Search results for "tractor"
showing 10 items of 219 documents
Polarization and modal attractors in conservative counterpropagating four-wave interaction
2005
An experimental and theoretical study of the resonant four-wave interaction scheme in the counterpropagating configuration reveals the existence of a novel attraction process in Hamiltonian systems. We show analytically that it is the specificity of the boundary conditions inherent in the counterpropagating configuration that makes attraction dynamics possible in spite of the reversible nature of the four-wave interaction. In the context of optics, this novel dynamical feature could be the basic mechanism of a universal polarizer performing total polarization conversion of unpolarized light with, in principle, 100% efficiency.
The great attractor and the COBE quadrupole
2008
A nonlinear model for the Great Attractor is built. It is based on the Tolman-Bondi solution of the Einstein equations. The angular temperature distribution of the Cosmic Microwave Background produced by the Great Attractor is numerically obtained. Several realizations of the Great Attractor are studied. In all the cases, the distance from the Great Attractor to the Local Group is ≈ 43h−1 Mpc, the density contrast reduces to a half of the central value at a radius of 9h−1 Mpc ⪯ Rc ⪯ 14h−1 Mpc, and the dipole due to the infall towards the inhomogeneity center is 1.33 × 10−3 ⪯ D ⪯ 1.8 × 10−3. A complete arbitrary background is assumed; the density parameter, Σ and the reduced Hubble constant,…
The imprints of the Great Attractor and the Virgo cluster on the microwave background
1993
A fully non-linear model based on the Tolman-Bondi solution of the Einstein equations is used to describe the Great Attractor and the Virgo cluster. The background is a Friedmann-Robertson-Walker universe, and the inhomogeneity develops from physically motivated initial profiles of the energy density and the peculiar velocity. Accurate numerical integrations of the field equations of the null geodesics are carried out, and thus the angular temperature distribution of the microwave background produced by the chosen overdensities is found. The observer is located in the Local Group. The quadrupole Q produced by each overdensity is computed and divided into two parts: the relativistic Doppler …
Phantom Dirac-Born-Infeld dark energy
2017
Motivated by the apparent discrepancy between Cosmic Microwave Background measurements of the Hubble constant and measurements from Type-Ia supernovae, we construct a model for Dark Energy with equation of state $w = p / ��< -1$, violating the Null Energy Condition. Naive canonical models of so-called "Phantom" Dark Energy require a negative scalar kinetic term, resulting in a Hamiltonian unbounded from below and associated vacuum instability. We construct a scalar field model for Dark Energy with $w < -1$, which nonetheless has a Hamiltonian bounded from below in the comoving reference frame, {\it i.e.} in the rest frame of the fluid. We demonstrate that the solution is a cosmologica…
Induced gravity and the attractor dynamics of dark energy/dark matter
2010
Attractor solutions that give dynamical reasons for dark energy to act like the cosmological constant, or behavior close to it, are interesting possibilities to explain cosmic acceleration. Coupling the scalar field to matter or to gravity enlarges the dynamical behavior; we consider both couplings together, which can ameliorate some problems for each individually. Such theories have also been proposed in a Higgs-like fashion to induce gravity and unify dark energy and dark matter origins. We explore restrictions on such theories due to their dynamical behavior compared to observations of the cosmic expansion. Quartic potentials in particular have viable stability properties and asymptotica…
A dynamical systems study of the inhomogeneous Lambda-CDM model
2010
We consider spherically symmetric inhomogeneous dust models with a positive cosmological constant, $\Lambda$, given by the Lemaitre-Tolman-Bondi metric. These configurations provide a simple but useful generalization of the Lambda-CDM model describing cold dark matter (CDM) and a Lambda term, which seems to fit current cosmological observations. The dynamics of these models can be fully described by scalar evolution equations that can be given in the form of a proper dynamical system associated with a 4-dimensional phase space whose critical points and invariant subspaces are examined and classified. The phase space evolution of various configurations is studied in detail by means of two 2-…
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.
Nearly-integrable dissipative systems and celestial mechanics
2010
The influence of dissipative effects on classical dynamical models of Celestial Mechanics is of basic importance. We introduce the reader to the subject, giving classical examples found in the literature, like the standard map, the Hénon map, the logistic mapping. In the framework of the dissipative standard map, we investigate the existence of periodic orbits as a function of the parameters. We also provide some techniques to compute the breakdown threshold of quasi-periodic attractors. Next, we review a simple model of Celestial Mechanics, known as the spin-orbit problem which is closely linked to the dissipative standard map. In this context we present the conservative and dissipative KA…
Rich dynamics and anticontrol of extinction in a prey-predator system
2019
This paper reveals some new and rich dynamics of a two-dimensional prey-predator system and to anticontrol the extinction of one of the species. For a particular value of the bifurcation parameter, one of the system variable dynamics is going to extinct, while another remains chaotic. To prevent the extinction, a simple anticontrol algorithm is applied so that the system orbits can escape from the vanishing trap. As the bifurcation parameter increases, the system presents quasiperiodic, stable, chaotic and also hyperchaotic orbits. Some of the chaotic attractors are Kaplan-Yorke type, in the sense that the sum of its Lyapunov exponents is positive. Also, atypically for undriven discrete sys…
One pendulum to run them all
2013
The analytical solution for the three-dimensional linear pendulum in a rotating frame of reference is obtained, including Coriolis and centrifugal accelerations, and expressed in terms of initial conditions. This result offers the possibility of treating Foucault and Bravais pendula as trajectories of the same system of equations, each of them with particular initial conditions. We compare them with the common two-dimensional approximations in textbooks. A previously unnoticed pattern in the three-dimensional Foucault pendulum attractor is presented.