Search results for " torus"
showing 10 items of 22 documents
Chaotic dynamics and partial hyperbolicity
2017
The dynamics of hyperbolic systems is considered well understood from topological point of view as well as from stochastic point of view. S. Smale and R. Abraham gave an example showing that, in general, the hyperbolic systems are not dense among all differentiable systems. In 1970s, M. Brin and Y. Pesin proposed a new notion: partial hyperbolicity to release the notion of hyperbolicity. One aim of this thesis is to understand the dynamics of certain partially hyperbolic systems from stochastic point of view as well as from topological point of view. From stochastic point of view, we prove the following results: — There exists an open and dense subset U of robustly transitive nonhyperbolic …
Efficient generation of energetic ions in multi-ion plasmas by radio-frequency heating
2017
We describe a new technique for the efficient generation of high-energy ions with electromagnetic ion cyclotron waves in multi-ion plasmas. The discussed ‘three-ion’ scenarios are especially suited for strong wave absorption by a very low number of resonant ions. To observe this effect, the plasma composition has to be properly adjusted, as prescribed by theory. We demonstrate the potential of the method on the world-largest plasma magnetic confinement device, JET (Joint European Torus, Culham, UK), and the high-magnetic-field tokamak Alcator C-Mod (Cambridge, USA). The obtained results demonstrate efficient acceleration of 3He ions to high energies in dedicated hydrogen–deuterium mixtures.…
Attractors/Basin of Attraction
2020
It is a controversial issue to decide who first coined the term “attractor”. According to Peter Tsatsanis, the editor of the English version of Prédire n’est pas expliquer, it was René Thom who first introduced such a term. It is necessary, however, to remember that Thom thought that it was first introduced by the American mathe- matician Steven Smale, “although Smale says it was Thom that coined the neolo- gism “attractor”“(Tsatsanis 2010: 63–64 n. 20). From this point of view, Bob Williams expressed a more cautious opinion by saying that “the word “attractor” was invented by these guys, Thom and Smale” (Cucker and Wong 2000: 183). But other mathematicians are of the opinion that the term …
Norms of harmonic projection operators on compact Lie groups
1988
In order to simplify the notation, we will assume throughout that G is connected, simply connected and semisimple. Sharp estimates for vp(z 0 when G = SU(2) have been obtained by Sogge [6], who proved that Vp(Zt) ~ d~ tl/v), where y(t) is the function which is affine on [1/2, 3/4] and on [3/4, 1] and is such that 7(1/2)=0, 7(3/4)=1/4, 7(1)=1. Two results in the literature give crucial estimates from below for vp(n) in the general case. The first estimate concernes the LP'-norm of the character X, : if ,~, is the highest weight of n and 0 is half the sum of the positive roots, then II x=llp,--> + 011-dimG/p" (1.2)
Computation of Yvon-Villarceau circles on Dupin cyclides and construction of circular edge right triangles on tori and Dupin cyclides
2014
Ring Dupin cyclides are non-spherical algebraic surfaces of degree four that can be defined as the image by inversion of a ring torus. They are interesting in geometric modeling because: (1) they have several families of circles embedded on them: parallel, meridian, and Yvon-Villarceau circles, and (2) they are characterized by one parametric equation and two equivalent implicit ones, allowing for better flexibility and easiness of use by adopting one representation or the other, according to the best suitability for a particular application. These facts motivate the construction of circular edge triangles lying on Dupin cyclides and exhibiting the aforementioned properties. Our first contr…
Actions de tores algébriques sur des corps de caractéristique zéro
2023
Over an algebraically closed field of characteristic zero, normal affine varieties endowed with an effective torus action were described by Altmann and Hausen in 2006 by a geometrico-combinatorial presentation.Using Galois descent tools, we extend this presentation to the case where the ground field is an arbitrary field of characteristic zero. In this context, the acting torus may be non split and may have non-trivial torsors, thus we need additional data to encode such varieties. We provide some situations where the generalized Altmann-Hausen presentation simplifies. For instance, if the acting torus is split, we recover mutatis mutandis the original Altmann-Hausen presentation. Finally, …
Comparison of the structure of the plasma-facing surface and tritium accumulation in beryllium tiles from JET ILW campaigns 2011-2012 and 2013-2014
2019
In this study, beryllium tiles from Joint European Torus (JET) vacuum vessel wall were analysed and compared regarding their position in the vacuum vessel and differences in the exploitation conditions during two campaigns of ITER-Like-Wall (ILW) in 2011-2012 (ILW1) and 2013-2014 (ILW2) Tritium content in beryllium samples were assessed. Two methods were used to measure tritium content in the samples - dissolution under controlled conditions and tritium thermal desorption. Prior to desorption and dissolution experiments, scanning electron microscopy and energy dispersive x-ray spectroscopy were used to study structure and chemical composition of plasma-facing-surfaces of the beryllium sampl…
Spectrometric analysis of inner divertor materials of JET carbon and ITER-like walls
2019
Abstract One of main reasons of the Joint European torus (JET) transformation from the carbon (JET-C) to ITER-like (JET-ILW) wall was high tritium retention of carbon. In order to compare the tritium retention, samples of analogous positions of the plasma-facing side of vertical tiles No. 3 of two campaigns: JET-C (2008–2009) and JET-ILW (2011–2012) were cut out. Temperature-programmed tritium desorption spectrometry in He + 0.1% H2 gas flow showed that JET-C sample without a tungsten coating had by a factor of >20 higher surface concentration of tritium than JET-ILW tungsten-coated sample: 4.9 × 1013 and 1.7–2.2 × 1012 T atoms/cm2 respectively. Installation of metallic plasma facing wall i…
Tritium sorption and desorption from JET beryllium tiles under temperature, electron radiation and magnetic field
2008
Abstract Tritium release at annealing of samples cut from beryllium tiles exposed to D + D, D + T plasma in the Joint European Torus (JET) was investigated under 5 MeV fast-electron radiation at the dose rate 14 MGy h −1 and in a magnetic field of 1.7 T separately and simultaneously in order to evaluate possible effects of these factors. Abundances of chemical forms of tritium—molecular T 2 (44%), atomic T 0 (42%), and ionic T + (14%) and their distribution were determined in the plasma-exposed beryllium samples with lyomethods. Fast-electron radiation considerably increased the fractional tritium release at annealing by a factor of approximately 5. The magnetic field increased the fraction…
Evolution by mean curvature flow of Lagrangian spherical surfaces in complex Euclidean plane
2016
We describe the evolution under the mean curvature flow of embedded Lagrangian spherical surfaces in the complex Euclidean plane $\mathbb{C}^2$. In particular, we answer the Question 4.7 addressed in [Ne10b] by A. Neves about finding out a condition on a starting Lagrangian torus in $\mathbb{C}^2$ such that the corresponding mean curvature flow becomes extinct at finite time and converges after rescaling to the Clifford torus.