Analytical Representation of the Longitudinal Hadronic Shower Development

The analytical representation of the longitudinal hadronic shower development from the face of a calorimeter is presented and compared with experimental data. The suggested formula is particularly useful at designing, testing and calibration of huge calorimeter complex like in ATLAS at LHC.Comment: 5 pages, 1 figur

Non-Compensation of the Barrel Tile Hadron Module-0 Calorimeter

The detailed experimental information about the electron and pion responses, the electron energy resolution and the e/h ratio as a function of incident energy E, impact point Z and incidence angle $\Theta$ of the Module-0 of the iron-scintillator barrel hadron calorimeter with the longitudinal tile configuration is presented. The results are based on the electron and pion beams data for E = 10, 20, 60, 80, 100 and 180 GeV at $\eta$ = -0.25 and -0.55, which have been obtained during the test beam period in 1996. The results are compared with the existing experimental data of TILECAL 1m prototype modules, various iron-scintillator calorimeters and with some Monte Carlo calculations.Comment: 33 pages, 20 figure

Non-compensation of an Electromagnetic Compartment of a Combined Calorimeter

The method of extraction of the $e/h$ ratio, the degree of non-compensation, of the electromagnetic compartment of the combined calorimeter is suggested. The $e/h$ ratio of $1.74\pm0.04$ has been determined on the basis of the 1996 combined calorimeter test beam data. This value agrees with the prediction that $e/h > 1.7$ for this electromagnetic calorimeter.Comment: LATEX, 17 pages, 7 figure

Longitudinal Hadronic Shower Development in a Combined Calorimeter

This work is devoted to the experimental study of the longitudinal hadronic shower development in the ATLAS barrel combined prototype calorimeter consisting of the lead-liquid argon electromagnetic part and the iron-scintillator hadronic part. The results have been obtained on the basis of the 1996 combined test beam data which have been taken on the H8 beam of the CERN SPS, with the pion beams of 10, 20, 40, 50, 80, 100, 150 and 300 GeV/c. The degree of description of generally accepted Bock parameterization of the longitudinal shower development has been investigated. It is shown that this parameterization does not give satisfactory description for this combined calorimeter. Some modification of this parameterization, in which the e/h ratios of the compartments of the combined calorimeter are used, is suggested and compared with the experimental data. The agreement between such parameterization and the experimental data is demonstrated.Comment: Latex, 21 pages, 10 figure

Separating Solution of a Quadratic Recurrent Equation

In this paper we consider the recurrent equation $$\Lambda_{p+1}=\frac1p\sum_{q=1}^pf\bigg(\frac{q}{p+1}\bigg)\Lambda_{q}\Lambda_{p+1-q}$$ for $p\ge 1$ with $f\in C[0,1]$ and $\Lambda_1=y>0$ given. We give conditions on $f$ that guarantee the existence of $y^{(0)}$ such that the sequence $\Lambda_p$ with $\Lambda_1=y^{(0)}$ tends to a finite positive limit as $p\to \infty$.Comment: 13 pages, 6 figures, submitted to J. Stat. Phy

Viscoelastic response of contractile filament bundles

The actin cytoskeleton of adherent tissue cells often condenses into filament bundles contracted by myosin motors, so-called stress fibers, which play a crucial role in the mechanical interaction of cells with their environment. Stress fibers are usually attached to their environment at the endpoints, but possibly also along their whole length. We introduce a theoretical model for such contractile filament bundles which combines passive viscoelasticity with active contractility. The model equations are solved analytically for two different types of boundary conditions. A free boundary corresponds to stress fiber contraction dynamics after laser surgery and results in good agreement with experimental data. Imposing cyclic varying boundary forces allows us to calculate the complex modulus of a single stress fiber.Comment: Revtex with 24 pages, 7 Postscript figures included, accepted for publication in Phys. Rev.

Use of Non-distractive Testing AU-E Technology to Evaluate Hearth Conditions at CherMK–SEVERSTAL

Intensive operation of blast furnace allows increase in production of hot metal and profitability of Iron & Steel Works. However, blast furnace life could be sacrificed if no measures are taken to protect refractory lining and to build stable accretion. CherMK and Hatch developed a systematic approach to monitor conditions of BF hearth lining using Acousto Ultrasonic-Echo (AU-E) non-destructive testing developed by Hatch. Multiple testing of blast furnaces revealed problematic areas with accelerated refractory deterioration and minimal thickness, formation of elephant foot, extent of accretion and speed of refractory wear, cracks and other anomalies. Improvement in coke quality, periodical staves washing, the addition of titania, grouting, etc., were recommended and implemented to prolong furnace life while maintaining the intensity of furnace operation. Keywords: blast furnace inspection and monitoring, non-destructive testing (NDT), refractory deterioration, blast furnace campaig

The graded Jacobi algebras and (co)homology

Jacobi algebroids (i.e. `Jacobi versions' of Lie algebroids) are studied in the context of graded Jacobi brackets on graded commutative algebras. This unifies varios concepts of graded Lie structures in geometry and physics. A method of describing such structures by classical Lie algebroids via certain gauging (in the spirit of E.Witten's gauging of exterior derivative) is developed. One constructs a corresponding Cartan differential calculus (graded commutative one) in a natural manner. This, in turn, gives canonical generating operators for triangular Jacobi algebroids. One gets, in particular, the Lichnerowicz-Jacobi homology operators associated with classical Jacobi structures. Courant-Jacobi brackets are obtained in a similar way and use to define an abstract notion of a Courant-Jacobi algebroid and Dirac-Jacobi structure. All this offers a new flavour in understanding the Batalin-Vilkovisky formalism.Comment: 20 pages, a few typos corrected; final version to be published in J. Phys. A: Math. Ge

Pion Energy Reconstruction by the Local Hadronic Calibration Method with ATLAS Combined Test Beam 2004 data

The pion energy reconstruction by the local hadronic calibration method on the basis of the 2004 combined test beam data in the energy range 10 -- 350 GeV and $\eta = 0.25$ is performed. In this method energies deposited in each cell are weighted. The weights are determined by the Monte Carlo simulation using Calibration Hits software. We have modified this method by applying cuts in weights. The obtained fractional energy resolution with the conventional method of determination of the energy deposit in the dead material between LAr and Tile calorimeters is $\sigma/E = (67\pm2)\%/\sqrt{E} \oplus (3.9\pm0.2)\% \oplus (95\pm22)\%/E$. This is about 1.5 times better than the results for the hadronic calibration method obtained by the Oxford-Stockholm group and slightly better than the H1 method results for CTB04 obtained by Pisa group. The energy linearity is within $\pm$1\%. We have determined the general normalization constant of 0.91 for which the mean value linearity for the weight cut of 1.05 is about 1. At using this normalization constant the energy resolution has not worsen. We have corrected the cesium miscalibration of the $Tile_1$ and $Tile_2$ longitudinal samplings. The mean value of energy linearity has been increased by about 1\% and becomes equal to 1.002$\pm$0.002. The energy resolution did not change. We have performed weighting without knowing of the beam energies. For this the special procedure has been developed. In this case the energy resolution shows 9\% degradation. Linearities are within $\pm$1\%. We have applied the Neural Networks to the determination of the energy deposit between LAr and Tile calorimeters. The essential improvement of energy resolution is obtained. In this case we have reached the projected energy resolution for hadrons in the ATLAS detector $\sigma/E = 50\%/\sqrt{E} \oplus 3\%$

The profile of a narrow line after single scattering by Maxwellian electrons: relativistic corrections to the kernel of the integral kinetic equation

The frequency distribution of photons in frequency that results from single Compton scattering of monochromatic radiation on thermal electrons is derived in the mildly relativistic limit. Algebraic expressions are given for (1) the photon redistribution function, K(nu,Omega -> nu',Omega'), and (2) the spectrum produced in the case of isotropic incident radiation, P(nu -> nu'). The former is a good approximation for electron temperatures kT_e < 25 keV and photon energies hnu < 50 keV, and the latter is applicable when hnu(hnu/m_ec^2) < kT_e < 25 keV, hnu < 50 keV. Both formulae can be used for describing the profiles of X-ray and low-frequency lines upon scattering in hot, optically thin plasmas, such as present in clusters of galaxies, in the coronae of accretion disks in X-ray binaries and AGNs, during supernova explosions, etc. Both formulae can also be employed as the kernels of the corresponding integral kinetic equations (direction-dependent and isotropic) in the general problem of Comptonization on thermal electrons. The K(nu,Omega -> nu',Omega') kernel, in particular, is applicable to the problem of induced Compton interaction of anisotropic low-frequency radiation of high brightness temperature with free electrons in the vicinity of powerful radiosources and masers. Fokker-Planck-type expansion (up to fourth order) of the integral kinetic equation with the P(nu -> nu') kernel derived here leads to a generalization of the Kompaneets equation. We further present (1) a simpler kernel that is necessary and sufficient to derive the Kompaneets equation and (2) an expression for the angular function for Compton scattering in a hot plasma, which includes temperature and photon energy corrections to the Rayleigh angular function.Comment: 29 pages, 17 figures, accepted for publication in ApJ, uses emulateapj.sty, corrects misprints in previous astro-ph versio