The Physics and Mathematics of the Second Law of Thermodynamics

The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of entropy in irreversible adiabatic processes that take one equilibrium state to another. The entropy constructed here is defined only for equilibrium states and no attempt is made to define it otherwise. Statistical mechanics does not enter these considerations. One of the main concepts that makes everything work is the comparison principle (which, in essence, states that given any two states of the same chemical composition at least one is adiabatically accessible from the other) and we show that it can be derived from some assumptions about the pressure and thermal equilibrium. Temperature is derived from entropy, but at the start not even the concept of `hotness' is assumed. Our formulation offers a certain clarity and rigor that goes beyond most textbook discussions of the second law.Comment: 93 pages, TeX, 8 eps figures. Updated, published version. A summary appears in Notices of the Amer. Math. Soc. 45 (1998) 571-581, math-ph/980500

Notes on the Third Law of Thermodynamics.I

We analyze some aspects of the third law of thermodynamics. We first review both the entropic version (N) and the unattainability version (U) and the relation occurring between them. Then, we heuristically interpret (N) as a continuity boundary condition for thermodynamics at the boundary T=0 of the thermodynamic domain. On a rigorous mathematical footing, we discuss the third law both in Carath\'eodory's approach and in Gibbs' one. Carath\'eodory's approach is fundamental in order to understand the nature of the surface T=0. In fact, in this approach, under suitable mathematical conditions, T=0 appears as a leaf of the foliation of the thermodynamic manifold associated with the non-singular integrable Pfaffian form $\delta Q_{rev}$. Being a leaf, it cannot intersect any other leaf $S=$ const. of the foliation. We show that (N) is equivalent to the requirement that T=0 is a leaf. In Gibbs' approach, the peculiar nature of T=0 appears to be less evident because the existence of the entropy is a postulate; nevertheless, it is still possible to conclude that the lowest value of the entropy has to belong to the boundary of the convex set where the function is defined.Comment: 29 pages, 2 figures; RevTex fil

Being Able to Learn: Researching the History of a Therapeutic Community

This article uses grounded theory methods to research the history of a therapeutic community and highlights the possibilities of ‘being able to learn’ as an aim for history of medicine research. For this case study, processes of research and learning allow consideration of the ‘dilemma of paternalism’ and the interaction between history, policy and practice. How can students enter into discourses about learning? How could this discourse help to make university systems of administration and assessment provide a more appropriate environment for staff and students to ‘be able to learn’

Integration of range images in a multi-view stereo system

A novel method for integrating multiple range images in a multi-view stereo imaging system is presented here. Due to self-occlusion an individual range image provides only a partial model of an object surface. Therefore multiple range images from differing viewpoints must be captured and merged to extend the surface area that can be captured. In our approach range images are decomposed into subset patches and then evaluated in a "confidence competition". Redundant patches are removed whilst winning patches are merged to complete a single plausible mesh that represents the acquired object surface

Comprehensive Researcher Achievement Model (CRAM): A framework for measuring researcher achievement, impact and influence derived from a systematic literature review of metrics and models

Objectives Effective researcher assessment is key to decisions about funding allocations, promotion and tenure. We aimed to identify what is known about methods for assessing researcher achievements, leading to a new composite assessment model. Design We systematically reviewed the literature via the Preferred Reporting Items for Systematic Review and Meta-Analysis Protocols framework. Data sources All Web of Science databases (including Core Collection, MEDLINE and BIOSIS Citation Index) to the end of 2017. Eligibility criteria (1) English language, (2) published in the last 10 years (2007-2017), (3) full text was available and (4) the article discussed an approach to the assessment of an individual researcher's achievements. Data extraction and synthesis Articles were allocated among four pairs of reviewers for screening, with each pair randomly assigned 5% of their allocation to review concurrently against inclusion criteria. Inter-rater reliability was assessed using Cohen's Kappa (A). The A statistic showed agreement ranging from moderate to almost perfect (0.4848-0.9039). Following screening, selected articles underwent full-text review and bias was assessed. Results Four hundred and seventy-eight articles were included in the final review. Established approaches developed prior to our inclusion period (eg, citations and outputs, h-index and journal impact factor) remained dominant in the literature and in practice. New bibliometric methods and models emerged in the last 10 years including: measures based on PageRank algorithms or 'altmetric' data, methods to apply peer judgement and techniques to assign values to publication quantity and quality. Each assessment method tended to prioritise certain aspects of achievement over others. Conclusions All metrics and models focus on an element or elements at the expense of others. A new composite design, the Comprehensive Researcher Achievement Model (CRAM), is presented, which supersedes past anachronistic models. The CRAM is modifiable to a range of applications

The Clinical Assessment Study of the Hand (CAS-HA): a prospective study of musculoskeletal hand problems in the general population

<p>Abstract</p> <p>Background</p> <p>Pain in the hand affects an estimated 12–21% of the population, and at older ages the hand is one of the most common sites of pain and osteoarthritis. The association between symptomatic hand osteoarthritis and disability in everyday life has not been studied in detail, although there is evidence that older people with hand problems suffer significant pain and disability. Despite the high prevalence of hand problems and the limitations they cause in older adults, little attention has been paid to the hand by health planners and policy makers. We plan to conduct a prospective, population-based, observational cohort study designed in parallel with our previously reported cohort study of knee pain, to describe the course of musculoskeletal hand problems in older adults and investigate the relative merits of different approaches to classification and defining prognosis.</p> <p>Methods/Design</p> <p>All adults aged 50 years and over registered with two general practices in North Staffordshire will be invited to take part in a two-stage postal survey. Respondents to the survey who indicate that they have experienced hand pain or problems within the previous 12 months will be invited to attend a research clinic for a detailed assessment. This will consist of clinical interview, hand assessment, screening test of lower limb function, digital photography, plain x-rays, anthropometric measurement and brief self-complete questionnaire. All consenting clinic attenders will be followed up by (i) general practice medical record review, (ii) repeat postal questionnaire at 18-months, and (iii) repeat postal questionnaire at 3 years.</p> <p>Discussion</p> <p>This paper describes the protocol for the Clinical Assessment Study of the Hand (CAS-HA), a prospective, population-based, observational cohort study of community-dwelling older adults with hand pain and hand problems based in North Staffordshire.</p

The transformative role of interaction rituals within therapeutic communities

Mental health settings are fraught with emotion as clients address difficult life experiences and relational patterns. Clients spend a substantial amount of time together outside of structured therapy, but little is known about how these moments are potentially therapeutic, especially as sites of emotional change. We draw on interaction ritual chain theory to explore how negative emotions in situations outside of formal therapy can be transformed into positive emotions and facilitate personal change. The research is based upon a narrative ethnography of two therapeutic communities for individuals with a diagnosis of personality disorder. Despite the presence of negative transient emotions in these rituals, clients experienced positive feelings of solidarity and belonging, and the majority of clients reported increased feelings of confidence and positive change. Conversely, dynamics between clients showed clients were not always supportive of one another and at times, could exclude others, resulting in isolation and alienation. We argue interactions that generate feelings of inclusion or exclusion over time area key component in whether clients gain positive or negative emotional feeling and experience personal change

Cuts from residues: the one-loop case

Using the multivariate residue calculus of Leray, we give a precise definition of the notion of a cut Feynman integral in dimensional regularization, as a residue evaluated on the variety where some of the propagators are put on shell. These are naturally associated to Landau singularities of the first type. Focusing on the one-loop case, we give an explicit parametrization to compute such cut integrals, with which we study some of their properties and list explicit results for maximal and next-to-maximal cuts. By analyzing homology groups, we show that cut integrals associated to Landau singularities of the second type are specific combinations of the usual cut integrals, and we obtain linear relations among different cuts of the same integral. We also show that all one-loop Feynman integrals and their cuts belong to the same class of functions, which can be written as parametric integrals.Comment: v2: fixed minor typos in the normalisation of cut integral