Search results for "Torus"
showing 10 items of 100 documents
Transitive partially hyperbolic diffeomorphisms on 3-manifolds
2005
Abstract The known examples of transitive partially hyperbolic diffeomorphisms on 3-manifolds belong to 3 basic classes: perturbations of skew products over an Anosov map of T 2 , perturbations of the time one map of a transitive Anosov flow, and certain derived from Anosov diffeomorphisms of the torus T 3 . In this work we characterize the two first types by a local hypothesis associated to one closed periodic curve.
Damping effect on the ITER vacuum vessel displacements during slow downward locked and rotating asymmetric vertical displacement events
2018
Abstract In this paper, we present the electromechanical coupled analysis of the ITER vacuum vessel in case of slow downward locked and rotating Asymmetric VDEs. The numerical model for simulating the AVDE includes the asymmetric distribution of the halo currents obtained by a suitable 3D kink perturbation of a slow VDE downward computed by the 2D code DINA. In the case of a rotational AVDE, the rotation frequency of the kink asymmetry has been chosen to be ω = 2π × 5 rad/s. The model includes the mesh of the main passive components facing the plasma. The whole torus (360 degrees) has been discretized. It is shown that the very high complexity of the numerical model can be suitably treated.…
Domains of Convergence of Kam Type Iterations for Eigenvalue Problems
1999
The KAM technique was first introduced to deal with small denominator problems appearing in perturbation of invariant tori in classical mechanics [1, 2]. Similar methods were later applied to many different problems, like e.g. eigenvalue problems for time dependent problems in the Floquet representation [3, 4, 5, 6]. Most of the known results are valid for sufficiently small perturbation of some simple (integrable) system. The phenomena arising for large perturbations, in particular critical perturbations at which a given torus loses its stability, have been discussed in the framework of some approximate schemes inspired in renormalization group ideas [7, 8, 9]. In this framework, an iterat…
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…
Tailoring a pair of pants
2021
Abstract We show how to deform the map Log : ( C ⁎ ) n → R n such that the image of the complex pair of pants P ∘ ⊂ ( C ⁎ ) n is the tropical hyperplane by showing an (ambient) isotopy between P ∘ ⊂ ( C ⁎ ) n and a natural polyhedral subcomplex of the product of the two skeleta S × Σ ⊂ A × C of the amoeba A and the coamoeba C of P ∘ . This lays the groundwork for having the discriminant to be of codimension 2 in topological Strominger-Yau-Zaslow torus fibrations.
Mappings of Finite Distortion : Compactness of the Branch Set
2017
We show that an entire branched cover of finite distortion cannot have a compact branch set if its distortion satisfies a certain asymptotic growth condition. We furthermore show that this bound is strict by constructing an entire, continuous, open and discrete mapping of finite distortion which is piecewise smooth, has a branch set homeomorphic to an (n - 2)-dimensional torus and distortion arbitrarily close to the asymptotic bound. Peer reviewed
On the dynamics of tilted black hole-torus systems
2016
We present results from three-dimensional, numerical relativity simulations of a {\it tilted} black hole-thick accretion disc system. The simulations are analysed using tracer particles in the disc which are advected with the flow. Such tracers, which we employ in these new simulations for the first time, provide a powerful means to analyse in detail the complex dynamics of tilted black hole-torus systems. We show how its use helps to gain insight in the overall dynamics of the system, discussing the origin of the observed black hole precession and the development of a global non-axisymmetric $m=1$ mode in the disc. Our three-dimensional simulations show the presence of quasi-periodic oscil…
Magnetised Polish doughnuts revisited
2017
We discuss a procedure to build new sequences of magnetised, equilibrium tori around Kerr black holes which combines two approaches previously considered in the literature. For simplicity we assume that the test-fluid approximation holds, and hence we neglect the self-gravity of the fluid. The models are built assuming a particular form of the angular momentum distribution from which the location and morphology of equipotential surfaces can be computed. This ansatz includes, in particular, the constant angular momentum case originally employed in the construction of thick tori - or Polish doughnuts - and it has already been used to build equilibrium sequences of purely hydrodynamical models…
Non-linear evolutions of magnetized thick discs around black holes: dependence on the initial data
2020
We build equilibrium solutions of magnetised thick discs around a highly spinning Kerr black hole and evolve these initial data up to a final time of about 100 orbital periods. The numerical simulations reported in this paper solve the general relativistic magnetohydrodynamics equations using the BHAC code and are performed in axisymmetry. Our study assumes non-self-gravitating, polytropic, constant angular momentum discs endowed with a purely toroidal magnetic field. In order to build the initial data we consider three approaches, two of which incorporate the magnetic field in a self-consistent way and a third approach in which the magnetic field is included as a perturbation on to an othe…
Using evolutionary algorithms to model relativistic jets
2019
High-resolution Very-Long-Baseline Interferometry observations of NGC 1052 show a two sided jet with several regions of enhanced emission and a clear emission gap between the two jets.This gap shrinks with increasing frequency and vanishes around $\nu\sim43$ GHz. The observed structures are due to both the macroscopic fluid dynamics interacting with the surrounding ambient medium including an obscuring torus and the radiation microphysics. In this paper we investigate the possible physical conditions in relativistic jets of NGC 1052 by directly modelling the observed emission and spectra via state-of-the-art special-relativistic hydrodynamic (SRHD) simulations and radiative transfer calcula…