Vol 23, No 1 (2023)

Background and Objectives: The Josephson effect is widely used for both generating and receiving very high frequency signals. The approaches and methods of nonlinear dynamics are commonly used: construction of phase portraits, bifurcation analysis, Kuramoto model approach, etc. Usually large arrays of identical junctions are considered. However, the non-identity of junctions leads to new and interesting effects. A very popular model is a chain of junctions connected via an RLC circuit. In this case, two types of non-identity are possible – in terms of critical currents IN through the junctions and in terms of the value rN of junction resistances. An increase in the number of junctions from two to three leads to the possibility of quasiperiodic dynamics with invariant tori of dimensions both two and three and to a complex structure of the parameter space. Materials and Methods: In this paper, we will mainly consider three junctions that are not identical in terms of resistance. As the main research tool, we will use the method of construction of Lyapunov exponent charts. Within the framework of this method, the type of dynamics of the system is determined by the signature of the spectrum of Lyapunov exponents. The parameter plane is scanned and the types of modes are identified at each point. The method is effective in that it allows one to study all types of possible regimes and fine details of the parameter space arrangement. Results: For the analysis of the dynamics of non-identical Josephson junctions, the method of Lyapunov exponent charts is effective. With its help, the regions of periodic regimes, regimes of two-frequency and three-frequency quasiperiodicity, chaos have been revealed. As a rule, the regions of two-frequency quasiperiodicity have the form of bands of different widths immersed in the region of three-frequency quasiperiodicity, which form the structure of the Arnold’s resonant web. Conclusion: The boundaries of the regions of two-frequency quasiperiodicity are the lines of saddle-node bifurcations of invariant tori. As the area of chaos increases, the Arnold’s resonant web can collapse. Changing the type of external circuit coupling the junctions does not fundamentally affect the dynamics of the system. 

Background and Objectives: Impedance plethysmography and Doppler ultrasound, in most cases, are considered as independent methods for analyzing hemodynamics. This work shows the presence of similarities in the shape of pulse waves recorded by the two indicated methods at rest and during exercise tests. The dynamics of the volume and velocity of blood flow in the radial artery was studied at rest, during an occlusive test and a test with a deep breath. Materials and Methods: The method of impedance rheography was used to determine the dynamics of the blood volume in the artery, and the method of ultrasound dopplerography was used to determine the linear velocity of arterial blood flow. The equation that considers the irregular distribution of erythrocytes velocity in the cross-section of a blood vessel has been obtained for a correct quantitative description of the dynamics of the volumetric blood flow velocity. Results: It has been determined that both the deep breath test and the occlusive test lead to vasodilation of the radial artery. In this case, the test with deep breath causes the appearance of an additional peak in the diastole which agrees in time with the negative (retrograde) diastolic peak of the blood flow velocity. Comparative analysis of the integrated velocity and volume waves demonstrates phase matching and a linear dependence of the shape of these waves at rest which are disrupted during the deep breath test. Conclusions: The proposed equation for calculating volumetric blood flow enables one to study the processes of autoregulation of blood flow in vessels by controlling the balance of changes in blood volume and velocity by the methods of impedance rheography and ultrasound dopplerography and can potentially form the basis for the development of appropriate methods of functional diagnostics.

Background and Objectives: The method of identification of symbolic sequences associated with the genetic structure of biological objects using the principles of small-angle polarimetry is considered. This method of analyzing and visualizing symbolic sequences obtained by sequencing DNA fragments can be defined as small-angle polarimetry of phase-modulating structures associated with genetic information. Materials and Methods: The analyzed symbolic sequence is represented by a two-dimensional phase-modulating matrix, each element of which corresponds to one of the four basic nucleotides (adenine, cytosine, thymine, guanine), and the depth of modulation of the phase of the reading coherent linearly polarized beam is determined by the content of this nucleotide in the corresponding triplet in the nucleotide sequence. As a result of the diffraction of a reading coherent beam with a polarization plane oriented at an angle of 45° to the sides of the phase-modulating matrix, a spatial distribution of local polarization states of the reading field diffracted on the matrix is formed in the paraxial region of the far diffraction zone. Discrimination of local polarization states in accordance with the proposed algorithm makes it possible to synthesize a binary spatial distribution, which is a unique identifier of the analyzed symbol sequence. Results: Modeling of the processes of phase coding and subsequent analysis of local polarization states in the near-axial region using sequencing results for the strains “Wuhan”, “Delta” and “Omicron” of the SARS-CoV-2 virus has shown a high sensitivity of the method to local changes in the structure of nucleotide sequences. Conclusion: The results of the simulation allow us to conclude that binary distributions of local polarization states of light fields diffracted on DNA-associated phase-modulating structures recorded in the axial region are characterized by high sensitivity to local mutational changes in the structure of nucleotide sequences. The results obtained can be used as a basis for creating effective hybrid methods for analyzing genetic information using the principles of polarization coding and small-angle polarimetry.

Background and Objectives: The purpose of the paper is to reflect on the development of physical and mathematical education in Saratov in 1920–1930 using the biographies of the Gnedenko brothers, Gleb V. Gnedenko (1909–1943) and Boris V. Gnedenko (1912–1995). In April 1925, the Gnedenko family moved to Saratov motivated by the parents’ desire to give their children good education. In 1932, the older brother, Gleb Gnedenko, received a diploma from the Saratov Pedagogical Institute. The younger brother, Boris Gnedenko, entered the Physics and Technology Department of the Pedagogical Faculty of Saratov University in 1927, at the age of 15, and graduated in 1930, well ahead of the schedule. Over the years of learning, the talented Gnedenko brothers stood out for their dedication to knowledge and their desire to help their classmates. Gleb Gnedenko, after completing his postgraduate studies at the K. Liebkhnecht Pedagogical Institute in Moscow and working at the Tyumen Pedagogical Institute, returned to teaching in Saratov, where he had worked at the Saratov Pedagogical Institute and at the German Pedagogical Institute (Engels city). With the beginning of the Great War II, he was enlisted into the Soviet Army and died heroically in October 1943 while crossing the Dnieper River in Ukraine. In Saratov city, his name is listed on the obelisk in memory of the Pedagogical Institute’s lecturers who did not return from the war. Boris V. Gnedenko was an outstanding mathematician who worked in the field of probability theory and its applications. He is known for his achievements in the probability theory and mathematical statistics, the queuing theory, and the reliability theory. He was an expert in history,methodology and philosophy ofmathematics. His book “A Course in Probability Theory” has been a worldwide bestseller for decades. Boris V. Gnedenko stood at the origins of the creation of computer technology in the former Soviet Union. His total number of scientific, methodological, and popular publications is close to 1300. Materials and Methods: The article uses family archives, Boris V. Gnedenko’s memoirs, and his students’ recollections, as well as the archive materials on the history of the Saratov State University. Conclusion: The Gnedenko brothers were people of great spiritual generosity, modesty, and chivalrous quality. They were being easy to communicate with and at the same time firm and principled in defending their views and beliefs. The brothers’ personal life and professional activities reflect very well the character and history of the pedagogical, physical, and mathematical departments at the Saratov University and at the Saratov Pedagogical Institute in the 1920s-1930s.