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from Dialogues in Art and Design: Promoting and sharing ExcellenceUo

Centre for Learner Development

CETL Briefing Paper - HEFCE Website. HEFCE CETL.HEFC

Des equations de Dirac et de Schrodinger pour la transformation de Fourier

Dyson a associe aux determinants de Fredholm des noyaux de Dirichlet pairs (resp. impairs) une equation de Schrodinger sur un demi-axe et a employe les methodes du scattering inverse de Gel'fand-Levitan et de Marchenko, en tandem, pour etudier l'asymptotique de ces determinants. Nous avons propose suite a notre mise-au-jour de l'operateur conducteur de chercher a realiser la transformation de Fourier elle-meme comme un scattering, et nous obtenons ici dans ce but deux systemes de Dirac sur l'axe reel tout entier et qui sont associes intrinsequement, respectivement, aux transformations en cosinus et en sinus. (Dyson has associated with the Fredholm determinants of the even (resp. odd) Dirichlet kernels a Schrodinger equation on the half-axis and has used, in tandem, the Gel'fand-Levitan and Marchenko methods of inverse scattering theory to study the asymptotics of these determinants. We have proposed following our unearthing of the conductor operator to seek to realize the Fourier transform itself as a scattering, and we obtain here to this end two Dirac systems on the entire real axis which are intrinsically associated, respectively, to the cosine and to the sine transforms.)Comment: 8 pages, with a summary in English. One or two things adde

Testing Hall-Post Inequalities With Exactly Solvable N-Body Problems

The Hall--Post inequalities provide lower bounds on $N$-body energies in terms of $N'$-body energies with $N'<N$. They are rewritten and generalized to be tested with exactly-solvable models of Calogero-Sutherland type in one and higher dimensions. The bound for $N$ spinless fermions in one dimension is better saturated at large coupling than for noninteracting fermions in an oscillatorComment: 7 pages, Latex2e, 2 .eps figure

Velocity fluctuations in forced Burgers turbulence

We propose a simple method to compute the velocity difference statistics in forced Burgers turbulence in any dimension. Within a reasonnable assumption concerning the nucleation and coalescence of shocks, we find in particular that the `left' tail of the distribution decays as an inverse square power, which is compatible with numerical data. Our results are compared to those of various recent approaches: instantons, operator product expansion, replicas.Comment: 10 pages latex, one postcript figur

New Lower Bound on Fermion Binding Energies

We derive a new lower bound for the ground state energy $E^{\rm F}(N,S)$ of N fermions with total spin S in terms of binding energies $E^{\rm F}(N-1,S \pm 1/2)$ of (N-1) fermions. Numerical examples are provided for some simple short-range or confining potentials.Comment: 4 pages, 1 eps figur

Physics of accretion flows around compact objects

Several physical and astrophysical problems related to accretion onto black holes and neutron stars are shortly reviewed. I discuss the observed differences between these two types of compact objects in quiescent Soft X-ray Transients. Then I review the status of various non-standard objects suggested as an alternative to black-holes. Finally I present new results and suggestions about the nature of the jet activity in Active Galactic Nuclei. {To cite this article: J.-P. Lasota, C. R. Physique 6 (2006).}Comment: Submitted to Elsevier Scienc

Robust High-performance Dye-sensitized Solar Cells Based on Ionic Liquid-sulfolane Composite Electrolytes

Novel ionic liquid-sulfolane composite electrolytes based on the 1,2,3-triazolium family of ionic liquids were developed for dye-sensitized solar cells. The best performing device exhibited a short-circuit current density of 13.4 mA cm(-2), an open-circuit voltage of 713 mV and a fill factor of 0.65, corresponding to an overall power conversion efficiency (PCE) of 6.3%. In addition, these devices are highly stable, retaining more than 95% of the initial device PCE after 1000 hours of light-and heat-stress. These composite electrolytes show great promise for industrial application as they allow for a 14.5% improvement in PCE, compared to the solvent-free eutectic ionic liquid electrolyte system, without compromising device stability

Implementation of U.K. Earth system models for CMIP6

We describe the scientific and technical implementation of two models for a core set of experiments contributing to the sixth phase of the Coupled Model Intercomparison Project (CMIP6). The models used are the physical atmosphere-land-ocean-sea ice model HadGEM3-GC3.1 and the Earth system model UKESM1 which adds a carbon-nitrogen cycle and atmospheric chemistry to HadGEM3-GC3.1. The model results are constrained by the external boundary conditions (forcing data) and initial conditions.We outline the scientific rationale and assumptions made in specifying these. Notable details of the implementation include an ozone redistribution scheme for prescribed ozone simulations (HadGEM3-GC3.1) to avoid inconsistencies with the model's thermal tropopause, and land use change in dynamic vegetation simulations (UKESM1) whose influence will be subject to potential biases in the simulation of background natural vegetation.We discuss the implications of these decisions for interpretation of the simulation results. These simulations are expensive in terms of human and CPU resources and will underpin many further experiments; we describe some of the technical steps taken to ensure their scientific robustness and reproducibility

Crises and collective socio-economic phenomena: simple models and challenges

Financial and economic history is strewn with bubbles and crashes, booms and busts, crises and upheavals of all sorts. Understanding the origin of these events is arguably one of the most important problems in economic theory. In this paper, we review recent efforts to include heterogeneities and interactions in models of decision. We argue that the Random Field Ising model (RFIM) indeed provides a unifying framework to account for many collective socio-economic phenomena that lead to sudden ruptures and crises. We discuss different models that can capture potentially destabilising self-referential feedback loops, induced either by herding, i.e. reference to peers, or trending, i.e. reference to the past, and account for some of the phenomenology missing in the standard models. We discuss some empirically testable predictions of these models, for example robust signatures of RFIM-like herding effects, or the logarithmic decay of spatial correlations of voting patterns. One of the most striking result, inspired by statistical physics methods, is that Adam Smith's invisible hand can badly fail at solving simple coordination problems. We also insist on the issue of time-scales, that can be extremely long in some cases, and prevent socially optimal equilibria to be reached. As a theoretical challenge, the study of so-called "detailed-balance" violating decision rules is needed to decide whether conclusions based on current models (that all assume detailed-balance) are indeed robust and generic.Comment: Review paper accepted for a special issue of J Stat Phys; several minor improvements along reviewers' comment