Motion of a Vector Particle in a Curved Spacetime. II First Order Correction to a Geodesic in a Schwarzschild Background

The influence of spin on a photon's motion in a Schwarzschild and FRW spacetimes is studied. The first order correction to the geodesic motion is found. It is shown that unlike the world-lines of spinless particles, the photons world-lines do not lie in a plane.Comment: 14 pages, LaTeX2e, second paper in the series (the first one: gr-qc/0110067), replaced with typos and style corrected version, accepted in MPL

Restricted three-body problem in effective-field-theory models of gravity

One of the outstanding problems of classical celestial mechanics was the restricted 3-body prob- lem, in which a planetoid of small mass is subject to the Newtonian attraction of two celestial bodies of large mass, as it occurs, for example, in the sun-earth-moon system. On the other hand, over the last decades, a systematic investigation of quantum corrections to the Newtonian potential has been carried out in the literature on quantum gravity. The present paper studies the effect of these tiny quantum corrections on the evaluation of equilibrium points. It is shown that, despite the extreme smallness of the corrections, there exists no choice of sign of these corrections for which all qualitative features of the restricted 3-body problem in Newtonian theory remain unaffected. Moreover, first-order stability of equilibrium points is characterized by solving a pair of algebraic equations of fifth degree, where some coefficients depend on the Planck length. The coordinates of stable equilibrium points are slightly changed with respect to Newtonian theory, because the planetoid is no longer at equal distance from the two bodies of large mass. The effect is conceptually interesting but too small to be observed, at least for the restricted 3-body problems available in the solar system.Comment: 20 pages, latex, 8 figure

Routh reduction for singular Lagrangians

This paper concerns the Routh reduction procedure for Lagrangians systems with symmetry. It differs from the existing results on geometric Routh reduction in the fact that no regularity conditions on either the Lagrangian $L$ or the momentum map $J_L$ are required apart from the momentum being a regular value of $J_L$. The main results of this paper are: the description of a general Routh reduction procedure that preserves the Euler-Lagrange nature of the original system and the presentation of a presymplectic framework for Routh reduced systems. In addition, we provide a detailed description and interpretation of the Euler-Lagrange equations for the reduced system. The proposed procedure includes Lagrangian systems with a non-positively definite kinetic energy metric.Comment: 34 pages, 2 figures, accepted for publicaton in International Journal of Geometric Methods in Modern Physics (IJGMMP

Routhian reduction for quasi-invariant Lagrangians

In this paper we describe Routhian reduction as a special case of standard symplectic reduction, also called Marsden-Weinstein reduction. We use this correspondence to present a generalization of Routhian reduction for quasi-invariant Lagrangians, i.e. Lagrangians that are invariant up to a total time derivative. We show how functional Routhian reduction can be seen as a particular instance of reduction of a quasi-invariant Lagrangian, and we exhibit a Routhian reduction procedure for the special case of Lagrangians with quasi-cyclic coordinates. As an application we consider the dynamics of a charged particle in a magnetic field.Comment: 24 pages, 3 figure

The classical dynamics of two-electron atoms near the triple collision

The classical dynamics of two electrons in the Coulomb potential of an attractive nucleus is chaotic in large parts of the high-dimensional phase space. Quantum spectra of two-electron atoms, however, exhibit structures which clearly hint at the existence of approximate symmetries in this system. In a recent paper,(Phys. Rev. Lett. 93, 054302 (2004)), we presented a study of the dynamics near the triple collision as a first step towards uncovering the hidden regularity in the classical dynamics of two electron atoms. The non-regularisable triple collision singularity is a main source of chaos in three body Coulomb problems. Here, we will give a more detailed account of our findings based on a study of the global structure of the stable and unstable manifolds of the triple collision.Comment: 21 pages, 17 figure

Lagrangian Framework for Systems Composed of High-Loss and Lossless Components

Using a Lagrangian mechanics approach, we construct a framework to study the dissipative properties of systems composed of two components one of which is highly lossy and the other is lossless. We have shown in our previous work that for such a composite system the modes split into two distinct classes, high-loss and low-loss, according to their dissipative behavior. A principal result of this paper is that for any such dissipative Lagrangian system, with losses accounted by a Rayleigh dissipative function, a rather universal phenomenon occurs, namely, selective overdamping: The high-loss modes are all overdamped, i.e., non-oscillatory, as are an equal number of low-loss modes, but the rest of the low-loss modes remain oscillatory each with an extremely high quality factor that actually increases as the loss of the lossy component increases. We prove this result using a new time dynamical characterization of overdamping in terms of a virial theorem for dissipative systems and the breaking of an equipartition of energy.Comment: 53 pages, 1 figure; Revision of our original manuscript to incorporate suggestions from refere

Hepatosteatoz olgularında elastografi bulguları

OBJECTIVE: This study evaluates whether dynamic elastography could better characterize and differentiate the non-alcoholic fatty liver disease (NAFLD) and patient pool for biopsy. MATERIALS AND METHODS: 18 patients with NAFLD were examined by ultrasound (US) and elastography at the Department of Radiology. The patients, none of whom had any chronic liver disease, were 54±9.5 (35-71) years old (8 men; 10 women). Biochemical markers were evaluated. Patients with high liver echogenicity were classified as Stage III NAFLD. B-mode US equipment includes a Hitachi HI VISION Preirus system with an embedded elastography (EL) module (Hitachi Medical Systems Europe) and 6.5 MHz linear probe. RESULTS: Of the cases, 55.6% were female and 44.4% were male. All cases with Stage I NAFLD were female (n:5). Only 33.3% of the cases with Stage III NAFLD were female (n:2). According to the results of elastography, no intergroup difference was differentiated when the stages of NAFLD were compared. When biochemical and hepatomegaly values were considered, differences were only detected in GGT and hepatomegaly values among the NAFLD groups (p:0.015). CONCLUSION: In the study, the stages of hepatosteatosis could not be differentiated with the EL examination. Therefore, it was thought to be of no benefit to the selection.AMAÇ: Bu çalışma alkolik olmayan yağlı karaciğer (NAFLD) olgularının biopsi öncesi değerlendiriminde elastografinin etkinliğini araştırmak için planlandı. GEREÇ VE YÖNTEMLER: Radyoloji bölümünde 18 NAFLD hastası B mod ultrason ile incelendikten sonra elastografi ile değerlendirildi . Olguların hiçbirinde kronik karaciğer hastalığı yoktu. Yaşları 35 ila 71 arasında değişen 8 erkek hasta ile 10 kadın hasta çalışmaya dahil edildi ( ortalama 54±9.5). Son 6 ay içerisindeki biyokimyasal değerlendirmeleri de kayıt altına alındı. Karaciğer dalak ile karşılaştırılarak ekojenite artışına göre I., II. ve III. derecelerde ile sınıflandıırldı. B mod ve elastografi değerlendirilmesi Hitachi HI VISION Preirus sistemi ile 6.5 MHz lineer prob ile yapıldı. BULGULAR: Olguların %55,6’sı kadın, %44’ ü erkek idi. Evre I NAFLD olgularının tümü kadın idi (n:5). Evre III olgularının sadece %33,3’ü kadın idi (n:2). Gruplar arası hepatosteatoz evresi göz önüne alındığında elastografi sonuçları arasında fark saptanmadı. Biyokimyasal değerler ve hepatomegali ölçüm değerleri göz önüne alındığında GGT ve hepatomegali ölçümleri gruplar arası farklılık göstermekte idi (p:0.015). SONUÇ: Bu çalışmada, B mod ultrasonda sıklıkla kullanılan hepatosteatoz evreleme sistemi elastografi tekniği ile doğrulanamadı. Böylelikle NAFLD tanısı ile biyopsi gereken ile gerekmeyen takipteki olgular arasında ayrım yapılamadı. Bu veri transient elastografi bulgularından oldukça farklı idi

Dissipative Properties of Systems Composed of High-Loss and Lossless Components

We study here dissipative properties of systems composed of two components one of which is highly lossy and the other is lossless. A principal result of our studies is that all the eigenmodes of such a system split into two distinct classes characterized as high-loss and low-loss. Interestingly, this splitting is more pronounced the higher the loss of the lossy component. In addition, the real frequencies of the high-loss eigenmodes can become very small and even can vanish entirely, which is the case of overdamping.Comment: Revision; Improved exposition and typos corrected; 45 pages, 4 figure

Conservation of energy and momenta in nonholonomic systems with affine constraints

We characterize the conditions for the conservation of the energy and of the components of the momentum maps of lifted actions, and of their `gauge-like' generalizations, in time-independent nonholonomic mechanical systems with affine constraints. These conditions involve geometrical and mechanical properties of the system, and are codified in the so-called reaction-annihilator distribution

Nonholonomic Constraints with Fractional Derivatives

We consider the fractional generalization of nonholonomic constraints defined by equations with fractional derivatives and provide some examples. The corresponding equations of motion are derived using variational principle.Comment: 18 page