Integrated Safety and Environment Group: Annual Report 2003

This report summarizes the main activities of the Integrated Safety and Environment (IE) Group of the Safety Commission (TIS) during the year 2003, and the results obtained. The different topics in which the group is active are covered: environment, quality management, safety training and major accidents follow-up

Abelian Sandpile Model on the Honeycomb Lattice

We check the universality properties of the two-dimensional Abelian sandpile model by computing some of its properties on the honeycomb lattice. Exact expressions for unit height correlation functions in presence of boundaries and for different boundary conditions are derived. Also, we study the statistics of the boundaries of avalanche waves by using the theory of SLE and suggest that these curves are conformally invariant and described by SLE2.Comment: 24 pages, 5 figure

On the Mixing of Diffusing Particles

We study how the order of N independent random walks in one dimension evolves with time. Our focus is statistical properties of the inversion number m, defined as the number of pairs that are out of sort with respect to the initial configuration. In the steady-state, the distribution of the inversion number is Gaussian with the average ~N^2/4 and the standard deviation sigma N^{3/2}/6. The survival probability, S_m(t), which measures the likelihood that the inversion number remains below m until time t, decays algebraically in the long-time limit, S_m t^{-beta_m}. Interestingly, there is a spectrum of N(N-1)/2 distinct exponents beta_m(N). We also find that the kinetics of first-passage in a circular cone provides a good approximation for these exponents. When N is large, the first-passage exponents are a universal function of a single scaling variable, beta_m(N)--> beta(z) with z=(m-)/sigma. In the cone approximation, the scaling function is a root of a transcendental equation involving the parabolic cylinder equation, D_{2 beta}(-z)=0, and surprisingly, numerical simulations show this prediction to be exact.Comment: 9 pages, 6 figures, 2 table

Complete positivity of nonlinear evolution: A case study

Simple Hartree-type equations lead to dynamics of a subsystem that is not completely positive in the sense accepted in mathematical literature. In the linear case this would imply that negative probabilities have to appear for some system that contains the subsystem in question. In the nonlinear case this does not happen because the mathematical definition is physically unfitting as shown on a concrete example.Comment: extended version, 3 appendices added (on mixed states, projection postulate, nonlocality), to be published in Phys. Rev.

The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry

The closest tensors of higher symmetry classes are derived in explicit form for a given elasticity tensor of arbitrary symmetry. The mathematical problem is to minimize the elastic length or distance between the given tensor and the closest elasticity tensor of the specified symmetry. Solutions are presented for three distance functions, with particular attention to the Riemannian and log-Euclidean distances. These yield solutions that are invariant under inversion, i.e., the same whether elastic stiffness or compliance are considered. The Frobenius distance function, which corresponds to common notions of Euclidean length, is not invariant although it is simple to apply using projection operators. A complete description of the Euclidean projection method is presented. The three metrics are considered at a level of detail far greater than heretofore, as we develop the general framework to best fit a given set of moduli onto higher elastic symmetries. The procedures for finding the closest elasticity tensor are illustrated by application to a set of 21 moduli with no underlying symmetry.Comment: 48 pages, 1 figur

Intrinsic and extrinsic properties of quantum systems

The paper attempts to convince that the orthodox interpretation of quantum mechanics does not contradict philosophical realism by throwing light onto certain properties of quantum systems that seem to have escaped attention as yet. The exposition starts with the philosophical notions of realism. Then, the quantum mechanics as it is usually taught is demoted to a mere part of the theory called phenomenology of observations, and the common impression about its contradiction to realism is explained. The main idea of the paper, the physical notion of intrinsic properties, is introduced and many examples thereof are given. It replaces the irritating dichotomy of quantum and classical worlds by a much softer difference between intrinsic and extrinsic properties, which concern equally microscopic and macroscopic systems. Finally, the classicality and the quantum measurement are analyzed and found to present some still unsolved problems. A possible way of dealing with the Schr\"{o}dinger cat is suggested that is based on the intrinsic properties. A simple quantum model of one classical property illustrates how our philosophy may work.Comment: 20 pages, no figure. Comments are wellcom

Manufacturing features and performances of long models and first prototype for the LHC project

This paper reports about the 10-m-long models and one 15-m-long prototype. Their main design features are a 5-block coil cross section, an intra-beam distance of 194 mm at room temperature and a 15-mm-wide superconducting cable. The collared coil of the 10-m-long models were built in Industry and the assembly of the magnetic circuit and cold mass was done at CERN while the 15-m-long prototype was entirely made in Industry. Manufacturing features, assembly steps and quench performances of each magnet are presented. Results of magnetic measurements taken in the course of magnet assembly, during and after the cold test campaigns are also given

Test results on the long models and full scale prototypes of the second generation LHC arc dipoles

With the test of the first full scale prototype in June-July 1998, the R&D on the long superconducting dipoles based on the LHC design of 1993-95 has come to an end. This second generation of long magnets has a 56 mm coil aperture, is wound with 15 mm wide cable arranged in a 5 coil block layout. The series includes four 10 m long model dipoles, whose coils have been wound and collared in industry and the cold mass assembled and cryostated at CERN, as well as one 15 m long dipole prototype, manufactured totally in industry in the framework of a CERN-INFN collaboration for the LHC. After a brief description of particular features of the design and of the manufacturing, test results are reported and compared with the expectations. One magnet reached the record field for long model dipoles of 9.8 T but results have not been well reproducible from magnet to magnet. Guidelines for modifications that will appear in the next generation of long magnets, based on a six block coil design, are indicated in the conclusions. (10 refs)