Search results for "Torus"
showing 10 items of 100 documents
Transition to turbulence in toroidal pipes
2011
AbstractIncompressible flow in toroidal pipes of circular cross-section was investigated by three-dimensional, time-dependent numerical simulations using a finite volume method. The computational domain included a whole torus and was discretized by up to ${\ensuremath{\sim} }11. 4\ensuremath{\times} 1{0}^{6} $ nodes. Two curvatures $\delta $ (radius of the cross-section/radius of the torus), namely 0.3 and 0.1, were examined; a streamwise forcing term was imposed, and its magnitude was made to vary so that the bulk Reynolds number ranged between ${\ensuremath{\sim} }3500$ and ${\ensuremath{\sim} }14\hspace{0.167em} 700$. The results were processed by different techniques in order to confirm…
OUTFLOWS FROM ACTIVE GALACTIC NUCLEI: KINEMATICS OF THE NARROW-LINE AND CORONAL-LINE REGIONS IN SEYFERT GALAXIES,
2011
As part of an extensive study of the physical properties of active galactic nuclei (AGN) we report high spatial resolution near-IR integral-field spectroscopy of the narrow-line region (NLR) and coronal-line region (CLR) of seven Seyfert galaxies. These measurements elucidate for the first time the two-dimensional spatial distribution and kinematics of the recombination line Br{\gamma} and high-ionization lines [Sivi], [Alix] and [Caviii] on scales <300 pc from the AGN. The observations reveal kinematic signatures of rotation and outflow in the NLR and CLR. The spatially resolved kinematics can be modeled as a combination of an outflow bicone and a rotating disk coincident with the molecula…
Kolmogorov-Arnold-Moser–Renormalization-Group Analysis of Stability in Hamiltonian Flows
1997
We study the stability and breakup of invariant tori in Hamiltonian flows using a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. We implement the scheme numerically for a family of Hamiltonians quadratic in the actions to analyze the strong coupling regime. We show that the KAM iteration converges up to the critical coupling at which the torus breaks up. Adding a renormalization consisting of a rescaling of phase space and a shift of resonances allows us to determine the critical coupling with higher accuracy. We determine a nontrivial fixed point and its universality properties.
Large data scattering for NLKG on waveguide ℝd × 𝕋
2020
We consider the pure-power defocusing nonlinear Klein–Gordon equation, in the [Formula: see text]-subcritical case, posed on the product space [Formula: see text], where [Formula: see text] is the one-dimensional flat torus. In this framework, we prove that scattering holds for any initial data belonging to the energy space [Formula: see text] for [Formula: see text]. The strategy consists in proving a suitable profile decomposition theorem on the whole manifold to pursue a concentration-compactness and rigidity method along with the proofs of (global in time) Strichartz estimates.
The Ising transition in 2D simplicial quantum gravity - can Regge calculus be right?
1995
We report a high statistics simulation of Ising spins coupled to 2D quantum gravity in the Regge calculus approach using triangulated tori with up to $512^2$ vertices. For the constant area ensemble and the $dl/l$ functional measure we definitively can exclude the critical exponents of the Ising phase transition as predicted for dynamically triangulated surfaces. We rather find clear evidence that the critical exponents agree with the Onsager values for static regular lattices, independent of the coupling strength of an $R^2$ interaction term. For exploratory simulations using the lattice version of the Misner measure the situation is less clear.
Modelling of the magnetic field structures and first measurements of heat fluxes for TEXTOR-DED operation
2004
The dynamic ergodic divertor (DED) was recently installed at the TEXTOR tokamak. One of the aims of the DED is to control and study heat and particle deposition on a plasma wall via modification of the plasma edge by external perturbation coils. Sixteen perturbation coils are mounted on the high-field side of the torus. The external magnetic perturbation creates a zone of chaotic field lines at the plasma edge by destroying several resonant surfaces. These structures have the properties of an open chaotic system while the field lines intersect the tokamak vessel. In order to study the topology of the field lines in different regimes, a set of tools called Atlas was created. Atlas uses a sym…
The Ising–Bloch transition in degenerate optical parametric oscillators
2003
Domain walls in type I degenerate optical parametric oscillators are numerically investigated. Both steady Ising and moving Bloch walls are found, bifurcating one into another through a nonequilibrium Ising--Bloch transition. Bloch walls are found that connect either homogeneous or roll planforms. Secondary bifurcations affecting Bloch wall movement are characterized that lead to a transition from a steady drift state to a temporal chaotic movement as the system is moved far from the primary, Ising--Bloch bifurcation. Two kinds of routes to chaos are found, both involving tori: a usual Ruelle-Takens and an intermittent scenarios.
Multiple Noncommutative Tori and Hopf Algebras
2001
We derive the Kac-Paljutkin finite-dimensional Hopf algebras as finite fibrations of the quantum double torus and generalize the construction for quantum multiple tori.
Three-dimensional axisymmetric cloak based on the cancellation of acoustic scattering from a sphere.
2013
This Letter presents the design, fabrication, and experimental characterization of a directional threedimensional acoustic cloak for airborne sound. The cloak consists of 60 concentric acoustically rigid tori surrounding the cloaked object, a sphere of radius 4 cm. The major radii and positions of the tori along the symmetry axis are determined using the condition of complete cancellation of the acoustic field scattered from the sphere. They are obtained through an optimization technique that combines genetic algorithm and simulated annealing. The scattering cross section of the sphere with the cloak, which is the magnitude that is minimized, is calculated using the method of fundamental so…
Types I and II intermittencies in a cascade laser model
1995
Abstract We report on types I and II intermittencies found in a cascade laser model. A continuous transition from one to another type of intermittency, which involves the coexistence of both types of laminar phases within the same time series, is found. Type II intermittency has special characteristics such as its origin at a frequency locked two-torus. When frequency unlocked this torus bifurcates to a three-torus, further giving rise to a type II intermittent like behaviour with new features during the laminar phases.