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Nonlinear Phenomena in Complex Systems, 1999, Vol.2, No.4

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Nonlinear Phenomena in Complex Systems, 1999, Vol.2, No.4

An Interdisciplinary Journal

Published by The "Education and Upbringing" Publishing Company, Minsk, Republic of Belarus

Volume 2, Number 4, 1999

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Yu.L . Klimontovich
Entropy, Information, and Criteria of Order in Open Systems. pp. 1--25

Summary: Entropy, information and relative criteria of order for states of open systems are considered. In the theory of communication two definitions of concept "information" are known. One of them coincides in form with the Boltzmann entropy. The second definition of information is defined as the difference between unconditional and conditional entropies. In the present work the latter is used for the definition of information about states of open systems with various meanings of controlling (governing) parameter. Two kinds of open systems are considered. Those systems belong to the first kind that with zero value of controling parameter are in the equilibrium state. The information about the equilibrium state is equal to zero. During self-organization in the process of removal from the equilibrium state the information is increased. For open systems of this class the conservation law for the sum of information and entropy with all values of controlling parameter is proved. In open systems of the second class the equilibrium is impossible. For them the concept ''norm of chaoticity '' is introduced. It allows to consider two kinds of self-organization processes and to give the corresponding definitions of information. The treatment is carried out on a number (classical and quantum) of examples of physical systems. The example of a medico-biological system is also considered.

P.C. Hendry, P.V.E. McClintock
Cosmological experiments in liquid helium. pp. 26--35

Summary: Fast passage through a continuous phase transition is expected to result in the creation of topical defects via the Kibble mechanism. Recent experiments involving the expansion of a small volume of liquid 4He through the lambda (superfluid) transition, as a model of the GUT (grand unified theory) symmetry-breaking transition of the early universe, are discussed and set in context. Copious creation of quantized vortices, analogous to cosmic strings, is expected but not observed. The possibility of developing a more sensitive version of the experiment is considered.

A. Cenys, A.Tamasevicius, G. Mykolaitis, A. Namajunas
Hyperchaos with High Metric Entropy. pp. 36--40

Summary: A new design of the hyperchaotic systems with arbitrarily highnumber of positive Lyapunov exponents is suggested. It exploits asa linear subsystem chain of harmonic oscillators corresponding tohigh-pass filter. In the new design characteristic frequency ofthe system is increasing proportionally to the number of identicallinear elements. As a result both number of the positive Lyapunov exponents and metric entropy increase when identical linearelements are added to the system.

K. G. Kyritsi, L. Gallos, A. N. Anagnostopoulos, A. Cenys, G. L. Bleris
Chaotic Photoconductivity. pp. 41--47

Summary: In modern optoelectronics, light sensors are playing a main role. The present work examines the conditions of their performance, concerning photoconductivity. The model of a n-type photosensitive semiconductor containing two localized levels in its energy gap is considered. The semiconductor is illuminated homogeneously with bandgap-light and a constant electric field is applied. Electrons are excited by the illumination from the valence- to the conduction-band and by the electric field from the localized levels to the conduction-band. Electrons are also recombining from the conduction- to the valence-band and from the conduction-band to the localized levels. Depending on the parameters of the system (i.e. generation- and recombination rates, electric field strength, capture- and reemission-coefficients of the levels, ambient temperature, etc) the semiconductor is exhibiting periodic or chaotic conductivity. Different routes to chaos were observed in this system, like period doubling, intermittency and crisis induced intermittency.

Yu. Andreyev, A. Dmitriev, A. Ovsyannikov
Chaotic processors and content-based search of information in unstructured data bases. pp. 48--53

Summary: In this report, we discuss an approach to construction of information searching systems based on dynamic chaos and intended to operate in computer networks, local area or Internet. Also we discuss an application of this technology to the problems of searching for information in unstructured text databases with natural-language requests.

T.A. King, W. Hogervorst, N.S. Kazak, V.A. Tugbaev, V.N.Belyi, N.A.Khilo, A.A.Ryzhevich
Investigation of properties of nonlinear optical frequency-conversion and parametric interactions using Bessel nondiffracting light beams. pp. 54--60

Summary: The fundamental possibility of the formation of higher-order Bessel light beams is confirmed. The transformation of beam order is observed when propagating circularly polarized light along the optical axis of biaxial crystal under conditions of internal conical refraction. Theoretical and experimental investigations were made of the characteristic features of frequency doubling of Bessel light beams by the oe-e interaction in a KTP crystal. All possible vector and scalar interactions of plane-wave components of Bessel beams were observed experimentally. Parametric generation of light by pumping with Bessel light beams is considered. A theory of azimuth-matched nonlinear interaction of Bessel light beams is developed.

A. Antonevich
The Schroedinger operator with d-potential: Finite-dimensional perturbations approach. pp. 61--71

Summary: The lecture presents the results on approximations of the Schroedinger operator with d-potential by means of approximations of the operator of multiplication by a d - function by families of finite range operators. The resolvents behaviour is investigated and the resonance cases when the limit operator does not coincide with the Laplace operator are singled out.

S. Ya. Kilin, D. B. Horoshko
Quantum theory of photodetection in the presence of feedback. pp. 72--77

Summary: We develop a theory of photodetection in the presence of feedback valid for arbitrary time delay in the feedback loop and any degree of field fluctuation. As a result we obtain an expression for the in-loop photocurrent autocorrelation function which differs from the traditional one by replacing the delta-function by the Green function of the feedback loop. We discuss two main consequences of the new formula: frequency-dependent standard quantum limit in the presence of feedback, and the violation of statistical equivalence between the photon flux and the photocurrent in the feedback loop.

A. Ruffing, D. Heim, C. Dingwall, U. Pforzheimer, B. Lampe
Revising moment problems of polarized densities in quantum chromodynamics. pp. 78--88

Summary: The sensititivity of various future polarization experiments to the first moment ?g of the polarized gluon density is elucidated in detail. It is shown to what extent the first moment can be extracted from the future data as compared to the higher moments. We concentrate on two processes which in the near future will become an important source of information on the polarized gluon density, namely the photoproduction of open charm to be studied at CERN (COMPASS) and SLAC and the production of direct photons at RHIC.

Mathematical modelling of intracellular calcium signal transduction. pp. 89--92

Summary: Two problems concerning intracellular regulating processes are considered. 1. Calcium wave propagation taking into account cooperative action of two distinct classes of calcium channels. Such a system appear to exibit a wide variety of spatial-temporal patterns including calcium oscillations with different periods coexhisting in different space regions. 2. The system of reactions is proposed possessing the resonans property with respect to alternating modulation by externel factor. Such a processes may serve as a mechanism of frequensy-selective cellular response.

A. D. Linkevich
Representation of information in dynamical systems: measures, entropy and fractals. pp. 93--104

Summary: An approach is suggested in which information encoding and information processing are implemented through Borel measures supported on spaces associated with neural networks. To develop tools to read out pieces of information stored in the system, the functional integration method is exploited. A special emphasis is put on fractal sets and fractal measures.

I.V. Babushkin, Yu.A. Logvin, and N.A. Loiko
Stationary and nonstationary symmetry-breaking optical patterns in a resonant bilayer. pp. 105--110

Summary: Optical pattern formation is studied in a system consisting of two identical thin layers of resonance medium illuminated by light fields of equal intensity from both sides. It is shown that transverse optical patterns emerged in the system may be either symmetrical (identical for both layers) or symmetry-breaking. The influence of the inter-layer mistuning (distance between the layers) on the type of instability is elucidated. When delay effects are taken into account, a relationship between the symmetry-breaking, bistability and the Hopf--Ikeda transverse instabilities is revealed.

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