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An informal introduction is provided to a range of topics in fluid dynamics having a topological character. These topics include flows with boundary singularities, Lagrangian chaos, frozen-in fields, magnetohydrodynamic analogies, fast- and slow-dynamo mechanisms, magnetic relaxation, minimum-energy states, knotted flux tubes, vortex reconnection and the finite-time singularity problem. The paper concludes with a number of open questions concerning the above topics.

Many physics and engineering applications demand partial differential equations (PDE) property evaluations that are traditionally computed with resource-intensive high-fidelity numerical solvers. Data-driven surrogate models provide an efficient alternative but come with a substantial cost of training. Emerging applications would benefit from surrogates with an improved accuracy–cost tradeoff when studied at scale. Here we present a ‘physics-enhanced deep-surrogate’ (PEDS) approach towards developing fast surrogate models for complex physical systems, which is described by PDEs. Specifically, a combination of a low-fidelity, explainable physics simulator and a neural network generator is proposed, which is trained end-to-end to globally match the output of an expensive high-fidelity numerical solver. Experiments on three exemplar test cases, diffusion, reaction–diffusion and electromagnetic scattering models, show that a PEDS surrogate can be up to three times more accurate than an ensemble of feedforward neural networks with limited data (approximately 10 3 training points), and reduces the training data need by at least a factor of 100 to achieve a target error of 5%. Experiments reveal that PEDS provides a general, data-driven strategy to bridge the gap between a vast array of simplified physical models with corresponding brute-force numerical solvers modelling complex systems, offering accuracy, speed and data efficiency, as well as physical insights into the process. Data-driven surrogate models are used in computational physics and engineering to greatly speed up evaluations of the properties of partial differential equations, but they come with a heavy computational cost associated with training. Pestourie et al. combine a low-fidelity physics model with a generative deep neural network and demonstrate improved accuracy–cost trade-offs compared with standard deep neural networks and high-fidelity numerical solvers.

James Clerk Maxwell's 1856 essay \"Are There Real Analogies in Nature?\" asks whether analogies can be said to exist in nature or whether they are a construction of the human mind. I argue that Maxwell's answer to this question is articulated compellingly through an analogy he sets up between the structure of crystals and the structure of the human mind: like crystals, Maxwell suggests, which attain form in response to their environment, the mind is shaped by the natural world it tries to know. Paying attention to Maxwell's educational history and building on more recent philosophy, I argue that his essay cultivates a \"naturalist idealism\" that seeks to mend the ontological gap between mind and matter instituted by an earlier generation of Cambridge scientists. As such, I stress the extent to which naturalism and idealism—although often thought of as opposing positions in the history of philosophy—could in fact be deeply complementary in Victorian scientific culture.

Theoretical equivalence and duality are two closely related notions: but their interconnection has so far not been well understood. In this paper I explicate the contribution of a recent schema for duality to discussions of theoretical equivalence. I argue that duality suggests a construal of theoretical equivalence in the physical sciences. The construal is in terms of the isomorphism of models, as defined by the schema. This construal gives interpretative constraints that should be useful for discussions of theoretical equivalence more generally. I illustrate the construal in various formulations of Maxwell’s electromagnetic theory.

Background Peer support is effective in improving psychological well-being of family caregivers of people with conditions such as dementia, cancer, and brain injury. However, there are limited data on effective psychological interventions for family caregivers of people living with motor neurone disease. Our objective is to evaluate the efficacy of a virtual peer support programme for improving caregiver psychological wellbeing and caregiving related outcomes. Methods We will conduct a multi-centre parallel group randomised controlled superiority trial. Using a multi-modal recruitment strategy, we will recruit informal caregivers from UK MND clinics, in-patient units, and hospices. We will randomise (1:1, stratified by gender) participants to either a 12-week virtual peer support programme or usual care comprising provision of online information resources publicly available via the MND Association website. Peer support programme elements will be delivered via a secure digital e-platform aTouchAway™ (Aetonix, Canada). Our target sample size is 160 (80 each arm). Our primary outcome is the Hospital Anxiety and Depression Scale (HADS) assessed at 12 weeks (primary endpoint). Secondary outcomes that will also be assessed at 12 weeks include the Zarit Burden Interview, Pearlin Mastery Scale, Personal Gain Scale, Positive Affect Scale, and the Brief COPE. Outcome assessors will be blinded to allocation. Tertiary outcomes include perceived usability (1 item 9-point Likert scale) and acceptability (semi-structured qualitative interviews) of the peer support programme. Intervention fidelity measures will comprise frequency, type (text, audio, video), and duration (audio and video) of peer support contact downloaded from the aTouchAway AWS server. We will use a mixed-effects linear model to test the effect of the intervention on the primary outcome. Secondary outcomes will be analysed using linear regression. We have ethical approval (21/NW/0269) from the North-West Research Ethics Committee, UK. Discussion This single-blinded randomised controlled trial will determine the effect of a virtual peer support programme on caregiver psychological wellbeing and caregiver burden. This study will examine the impact of a virtual peer support intervention on quality-of-life measures in informal caregivers of individuals with MND living in the community. Trial registration ClinicalTrials.gov: NCT04695210

Time asymmetric phenomena are successfully predicted by statistical mechanics. Yet the foundations of this theory are surprisingly shaky. Its explanation for the ease of mixing milk with coffee is incomplete, and even implies that un-mixing them should be just as easy. In this book the authors develop a new conceptual foundation for statistical mechanics that addresses this difficulty. Explaining the notions of macrostates, probability, measurement, memory, and the arrow of time in statistical mechanics, they reach the startling conclusion that Maxwell's Demon, the famous perpetuum mobile, is consistent with the fundamental physical laws. Mathematical treatments are avoided where possible, and instead the authors use novel diagrams to illustrate the text. This is a fascinating book for graduate students and researchers interested in the foundations and philosophy of physics.

The Dictionary of National Biography, published between 1885 and 1900, was one of Britain's biggest cyclopedia projects. The rampant expansion of the nation's archives, private collections, and museums produced an abundance of materials that frustrated the dictionary's editors, Leslie Stephen and Sidney Lee, especially because methodologies for making order of such materials were underdeveloped. Adding to their frustration was the sense of impending doom felt generally in Britain after the discovery of the second law of thermodynamics in 1859. Entropy put an end to the presiding belief in the infinite energy that fueled Britain's economic development and therefore challenged Victorian biography's premise that the capacity for self-development was boundless. Like the physicists of the era, these dictionary makers searched for ways to circumvent entropy's deadening force and reenergize their world. This project would not actually be achieved, however, until the twentieth century when Claude Shannon published his “Information Theory” in 1948. I argue that in an attempt to get out from under the chaos of information overload, the editors of the DNB invented new methods to organize information that anticipated Shannon's revolutionary theory and changed the way that we think, write, and work.

J. M. Barrie's Neverland functions as a fantasy space of alternative energy that defies the laws of thermodynamics. Barrie, whose interest in science remains underrepresented, studied under the eminent physicist Peter Guthrie Tait. In Peter and Wendy (1911), the mysterious forces in Neverland amass and reuse reality's waste, ultimately demonstrating the cyclical immortality of stories.

James Clerk Maxwell's theories of electromagnetism are uniquely Victorian products. Maxwell and his physics have traditionally been viewed as aloof and disinterested, dating to the mid-to-late-19th century, but not party to the cultural, industrial, political, economic, and environmental turmoil of the era. This dissertation examines often ignored corners of Maxwell's electromagnetic theories and those of his successors to demonstrate that they were shaped by the technologies of their time. These technologies, steam engine governors, capacitors, and undersea telegraph cables are each, in their own way, responsible for the varying forms taken by Maxwellian electromagnetic theory. Each of these technologies also has its own history. These histories connect these technologies and thus Maxwellian theory to the newly emerging concept of efficiency, as well as the colonialism, economics, religion, and ecology of the British Empire. Governors, capacitors, and submarine telegraph cables serve as a historiographical bridge, allowing for the exploration of how empire-wide forces shaped the minutiae of Maxwellian electromagnetic theory.