MODELLING THE ELECTRON WITH COSSERAT ELASTICITY

Interactions between a finite number of bodies and the surrounding fluid, in a channel for instance, are investigated theoretically. In the planar model here the bodies or modelled grains are thin solid bodies free to move in a nearly parallel formation within a quasi-inviscid fluid. The investigation involves numerical and analytical studies and comparisons. The three main features that appear are a linear instability about a state of uniform motion, a clashing of the bodies (or of a body with a side wall) within a finite scaled time when nonlinear interaction takes effect, and a continuum-limit description of the body–fluid interaction holding for the case of many bodies

Invertibility in groupoid C*-algebras

Given a second-countable, Hausdorff, \'etale, amenable groupoid G with compact unit space, we show that an element a in C*(G) is invertible if and only if \lambda_x(a) is invertible for every x in the unit space of G, where \lambda_x refers to the "regular representation" of C*(G) on l_2(G_x). We also prove that, for every a in C*(G), there exists some x in G^{(0)} such that ||a|| = ||\lambda_x(a)||.Comment: 8 page

Minimal symmetric Darlington synthesis

We consider the symmetric Darlington synthesis of a p x p rational symmetric Schur function S with the constraint that the extension is of size 2p x 2p. Under the assumption that S is strictly contractive in at least one point of the imaginary axis, we determine the minimal McMillan degree of the extension. In particular, we show that it is generically given by the number of zeros of odd multiplicity of I-SS*. A constructive characterization of all such extensions is provided in terms of a symmetric realization of S and of the outer spectral factor of I-SS*. The authors's motivation for the problem stems from Surface Acoustic Wave filters where physical constraints on the electro-acoustic scattering matrix naturally raise this mathematical issue

Some geometric invariants from resolutions of Hilbert modules

The model theory of Sz.-Nagy and Foias for contractions was reformulated in [15, chapter 3]. The existence of a unique minimal unitary dilation amounts to the exis-tence of a Silov resolution for contractive Hilbert modulesM over the disc algebra A(D) along with the fact that any two minimal Silov resolutions are isomorphic

Platinized counter-electrodes for dye-sensitised solar cells from waste thermocouples: A case study for resource efficiency, industrial symbiosis and circular economy

A study of a local industrial symbiosis involving the recovery of platinum from waste thermocouples which is then used for the preparation of catalytic electrodes suitable for dye-sensitized solar cell production is reported. The small quantity of platinum in the filaments of used thermocouples, thousands of which are discarded each year by metal foundries, can be economically recovered by conversion to chloroplatinic acid hydrate, an ‘added value’ product, which can then be used in the fabrication of dye-sensitized solar cell counter-electrodes. 91% recovery of platinum from filaments as chloroplatinic acid hydrate has been achieved by aqua regia digestion of manually isolated filaments. Cost-benefit analysis shows the proposed process derives sufficient value to cover landfill costs for what is left of the waste thermocouples after platinum removal; provide ∼5 days employment; and provide 63% materials cost savings for electrode preparation in comparison to purchasing commercially available chloroplatinic acid hydrate. The proposed local industrial symbiosis would, per year, divert ∼50  g of platinum from landfill, avoid up to 1400 kg of CO2 emissions associated with primary production of an equivalent quantity of platinum, and give enough platinum to produce catalytic electrodes for ∼500 m2 of dye-sensitized solar cells, which could supply clean energy for 12 homes in the locality. The process exemplifies the environmental, economic and social benefits available through adoption of circular practices, which make use of secondary materials available within the local economy by valorizing wastes. The process also overcomes economic barriers to critical raw materials (CRMs) recovery from dissipative applications

Operator theory and function theory in Drury-Arveson space and its quotients

The Drury-Arveson space $H^2_d$, also known as symmetric Fock space or the $d$-shift space, is a Hilbert function space that has a natural $d$-tuple of operators acting on it, which gives it the structure of a Hilbert module. This survey aims to introduce the Drury-Arveson space, to give a panoramic view of the main operator theoretic and function theoretic aspects of this space, and to describe the universal role that it plays in multivariable operator theory and in Pick interpolation theory.Comment: Final version (to appear in Handbook of Operator Theory); 42 page

Generality of shear thickening in suspensions

Suspensions are of wide interest and form the basis for many smart fluids. For most suspensions, the viscosity decreases with increasing shear rate, i.e. they shear thin. Few are reported to do the opposite, i.e. shear thicken, despite the longstanding expectation that shear thickening is a generic type of suspension behavior. Here we resolve this apparent contradiction. We demonstrate that shear thickening can be masked by a yield stress and can be recovered when the yield stress is decreased below a threshold. We show the generality of this argument and quantify the threshold in rheology experiments where we control yield stresses arising from a variety of sources, such as attractions from particle surface interactions, induced dipoles from applied electric and magnetic fields, as well as confinement of hard particles at high packing fractions. These findings open up possibilities for the design of smart suspensions that combine shear thickening with electro- or magnetorheological response.Comment: 11 pages, 9 figures, accepted for publication in Nature Material

de Branges-Rovnyak spaces: basics and theory

For $S$ a contractive analytic operator-valued function on the unit disk ${\mathbb D}$, de Branges and Rovnyak associate a Hilbert space of analytic functions ${\mathcal H}(S)$ and related extension space ${\mathcal D(S)}$ consisting of pairs of analytic functions on the unit disk ${\mathbb D}$. This survey describes three equivalent formulations (the original geometric de Branges-Rovnyak definition, the Toeplitz operator characterization, and the characterization as a reproducing kernel Hilbert space) of the de Branges-Rovnyak space ${\mathcal H}(S)$, as well as its role as the underlying Hilbert space for the modeling of completely non-isometric Hilbert-space contraction operators. Also examined is the extension of these ideas to handle the modeling of the more general class of completely nonunitary contraction operators, where the more general two-component de Branges-Rovnyak model space ${\mathcal D}(S)$ and associated overlapping spaces play key roles. Connections with other function theory problems and applications are also discussed. More recent applications to a variety of subsequent applications are given in a companion survey article

d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories

We study three dimensional O(N)_k and U(N)_k Chern-Simons theories coupled to a scalar field in the fundamental representation, in the large N limit. For infinite k this is just the singlet sector of the O(N) (U(N)) vector model, which is conjectured to be dual to Vasiliev's higher spin gravity theory on AdS_4. For large k and N we obtain a parity-breaking deformation of this theory, controlled by the 't Hooft coupling lambda = 4 \pi N / k. For infinite N we argue (and show explicitly at two-loop order) that the theories with finite lambda are conformally invariant, and also have an exactly marginal (\phi^2)^3 deformation. For large but finite N and small 't Hooft coupling lambda, we show that there is still a line of fixed points parameterized by the 't Hooft coupling lambda. We show that, at infinite N, the interacting non-parity-invariant theory with finite lambda has the same spectrum of primary operators as the free theory, consisting of an infinite tower of conserved higher-spin currents and a scalar operator with scaling dimension \Delta=1; however, the correlation functions of these operators do depend on lambda. Our results suggest that there should exist a family of higher spin gravity theories, parameterized by lambda, and continuously connected to Vasiliev's theory. For finite N the higher spin currents are not conserved.Comment: 34 pages, 29 figures. v2: added reference

Comparison of breast and bowel cancer screening uptake patterns in a common cohort of South Asian women in England

Background: Inequalities in uptake of cancer screening by ethnic minority populations are well documented in a number of international studies. However, most studies to date have explored screening uptake for a single cancer only. This paper compares breast and bowel cancer screening uptake for a cohort of South Asian women invited to undertake both, and similarly investigates these women's breast cancer screening behaviour over a period of fifteen years. Methods: Screening data for rounds 1, 2 and 5 (1989-2004) of the NHS breast cancer screening programme and for round 1 of the NHS bowel screening pilot (2000-2002) were obtained for women aged 50-69 resident in the English bowel screening pilot site, Coventry and Warwickshire, who had been invited to undertake breast and bowel cancer screening in the period 2000-2002. Breast and bowel cancer screening uptake levels were calculated and compared using the chi-squared test. Results: 72,566 women were invited to breast and bowel cancer screening after exclusions. Of these, 3,539 were South Asian and 69,027 non-Asian; 18,730 had been invited to mammography over the previous fifteen years (rounds 1 to 5). South Asian women were significantly less likely to undertake both breast and bowel cancer screening; 29.9% (n = 1,057) compared to 59.4% (n = 40,969) for non-Asians (p < 0.001). Women in both groups who consistently chose to undertake breast cancer screening in rounds 1, 2 and 5 were more likely to complete round 1 bowel cancer screening. However, the likelihood of completion of bowel cancer screening was still significantly lower for South Asians; 49.5% vs. 82.3% for non-Asians, p < 0.001. South Asian women who undertook breast cancer screening in only one round were no more likely to complete bowel cancer screening than those who decided against breast cancer screening in all three rounds. In contrast, similar women in the non-Asian population had an increased likelihood of completing the new bowel cancer screening test. The likelihood of continued uptake of mammography after undertaking screening in round 1 differed between South Asian religio-linguistic groups. Noticeably, women in the Muslim population were less likely to continue to participate in mammography than those in other South Asian groups. Conclusions: Culturally appropriate targeted interventions are required to reduce observed disparities in cancer screening uptakes