A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations

The purpose of this paper is to enhance a correspondence between the dynamics of the differential equations $\dot y(t)=g(y(t))$ on $\mathbb{R}^d$ and those of the parabolic equations $\dot u=\Delta u +f(x,u,\nabla u)$ on a bounded domain $\Omega$. We give details on the similarities of these dynamics in the cases $d=1$, $d=2$ and $d\geq 3$ and in the corresponding cases $\Omega=(0,1)$, $\Omega=\mathbb{T}^1$ and dim($\Omega$)$\geq 2$ respectively. In addition to the beauty of such a correspondence, this could serve as a guideline for future research on the dynamics of parabolic equations

What’s D&T for? Gathering and comparing the values of design and technology academics and trainee teachers

Some who read and research about Design & Technology (D&T) would say that the concept of value is key to understanding and defining D&T. Closer inspection reveals though that there are two ways in which values are defined in D&T: how values are taught and learnt about in D&T to use them to make judgments in D&T lessons, and also how values are developed in pupils as a result of studying D&T. Layton’s seminal keynote speech is the notable exception to these two classifications. In 1992 he shared a new perspective of values and D&T: how different stakeholders value the school subject D&T (1992a). The work presented here builds on Layton’s ‘new’ perspective and compares how two D&T stakeholder groups value D&T. The opinions of trainee D&T teachers and D&T academics, both directly affected by these changes were analysed using a grounded theory coded method. This resulted in a series of twenty-two values that facilitated comparison of the two group’s values. Further analysis revealed there were many similarities between the two groups, and only a few differences. However these differences showed the trainees did not believe D&T can be about the process of designing or identifying the needs of others, both values central to the original purpose of D&T in England and recognised by the academics. One implication for this, as schools take more ownership of teacher training, is that the value of D&T is likely to move further away from the D&T academics’ influence and be based upon the ‘spontaneous’ (Dow 2014, p.151) values developed through classroom practice with little reference to external opinion. Future work could widen the scope of the research, incorporating the values of other stakeholder groups into the values series and hence become a new tool to support the development of design and technology education, which hopefully will benefit others as they reflect on why they teach, research or use D&T

Innovation, competition and incentives for R&D

This paper analyses the relationship between past innovation output, competition, and future innovation input in a dynamic econometric setting. We distinguish two dimensions of competition that correspond to the concepts of product substitutability and entry barriers due to fixed costs. Based on firm-level panel data for Germany and Switzerland we obtain consistent results for both countries. Innovation output in t-1 as measured by the sales share of innovative products is positively related to the degree of product obsolescence in t, and negatively to the degree of substitutability in t in both countries. Further, we find that rapid product obsolescence provides positive incentives for higher - primarily product-oriented - R&D investments in t+1, while high substitutability exerts negative incentives for future R&D investment. --Innovation,R&D,Competition

Higgs boson form factor effects in ttˉt\bar t production by W−W+W^-W^+ and ZZZZ fusion

We study the fusion processes $W^-W^+\to t\bar t$ and $ZZ\to t\bar t$ observable at a future $e^-e^+$ collider and we discuss their sensitivity to an $Htt$ form factor which may be due to compositeness, in particular when the $H$ and the top quark have common constituents. We make an amplitude analysis and illustrate which helicity amplitudes and cross sections for specific final $t\bar t$ polarizations are especially sensitive to this form factor.Comment: 24 pages, 37 figures, version including changes suggested by the Physical Review D publication tea

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

News vs Information

We consider the relative entropy between the vacuum state and a coherent state in linearized quantum gravity around a stationary black hole spacetime. Combining recent results by Casini et al. and Longo with the Raychaudhuri equation, the following result is obtained: Let $\frak A$ be the algebra of observables assoiciated with a region that is the causal future of some compact set in the interior of the spacetime. Let $S$ be the relative entropy with respect to this algebra, $A$ the area of the horizon cross section defined by the region, computed to second order in the gravitational perturbation. If the region is time-translated by the Killing parameter $t$, then $\frac{d}{d t}(S+A/4)= 2\pi F$, with $F$ the flux of the gravitational/matter radiation (integrated squared news tensor) emitted towards the future of the region.Comment: 11 pages, 1 figure. arXiv admin note: text overlap with arXiv:1903.07508, v2: some details added on function spaces and decay of solutions, refs. adde