Hamiltonian flows on null curves

The local motion of a null curve in Minkowski 3-space induces an evolution equation for its Lorentz invariant curvature. Special motions are constructed whose induced evolution equations are the members of the KdV hierarchy. The null curves which move under the KdV flow without changing shape are proven to be the trajectories of a certain particle model on null curves described by a Lagrangian linear in the curvature. In addition, it is shown that the curvature of a null curve which evolves by similarities can be computed in terms of the solutions of the second Painlev\'e equation.Comment: 14 pages, v2: final version; minor changes in the expositio

Closed trajectories of a particle model on null curves in anti-de Sitter 3-space

We study the existence of closed trajectories of a particle model on null curves in anti-de Sitter 3-space defined by a functional which is linear in the curvature of the particle path. Explicit expressions for the trajectories are found and the existence of infinitely many closed trajectories is proved.Comment: 12 pages, 1 figur

Lagrangian bias in the local bias model

It is often assumed that the halo-patch fluctuation field can be written as a Taylor series in the initial Lagrangian dark matter density fluctuation field. We show that if this Lagrangian bias is local, and the initial conditions are Gaussian, then the two-point cross-correlation between halos and mass should be linearly proportional to the mass-mass auto-correlation function. This statement is exact and valid on all scales; there are no higher order contributions, e.g., from terms proportional to products or convolutions of two-point functions, which one might have thought would appear upon truncating the Taylor series of the halo bias function. In addition, the auto-correlation function of locally biased tracers can be written as a Taylor series in the auto-correlation function of the mass; there are no terms involving, e.g., derivatives or convolutions. Moreover, although the leading order coefficient, the linear bias factor of the auto-correlation function is just the square of that for the cross-correlation, it is the same as that obtained from expanding the mean number of halos as a function of the local density only in the large-scale limit. In principle, these relations allow simple tests of whether or not halo bias is indeed local in Lagrangian space. We discuss why things are more complicated in practice. We also discuss our results in light of recent work on the renormalizability of halo bias, demonstrating that it is better to renormalize than not. We use the Lognormal model to illustrate many of our findings.Comment: 14 pages, published on JCA

The spin 1/2 Calogero-Gaudin System and its q-Deformation

The spin 1/2 Calogero-Gaudin system and its q-deformation are exactly solved: a complete set of commuting observables is diagonalized, and the corresponding eigenvectors and eigenvalues are explicitly calculated. The method of solution is purely algebraic and relies on the co-algebra simmetry of the model.Comment: 15 page

The Interconnections of the LHC Cryomagnets at CERN: Strategy Applied and First Results of the Industrialization Process

The final interconnections of the LHC superconducting magnets in the underground tunnel are performed by a contractor on a result-oriented basis. A consortium of firms was awarded the contract after competitive tendering based on a technical and commercial specification. The implementation of the specific technologies and tooling developed and qualified by CERN has required an important effort to transfer the know-how and implement the follow-up of the contractor. This paper summarizes the start-up phase and the difficulties encountered. The organization and management tools put in place during the ramping-up phase are presented. In addition to contractual adaptations of the workforce, several configuration changes to the workflows were necessary to reach production rates compatible with the overall schedule and with the different constraints: availability of magnets, co-activities with magnets transport and alignment, handling of non-conformities, etc. Also the QA procedures underwent many changes to reach the high level of quality mandatory to ensure the LHC performance. The specificities of this worksite are underlined and first figures of merit of the learning process are presented

Elementary Darboux transformations and factorization

A general theorem on factorization of matrices with polynomial entries is proven and it is used to reduce polynomial Darboux matrices to linear ones. Some new examples of linear Darboux matrices are discussed.Comment: 10 page

Leak-Tight Welding Experience from the Industrial Assembly of the LHC Cryostats at CERN

The assembly of the approximately 1700 LHC main ring cryostats at CERN involved extensive welding of cryogenic lines and vacuum vessels. More than 6 km of welding requiring leak tightness to a rate better than 1.10-9 mbar.l.s-1 on stainless steel and aluminium piping and envelopes was made, essentially by manual welding but also making use of orbital welding machines. In order to fulfil the safety regulations related to pressure vessels and to comply with the leak-tightness requirements of the vacuum systems of the machine, welds were executed according to high qualification standards and following a severe quality assurance plan. Leak detection by He mass spectrometry was extensively used. Neon leak detection was used successfully to locate leaks in the presence of helium backgrounds. This paper presents the quality assurance strategy adopted for welds and leak detection. It presents the statistics of non-conformities on welds and leaks detected throughout the entire production and the advances in the use of alternative leak detection methods in an industrial environment

Videogame Addiction Scale for Children: Psychometric Properties and Gamer Profiles in the Italian Context

Given the few studies examining the evaluation of screening tools for videogame addiction among children aged 12 years and under, the present study analyzed (i) the psychometric properties (factorial structure, reliability indices and criterion validity) of the Italian version of the Videogame Addiction Scale for Children (VASC) and (ii) its construct validity using a person-centered approach. Two studies were carried out. In study 1, 728 participants completed a survey including demographic information, questions concerning the amount of time spent in playing videogames, and the Italian version of the VASC. In study 2, 1008 participants completed a survey comprising demographic information, the Italian version of the VASC, the Big Five Questionnaire for Children, and the social dimension subscale of the Multidimensional Self-Concept Scale. Findings supported (i) the four-dimensional first-order factor structure, (ii) full scalar invariance across age groups and partial scalar equivalence across gender, and (iii) reliability and criterion validity of the VASC. The construct validity of the VASC was confirmed by the identification of two distinct profiles (high videogame players vs. low videogame players) and their specific patterns of associations with personality traits and social self-concept. Interaction effects of gender × profiles on personality traits were evidenced. Overall, the findings provided validity for the use of the Italian version of the VASC and extending the body of literature on videogame addiction