOD), extinction-to-backscatter ratios (lidar ratios, LR), and linear depolarization ratios of desert aerosols ranged from 0.1 to 0.25 at the wavelength of 355 or 351 nm, 30 to 80 sr at 355 or 351 nm, and 10 to 25% at 532 nm, respectively, within the lofted dust plumes. In these plumes typical Saharan dust backscatter coefficients ranged from 0.5 to 2 Mm−1sr−1. Southern European stations presented higher variability of the LR values and the backscatter-related Ångström exponent values (BRAE) (LR: 20–100 sr; BRAE: −0.5 to 3) than northern ones (LR: 30–80 sr; BRAE: −0.5 to 1)

In this article we use 5-brane junctions to study the 5D T N SCFTs corresponding to the 5D N = 1 uplift of the 4D N = 2 strongly coupled gauge theories, which are obtained by compactifying N M5 branes on a sphere with three full punctures. Even though these theories have no Lagrangian description, by using the 5-brane junctions proposed by Benini, Benvenuti and Tachikawa, we are able to derive their Seiberg-Witten curves and Nekrasov partition functions. We cross-check our results with the 5D superconformal index proposed by Kim, Kim and Lee. Through the AGTW correspondence, we discuss the relations between 5D superconformal indices and n-point functions of the q-deformed W N Toda theories.

We use modern bootstrap techniques to study half-BPS line defects in 4d N = 4 superconformal theories. Specifically, we consider the 1d CFT with OSP(4 * |4) superconformal symmetry living on such a defect. Our analysis is general and based only on symmetries, it includes however important examples like Wilson and 't Hooft lines in N = 4 super Yang-Mills. We present several numerical bounds on OPE coefficients and conformal dimensions. Of particular interest is a numerical island obtained from a mixed correlator bootstrap that seems to imply a unique solution to crossing. The island is obtained if some assumptions about the spectrum are made, and is consistent with Wilson lines in planar N = 4 super Yang-Mills at strong coupling. We further analyze the vicinity of the strong-coupling point by calculating perturbative corrections using analytic methods. This perturbative solution has the sparsest spectrum and is expected to saturate the numerical bounds, explaining some of the features of our numerical results. B Comments on the derivation of the crossing equations 36 C The analytic solutions to the crossing equations 37 D First order perturbation of D 1 D 1 D 1 D 1 (1,0) 41 8 The function θ(O) is included due to the fact that only operators in D 1 × D 1 contribute to the A {1,1,2,2} function.

In Phys. Rev. Lett. 116 (2016) 062001, the space of planar pentagon functions that describes all two-loop on-shell five-particle scattering amplitudes was introduced. In the present paper we present a natural extension of this space to non-planar pentagon functions. This provides the basis for our pentagon bootstrap program. We classify the relevant functions up to weight four, which is relevant for two-loop scattering amplitudes. We constrain the first entry of the symbol of the functions using information on branch cuts. Drawing on an analogy from the planar case, we introduce a conjectural second-entry condition on the symbol. We then show that the information on the function space, when complemented with some additional insights, can be used to efficiently bootstrap individual Feynman integrals. The extra information is read off of Mellin-Barnes representations of the integrals, either by evaluating simple asymptotic limits, or by taking discontinuities in the kinematic variables. We use this method to evaluate the symbols of two non-trivial non-planar five-particle integrals, up to and including the finite part.

The eruption of the Icelandic volcano Eyjafjallajökull in April- May 2010 represents a "natural experiment" to study the impact of volcanic emissions on a continental scale. For the first time, quantitative data about the presence, altitude, and layering of the volcanic cloud, in conjunction with optical information, are available for most parts of Europe derived from the observations by the European Aerosol Research Lidar NETwork (EARLINET). Based on multi-wavelength Raman lidar systems, EARLINET is the only instrument worldwide that is able to provide dense time series of high-quality optical data to be used for aerosol typing and for the retrieval of particle microphysical properties as a function of altitude. In this work we show the four-dimensional (4-D) distribution of the Eyjafjallajökull volcanic cloud in the troposphere over Europe as observed by EARLINET during the entire volcanic event (15 April-26 May 2010). All optical properties directly measured (backscatter, extinction, and particle linear depolarization ratio) are stored in the EARLINET database available at http://www.earlinet.org. A specific relational database providing the volcanic mask over Europe, realized ad hoc for this specific event, has been developed and is available on request at http://www.earlinet.org.During the first days after the eruption, volcanic particles were detected over Central Europe within a wide range of altitudes, from the upper troposphere down to the local planetary boundary layer (PBL). After 19 April 2010, volcanic particles were detected over southern and south-eastern Europe. During the first half of May (5-15 May), material emitted by the Eyjafjallajökull volcano was detected over Spain and Portugal and then over the Mediterranean and the Balkans. The last observations of the event were recorded until 25 May in Central Europe and in the Eastern Mediterranean area.The 4-D distribution of volcanic aerosol layering and optical properties on European scale reported here provides an unprecedented data set for evaluating satellite data and aerosol dispersion models for this kind of volcanic events