Realms: A Structure for Consolidating Knowledge about Mathematical Theories

Since there are different ways of axiomatizing and developing a mathematical theory, knowledge about a such a theory may reside in many places and in many forms within a library of formalized mathematics. We introduce the notion of a realm as a structure for consolidating knowledge about a mathematical theory. A realm contains several axiomatizations of a theory that are separately developed. Views interconnect these developments and establish that the axiomatizations are equivalent in the sense of being mutually interpretable. A realm also contains an external interface that is convenient for users of the library who want to apply the concepts and facts of the theory without delving into the details of how the concepts and facts were developed. We illustrate the utility of realms through a series of examples. We also give an outline of the mechanisms that are needed to create and maintain realms.Comment: As accepted for CICM 201

The Multi-Configurational Hartree-Fock close-coupling ansatz: application to Argon photoionization cross section and delays

We present a robust, ab initio method for addressing atom-light interactions and apply it to photoionization of argon. We use a close-coupling ansatz constructed on a multi-configurational Hartree-Fock description of localized states and B-spline expansions of the electron radial wave functions. In this implementation, the general many-electron problem can be tackled thanks to the use of the ATSP2K libraries [CPC 176 (2007) 559]. In the present contribution, we combine this method with exterior complex scaling, thereby allowing for the computation of the complex partial amplitudes that encode the whole dynamics of the photoionization process. The method is validated on the 3s3p6np series of resonances converging to the 3s extraction. Then, it is used for computing the energy dependent differential atomic delay between 3p and 3s photoemission, and agreement is found with the measurements of Gu\'enot et al. [PRA 85 (2012) 053424]. The effect of the presence of resonances in the one-photon spectrum on photoionization delay measurements is studied.Comment: 15 pages, 8 figures, 4 table

Ab initio calculations of the {33}S 3p4 3P_J and {33}S- / {37,35}Cl 3p5 2Po_J hyperfine structures

We present highly correlated multi-configuration Hartree-Fock (MCHF) calculations of the hyperfine structure of the 3p5 2Po_J levels of {33}S- and {35,37}Cl. We obtain a good agreement with observation. The hyperfine structure of the neutral sulfur {33}S 3p4 3P_J lowest multiplet that has never been measured to the knowledge of the authors, is also estimated theoretically. We discuss some interesting observations made on the description of the atomic core in MCHF theory.Comment: 14 pages, 2 figures (10 subfigures

The use of 3D printing in the development of gaseous radiation detectors

Fused Deposition Modelling has been used to produce a small, single wire, Iarocci-style drift tube to demonstrate the feasibility of using the Additive Manufacturing technique to produce cheap detectors, quickly. Recent technological developments have extended the scope of Additive Manufacturing, or 3D printing, to the possibility of fabricating Gaseous Radiation Detectors, such as Single Wire Proportional Counters and Time Projection Chambers. 3D printing could allow for the production of customisable, modular detectors; that can be easily created and replaced and the possibility of printing detectors on-site in remote locations and even for outreach within schools. The 3D printed drift tube was printed using Polylactic acid to produce a gas volume in the shape of an inverted triangular prism; base length of 28 mm, height 24.25 mm and tube length 145 mm. A stainless steel anode wire was placed in the centre of the tube, mid-print. P5 gas (95% Argon, 5% Methane) was used as the drift gas and a circuit was built to capacitively decouple signals from the high voltage. The signal rate and average pulse height of cosmic ray muons were measured over a range of bias voltages to characterise and prove correct operation of the printed detector