Substructures in lens galaxies: PG1115+080 and B1555+375, two fold configurations

We study the anomalous flux ratio which is observed in some four-image lens systems, where the source lies close to a fold caustic. In this case two of the images are close to the critical curve and their flux ratio should be equal to unity, instead in several cases the observed value differs significantly. The most plausible solution is to invoke the presence of substructures, as for instance predicted by the Cold Dark Matter scenario, located near the two images. In particular, we analyze the two fold lens systems PG1115+080 and B1555+375, for which there are not yet satisfactory models which explain the observed anomalous flux ratios. We add to a smooth lens model, which reproduces well the positions of the images but not the anomalous fluxes, one or two substructures described as singular isothermal spheres. For PG1115+080 we consider a smooth model with the influence of the group of galaxies described by a SIS and a substructure with mass $\sim 10^{5} M_{\odot}$ as well as a smooth model with an external shear and one substructure with mass $\sim 10^{8} M_{\odot}$ . For B1555+375 either a strong external shear or two substructures with mass $\sim 10^{7} M_{\odot}$ reproduce the data quite well.Comment: 26 pages, updated bibliography, Accepted for publication in Astrophysics & Space Scienc

Long-range Angular Correlations On The Near And Away Side In P-pb Collisions At √snn=5.02 Tev

7191/Mar294

Inverse dynamics based tuning of a fuzzy logic controller for a single-link flexible manipulator

Since its introduction to engineering applications, fuzzy logic has attracted many researchers because of its simplicity and robustness. Experience with a system is translated into heuristic rules which can be used to control that system. This article proposes a novel method for a generalized inverse dynamics based fuzzy logic controller (FLC) of a single-link flexible manipulator. The deflection of the flexible link was modeled using the assumed modes method. The control action is distributed between two FLCs: A joint angle controller and a tip controller. Each controller produces a torque value. The torque values are summed, and the resulting control action is used to drive the manipulator. A novel method for varying the ranges of the variables of the two controllers as a function of the motion parameters and the inverse dynamics of the system is presented. The relative shapes and distribution of the fuzzy membership sets (with respect to each other) are kept fixed. Simulation results show that joint trajectory tracking is accomplished, and that the residual vibration of the flexible link is suppressed