A 2-chain can interlock with a k-chain

One of the open problems posed in [3] is: what is the minimal number k such that an open, flexible k-chain can interlock with a flexible 2-chain? In this paper, we establish the assumption behind this problem, that there is indeed some k that achieves interlocking. We prove that a flexible 2-chain can interlock with a flexible, open 16-chain.Comment: 10 pages, 6 figure

A 2-chain can interlock with an open 10-chain

It is an open problem, posed in \cite{SoCG}, to determine the minimal $k$ such that an open flexible $k$-chain can interlock with a flexible 2-chain. It was first established in \cite{GLOSZ} that there is an open 16-chain in a trapezoid frame that achieves interlocking. This was subsequently improved in \cite{GLOZ} to establish interlocking between a 2-chain and an open 11-chain. Here we improve that result once more, establishing interlocking between a 2-chain and a 10-chain. We present arguments that indicate that 10 is likely the minimum.Comment: 9 pages, 6 figure

Fibre Monitoring System for the Beam Permit Loops at the LHC and Future Evolution of the Beam Interlock System

The optical fibres that transmit the beam permit loop signals at the CERN accelerator complex are deployed along radiation areas. This may result in increased attenuation of the fibres, which reduces the power margin of the links. In addition, other events may cause the links to not function properly and result in false dumps, reducing the availability of the accelerator chain and affecting physics data taking. In order to evaluate the state of the fibres, an out-of-band fibre monitoring system is proposed, working in parallel to the actual beam permit loops. The future beam interlock system to be deployed during LHC long shutdown 2 will implement online, real-time monitoring of the fibres, a feature the current system lacks. Commercial off-the-shelf components to implement the optical transceivers are proposed whenever possible instead of ad-hoc designs.Comment: Presented in IPAC 201

Introduction to Machine Protection

Protection of accelerator equipment is as old as accelerator technology and was for many years related to high-power equipment. Examples are the protection of powering equipment from overheating (magnets, power converters, high-current cables), of superconducting magnets from damage after a quench and of klystrons. The protection of equipment from beam accidents is more recent, although there was one paper that discussed beam-induced damage for the SLAC linac (Stanford Linear Accelerator Center) as early as in 1967. It is related to the increasing beam power of high-power proton accelerators, to the emission of synchrotron light by electron-positron accelerators and to the increase of energy stored in the beam. Designing a machine protection system requires an excellent understanding of accelerator physics and operation to anticipate possible failures that could lead to damage. Machine protection includes beam and equipment monitoring, a system to safely stop beam operation (e.g. dumping the beam or stopping the beam at low energy) and an interlock system providing the glue between these systems. The most recent accelerator, LHC, will operate with about 3 x 10$^{14}$ protons per beam, corresponding to an energy stored in each beam of 360 MJ. This energy can cause massive damage to accelerator equipment in case of uncontrolled beam loss, and a single accident damaging vital parts of the accelerator could interrupt operation for years. This lecture will provide an overview of the requirements for protection of accelerator equipment and introduces various protection systems. Examples are mainly from LHC and ESS.Comment: 20 pages, contribution to the 2014 Joint International Accelerator School: Beam Loss and Accelerator Protection, Newport Beach, CA, USA , 5-14 Nov 2014. arXiv admin note: text overlap with arXiv:1601.0520

Decision making dynamics in corporate boards

Members of boards of directors of large corporations who also serve together on an outside board, form the so called interlock graph of the board and are assumed to have a strong influence on each others' opinion. We here study how the size and the topology of the interlock graph affect the probability that the board approves a strategy proposed by the Chief Executive Officer. We propose a measure of the impact of the interlock on the decision making, which is found to be a good predictor of the decision dynamics outcome. We present two models of decision making dynamics, and we apply them to the data of the boards of the largest US corporations in 1999.Comment: 20 pages, 10 figures, submitte