Search results for "Torus"
showing 10 items of 100 documents
Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems
2001
We consider a class of Hamiltonians with three degrees of freedom that can be mapped into quasi-periodically driven pendulums. The purpose of this paper is to determine the threshold of the break-up of invariant tori with a specific frequency vector. We apply two techniques: the frequency map analysis and renormalization-group methods. The renormalization transformation acting on a Hamiltonian is a canonical change of coordinates which is a combination of a partial elimination of the irrelevant modes of the Hamiltonian and a rescaling of phase space around the considered torus. We give numerical evidence that the critical coupling at which the renormalization transformation starts to diverg…
Massless Spectra and Gauge Couplings at One-Loop on Non-Factorisable Toroidal Orientifolds
2018
So-called `non-factorisable' toroidal orbifolds can be rewritten in a factorised form as a product of three two-tori by imposing an additional shift symmetry. This finding of Blaszczyk et al., arXiv:1111.5852, provides a new avenue to Conformal Field Theory methods, by which the vector-like massless matter spectrum - and thereby the type of gauge group enhancement on orientifold invariant fractional D6-branes - and the one-loop corrections to the gauge couplings in Type IIA orientifold theories can be computed in addition to the well-established chiral matter spectrum derived from topological intersection numbers among three-cycles. We demonstrate this framework for the $\mathbb{Z}_4 \times…
Critical Attractor and Universality in a Renormalization Scheme for Three Frequency Hamiltonian Systems
1998
We study an approximate renormalization-group transformation to analyze the breakup of invariant tori for three degrees of freedom Hamiltonian systems. The scheme is implemented for the spiral mean torus. We find numerically that the critical surface is the stable manifold of a critical nonperiodic attractor. We compute scaling exponents associated with this fixed set, and find that they can be expected to be universal.
Nondegeneracy in the Perturbation Theory of Integrable Dynamical Systems
1990
The most general nondegeneracy condition for the existence of invariant tori in nearly integrable and analytic Hamiltonian systems is formulated.
Neutron-star merger ejecta as obstacles to neutrino-powered jets of gamma-ray bursts
2015
We present the first special relativistic, axisymmetric hydrodynamic simulations of black hole-torus systems (approximating general relativistic gravity) as remnants of binary-neutron star (NS-NS) and neutron star-black hole (NS-BH) mergers, in which the viscously driven evolution of the accretion torus is followed with self-consistent energy-dependent neutrino transport and the interaction with the cloud of dynamical ejecta expelled during the NS-NS merging is taken into account. The modeled torus masses, BH masses and spins, and the ejecta masses, velocities, and spatial distributions are adopted from relativistic merger simulations. We find that energy deposition by neutrino annihilation…
Influence of self-gravity on the runaway instability of black-hole-torus systems.
2010
Results from the first fully general relativistic numerical simulations in axisymmetry of a system formed by a black hole surrounded by a self-gravitating torus in equilibrium are presented, aiming to assess the influence of the torus self-gravity on the onset of the runaway instability. We consider several models with varying torus-to-black hole mass ratio and angular momentum distribution orbiting in equilibrium around a non-rotating black hole. The tori are perturbed to induce the mass transfer towards the black hole. Our numerical simulations show that all models exhibit a persistent phase of axisymmetric oscillations around their equilibria for several dynamical timescales without the …
Accurate evolutions of unequal-mass neutron-star binaries: properties of the torus and short GRB engines
2010
We present new results from accurate and fully general-relativistic simulations of the coalescence of unmagnetized binary neutron stars with various mass ratios. The evolution of the stars is followed through the inspiral phase, the merger and prompt collapse to a black hole, up until the appearance of a thick accretion disk, which is studied as it enters and remains in a regime of quasi-steady accretion. Although a simple ideal-fluid equation of state with \Gamma=2 is used, this work presents a systematic study within a fully general relativistic framework of the properties of the resulting black-hole--torus system produced by the merger of unequal-mass binaries. More specifically, we show…
Remarks on the reduced phase space of -dimensional gravity on a torus in the Ashtekar formulation
1998
We examine the reduced phase space of the Barbero-Varadarajan solutions of the Ashtekar formulation of (2 + 1)-dimensional general relativity on a torus. We show that it is a finite-dimensional space due to the existence of an infinite-dimensional residual gauge invariance which reduces the infinite-dimensional space of solutions to a finite-dimensional space of gauge-inequivalent solutions. This is in agreement with general arguments which imply that the number of physical degrees of freedom for (2 + 1)-dimensional Ashtekar gravity on a torus is finite.
Towards modelling the central engine of short GRBs
2011
Numerical relativity simulations of non-vacuum spacetimes have reached a status where a complete description of the inspiral, merger and post-merger stages of the late evolution of close binary neutron systems is possible. Determining the properties of the black-hole-torus system produced in such an event is a key aspect to understand the central engine of short-hard gamma-ray bursts (sGRBs). Of the many properties characterizing the torus, the total rest-mass is the most important one, since it is the torus' binding energy which can be tapped to extract the large amount of energy necessary to power the sGRB emission. In addition, the rest-mass density and angular momentum distribution in t…
On the runaway instability of self-gravitating torus around black holes
2010
Black holes surrounded by self-gravitating tori are astrophysical systems which may naturally form following the core collapse of a massive star or the merger of two neutron stars. We present here results from fully general relativistic numerical simulations of such systems in order to assess the influence of the torus self-gravity on the onset of the so-called runaway instability. This instability, which might drive the rapid accretion of the disk on shorter timescales than those required to power a relativistic fireball, potentially challenges current models of gamma-ray bursts. Our simulations indicate that the self-gravity of the torus does not actually favour the onset of the instabili…