Modeshapes recognition using Fourier descriptors: a simple SHM example

The main objective of this study is to develop an alternative criterion for modeshape classification, as the currently available one, MAC (Modal Assurance Criteria), is only a vector correlation representing modeshape similarities. This new method is developed to provide a set of features (Fourier Descriptors) for comparing modeshapes with “local” similarities of higher interest than “global” similarities using nodal lines. These lines are able to characterize modeshapes very easily. So when damage occurs, we are able to track the few descriptors changes to localise the damage. We validated our method on a CFCF plate demonstrating the quality of the damage localisation and possible use in a “mode tracking” application (space structure)

On the application of differences in intrinsic fluctuations of Cherenkov light images for separation of air showers

The sensitivity of ground-based imaging atmospheric Cherenkov gamma-ray observatories depends critically on the primary particle identification methods which are used to retain photon-initiated events and suppress the spurious background produced by cosmic rays. We suggest a new discrimination technique which utilizes differences in the fluctuations of the light intensity in the images of showers initiated by photons and those initiated by protons or heavier nuclei. The database of simulated events for the proposed VERITAS observatory has been used to evaluate the efficiency of the new technique. Analysis has been performed for both a single VERITAS imaging telescope, and a system of these telescopes. We demonstrate that a discrimination efficiency of > 1.5 - 2.0 can be achieved in addition to traditional background rejection methods based on image shape parameters.Comment: 17 pages, 9 figures, accepted for publucation in Astropart. Phy

Strong field limit of black hole gravitational lensing

We give the formulation of the gravitational lensing theory in the strong field limit for a Schwarzschild black hole as a counterpart to the weak field approach. It is possible to expand the full black hole lens equation to work a simple analytical theory that describes at a high accuracy degree the physics in the strong field limit. In this way, we derive compact and reliable mathematical formulae for the position of additional critical curves, relativistic images and their magnification, arising in this limit.Comment: 11 pages, 3 figure

Linear And Nonlinear Arabesques: A Study Of Closed Chains Of Negative 2-Element Circuits

In this paper we consider a family of dynamical systems that we call "arabesques", defined as closed chains of 2-element negative circuits. An $n$-dimensional arabesque system has $n$ 2-element circuits, but in addition, it displays by construction, two $n$-element circuits which are both positive vs one positive and one negative, depending on the parity (even or odd) of the dimension $n$. In view of the absence of diagonal terms in their Jacobian matrices, all these dynamical systems are conservative and consequently, they can not possess any attractor. First, we analyze a linear variant of them which we call "arabesque 0" or for short "A0". For increasing dimensions, the trajectories are increasingly complex open tori. Next, we inserted a single cubic nonlinearity that does not affect the signs of its circuits (that we call "arabesque 1" or for short "A1"). These systems have three steady states, whatever the dimension is, in agreement with the order of the nonlinearity. All three are unstable, as there can not be any attractor in their state-space. The 3D variant (that we call for short "A1\_3D") has been analyzed in some detail and found to display a complex mixed set of quasi-periodic and chaotic trajectories. Inserting $n$ cubic nonlinearities (one per equation) in the same way as above, we generate systems "A2\_$n$D". A2\_3D behaves essentially as A1\_3D, in agreement with the fact that the signs of the circuits remain identical. A2\_4D, as well as other arabesque systems with even dimension, has two positive $n$-circuits and nine steady states. Finally, we investigate and compare the complex dynamics of this family of systems in terms of their symmetries.Comment: 22 pages, 12 figures, accepted for publication at Int. J. Bif. Chao

Matter in extremis: ultrarelativistic nuclear collisions at RHIC

We review the physics of nuclear matter at high energy density and the experimental search for the Quark-Gluon Plasma at the Relativistic Heavy Ion Collider (RHIC). The data obtained in the first three years of the RHIC physics program provide several lines of evidence that a novel state of matter has been created in the most violent, head-on collisions of $Au$ nuclei at $\sqrt{s}=200$ GeV. Jet quenching and global measurements show that the initial energy density of the strongly interacting medium generated in the collision is about two orders of magnitude larger than that of cold nuclear matter, well above the critical density for the deconfinement phase transition predicted by lattice QCD. The observed collective flow patterns imply that the system thermalizes early in its evolution, with the dynamics of its expansion consistent with ideal hydrodynamic flow based on a Quark-Gluon Plasma equation of state.Comment: 93 pages, 46 figures; final version for journal incorporating minor changes and correction