Chaos in a Relativistic 3-body Self-Gravitating System

We consider the 3-body problem in relativistic lineal gravity and obtain an exact expression for its Hamiltonian and equations of motion. While general-relativistic effects yield more tightly-bound orbits of higher frequency compared to their non-relativistic counterparts, as energy increases we find in the equal-mass case no evidence for either global chaos or a breakdown from regular to chaotic motion, despite the high degree of non-linearity in the system. We find numerical evidence for a countably infinite class of non-chaotic orbits, yielding a fractal structure in the outer regions of the Poincare plot.Comment: 9 pages, LaTex, 3 figures, final version to appear in Phys. Rev. Let

Chaos in an Exact Relativistic 3-body Self-Gravitating System

We consider the problem of three body motion for a relativistic one-dimensional self-gravitating system. After describing the canonical decomposition of the action, we find an exact expression for the 3-body Hamiltonian, implicitly determined in terms of the four coordinate and momentum degrees of freedom in the system. Non-relativistically these degrees of freedom can be rewritten in terms of a single particle moving in a two-dimensional hexagonal well. We find the exact relativistic generalization of this potential, along with its post-Newtonian approximation. We then specialize to the equal mass case and numerically solve the equations of motion that follow from the Hamiltonian. Working in hexagonal-well coordinates, we obtaining orbits in both the hexagonal and 3-body representations of the system, and plot the Poincare sections as a function of the relativistic energy parameter $\eta$. We find two broad categories of periodic and quasi-periodic motions that we refer to as the annulus and pretzel patterns, as well as a set of chaotic motions that appear in the region of phase-space between these two types. Despite the high degree of non-linearity in the relativistic system, we find that the the global structure of its phase space remains qualitatively the same as its non-relativisitic counterpart for all values of $\eta$ that we could study. However the relativistic system has a weaker symmetry and so its Poincare section develops an asymmetric distortion that increases with increasing $\eta$. For the post-Newtonian system we find that it experiences a KAM breakdown for $\eta \simeq 0.26$: above which the near integrable regions degenerate into chaos.Comment: latex, 65 pages, 36 figures, high-resolution figures available upon reques

Initial Approach Toward Self-configuration and Self-optimization in IP Networks

The growing heterogeneity and scalability of Internet services has complicated, beyond human capabilities, the management of network devices. Therefore, a new paradigm called autonomic networking is being introduced to control, in an efficient and automatic manner, this complex environment. This approach aims to enhance network elements with capabilities that allow them to choose their own behavior for achieving high-level directives. This so called autonomic network element should be able to optimize its configuration, ensure its protection, detect/repair unpredicted conflicts between services requirements and coordinate its behavior with other network elements. In this paper, we present a research activity that investigates this new concept, and applies it to facilitate the configuration and the optimization of a multi-services IP network. This approach is a first step toward building a self-configured and self-optimized IP network that automatically supports the QoS requirements of heterogeneous applications without any external intervention. Different paradigms have been explored in order to model this behavior and to render network equipment autonomic. A laboratory prototype has been developed to highlight the autonomic behavior of the network to achieve heterogeneous QoS requirements of multimedia and data applications

Hypovitaminosis D and Its Associated Factors in North Algerian Postmenopausal Women: Results of a Cross-Sectional Study

Purpose. As the vitamin D status of Algerian postmenopausal women was poorly described, this cross-sectional study investigated the prevalence of low vitamin D status in a sample population. Secondarily, predictive factors of this hypovitaminosis D were explored. Methods. All the 336 selected women ≥ 45 years from Douera were interviewed to get anthropometric and lifestyle data, reproductive and medical history, medications, and calcium/vitamin D intakes. A blood sample was collected to measure 25-hydroxyvitamin D (25(OH)D) concentrations. Results. Approximately 86% of subjects had low vitamin D status (<20 ng/mL). Mean 25(OH)D level was 14.4 ± 5.3 ng/mL with a clear seasonal dynamic and a significant negative correlation with PTH levels (r  = −0.15, p=0.006). A multiple regression analysis using the 25(OH)D cutoff value of 17 ng/mL instead of the generally admitted level of 20 ng/mL was performed to increase statistical power. Other seasons than summer (OR 4.159 and 95% CI 2.456–7.043), obesity (≥30 kg/m2, OR 1.826, 95% CI 1.081–3.083), and veiling (OR 3.526, 95% CI 1.090–11.400) were significantly associated with 25(OH)D concentrations <17 ng/mL. Conclusions. In North Algeria, the abundant sunlight appears insufficient to fully offset hypovitaminosis D risk factors in postmenopausal women, especially obesity and veiling. It suggests the major need to increase vitamin D supplementation in this subpopulation