This volume presents lectures given at the Wisła 20-21 Winter School and Workshop: Groups, Invariants, Integrals, and Mathematical Physics, organized by the Baltic Institute of Mathematics. The lectures were dedicated to differential invariants – with a focus on Lie groups, pseudogroups, and their orbit spaces – and Poisson structures in algebra and geometry and are included here as lecture notes comprising the first two chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and category theory. Specific topics covered include: The multisymplectic and variational nature of Monge-Ampère equations in dimension four Integrability of fifth-order equations admitting a Lie symmetry algebra Applications of the van Kampen theorem for groupoids to computation of homotopy types of striped surfaces A geometric framework to compare classical systems of PDEs in the category of smooth manifolds Groups, Invariants, Integrals, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry and category theory is assumed.

Reliability, Risk and Safety: Back to the Future covers topics on reliability, risk and safety issues, including risk and reliability analysis methods, maintenance optimization, human factors, and risk management. The application areas range from nuclear engineering, oil and gas industry, electrical and civil engineering to information technology and communication, security, transportation, health and medicine or critical infrastructures. Significant attention is paid to societal factors influencing the use of reliability and risk assessment methods, and to combinatorial analysis, which has found its way into the analysis of probabilities and risk, from which quantified risk analysis developed. Integral demonstrations of the use of risk analysis and safety assessment are provided in many practical applications concerning major technological systems and structures. Reliability, Risk and Safety: Back to the Future will be of interest to academics and engineers interested in nuclear engineering, oil and gas engineering, electrical engineering, civil engineering, information technology, communication, and infrastructure.

Synchrotron radiation is the name given to the radiation which occurs when charged particles are accelerated in a curved path or orbit. Classically, any charged particle which moves in a curved path or is accelerated in a straight-line path will emit electromagnetic radiation. Various names are given to this radiation in different contexts. Thus circular particle accelerators are called synchrotrons, this is where charged particles are accelerated to very high speeds and the radiation is referred to as synchrotron radiation.Suitable for a summer short course or one term lecture series this text introduces the subject, starting with some historical background then covering basic concepts such as flux, intensity, brilliance, emittance and Liouville's theorem. The book then covers the properties of synchrotron radiation, insertion devices, beamlines and monochromators before finishing with an introduction to free electron lasers and an overview of the most common techniques and applications of this technology.

As technology advances, education has expanded from the classroom into other formats including online delivery, flipped classrooms and hybrid delivery. Congruent with these is the need for alternative formats for laboratory experiences. This explosion in technology has also placed in the hands of a majority of students a sensor suite tucked neatly into their smartphones or smart tablets. The popularity of these devices provides a new avenue for the non-traditional kinematic lab experience. This book addresses this issue by providing 13 labs spanning the common topics in the first semester of university-level physics. Each lab is designed to use only the student's smartphone, laptop and items easily found in big-box stores or a hobby shop. Each lab contains theory, set-up instructions and basic analysis techniques. All of these labs can be performed outside of the traditional university lab setting and initial costs averaging less than $8 per student, per lab, excluding the smartphone and laptop.

The development of man's understanding of planetary motions is the crown jewel of Newtonian mechanics. This book offers a concise but self-contained handbook-length treatment of this historically important topic for students at about the third-year-level of an undergraduate physics curriculum. After opening with a review of Kepler's three laws of planetary motion, it proceeds to analyze the general dynamics of 'central force' orbits in spherical coordinates, how elliptical orbits satisfy Newton's gravitational law, and how the geometry of ellipses relates to physical quantities, such as energy and momentum. Exercises are provided, and derivations are set up in such a way that readers can gain analytic practice by filling in the missing steps. A brief bibliography lists sources for readers who wish to pursue further study on their own.

Biophotonic diagnostics/biomedical spectroscopy can revolutionise the medical environment by providing a responsive and objective diagnostic environment. This book aims to explain the fundamentals of the physical techniques used combined with the particular requirements of analysing medical/clinical samples as a resource for any interested party. In addition, it will show the potential of this field for the future of medical science and act as a driver for translation across many different biological problems/questions.

Electromagnetic homogenization is the process of estimating the effective electromagnetic properties of composite materials in the long-wavelength regime, wherein the length scales of nonhomogeneities are much smaller than the wavelengths involved. This is a bird's-eye view of currently available homogenization formalisms for particulate composite materials. It presents analytical methods only, with focus on the general settings of anisotropy and bianisotropy. The authors largely concentrate on 'effective' materials as opposed to 'equivalent' materials, and emphasize the fundamental (but sometimes overlooked) differences between these two categories of homogenized composite materials. The properties of an 'effective' material represents those of its composite material, regardless of the geometry and dimensions of the bulk materials and regardless of the orientations and polarization states of the illuminating electromagnetic fields. In contrast, the properties of 'equivalent' materials only represent those of their corresponding composite materials under certain restrictive circumstances.

Today, air-to-surface vessel (ASV) radars, or more generally maritime surveillance radars, are installed on maritime reconnaissance aircraft for long-range detection, tracking and classification of surface ships (ASuW - Air to Surface Warfare) and for hunting submarines (ASW - anti-submarine warfare). Such radars were first developed in the UK during WWII as part of the response to the threat to shipping from German U-Boats. This book describes the ASV radars developed in the UK after WWII (1946-2000) and used by the RAF for long-range maritime surveillance.

Physics and the Environment directly connects the physical world to environmental issues that the world is facing today and will face in the future. It shows how the first and second laws of thermodynamics limit the efficiencies of fossil fuel energy conversions to less than 100%, while also discussing how clever technologies can enhance overall performance. It also extensively discusses renewable forms of energy, their physical constraints and how we must use science and engineering as tools to solve problems instead of opinion and politics. Dr. Kyle Forinash takes you on a journey of understanding our mature and well developed technologies for using fossil fuel resources and how we are unlikely to see huge gains in their efficiency as well as why their role in climate change ought to be an argument for their replacement sooner rather than later. He also discusses the newest technologies in employing renewable resources and how it is important to understand their physical constrains in order to make a smooth transition to them. An entire chapter is dedicated to energy storage, a core question in renewable energy as well as another chapter on the technical issues of nuclear energy. The book ends with a discussion on how no environmental solution, no matter how clever from a technical aspect, will succeed if there are cheaper alternative, even if those alternatives have undesirable features associated with them.

Domain theory, a subject that arose as a response to natural concerns in the semantics of computation, studies ordered sets which possess an unusual amount of mathematical structure. This book explores its connection with quantum information science and the concept that relates them: disorder. This is not a literary work. It can be argued that its subject, domain theory and quantum information science, does not even really exist, which makes the scope of this alleged 'work' irrelevant. BUT, it does have a purpose and to some extent, it can also be said to have a method. I leave the determination of both of those largely to you, the reader. Except to say, I am hoping to convince the uninitiated to take a look. A look at what? Twenty years ago, I failed to satisfactorily prove a claim that I still believe: that there is substantial domain theoretic structure in quantum mechanics and that we can learn a lot from it. One day it will be proven to the point that people will be comfortable dismissing it as a 'well-known' idea that many (possibly including themselves) had long suspected but simply never bothered to write down. They may even call it "obvious!" I will not bore you with a brief history lesson on why it is not obvious, except to say that we have never been interested in the difficulty of proving the claim only in establishing its validity. This book then documents various attempts on my part to do just that.