Dynamical Characteristics of Traveling Wave Packets of Total Electron Content Disturbances

Using the COPHASE method and the GPS interferometry method for travelling ionospheric disturbances, we analyze in detail the spatio-temporal properties of travelling wave packets (TWP) of total electron content (TEC) disturbances. The analysis is performed on the example of a clearest TWP manifestation observed in California, USA, in October 18, 2001, using the GLOBDET technique, developed at the Institute of Solar-Terrestrial Physics of the Siberian Branch of RAS for global detection and monitoring of natural and technogenic ionospheric disturbances on the basis of TEC variations retrieved from the global network of GPS receivers. In the time domain, TWPs are quasi-periodic TEC oscillations of duration about 1 h, period of 10–20 min, and amplitude exceeding that of the background TEC fluctuations by at least one order of magnitude. The velocity and direction of TWP motion are similar to those of mid-latitude mesoscale travelling ionospheric disturbances, as obtained earlier from the analysis of phase parameters of HF radio signals and the signals of geostationary satellites and discrete space radio sources.     

Statistical properties of 2-D generalized hyperbolic attractors

Recently Pesin introduced a large class of hyperbolic attractors, and for those attractors he established the Smale spectral decomposition. In this paper our main results are a stretched exponential bound on the decay of correlations and the central limit theorem. Also we will obtain conditions under which two well known attractors-those of Belykh and Lozi-are subject to our main results. (c) 1995 American Institute of Physics.     

Spatial chaotic structure of attractors of reaction-diffusion systems

The dynamics described by a system of reaction-diffusion equations with a nonlinear potential exhibits complicated spatial patterns. These patterns emerge from preservation of homotopy classes of solutions with bounded energies. Chaotically arranged stable patterns exist because of realizability of all elements of a fundamental homotopy group of a fixed degree. This group corresponds to level sets of the potential. The estimates of homotopy complexity of attractors are obtained in terms of geometric characteristics of the potential and other data of the problem.

     

Space-time complexity in Hamiltonian dynamics

New notions of the complexity function C(epsilon;t,s) and entropy function S(epsilon;t,s) are introduced to describe systems with nonzero or zero Lyapunov exponents or systems that exhibit strong intermittent behavior with "flights," trappings, weak mixing, etc. The important part of the new notions is the first appearance of epsilon-separation of initially close trajectories. The complexity function is similar to the propagator p(t(0),x(0);t,x) with a replacement of x by the natural lengths s of trajectories, and its introduction does not assume of the space-time independence in the process of evolution of the system. A special stress is done on the choice of variables and the replacement t-->eta=ln t, s-->xi=ln s makes it possible to consider time-algebraic and space-algebraic complexity and some mixed cases. It is shown that for typical cases the entropy function S(epsilon;xi,eta) possesses invariants (alpha,beta) that describe the fractal dimensions of the space-time structures of trajectories. The invariants (alpha,beta) can be linked to the transport properties of the system, from one side, and to the Riemann invariants for simple waves, from the other side. This analog provides a new meaning for the transport exponent mu that can be considered as the speed of a Riemann wave in the log-phase space of the log-space-time variables. Some other applications of new notions are considered and numerical examples are presented.     

A spectral-polarization method for analyzing the interference pattern of a radio signal

In this paper, we propose a spectral-polarization method for recovering the shape and measuring the displacement velocity of an interference pattern (IP) by analyzing three mutually orthogonal projections of the radio-signal field vector using one receiving antenna. At the first stage of analysis, the complex Doppler spectra of the time variations of these projections are calculated. Then these data are used to determine the spectra of the arrival angles for each component of the spectra. Together with the data on the Doppler shift, this allows us to recover the IP shape and estimate its velocity and displacement direction. Formulas illustrating the proposed method and numerical simulation results demonstrating practical implementation of the idea are given. Institute of Solar and Terrestrial Physics, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 6, pp. 723–734, June, 1998.     

Determining the velocity of the interference pattern by analysis of three mutually orthogonal projections of the radio-signal field vector. part II. Experiment in the HF range

We present the results of experimental verification of the spectral-polarization method which we proposed earlier to measure the interference pattern velocity by analysis of three mutually orthogonal projections of the radio-signal field vector using a single receiving antenna. Measurements were performed for an HF radio path about 100 km in length, with the simultaneous monitoring of the ionospheric situation by an oblique-incidence sounding chirp ionosonde. We used nighttime periods in which we observed a stable one-mode reflected radio signal to eliminate multipath effects in the analysis. The mean values of azimuthal and zenith angles obtained by this method differ by no more than 2°–5° from the calculated values. The mean velocity of traveling ionospheric disturbances (of the order of 50 m/sec) and their propagation directions (north-western, changing to northern in the morning hours) for these periods of time are consistent with the existing data. Institute of Solar-Terrestrial Physics of the Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 1, pp. 60–72, January. 1999.