Geometric shape of invariant manifolds for a class of stochastic partial differential equations

Invariant manifolds play an important role in the study of the qualitative dynamical behaviors for nonlinear stochastic partial differential equations. However, the geometric shape of these manifolds is largely unclear. The purpose of the present paper is to try to describe the geometric shape of invariant manifolds for a class of stochastic partial differential equations with multiplicative white noises. The local geometric shape of invariant manifolds is approximated, which holds with significant likelihood. Furthermore, the result is compared with that for the corresponding deterministic partial differential equations

Studies of the Response of the Prototype CMS Hadron Calorimeter, Including Magnetic Field Effects, to Pion, Electron, and Muon Beams

We report on the response of a prototype CMS hadron calorimeter module to charged particle beams of pions, muons, and electrons with momenta up to 375 GeV/c. The data were taken at the H2 and H4 beamlines at CERN in 1995 and 1996. The prototype sampling calorimeter used copper absorber plates and scintillator tiles with wavelength shifting fibers for readout. The effects of a magnetic field of up to 3 Tesla on the response of the calorimeter to muons, electrons, and pions are presented, and the effects of an upstream lead tungstate crystal electromagnetic calorimeter on the linearity and energy resolution of the combined calorimetric system to hadrons are evaluated. The results are compared with Monte Carlo simulations and are used to optimize the choice of total absorber depth, sampling frequency, and longitudinal readout segmentation.Comment: 89 pages, 41 figures, to be published in NIM, corresponding author: P de Barbaro, [email protected]

Response of plastic scintillators in magnetic fields

The dependence of the light yield on magnetic field has been measured up to 0.45 T for the plastic scintillators NE-102A, SCSN-38, and Polivar. The scintillators were excited by 25-MeV protons, 5.9-keV X-rays, and UV light. When excited with ionizing radiation an increase of light yield is observed. For SCSN-38 of 2.7-mm thickness it amounts to 0.3%, 0.9%, 1.1%, and 3.3% at 1, 10, 100 and 450 mT, respectively. Ne-102A behaves similarly whereas a polymethyl methacrylate (PMMA)-based scintillator shows a stronger field dependenc