A first estimation of the contraction related to vertical axis rotation: the case of the Ibero-Armorican Arc formation

Different models have been proposed to explain the formation of the Ibero-Armorican Arc, which require significant vertical axis rotations, at the end of the Variscan orogeny. Estimates of the amount of contraction (horizontal shortening) needed for these rotations range from 54 % to 91 % perpendicularly to the arc. These estimates are compared with coeval deformational structures developed in two areas of the orogen, one in the autochthonous hinterland underlying the Galicia-Trás-os-Montes Zone in the southern branch of the arc, and the other in the Cantabrian Zone foreland in the core of the arc. From this analysis it follows that the late Variscan deformation together with the subsequent Alpine contraction is not sufficient to explain the formation of the Ibero-Armorican Arc as a secondary structure by means of vertical axis rotations. Our analysis suggests this arc is mainly a primary, or non-rotational curve, slightly modified by ca. 10 % of superposed contraction during late Carboniferous and/or Alpine times. Moreover, we propose that the assumptions underlying the interpreted geometry of the arc be re-evaluated, and we discuss the role of late-Variscan regional strike-slip faults in the Iberian and in the Armorican massifs that probably acted consecutively before and during the contraction of the arc.

Newtonian and modified newtonian gravitational simulation of spiral galaxies

One of the most powerful tools for any stellar dynamics is the N-body simulation. In an N-body simulation the motion of N particles is followed under their mutual gravitational attraction. In this paper the gravitational N-body simulation is described to investigate Newtonian and non- Newtonian (modified Newtonian dynamics) interaction between the stars of spiral galaxies. It is shown that standard Newtonian interaction requires dark matter to produce the flat rotational curves of the systems under consideration, while modified Newtonian dynamics (MOND) theorem provides a flat rotational curve and gives a good agreement with the observed rotation curve; MOND was tested as an alternative to the dark matter hypothesis. So that MOND hypothesis has generated better rotation curves than Newtonian theorem.

UNIMODULAR CONSTRAINT ON GLOBAL SCALE INVARIANCE

We study a model with global scale invariance within the framework of unimodular gravity. The global scale invariant gravitational action which follows the unimodular general coordinate transformations is considered without invoking any scalar field. This is generalization of conformal theory described [P. D. Mannheim and D. Kazanas, Astrophys. J. 342, 635 (1989)]. The possible solutions for the gravitational potential under static linear field approximation are discussed. The new modified solution has additional corrections to the Schwarzschild solution which describe the galactic rotational curve. A comparative study of unimodular theory with conformal theory is also presented. Furthermore, the cosmological solution is studied and it is shown that the unimodular constraint preserve the de Sitter solution explaining the dark energy of the universe.

Induced energy polarization of the vacuum and the rotational curve for the Galaxy

The theory of an induced energy polarized vacuum, as previously presented by the author (Penner. Can. J. Phys. 90, 315 (2012)), is used to generate a theoretical rotational curve for the Galaxy. The theoretical curve generated is found to be in good agreement with Sofue's (Publ. Astron. Soc. Jpn. 64, (In press) (2012)) compilation of observations. For the baryonic mass distribution and baryonic Tully–Fisher relationship that is used, the theoretical orbital velocity at the Sun's location is found to be (235 ± 15) km s−1. The galactic rotational velocity is then found to slowly fall from this value as it asymptotically approaches the value of (192 ± 15) km s−1.

Stability of the Shallow Axisymmetric Parabolic-Conic Bimetallic Shell by Nonlinear Theory

In this contribution, we discuss the stress, deformation, and snap-through conditions of thin, axi-symmetric, shallow bimetallic shells of so-called parabolic-conic and plate-parabolic type shells loaded by thermal loading. According to the theory of the third order that takes into account the balance of forces on a deformed body, we present a model with a mathematical description of the system geometry, displacements, stress, and thermoelastic deformations. The equations are based on the large displacements theory. We numerically calculate the deformation curve and the snap-through temperature using the fourth-order Runge-Kutta method and a nonlinear shooting method. We show how the temperature of both snap-through depends on the point where one type of the rotational curve transforms into another.

The Internal Rotation Rate Inferred from Lowl and Gong Data: Using a Forward Method

Recently the LOWL Group has made available 2-year averages of frequency splitting data obtained mainly for low values of the degree ℓ. Charbonneau et al. (1997) find a nearly flat rotational curve in the deep radiative core from these data using a Genetic Forward Modeling method. Subsequently, they test the assumption of latitude independence for r < 0.5 by performing a 1.5-D inversion, and find a rotation rate which is 25% greater at the pole than at the equator for 0.1 < r < 0.2.

ELLIPTIC NON-BIRKHOFF PERIODIC ORBITS IN THE TWIST MAPS

We consider a perturbed twist map when the perturbation is big enough to destroy the invariant rotational curve (IRC) with a given irrational rotation number. Then an invariant Cantorian set appears. From another point of view, the destruction of the IRC is associated with the appearance of heteroclinic connections between hyperbolic periodic points. Furthermore the destruction of the IRC is also associated with the existence of non-Birkhoff orbits. In this paper we relate the different approaches. In order to explain the creation of non-Birkhoff orbits, we provide qualitative and quantitative models. We show the existence of elliptic non-Birkhoff periodic orbits for an open set of values of the perturbative parameter. The bifurcations giving rise to the elliptic non-Birkhoff orbits and other related bifurcations are analysed. In the last section, we show a celestial mechanics example displaying the described behavior.