Hyperbolic Chaos of Turing Patterns

We consider time evolution of Turing patterns in an extended system governed by an equation of the Swift-Hohenberg type, where due to an external periodic parameter modulation long-wave and short-wave patterns with length scales related as 1:3 emerge in succession. We show theoretically and demonstrate numerically that the spatial phases of the patterns, being observed stroboscopically, are governed by an expanding circle map, so that the corresponding chaos of Turing patterns is hyperbolic, associated with a strange attractor of the Smale-Williams solenoid type. This chaos is shown to be robust with respect to variations of parameters and boundary conditions.Comment: 4 pages, 4 figure

Can Any "Invariants" Be Revealed in Quasi-periodic Phenomena Observed From Sco X-1?

Using large number of Rossi X-ray Time Explorer observations of Sco X-1 we present a detailed investigation of the transition layer (TL) and the relativistic precession (RP) models. These models predict the existence of the invariant quantities: an inclination angle delta of the magnetospheric axis with the normal to the disk for the TLM and a neutron star (NS) mass M_{NS} for the RPM. Theoretical predictions of both models are tested and their self-consistency is checked. We establish that: (1) The inferred delta angle is 5.56+/-0.09 degrees. Correlation of the delta-values with the horizontal branch oscillation (HBO) frequency is rather weak. (2) There is a strong correlation between an inferred M_{NS} and the HBO frequency in the RPM frameworks. (3) We infer M_{NS} for different assumptions regarding the relations between the HBO frequency and the nodal frequency. We find that the inferred M_{NS}=2.7+/-0.1 M_sun cannot be consistent with any EOS of NS matter. We conclude that RPM fails to describe the data while TLM seems to be compatible.Comment: Accepted for publication in Astrophysical Journal Letters (2002 June/571 issue), 5 pages, 4 figures, uses emulateapj5.st

Collective Phase Chaos in the Dynamics of Interacting Oscillator Ensembles

We study chaotic behavior of order parameters in two coupled ensembles of self-sustained oscillators. Coupling within each of these ensembles is switched on and off alternately, while the mutual interaction between these two subsystems is arranged through quadratic nonlinear coupling. We show numerically that in the course of alternating Kuramoto transitions to synchrony and back to asynchrony, the exchange of excitations between two subpopulations proceeds in such a way that their collective phases are governed by an expanding circle map similar to the Bernoulli map. We perform the Lyapunov analysis of the dynamics and discuss finite-size effects.Comment: 19 page

Correlations between X-ray Spectral and Timing Characteristics in Cyg X-2

Correlations between the quasi-periodic oscillations (QPOs) and the spectral power-law index have been reported for a number of black hole candidate sources and for four neutron star (NS) sources, 4U 0614+09, 4U 1608-52, 4U 1728-34 and Sco X-1. An examination of QPO frequencies and index relationship in Cyg X-2 is reported herein. The RXTE spectrum of Cyg X-2 can be adequately represented by a simple two-component model of Compton up-scattering with a soft photon electron temperature of about 0.7 keV and an iron K-line. Inferred spectral power-law index shows correlation with the low QPO frequencies. We find that the Thomson optical depth of the Compton cloud (CC) tau, in framework of spherical geometry, is in the range of ~4-6, which is consistent with the neutron star's surface being obscured. The NS high frequency pulsations are presumably suppressed as a result of photon scattering off CC electrons because of such high values of tau. We also point out a number of similarities in terms timing (presence of low and high frequency QPOs) and spectral (high CC optical depth and low CC plasma temperature) appearances between Cyg X-2 and Sco X-1.Comment: 7 pages, 4 figures, accepted for publication in ApJ (October 1, 2007, v667n2 issue

THE CONSTITUTION OF THE RUSSIAN FEDERATION IN THE ASPECT OF REQUIREMENTS FOR RUSSIAN AS A STATE LANGUAGE

On the results of the linguistic analysis of the text of the Constitution of the Russian Federation and the requirements that are imposed by legal discourse to the language of legal documents the authors reveal a set of obligatory characteristics of the language of the legal document, including definiteness, accuracy, clearness, stylistic neutrality, and language correctness. Application of these characteristics to assessing the quality of the text of Russian Constitution lead to finding some contextual gaps which might cause difficulties in understanding of some provisions in the basic law of the country. Violations of the accuracy and clarity of statements include those provisions of the Constitution in which lexical units are implemented in different meanings. In such cases, the distortion of meaning is possible at the stage of understanding (interpretation) of the verbal form. The articles of the Constitution also reveal a violation of clarity, which is accompanied by legal and linguistic uncertainty. The article provides examples of formulations that do not comply with the rules and norms of the use of language means in legal acts, as well as proposed ways to overcome these inconsistencies. It is argued that the development and application of a special linguistic methodology focused on communicative and rhetorical analysis of legally significant texts will allow more effective linguistic interpretation of normative legal acts, including the Constitution of the Russian Federation, as well as ensure uniformity of their application

SYSTEM OF LOAD DISTRIBUTION OF SHIP DIESEL GENERATORS BASED ON NEURAL NETWORKS

The dependence of the specific fuel consumption of the ship diesel-generator set on the generated electric power and the power factor is given. An algorithm for load distribution between parallel marine diesel generator sets is given, taking into account the dependencies of the specific fuel consumption on the generated power and the power factor of each marine diesel generator set. The possibility of using neural networks to solve the problem of minimizing the specific fuel consumption for parallel operation of ship diesel-generator sets in the steady state mode is considered. A neural network model for reducing fuel consumption is proposed by distributing the total electric load of a ship power plant between diesel generators operating in parallel. Such a model, based on the database obtained in the training process, which is implemented by microprocessor controllers with the algorithms of searching for a combination of capacities inherent in them for each of the parallel running generator, at which the minimum flow is reached, independently determines how it is necessary to load the units operating in parallel, to achieve a minimization of fuel consumption; and periodically checks the correspondence between the estimated (calculated) and the actual fuel costs, which ensures the control of the technical condition of the mechanisms