Mathematical Sciences - Book Chapters
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Item Determining finite strain: how far have we progressed?(Geological Society of London, 2020-01) McCarthy, Dave; Meere, Patrick A.; Mulchrone, Kieran; Bond, C. E.; Lebit, H. D.One of the main aims in the field of structural geology is the identification and quantification of deformation or strain. This pursuit has occupied geologists since the 1800s, but has evolved dramatically since those early studies. The quantification of strain in sedimentary lithologies was initially restricted to lithologies of known initial shape, such as fossils or reduction spots. In 1967, Ramsay presented a series of methods and calculations, which allowed populations of clasts to be used as strain markers. These methods acted as a foundation for modern strain analysis, and have influenced thousands of studies. This review highlights the significance of Ramsay's contribution to modern strain analysis. We outline the advances in the field over the 50 years since publication of Folding and Fracturing of Rocks, review the existing limitations of strain analysis methods and look to future developments.Item Spreading of infection on temporal networks: an edge-centered perspective(Springer, 2019-10-30) Koher, Andreas; Gleeson, James P.; Hövel, Philipp; Deutsche Forschungsgemeinschaft; Deutscher Akademischer Austauschdienst; Science Foundation IrelandWe discuss a continuous-time extension of the contact-based (CB) model, as proposed in [Koher et al. Phys. Rev. X 9, 031017 (2019)], for infections with permanent immunity on temporal networks. At the core of our methodology is a fundamental change to an edge-centered perspective, which allows for an accurate model on temporal networks, where the underlying time-aggregated graph has a tree structure. From the continuous-time CB model, we derive the infection propagator for the low prevalence limit and propose a novel spectral criterion to estimate the epidemic threshold. In addition, we explore the relation between the continuous-time CB model and the previously proposed edge-based compartmental model, as well as the message-passing framework.Item Novel approaches for genuine single phase room temperature magnetoelectric multiferroics(Wiley, 2016-05) Keeney, Lynette; Schmidt, Michael; Amann, Andreas; Maity, Tuhin; Deepak, Nitin; Faraz, Ahmad; Petkov, Nikolay; Roy, Saibal; Pemble, Martyn E.; Whatmore, Roger W.; Alguero, Miguel; Gregg, J. Marty; Mitoseriu, Liliana; Science Foundation IrelandThis chapter reviews approaches currently under investigation for the fabrication of single‐phase magnetoelectric multiferroics, from bulk ceramics to those in thin‐film form. It presents an approach of inserting magnetic ions into the Aurivillius phase, layer‐structured ferroelectric materials, whereby thin films of average composition Bi6Ti2.8Fe1.52Mn0.68O18 (B6TFMO) demonstrate room temperature ferroelectricity, ferromagnetism, and magnetoelectric coupling. The chapter also discusses the importance of careful microstructural analysis of the materials and the application of a statistical model to determine a confidence level that the observed effects are from genuine single‐phase magnetoelectric multiferroics. It reviews how careful phase analysis and statistical treatment of the data confirmed that the B6TFMO phase is a single‐phase multiferroic to a confidence level of 99.5%. Finally, it summarizes how direct evidence of magnetoelectric coupling in the B6TFMO thin films was obtained. This review demonstrates that with materials development and design, the development of room temperature multiferroic materials can be achieved.