| 1. |
- Herrmann, Sven, et al.
(författare)
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Optimal realizations of two-dimensional, totally-decomposable metrics
- 2015
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Ingår i: Discrete Mathematics. - : Elsevier BV. - 0012-365X .- 1872-681X. ; 338:8, s. 1289-1299
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Tidskriftsartikel (refereegranskat)abstract
- A realization of a metric d on a finite set X is a weighted graph (G, w) whose vertex set contains X such that the shortest-path distance between elements of X considered as vertices in G is equal to d. Such a realization (G, w) is called optimal if the sum of its edge weights is minimal over all such realizations. Optimal realizations always exist, although it is NP-hard to compute them in general, and they have applications in areas such as phylogenetics, electrical networks and internet tomography. A. Dress (1984) showed that the optimal realizations of a metric dare closely related to a certain polytopal complex that can be canonically associated to d called its tight-span. Moreover, he conjectured that the (weighted) graph consisting of the zero- and one-dimensional faces of the tight-span of d must always contain an optimal realization as a homeomorphic subgraph. In this paper, we prove that this conjecture does indeed hold for a certain class of metrics, namely the class of totally-decomposable metrics whose tight-span has dimension two. As a corollary, it follows that the minimum Manhattan network problem is a special case of finding optimal realizations of two-dimensional totally-decomposable metrics. (C) 2015 Elsevier B.V. All rights reserved.
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| 2. |
- Joffrin, E., et al.
(författare)
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Overview of the JET preparation for deuterium-tritium operation with the ITER like-wall
- 2019
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Ingår i: Nuclear Fusion. - : IOP Publishing. - 1741-4326 .- 0029-5515. ; 59:11
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Forskningsöversikt (refereegranskat)abstract
- 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 Alfven 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.
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