On the number of limit cycles of the Lienard equation

In this paper, we study a Lienard system of the form dot{x}=y-F(x), dot{y}=-x, where F(x) is an odd polynomial. We introduce a method that gives a sequence of algebraic approximations to the equation of each limit cycle of the system. This sequence seems to converge to the exact equation of each limit cycle. We obtain also a sequence of polynomials R_n(x) whose roots of odd multiplicity are related to the number and location of the limit cycles of the system.Comment: 10 pages, 5 figures. Submitted to Physical Review

Performance of Irradiated Thin Edgeless N-on-P Planar Pixel Sensors for ATLAS Upgrades

In view of the LHC upgrade phases towards the High Luminosity LHC (HL-LHC), the ATLAS experiment plans to upgrade the Inner Detector with an all-silicon system. Because of its radiation hardness and cost effectiveness, the n-on-p silicon technology is a promising candidate for a large area pixel detector. The paper reports on the joint development, by LPNHE and FBK of novel n-on-p edgeless planar pixel sensors, making use of the active trench concept for the reduction of the dead area at the periphery of the device. After discussing the sensor technology, a complete overview of the electrical characterization of several irradiated samples will be discussed. Some comments about detector modules being assembled will be made and eventually some plans will be outlined.Comment: 6 pages, 13 figures, to appear in the proceedings of the 2013 Nuclear Science Symposium and Medical Imaging Conference. arXiv admin note: text overlap with arXiv:1311.162

Electrical Characterization of a Thin Edgeless N-on-p Planar Pixel Sensors For ATLAS Upgrades

In view of the LHC upgrade phases towards the High Luminosity LHC (HL-LHC), the ATLAS experiment plans to upgrade the Inner Detector with an all-silicon system. Because of its radiation hardness and cost effectiveness, the n-on-p silicon technology is a promising candidate for a large area pixel detector. The paper reports on the joint development, by LPNHE and FBK of novel n-on-p edgeless planar pixel sensors, making use of the active trench concept for the reduction of the dead area at the periphery of the device. After discussing the sensor technology, and presenting some sensors' simulation results, a complete overview of the electrical characterization of the produced devices will be given.Comment: 9 pages, 9 figures, to appear in the proceedings of the 15th International Workshops on Radiation Imaging Detector

Development of Edgeless n-on-p Planar Pixel Sensors for future ATLAS Upgrades

The development of n-on-p "edgeless" planar pixel sensors being fabricated at FBK (Trento, Italy), aimed at the upgrade of the ATLAS Inner Detector for the High Luminosity phase of the Large Hadron Collider (HL-LHC), is reported. A characterizing feature of the devices is the reduced dead area at the edge, achieved by adopting the "active edge" technology, based on a deep etched trench, suitably doped to make an ohmic contact to the substrate. The project is presented, along with the active edge process, the sensor design for this first n-on-p production and a selection of simulation results, including the expected charge collection efficiency after radiation fluence of $1 \times 10^{15} {\rm n_{eq}}/{\rm cm}^2$ comparable to those expected at HL-LHC (about ten years of running, with an integrated luminosity of 3000 fb$^{-1}$) for the outer pixel layers. We show that, after irradiation and at a bias voltage of 500 V, more than 50% of the signal should be collected in the edge region; this confirms the validity of the active edge approach.Comment: 20 pages, 9 figures, submitted to Nucl. Instr. and Meth.

Novel Silicon n-on-p Edgeless Planar Pixel Sensors for the ATLAS upgrade

In view of the LHC upgrade phases towards HL-LHC, the ATLAS experiment plans to upgrade the Inner Detector with an all-silicon system. The n-on-p silicon technology is a promising candidate for the pixel upgrade thanks to its radiation hardness and cost effectiveness, that allow for enlarging the area instrumented with pixel detectors. We report on the development of novel n-in-p edgeless planar pixel sensors fabricated at FBK (Trento, Italy), making use of the "active edge" concept for the reduction of the dead area at the periphery of the device. After discussing the sensor technology and fabrication process, we present device simulations (pre- and post-irradiation) performed for different sensor configurations. First preliminary results obtained with the test-structures of the production are shown.Comment: 6 pages, 5 figures, to appear in the proceedings of the 9th International Conference on Radiation Effects on Semiconductor Materials Detectors and Device

An analytical approximation scheme to two point boundary value problems of ordinary differential equations

A new (algebraic) approximation scheme to find {\sl global} solutions of two point boundary value problems of ordinary differential equations (ODE's) is presented. The method is applicable for both linear and nonlinear (coupled) ODE's whose solutions are analytic near one of the boundary points. It is based on replacing the original ODE's by a sequence of auxiliary first order polynomial ODE's with constant coefficients. The coefficients in the auxiliary ODE's are uniquely determined from the local behaviour of the solution in the neighbourhood of one of the boundary points. To obtain the parameters of the global (connecting) solutions analytic at one of the boundary points, reduces to find the appropriate zeros of algebraic equations. The power of the method is illustrated by computing the approximate values of the ``connecting parameters'' for a number of nonlinear ODE's arising in various problems in field theory. We treat in particular the static and rotationally symmetric global vortex, the skyrmion, the Nielsen-Olesen vortex, as well as the 't Hooft-Polyakov magnetic monopole. The total energy of the skyrmion and of the monopole is also computed by the new method. We also consider some ODE's coming from the exact renormalization group. The ground state energy level of the anharmonic oscillator is also computed for arbitrary coupling strengths with good precision.Comment: 5 pages, 3 tables, Late