The ATLAS SCT grounding and shielding concept and implementation

This paper presents a complete description of Virgo, the French-Italian gravitational wave detector. The detector, built at Cascina, near Pisa (Italy), is a very large Michelson interferometer, with 3 km-long arms. In this paper, following a presentation of the physics requirements, leading to the specifications for the construction of the detector, a detailed description of all its different elements is given. These include civil engineering infrastructures, a huge ultra-high vacuum (UHV) chamber (about 6000 cubic metres), all of the optical components, including high quality mirrors and their seismic isolating suspensions, all of the electronics required to control the interferometer and for signal detection. The expected performances of these different elements are given, leading to an overall sensitivity curve as a function of the incoming gravitational wave frequency. This description represents the detector as built and used in the first data-taking runs. Improvements in different parts have been and continue to be performed, leading to better sensitivities. These will be detailed in a forthcoming paper

Chebyshev-Type Quadrature Formulas for New Weight Classes

We give Chebyshev-type quadrature formulas for certain new weight classes. These formulas are of highest possible degree when the number of nodes is a power of 2. We also describe the nodes in a constructive way, which is important for applications. One of our motivations to consider these type of problems is the Faraday cage phenomenon for discrete charges as discussed by J. Korevaar and his colleagues

The exponentially convergent trapezoidal rule

It is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line. The mathematics and history of this phenomenon are reviewed and it is shown that far from being a curiosity, it is linked with computational methods all across scientific computing, including algorithms related to inverse Laplace transforms, special functions, complex analysis, rational approximation, integral equations, and the computation of functions and eigenvalues of matrices and operators

A fast and well-conditioned spectral method for singular integral equations

We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almost-banded infinite-dimensional systems. This is accomplished by utilizing low rank approximations for sparse representations of the bivariate kernels. The resulting system can be solved in ${\cal O}(m^2n)$ operations using an adaptive QR factorization, where $m$ is the bandwidth and $n$ is the optimal number of unknowns needed to resolve the true solution. The complexity is reduced to ${\cal O}(m n)$ operations by pre-caching the QR factorization when the same operator is used for multiple right-hand sides. Stability is proved by showing that the resulting linear operator can be diagonally preconditioned to be a compact perturbation of the identity. Applications considered include the Faraday cage, and acoustic scattering for the Helmholtz and gravity Helmholtz equations, including spectrally accurate numerical evaluation of the far- and near-field solution. The Julia software package SingularIntegralEquations.jl implements our method with a convenient, user-friendly interface

A Note on the Kinetics of Diffusion-mediated Reactions

The prevalent scheme of a diffusion-mediated bimolecular reaction $A+B\rightarrow P$ is an adaptation of that proposed by Briggs and Haldane for enzyme action [{\em Biochem J.\/}, 19:338--339, 1925]. The purpose of this Note is to explain, {\em by using an argument involving no mathematics\/}, why the breakup of the encounter complex cannot be described, except in special circumstances, in terms of a first-order process $\{AB\}\rightarrow A+B$. Briefly, such a description neglects the occurrence of re-encounters, which lie at the heart of Noyes's theory of diffusion-mediated reactions. The relation k=\alpha k_{\mbox{\scriptsize e}} becomes valid only when $\alpha$ (the reaction probability per encounter) is very much smaller than unity (activation-controlled reactions), or when $\beta$ (the re-encounter probability) is negligible (as happens in a gas-phase reaction). References to some works (by the author and his collaborators) which propound the correct approach for finding $k$ are also supplied.Comment: 4 pages, 1 figur

KALwEN: a new practical and interoperable key management scheme for body sensor networks

Key management is the pillar of a security architecture. Body sensor networks (BSNs) pose several challenges–some inherited from wireless sensor networks (WSNs), some unique to themselves–that require a new key management scheme to be tailor-made. The challenge is taken on, and the result is KALwEN, a new parameterized key management scheme that combines the best-suited cryptographic techniques in a seamless framework. KALwEN is user-friendly in the sense that it requires no expert knowledge of a user, and instead only requires a user to follow a simple set of instructions when bootstrapping or extending a network. One of KALwEN's key features is that it allows sensor devices from different manufacturers, which expectedly do not have any pre-shared secret, to establish secure communications with each other. KALwEN is decentralized, such that it does not rely on the availability of a local processing unit (LPU). KALwEN supports secure global broadcast, local broadcast, and local (neighbor-to-neighbor) unicast, while preserving past key secrecy and future key secrecy (FKS). The fact that the cryptographic protocols of KALwEN have been formally verified also makes a convincing case. With both formal verification and experimental evaluation, our results should appeal to theorists and practitioners alike

The construction of Electromagnetism

Abstract We examine the construction of electromagnetism in its current form, and in an alternative form, from a point of view that combines a minimal realism with strict rational demands. We begin by discussing the requests of reason when constructing a theory and next, we follow the historical development as presented in the record of original publications, the underlying epistemology (often explained by the authors) and the mathematical constructions. The historical construction develops along socio-political disputes (mainly, the reunification of Germany and the second industrial revolution), epistemic disputes (at least two demarcations of science in conflict) and several theories of electromagnetism. Such disputes resulted in the militant adoption of the ether by some, a position that expanded in parallel with the expansion of Prussia. This way of thinking was facilitated by the earlier adoption of a standpoint that required, as a condition for understanding, the use of physical hypothesis in the form of analogies; an attitude that is antithetic to Newton's “hypotheses non fingo”. While the material ether was finally abandoned, the epistemology survived in the form of “substantialism” and a metaphysical ether: the space. The militants of the ether attributed certainties regarding the ether to Faraday and Maxwell, when they only expressed doubts and curiosity. Thus, the official story is not the real history. This was achieved by the operation of detaching Maxwell's electromagnetism from its construction and introducing a new game of formulae and interpretations. Large and important parts of Maxwell work are today not known, as for example, the rules for the transformation of the electromagnetic potentials between moving systems. When experiments showed that all the theories based in the material ether were incorrect, a new interpretation was offered: Special Relativity (SR). At the end of the transformation period a pragmatic view of science, well adapted to the industrial society, had emerged, as well as a new protagonist: the theoretical physicist. The rival theory of delayed action at distance initiated under the influence of Gauss was forgotten in the midst of the intellectual warfare. The theory is indistinguishable in formulae from Maxwell's and its earlier versions are the departing point of Maxwell for the construction of his equations. We show in a mathematical appendix that such (relational) theory can incorporate Lorentz' contributions as well as Maxwell's transformations and C. Neumann's action, without resource to the ether. Demarcation criteria was further changed at the end of the period making room for habits and intuitions. When these intuited criteria are examined by critical reason (seeking for the fundaments) they can be sharpened with the use of the Non Arbitrariness Principle, which throws light over the arbitrariness in the construction of SR. Under a fully rational view SR is not acceptable, it requires to adopt a less demanding epistemology that detaches the concept from the conception, such as Einstein's own view in this respect, inherited from Hertz. In conclusion: we have shown in this relevant exercise how the reality we accept depends on earlier, irrational, decisions that are not offered for examination but rather are inherited from the culture