Growth, profits and technological choice: The case of the Lancashire cotton textile industry

Using Lancashire textile industry company case studies and financial records, mainly from the period just before the First World War, the processes of growth and decline are re-examined. These are considered by reference to the nature of Lancashire entrepreneurship and the impact on technological choice. Capital accumulation, associated wealth distributions and the character of Lancashire business organisation were sybiotically linked to the success of the industry before 1914. However, the legacy of that accumulation in later decades, chronic overcapacity, formed a barrier to reconstruction and enhanced the preciptious decline of a once great industry

Comparison theory and smooth minimal C*-dynamics

We prove that the C*-algebra of a minimal diffeomorphism satisfies Blackadar's Fundamental Comparability Property for positive elements. This leads to the classification, in terms of K-theory and traces, of the isomorphism classes of countably generated Hilbert modules over such algebras, and to a similar classification for the closures of unitary orbits of self-adjoint elements. We also obtain a structure theorem for the Cuntz semigroup in this setting, and prove a conjecture of Blackadar and Handelman: the lower semicontinuous dimension functions are weakly dense in the space of all dimension functions. These results continue to hold in the broader setting of unital simple ASH algebras with slow dimension growth and stable rank one. Our main tool is a sharp bound on the radius of comparison of a recursive subhomogeneous C*-algebra. This is also used to construct uncountably many non-Morita-equivalent simple separable amenable C*-algebras with the same K-theory and tracial state space, providing a C*-algebraic analogue of McDuff's uncountable family of II_1 factors. We prove in passing that the range of the radius of comparison is exhausted by simple C*-algebras.Comment: 30 pages, no figure

Quantum gravitational contributions to quantum electrodynamics

Quantum electrodynamics describes the interactions of electrons and photons. Electric charge (the gauge coupling constant) is energy dependent, and there is a previous claim that charge is affected by gravity (described by general relativity) with the implication that the charge is reduced at high energies. But that claim has been very controversial with the situation inconclusive. Here I report an analysis (free from earlier controversies) demonstrating that that quantum gravity corrections to quantum electrodynamics have a quadratic energy dependence that result in the reduction of the electric charge at high energies, a result known as asymptotic freedom.Comment: To be published in Nature. 19 pages LaTeX, no figure

The Polymer Stress Tensor in Turbulent Shear Flows

The interaction of polymers with turbulent shear flows is examined. We focus on the structure of the elastic stress tensor, which is proportional to the polymer conformation tensor. We examine this object in turbulent flows of increasing complexity. First is isotropic turbulence, then anisotropic (but homogenous) shear turbulence and finally wall bounded turbulence. The main result of this paper is that for all these flows the polymer stress tensor attains a universal structure in the limit of large Deborah number \De\gg 1. We present analytic results for the suppression of the coil-stretch transition at large Deborah numbers. Above the transition the turbulent velocity fluctuations are strongly correlated with the polymer's elongation: there appear high-quality "hydro-elastic" waves in which turbulent kinetic energy turns into polymer potential energy and vice versa. These waves determine the trace of the elastic stress tensor but practically do not modify its universal structure. We demonstrate that the influence of the polymers on the balance of energy and momentum can be accurately described by an effective polymer viscosity that is proportional to to the cross-stream component of the elastic stress tensor. This component is smaller than the stream-wise component by a factor proportional to \De ^2 . Finally we tie our results to wall bounded turbulence and clarify some puzzling facts observed in the problem of drag reduction by polymers.Comment: 11 p., 1 Fig., included, Phys. Rev. E., submitte

Locally Trivial W*-Bundles

We prove that a tracially continuous W$^*$-bundle $\mathcal{M}$ over a compact Hausdorff space $X$ with all fibres isomorphic to the hyperfinite II$_1$-factor $\mathcal{R}$ that is locally trivial already has to be globally trivial. The proof uses the contractibility of the automorphism group $\mathrm{Aut}({\mathcal{R}})$ shown by Popa and Takesaki. There is no restriction on the covering dimension of $X$.Comment: 20 pages, this version will be published in the International Journal of Mathematic

Statistical mechanics of an ideal Bose gas in a confined geometry

We study the behaviour of an ideal non-relativistic Bose gas in a three-dimensional space where one of the dimensions is compactified to form a circle. In this case there is no phase transition like that for the case of an infinite volume, nevertheless Bose-Einstein condensation signified by a sudden buildup of particles in the ground state can occur. We use the grand canonical ensemble to study this problem. In particular, the specific heat is evaluated numerically, as well as analytically in certain limits. We show analytically how the familiar result for the specific heat is recovered as we let the size of the circle become large so that the infinite volume limit is approached. We also examine in detail the behaviour of the chemical potential and establish the precise manner in which it approaches zero as the volume becomes large.Comment: 13 pages, 2 eps figures, revtex

Pleistocene landscape evolution in the Avon valley, southern Britain: optical dating of terrace formation and Palaeolithic archaeology

This paper presents the first comprehensive Optically Stimulated Luminescence dating programme from a sequence of Pleistocene river terraces in the Avon valley (Wiltshire-Hampshire-Dorset), southern Britain. These results offer the most complete chronometric framework for Pleistocene landscape evolution and Palaeolithic occupation in the Avon valley, allowing for the first time: (1) an assessment of the timing of terrace formation and landscape evolution, (2) the dating of hominin presence in the area, and (3) an investigation of the relationship between terrace formation and Quaternary climatic change. Analysis of 25 samples collected from terraces 10 and 7 to 4 show that the middle Avon terraces formed in response to the main Pleistocene climatic oscillations (Marine Isotope Stage (MIS) 10, 8, 6) and that fluvial mechanisms changed through time, resulting in three different types of terrace architecture. The highest and oldest deposits are compound terraces deposited during the Early Pleistocene before the Mid Pleistocene Transition. The middle reach of the valley is characterised by well-developed strath terraces overlain with thick fluvial deposits, reflecting the greater degree of incision in response to the increased amplitude of climate cycles in the Middle Pleistocene. The youngest deposits in the confined modern floodplain represent cut-and-fill terraces deposited after MIS5e. The results indicate that the two main Palaeolithic sites in the area, Milford Hill and Woodgreen, date to between at least MIS 10 and 8 with a pre-MIS 10 human occupation at a third main site at Bemerton. This is significant because the sites date to a period previously associated with a decline in hominin presence in Britain. The dating of the Avon valley terrace sequence highlights the complex nature of terrace formation during the Pleistocene and the need to critically reassess the chronological understanding of these fluvial archives in southern Britain. This research demonstrates that with a detailed and multidisciplinary approach shifts in hominin landscape use can be discovered, providing new information on hominin behavioural change during the Pleistocene

Bose-Einstein condensation as symmetry breaking in compact curved spacetimes

We examine Bose-Einstein condensation as a form of symmetry breaking in the specific model of the Einstein static universe. We show that symmetry breaking never occursin the sense that the chemical potential $\mu$ never reaches its critical value.This leads us to some statements about spaces of finite volume in general. In an appendix we clarify the relationship between the standard statistical mechanical approaches and the field theory method using zeta functions.Comment: Revtex, 25 pages, 3 figures, uses EPSF.sty. To be published in Phys. Rev.

Rokhlin Dimension for Flows

This research was supported by GIF Grant 1137/2011, SFB 878 Groups, Geometry and Actions and ERC Grant No. 267079. Part of the research was conducted at the Fields institute during the 2014 thematic program on abstract harmonic analysis, Banach and operator algebras, and at the Mittag–Leffler institute during the 2016 program on Classification of Operator Algebras: Complexity, Rigidity, and Dynamics.Peer reviewedPostprin

Representing aggregate works in the digital library

This paper studies the challenge of representing aggregate works such as encyclopedias, collected poems and journals in heterogenous digital library collections. Reflecting on the materials used by humanities academics, we demonstrate the varied range of aggregate types and the problems of faithfully representing this in the DL interface. Aggregates are complex and pervasive, challenge common assumptions and confuse boundaries within organisational structures. Existing DL systems can only provide imperfect representation of aggregates, and alterations to document encoding are insufficient to create a faithful reproduction of the physical library. The challenge is amplified through concrete examples, and solutions are demonstrated in a well-known DL system and related to standard DL architecture