Izvestiya of Saratov University. Physics

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Background and Objectives: One of the most intriguing collective phenomena, which arise in systems of coupled oscillators of different nature, are chimera states. They are characterized by the emergence of coordinated spatial synchronization and desynchronization, in an initially homogeneous system. Materials and Methods: This paper discusses the results of studies of one-dimensional and two-dimensional systems of interacting neurons organized on the basis of the fractional Laplace operator and the superdiffusion kinetic mechanism. Their use significantly extends the possibilities of describing chimera-like phenomena from the position of the classical reaction-diffusion approach. Due to mathematical brevity and its ability to reproduce almost all known scenarios of point neural activity, Hindmarsh–Rose model functions were used as a nonlinear part. Results: The studies under discussion demonstrate that one-dimensional and two-dimensional systems, two and three-component reaction-superdiffusion equations organized on the basis the fractional Laplace operator are able to reproduce chimera states. Dynamic regimes in the parameter space of the fractional Laplace operator exponents associated with the shape-forming features of networks of interacting neurons have been analyzed. Parameter regions of synchronization modes, modes of incoherent behavior, and chimera states are discussed. Conclusion: The results of the presented studies can be used in computational neuroscience tasks and various interdisciplinary studies as an alternative to existing network models.

Background and Objectives: Changes in the secondary and tertiary structures of protein molecules during thermal denaturation lead to changes in their vibrational spectra. Vibrations corresponding to elements of the primary and secondary structure of the protein are manifested in the fingerprint range, while vibrational modes of large fragments corresponding to higher levels of the protein structural hierarchy can be observed in the low-frequency (40–500 cm−1) spectral range. The purpose of this work is to reveal changes in the vibrational spectra of proteins resulting from denaturation that can be used to characterize changes in the protein structure. Materials and Methods: Two proteins (collagen and chymotrypsin) having different secondary and tertiary structures are studied using Raman spectroscopy. The experimental data are analyzed using bandpass filtering of the Fourier transforms of the spectral curves. Results: Vibrational spectra of two proteins (collagen and chymotrypsin) having different secondary and tertiary structures, as well as the spectra of thermally denatured samples of these proteins have been measured in the fingerprint and low-frequency ranges. Several low-frequency spectral features that can be used to characterize structural changes of protein molecules have been considered. A few bands may correspond to vibrations of tertiary structure elements (both in the low-frequency range and in the “fingerprint” range). Conclusion: A comparison of the vibrational spectra of native and denatured (superhelical) collagen, as well as native and denatured (globular) chymotrypsin shows that changes in the amide I and amide III bands sensitive to the secondary structure are supplemented with spectral changes in bands that are not assigned to elements of the secondary structure and can be related to changes at higher levels of structural hierarchy. Comparison of the low-frequency vibrational spectra indicates a lower sensitivity of presumably tertiary structure of the globular protein to denaturation.

Background and Objectives: The high prevalence of varicose veins of the lower limbs(VVLL) emphasizes the importance of accurate and timely diagnosis of this pathology. Methods for diagnosing VVLL include, among others, infrared thermography (IRT), which is the safest method. It allows surface temperature mapping with a high spatial resolution. The purpose of this work is to mathematically model the distribution of heat along the back surface of the human shin in the presence of VVLL, compare the obtained distribution with the results of IRT, as well as study the effect of model parameters on the simulation results and assess the possibility of detecting varicose veins using IRT. Methods: А differential equation of thermal conductivity was used to simulate heat transfer processes taking into account blood flow in biological tissues. Biological tissues were defined in layers, the boundaries of which were determined based on the results of X-ray computed tomography. Inclusions reflecting the anatomical structure of the superficial and main veins, which are located directly in the main tissue layers, are considered as venous vessels. Numerical modeling of the process of heat propagation in the shin was carried out in order to investigate the dependence of the temperature change caused by VVLL on the posterior surface of the shin on the maximum depth of varicose veins, their diameters, their surface temperature, perfusion rate, and ambient temperature. The analysis of the possibility of recording such temperature changes with a modern IR thermograph is made. Results: Computational experiments to assess the influence of model parameters on the thermal picture of the surface of the back of the shin have shown that the created mathematical model provides sufficient agreement with the results of real thermographic studies. Most of the temperature dependences obtained in the calculations are consistent or do not contradict real studies. Conclusion: A comparison with experimental results available in the literature has shown that the performed mathematical modeling simulates the initial stages of VVLL.

Background and Objectives: One of the new and effective methods for treating skin cancer and other proliferative diseases, such as psoriasis, is phototherapy, but there is a problem of limiting the penetration of radiation into the depths of the tissue caused by the multiple scattering of the light waves. This problem can be solved by introducing optical clearing agents, many of which are hyperosmotic. In turn, the action of hyperosmotic agents can cause side effects that are induced by the appearance of additional external pressure, which can both increase and decrease the proliferation rate of cancer cells. Materials and Methods: In this work, numerical simulations of a two-dimensional model of an epidermal cell layer on a basal membrane under conditions of additional external pressure are performed. The paper studies the influence of the size of the area of localization of additional pressure, its magnitude and duration of exposure on the proliferation of cancer cells in the area of a binary surface consisting of healthy and cancer cells. Results: Studies were carried out at twofold and fivefold increase of pressure in the selected area (2 kPa and 5 kPa). The influence of the moment of introduction of additional pressure and its duration is also considered in this work. We have determined the parameters at which the rate of cancer cell proliferation slows down. It has been shown that the most pronounced inhibition occurs when applying an additional pressure of 2 kPa in the 1×1 mm region (the size of the entire system is 2×2 mm). The studies were carried out at a twofold and fivefold increase in pressure in the selected area (2 kPa and 5 kPa). Here we have also studied the effect of the duration of exposure if its introduction began at different moments t₀ of Phase 1. It has been shown that for t₀ = 240 the dependence of area covered by cancer cells Φ on the duration of short-term pressure is nonlinear, and for t₀ = 400 this dependence is linear, and the longer impact causes the slowdown of Φ growth.

The article is a recollection of Yuri Mikhailovich Romanovsky, a world-famous biophysicist, Honorary Professor of Lomonosov Moscow State Uаniversity, the stages of his life, scientific and personal destiny, of his sons – Mikhail and Alexander. The development of Yu. M. Romanovsky as a scientist and personality, the influence on him of his family, classmates, senior associates and friends, who represented the best people of Soviet and Russian science over the past 60 years, are described, as well as his personal contribution to world science – especially to mathematical biophysics. Much attention is paid to his scientific and social activities – from the chairman of the housing cooperative of scientists and teachers of Lomonosov Moscow State University to the collector of biographies of graduates of the Physics Department of Lomonosov Moscow State University, who made a huge contribution to the development of the scientific and industrial potential of our country. His enormous role in the development of cooperation between Lomonosov Moscow State University and Saratov State University in the field of biophysics and nonlinear dynamics is also presented.

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Background and Objectives: The methods to control the characteristics of microwave devices on photonic crystals are based on the high sensitivity of resonance states in the forbidden band to the creation of volume defect in the periodic structure and the features of its interface. The appearance of surface photonic Tamm states in microwave photonic crystals adjacent to the electromagnetic radiation absorber layer can be considered as interface states. Currently, there is an increasing interest in the possibility of using structures containing polar liquids, such as water, both in the form of continuous layers and in the form of individual periodically located drops as an absorber of electromagnetic energy in microwave technology, since water in the microwave range is characterized by both a significant value of the real part of the complex permittivity and an imaginary part of the complex permittivity. At the same time, microwave absorbers based on water-containing structures, compared to more traditional materials based on layers with high electrical conductivity, have a number of advantages, such as biocompatibility, availability, ease of adjustment, optical transparency. The appearance of analogs of photonic Tamm states is also possible in the presence of an interface in the form of a polar liquid layer characterized by a positive value of the real part of the complex permittivity and a significant value of the imaginary part of the complex permittivity. When choosing a polar liquid as an absorber, it is necessary to take into account that both the real and imaginary parts of the permittivity significantly depend on the frequency of the probing microwave signal. For the appearance of photonic Tamm states in a photonic crystal with an interface in the form of a polar liquid layer, the imaginary part of the complex permittivity of which is several orders of magnitude smaller than this value for metal nanolayers, the thickness of the liquid layer should be of the same order of the wavelength of electromagnetic radiation, unlike conducting nanolayers. In this case, the electric field of the electromagnetic wave turns out to be partially localized in the liquid layer. In this regard, it is of interest to carry out theoretical and experimental research of the resonance characteristics of microwave photonic crystals associated with the effect of the appearance of photonic Tamm states in the forbidden band, depending on the parameters of the interface based on a structure containing water in the form of a continuous layer. Materials and Methods: To carry out the research of Tamm states, a photonic crystal consisting of alternating layers of two types of dielectrics was created. Its last layer was separated from the distilled water layer by a thin dielectric film. The distance between the film and the last layer of the photonic crystal could be adjusted. A vector network analyzer was used to measure frequency characteristics in the frequency range of 7–13 GHz. Results: It has been established that with an increase of thickness of the distilled water layer, oscillations of the frequency and amplitude of the Tamm resonance are observed both in the first and in the second forbidden bands of the one-dimensional microwave Bragg structure, damping at a large thickness of the water layer. In this case, the greatest amplitude of the Tamm resonance is achieved for each thickness of the water layer at a certain value of the air gap. Conclusion: Based on the results of computer modeling using the transfer matrix method and experiment, the possibility to control photonic Tamm resonances by changing both the thickness of the distilled water layer and the size of the air gap between the photonic crystal and the water layer has been established.

Background and Objectives: It is already obvious today that the performance of modern microprocessors is approaching its limit. Increasing the clock frequency and increasing the performance of the transistors included in them by reducing their size is becoming increasingly difficult due to fundamental physical limitations. Possible ways to increase the performance of microprocessors can be found through the introduction of fundamentally new materials and technologies, which is associated with the need for partial or complete abandonment of modern technology for the production of electronic components. However, there is also a development option that makes it possible to increase the performance of microelectronic devices without abandoning familiar and established technologies, both in the field of creating integrated circuits and microarchitecture. The transition of digital technology from a binary base to a ternary number system, that is, the use of three possible states within one digit – false/uncertain/true – allows one to obtain a number of advantages and, in general, provides a real opportunity to increase the performance of microprocessor technology, all other things being equal. In this regard, the goal of the work is to develop analog models of ternary logic elements that are compatible in characteristics with modern series of binary CMOS logic elements that can allow one to correctly simulate complex digital circuitry devices containing such elements. Materials and Methods: A software package for analysis and automatic design of electronic circuits was used to develop analog models of ternary logic elements. This program made it possible to analyze transient processes, parameters and interaction features of the developed logical elements. Results: A working prototype of a ternary logic element has been completed using standard discrete electronic components, which confirms the correctness and efficiency of the developed models of ternary logic elements. Conclusion: The proposed analog models of ternary logic elements allow one to correctly simulate complex digital circuitry devices containing such elements. Based on the proposed models, the main units of the ternary processor have been subsequently designed.

Background and Objectives: Since the neural networks of the brain have a multilayer structure, multilayer networks of interconnected model neurons are used to simulate and study their complex dynamics. A central role in establishing and maintaining effective communication between brain regions is played by so-called hubs, which are network nodes connected to many other network nodes. The object of study in this work is a network of model neurons coupled via a hub. We used FitzHugh–Nagumo neurooscillators as node elements of the network. Materials and Methods: The spiking activity of a network consisting of interconnected excitable FitzHugh–Nagumo analog generators was experimentally studied. The collective behavior of elements is considered first in a ring of FitzHugh–Nagumo generators connected by repulsive diffusive couplings, and then in a three-layer network consisting of two such rings connected via a common hub, which is also a FitzHugh–Nagumo generator. Since in a real experimental setup it is impossible to achieve complete identity of analog electronic generators, we numerically studied the effect of weak non-identity of FitzHugh–Nagumo oscillators ontheir collective dynamics and compared the results obtained with experimental ones. The synchronization of analog generators in a three-layer network was studied when the coupling coefficient between the generators of one of the rings and the coupling coefficient between the hub and generators in both rings were varied. Results: Diagrams of the average frequency of spiking activity of generators in each layer of the network have been constructed when the coupling coefficients between the generators of the second ring and between the hub and generators in both rings are varied. It has been shown that in a ring of FitzHugh–Nagumo generators in a radio physical experiment, various oscillatory regimes are observed at fixed values of the parameters of the excitable generators. These regimes differ in the frequency of spikes and the phase shift between the oscillations of various generators in the ring. The existence of switchings between these oscillatory regimes has been revealed. It has been shown that with repulsive couplings of FitzHugh–Nagumo generators inside the rings and repulsive interlayer couplings (connections with the hub), frequency synchronization of all network generators occurs. Conclusion: The obtained results can be used when solving problems of synchronization control in spiking neural networks.

Background and Objectives: According to the quantum theory, a change in the states of a quantum system occurs either by continuous deterministic evolution or by almost instantaneous probabilistic projection into its own stationary states as a result of interaction with a classical measuring device. In the theory of quantum measurement, such projection can be carried out both at the beginning and at the end of the measuring chain. In the latter case, а paradoxical theoretical conclusion may arise that selection of the state to which reduction leads can only occur in the mind of the observer. This article proposes a model of measurements in which selection occurs dynamically in the quantum system itself being measured. Methods: A dynamic model of wave function reduction under quantum measurement is proposed. The reduction to a stationary state as a gate process was simulated, including evolution according to the Schrodinger equation and periodic zeroing of the imaginary part of the wave function. Conclusion: Modeling of dynamic reduction to various stationary states of a particle in a potential box and an oscillator has shown that the reduction occurs on a time scale of the order of several tens of the periods of oscillation of the ground state. Moreover, within the framework of this measurement model, the Zeno effect of freezing а resonant quantum transition has been confirmed. If a state decays, measurement cannot prevent decay, but it can slow it down. It is important that during dynamic measurement, the selection of the measured state is present in the measurement itself and leads to a result recorded by the device before the observer. We can also say that the Schrodinger equation is compatible with procedures for reduction of quantum states.