Invariant Lagrangians, mechanical connections and the Lagrange-Poincare equations

We deal with Lagrangian systems that are invariant under the action of a symmetry group. The mechanical connection is a principal connection that is associated to Lagrangians which have a kinetic energy function that is defined by a Riemannian metric. In this paper we extend this notion to arbitrary Lagrangians. We then derive the reduced Lagrange-Poincare equations in a new fashion and we show how solutions of the Euler-Lagrange equations can be reconstructed with the help of the mechanical connection. Illustrative examples confirm the theory.Comment: 22 pages, to appear in J. Phys. A: Math. Theor., D2HFest special issu

The inverse problem for Lagrangian systems with certain non-conservative forces

We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations with non-conservative forces of a generalized Rayleigh dissipation type, the other leading to Lagrangian equations with so-called gyroscopic forces. Our approach focusses primarily on obtaining coordinate-free conditions for the existence of a suitable non-singular multiplier matrix, which will lead to an equivalent representation of a given system of second-order equations as one of these Lagrangian systems with non-conservative forces.Comment: 28 page

Isometries, submetries and distance coordinates on Finsler manifolds

This paper considers fundamental issues related to Finslerian iso- metries, submetries, distance and geodesics. It is shown that at each point of a Finsler manifold there is a distance coordinate system. Us- ing distance coordinates, a simple proof is given for the Finslerian version of the Myers-Steenrod theorem and for the differentiability of Finslerian submetries

A setting for higher order differential equations fields and higher order Lagrange and Finsler spaces

We use the Fr\"olicher-Nijenhuis formalism to reformulate the inverse problem of the calculus of variations for a system of differential equations of order 2k in terms of a semi-basic 1-form of order k. Within this general context, we use the homogeneity proposed by Crampin and Saunders in [14] to formulate and discuss the projective metrizability problem for higher order differential equation fields. We provide necessary and sufficient conditions for higher order projectivpre-e metrizability in terms of homogeneous semi-basic 1-forms. Such a semi-basic 1-form is the Poincar\'e-Cartan 1-form of a higher order Finsler function, while the potential of such semi-basic 1-form is a higher order Finsler function.Comment: final, pre-published versio

Mitogen-Activated Protein Kinases Regulate Susceptibility to Ventilator-Induced Lung Injury

Background: Mechanical ventilation causes ventilator-induced lung injury in animals and humans. Mitogen-activated protein kinases have been implicated in ventilator-induced lung injury though their functional significance remains incomplete. We characterize the role of p38 mitogen-activated protein kinase/mitogen activated protein kinase kinase-3 and c-jun-NH2-terminal kinase-1 in ventilator-induced lung injury and investigate novel independent mechanisms contributing to lung injury during mechanical ventilation. Methodology and Principle Findings: C57/BL6 wild-type mice and mice genetically deleted for mitogen-activated protein kinase kinase-3 (mkk-3-/-) or c-Jun-NH2-terminal kinase-1 (jnk1-/-) were ventilated, and lung injury parameters were assessed. We demonstrate that mkk3-/- or jnk1-/- mice displayed significantly reduced inflammatory lung injury and apoptosis relative to wild-type mice. Since jnk1-/- mice were highly resistant to ventilator-induced lung injury, we performed comprehensive gene expression profiling of ventilated wild-type or jnk1-/- mice to identify novel candidate genes which may play critical roles in the pathogenesis of ventilator-induced lung injury. Microarray analysis revealed many novel genes differentially expressed by ventilation including matrix metalloproteinase-8 (MMP8) and GAFF45α. Functional characterization of MMP8 revealed that mmp8-/- mice were sensitized to ventilator-induced lung injury with increased lung vascular permeability. Conclusion: We demonstrate that mitogen-activated protein kinase pathways mediate inflammatory lung injury during ventilator-induced lung injury. C-Jun-NH2-terminal kinase was also involved in alveolo-capillary leakage and edema formation, whereas MMP8 inhibited alveolo-capillary protein leakage. © 2008 Dolinay et al

Beam test performance of a prototype module with Short Strip ASICs for the CMS HL-LHC tracker upgrade

The Short Strip ASIC (SSA) is one of the four front-end chips designed for the upgrade of the CMS Outer Tracker for the High Luminosity LHC. Together with the Macro-Pixel ASIC (MPA) it will instrument modules containing a strip and a macro-pixel sensor stacked on top of each other. The SSA provides both full readout of the strip hit information when triggered, and, together with the MPA, correlated clusters called stubs from the two sensors for use by the CMS Level-1 (L1) trigger system. Results from the first prototype module consisting of a sensor and two SSA chips are presented. The prototype module has been characterized at the Fermilab Test Beam Facility using a 120 GeV proton beam

Characterisation of irradiated thin silicon sensors for the CMS phase II pixel upgrade

The high luminosity upgrade of the Large Hadron Collider, foreseen for 2026, necessitates the replacement of the CMS experiment's silicon tracker. The innermost layer of the new pixel detector will be exposed to severe radiation, corresponding to a 1 MeV neutron equivalent fluence of up to Phi(eq) = 2x10(16) cm(-2), and an ionising dose of approximate to 5 MGy after an integrated luminosity of 3000 fb(-1). Thin, planar silicon sensors are good candidates for this application, since the degradation of the signal produced by traversing particles is less severe than for thicker devices. In this paper, the results obtained from the characterisation of 100 and 200 mu m thick p-bulk pad diodes and strip sensors irradiated up to fluences of Phi(eq) = 1.3 x 10(16) cm(-2) are shown.Peer reviewe

Selection of the silicon sensor thickness for the Phase-2 upgrade of the CMS Outer Tracker

During the operation of the CMS experiment at the High-Luminosity LHC the silicon sensors of the Phase-2 Outer Tracker will be exposed to radiation levels that could potentially deteriorate their performance. Previous studies had determined that planar float zone silicon with n-doped strips on a p-doped substrate was preferred over p-doped strips on an n-doped substrate. The last step in evaluating the optimal design for the mass production of about 200 m$^{2}$ of silicon sensors was to compare sensors of baseline thickness (about 300 μm) to thinned sensors (about 240 μm), which promised several benefits at high radiation levels because of the higher electric fields at the same bias voltage. This study provides a direct comparison of these two thicknesses in terms of sensor characteristics as well as charge collection and hit efficiency for fluences up to 1.5 × 10$^{15}$ n$_{eq}$/cm$^{2}$. The measurement results demonstrate that sensors with about 300 μm thickness will ensure excellent tracking performance even at the highest considered fluence levels expected for the Phase-2 Outer Tracker

The CMS Phase-1 pixel detector upgrade

The CMS detector at the CERN LHC features a silicon pixel detector as its innermost subdetector. The original CMS pixel detector has been replaced with an upgraded pixel system (CMS Phase-1 pixel detector) in the extended year-end technical stop of the LHC in 2016/2017. The upgraded CMS pixel detector is designed to cope with the higher instantaneous luminosities that have been achieved by the LHC after the upgrades to the accelerator during the first long shutdown in 2013–2014. Compared to the original pixel detector, the upgraded detector has a better tracking performance and lower mass with four barrel layers and three endcap disks on each side to provide hit coverage up to an absolute value of pseudorapidity of 2.5. This paper describes the design and construction of the CMS Phase-1 pixel detector as well as its performance from commissioning to early operation in collision data-taking.Peer reviewe