Entropies in investigation of dynamical systems

Interrelation of various approaches to the definition of the concept of entropy determines its wide using in applications. We consider entropy characteristics used in various research techniques for investigation of complex dynamical systems (including symbolic ones) behaviour. Methods of analysis of dynamical systems phase portraits, which are based on Rényi entropy, fractal and multifractal characteristics, and results of numerical experiments are given

On a method of applied symbolic dynamics for investigation of dynamical systems

We consider a method of applied symbolic dynamics which may be used to obtain wide spectrum of characteristics of complex dynamical systems: approximation of invariant sets, estimation of topological entropy and approximation of invariant measures. The method has received wide acceptance in studying complex dynamical systems. The main idea of the method is to describe the system behaviour approximately by means of an oriented graph (called symbolic image). Such a graph is a representation of symbolic dynamical system which is more appropriately known as topological Markov chain. There exists a correspondence between trajectories of a given system and paths on the graph, which allows us to design algorithms for estimation of topological entropy, approximate invariant measures of a given system by using stationary flows on the graph and calculate corresponding metric entropies. These values characterize complex behaviour of dynamical systems such as the existence of trajectories with large periods and chaotic regimes. The results of experiments are given for systems with chaotic dynamics

On application of dynamical system methods in biomedical engineering

The spectrum of various methods and tools used for solving bioengineering problems is sufficiently wide. Dynamical systems (including the symbolic ones) in many cases become a base for design and implementation of methods of investigation and computer modeling complex processes. Whereas for solving direct problems we have many well-developed methods, results for inverse problems are much more modest. We discuss two methods for such tasks: Takens’ method for reconstruction attractor by a time series, and the based on ideas of symbolic dynamics method for digital image analysis using stationary flow on graph and weighted entropy. The results of numerical experiments are given

Application of fractal analysis methods to images obtained by crystallization modified by an additive

The fractal and multifractal methods are now widely used for analysis and classification of digital images having complex structure. We present the results of the application of such methods to the images of crystallograms obtained by crystallization with additives. This technique was developed for studying images of blood crystals, and now finds increasing use in the analysis of medicines, checking food and soil quality. In this work we study images of crystallograms of various milk dilutions and crystallograms obtained with bean leave extracts. The results show that the proposed mathematical methods seem to be rather perspective both in comparing images of different classes and in obtaining classifying signs

Entropies in investigation of dynamical systems and their application to digital image analysis

We discuss entropy characteristics used in various research techniques for investigation of complex dynamical systems including symbolic ones. The dynamics of a system may be studied by analyzing the phase portrait of a system obtained as a digital image. Symbolic dynamics methods allow combining entropy of a given dynamical system with the entropy characteristics of its phase portrait. We apply methods of image analysis based on symbolic dynamics, Rényi entropy, fractal and multifractal characteristics to analyze high resolution images having a complex structure. We also describe the results of applications of described methods to images of biomedical preparations

Speeding up qubit control with bipolar single-flux-quantum pulse sequences

The development of quantum computers based on superconductors requires the improvement of the qubit state control approach aimed at the increase of the hardware energy efficiency. A promising solution to this problem is the use of superconducting digital circuits operating with single-flux-quantum (SFQ) pulses, moving the qubit control system into the cold chamber. However, the qubit gate time under SFQ control is still longer than under conventional microwave driving. Here we introduce the bipolar SFQ pulse control based on ternary pulse sequences. We also develop a robust optimization algorithm for finding a sequence structure that minimizes the leakage of the transmon qubit state from the computational subspace. We show that the appropriate sequence can be found for arbitrary system parameters from the practical range. The proposed bipolar SFQ control reduces a single qubit gate time by halve compared to nowadays unipolar SFQ technique, while maintaining the gate fidelity over 99.99%.Comment: 14 pages, 4 figure

Reactive co-sputter deposition of nanostructured cermet anodes for solid oxide fuel cells

The impact of a nanostructured NiO/yttria-stabilized zirconia (NiO/YSZ) and NiO/gadolinia-doped ceria (NiO/GDC) anode functional layers on low- and intermediate-temperature solid oxide fuel cell (SOFC) performance is investigated. NiO/YSZ and NiO/GDC thin films were reactively sputter-deposited by pulsed direct current magnetron sputtering from the Ni, Zr–Y, and Ce–Gd targets onto commercial NiO/YSZ substrates. Anode-supported SOFCs based on magnetron sputtered YSZ and GDC electrolytes (~4 µm) with and without the nanostructured anode layers are fabricated. A direct comparison of the YSZ- and GDC-based SOFCs in temperature range of 600–800 and 400–600 °C is made. The performance of cells with the nanostructured anode layers significantly increases as compared to that of the cell without it, especially at lower temperatures. Increase of cells performance was achieved by reduction of the total area-specific resistance by 26–30%

Magnetron sputtered LSC thin films for solid oxide fuel cell application

In this study, La0.6Sr0.4CoO3-d (LSC) thin films were deposited by pulsed DC magnetron sputtering at oblique angle of the LSC target. The effect of post-annealing temperature in the range of 600-1000°C on the film crystalline structure was investigated. The phase composition, crystalline structure and surface morphology of the films were determined using X-ray diffraction, scanning electron microscopy and atomic force microscopy, respectively. Anode-supported solid oxide fuel cells (SOFCs) with bi-layered thin-film yttria-stabilized zirconia (YSZ) / gadolinium-doped ceria (GDC) electrolyte and an LSC thin film interlayer were fabricated. Polarization curves were measured in the temperature range from 700 to 800°C. It was shown that the LSC interlayer improves SOFC power density. Our results demonstrate that magnetron sputtering provides a low-temperature synthesis route for realizing thin LSC films for intermediate-temperature SOFCs