Search results for "Tractor"

Great Attractor-like structures and large-scale anisotropy

1994

APPROXIMATE INERTIAL MANIFOLDS FOR THERMODIFFUSION EQUATIONS

2004

In this paper, we consider the two dimensional equations of thermohydraulics, i.e. the coupled system of equations of fluid and temperature in the Boussinesq approximation. We construct a family of approximate Inertial Manifolds whose order decreases exponentially fast with respect to the dimension of the manifold. We give the explicit expression of the order of the constructed manifolds.

Primordial Black Holes and Slow-Roll Violation

2017

For primordial black holes (PBH) to be the dark matter in single-field inflation, the slow-roll approximation must be violated by at least ${\cal O}(1)$ in order to enhance the curvature power spectrum within the required number of efolds between CMB scales and PBH mass scales. Power spectrum predictions which rely on the inflaton remaining on the slow-roll attractor can fail dramatically leading to qualitatively incorrect conclusions in models like an inflection potential and misestimate the mass scale in a running mass model. We show that an optimized temporal evaluation of the Hubble slow-roll parameters to second order remains a good description for a wide range of PBH formation models …

Relaxation, postponement, and features of the attractor in a driven varactor oscillator

1990

The driven varactor oscillator is investigated by numerical integration of its ODEs using the standard model of circuit theory. Attention is given to some properties of the basic relaxation mechanism. For time dependent amplitudes of the sinusoidal driving voltage the post-ponement of the bifurcations is characterized by transient Lyapunov numbers. The postponement of the first bifurcation shows the same dependence on the sweep velocity as in the case of the nonautonomous quadratic map. The shapes of the attractors are displayed in extended phase space. Generalized Renyi-dimensionsD 0 andD 1 have been determined in the chaotic region. A corresponding twodimensional Pioncare map indicates se…

Physical interpretation of laser phase dynamics

1990

The basic features characterizing the dynamical evolution of the phase of a detuned-laser field under an unstable regime are physically interpreted in terms of dispersive and dynamical effects. A general method for obtaining any attractor projection containing the phase information is established, which provides evidence for the heteroclinic character of the attractor in the presence of cavity detuning for any emission regime.

Attracteur de polarisation dans les fibres optiques

2004

Nous etudions la dynamique non lineaire des etats de polarisation de deux ondes coherentes ou incoherentes se propageant dans une fibre optique. Nous presentons en particulier un effet original d'attraction de la polarisation.

Phenomenological approaches of inflation and their equivalence

2014

In this work, we analyze two possible alternative and model-independent approaches to describe the inflationary period. The first one assumes a general equation of state during inflation due to Mukhanov, while the second one is based on the slow-roll hierarchy suggested by Hoffman and Turner. We find that, remarkably, the two approaches are equivalent from the observational viewpoint, as they single out the same areas in the parameter space, and agree with the inflationary attractors where successful inflation occurs. Rephrased in terms of the familiar picture of a slowly rolling, canonically normalized scalar field, the resulting inflaton excursions in these two approaches are almost ident…

Experimental observation of modal attraction in optical fibers

2002

We investigate experimentally nonlinear optical attractors based on four-photon mixing interaction of counterpropagating waves in optical fibers.

Structural similarities and differences among attractors and their intensity maps in the laser-Lorenz model

1995

Abstract Numerical studies of the laser-Lorenz model using parameters reasonably accessible for recent experiments with a single mode homogeneously broadened laser demonstrate that the form of the return map of successive peak values of the intensity changes from a sharply cusped map in resonance to a map with a smoothly rounded maximum as the laser is detuned into the period doubling regime. This transformation appears to be related to the disappearance (with detuning) of the heteroclinic structural basis for the stable manifold which exists in resonance. This is in contrast to the evidence reported by Tang and Weiss (Phys. Rev. A 49 (1994) 1296) of a cusped map for both the period doublin…

Models, predictions, and experimental measurements of far-infrared NH3-laser dynamics and comparisons with the Lorenz-Haken model

1995

Dynamics of the intensity and optical field amplitude of a coherently pumped far-infrared NH3-laser are measured and characterized. The experimental findings in certain parameter ranges closely follow the dynamics of the Lorenz model and its generalization for laser systems. Similarities and some specific differences are found in geometrical or statistical characterizations of the attractors. The experimental results are also consistent with the results of a model of optically pumped three-level lasers which takes into account the presence of a multiplicity of velocity groups as well as three-level coherence effects. For a certain region in parameter space, this far more complex model with …