An elementary approach to rigorous approximation of invariant measures

We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general statement on the approximation of fixed points for operators between normed vector spaces, allowing an explicit estimation of the error. We show the flexibility of our approach by applying it to piecewise expanding maps and to maps with indifferent fixed points. We show how the required estimations can be implemented to compute invariant densities up to a given error in the $L^{1}$ or $L^\infty$ distance. We also show how to use this to compute an estimation with certified error for the entropy of those systems. We show how several related computational and numerical issues can be solved to obtain working implementations, and experimental results on some one dimensional maps.Comment: 27 pages, 10 figures. Main changes: added a new section in which we apply our method to Manneville-Pomeau map

Comparison of LHC collimator beam-based alignment to BPM-interpolated centers

The beam centers at the Large Hadron Collider collimators are determined by beam-basedalignment, where both jaws of a collimator are moved in separately until a loss spike isdetected on a Beam Loss Monitor downstream. Orbit drifts of more than a few hundredmicrometers cannot be tolerated, as they would compromise the performance of thecollimation system. Beam Position Monitors (BPMs) are installed at various locations aroundthe LHC ring, and a linear interpolation of the orbit can be obtained at the collimatorpositions. In this paper, the results obtained from beam-based alignment are compared withthe orbit interpolated from the BPM data throughout the 2011 and 2012 LHC proton runs.Louisiana State University (LSU),U.S. Department of Energy, Office of Science,COSYLAB,DIMTEL,Muons, Inc.peer-reviewe

Bose-Einstein correlations of same-sign charged pions in the forward region in pp collisions at √s=7 TeV

Bose-Einstein correlations of same-sign charged pions, produced in protonproton collisions at a 7 TeV centre-of-mass energy, are studied using a data sample collected by the LHCb experiment. The signature for Bose-Einstein correlations is observed in the form of an enhancement of pairs of like-sign charged pions with small four-momentum difference squared. The charged-particle multiplicity dependence of the Bose-Einstein correlation parameters describing the correlation strength and the size of the emitting source is investigated, determining both the correlation radius and the chaoticity parameter. The measured correlation radius is found to increase as a function of increasing charged-particle multiplicity, while the chaoticity parameter is seen to decreas

The Italian Museo Nazionale dell’Antartide

These abstract proceedings were produced based on the program for the POLAR2018 SCAR/IASC Open Science Conference, updated until 25 May 2018