Isospectral deformations of the Dirac operator

We give more details about an integrable system in which the Dirac operator D=d+d^* on a finite simple graph G or Riemannian manifold M is deformed using a Hamiltonian system D'=[B,h(D)] with B=d-d^* + i b. The deformed operator D(t) = d(t) + b(t) + d(t)^* defines a new exterior derivative d(t) and a new Dirac operator C(t) = d(t) + d(t)^* and Laplacian M(t) = d(t) d(t)^* + d(t)* d(t) and so a new distance on G or a new metric on M.Comment: 32 pages, 8 figure

What do others think is the point of design and technology education?

As a result of a national curriculum review in England (Department for Education [DfE], 2011), a new curriculum for design and technology (D&T) is being taught in secondary schools from September 2014 (Department of Education [DoE], 2013a). This curriculum is compulsory for a decreasing number of schools; two potential consequences are the nature of D&T in secondary schools changing to reflect local perceptions of the subject and maybe D&T being removed from the curriculum completely. The pressure on D&T’s curriculum content is likely to come from different stakeholders such as senior school leaders, D&T teachers, and pupils. D&T school departments could respond to this pressure by adapting the curriculum to popularise the subject or produce high exam results with a consequence that much of the subject’s value is lost. This paper reports on a small research project conducted in two secondary schools where stakeholder representatives were interviewed to identify their values of D&T. These different stakeholders were interviewed using the active interview method (Holstein & Gubrium, 1995), coded following Aurebach and Silverstein’s method (2003) and their values compared to Hardy’s values framework (Hardy, 2013b). Analysis shows most stakeholders believe a key value of D&T is to provide ‘practical life skills’ (Hardy, p.226), whilst only one recognizes that learning in D&T involves ‘identifying problems to be solved’. The outcomes from the research are being used to support critically reflective conversations within both D&T departments (Zwozdiak-Myers, 2012) framing their evaluation of their local curriculum and making changes to their curriculum

Finite temperature Drude weight of an integrable Bose chain

We study the Drude weight $D(T)$ at finite temperatures $T$ of an integrable bosonic model where the particles interact via nearest-neighbour coupling on a chain. At low temperatures, $D(T)$ is shown to be universal in the sense that this region is equivalently described by a Gaussian model. This low-temperature limit is also relevant for the integrable one-dimensional Bose gas. We then use the thermodynamic Bethe ansatz to confirm the low-temperature result, to obtain the high temperature limit of $D(T)$ and to calculate $D(T)$ numerically.Comment: 11 pages, 2 figure

Coupling iterated Kolmogorov diffusions

The Kolmogorov (1934) diffusion is the two-dimensional diffusion generated by real Brownian motion B and its time integral integral B d t. In this paper we construct successful co-adapted couplings for iterated Kolmogorov diffusions defined by adding iterated time integrals integral integral B d s d t,... as further components to the original Kolmogorov diffusion. A Laplace-transform argument shows it is not possible successfully to couple all iterated time integrals at once; however we give an explicit construction of a successful co-adapted coupling method for (B, integral B d t, integral integral B d s d t); and a more implicit construction of a successful co-adapted coupling method which works for finite sets of iterated time integrals

Overview of the JET preparation for deuterium-tritium operation with the ITER like-wall

For the past several years, the JET scientific programme (Pamela et al 2007 Fusion Eng. Des.82 590) has been engaged in a multi-campaign effort, including experiments in D, H and T, leading up to 2020 and the first experiments with 50%/50% D–T mixtures since 1997 and the first ever D–T plasmas with the ITER mix of plasma-facing component materials. For this purpose, a concerted physics and technology programme was launched with a view to prepare the D–T campaign (DTE2). This paper addresses the key elements developed by the JET programme directly contributing to the D–T preparation. This intense preparation includes the review of the physics basis for the D–T operational scenarios, including the fusion power predictions through first principle and integrated modelling, and the impact of isotopes in the operation and physics of D–T plasmas (thermal and particle transport, high confinement mode (H-mode) access, Be and W erosion, fuel recovery, etc). This effort also requires improving several aspects of plasma operation for DTE2, such as real time control schemes, heat load control, disruption avoidance and a mitigation system (including the installation of a new shattered pellet injector), novel ion cyclotron resonance heating schemes (such as the three-ions scheme), new diagnostics (neutron camera and spectrometer, active Alfvèn eigenmode antennas, neutral gauges, radiation hard imaging systems...) and the calibration of the JET neutron diagnostics at 14 MeV for accurate fusion power measurement. The active preparation of JET for the 2020 D–T campaign provides an incomparable source of information and a basis for the future D–T operation of ITER, and it is also foreseen that a large number of key physics issues will be addressed in support of burning plasmas.This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 and 2019–2020 under grant agreement No. 633053Postprint (published version