Pub Date : 2023-01-01DOI: 10.18500/0869-6632-003056
Olga Vershinina, Mihail Ivanchenko
The purpose of this study is to investigate collective dynamics of coupled communities that evolve according to the population game «Battle of the Sexes». A separate community includes two interacting populations of players of opposite sex, where each player has one of two possible competing behavior strategies. It is necessary to determine the possibility of mutual synchronization of oscillations in the number of players adhering to a particular strategy, build a synchronization region, and also evaluate the dependence of the properties of oscillations on the coupling strength. Methods. In this paper, we study the system of evolutionary games «Battle of the Sexes» interacting through migration. To simulate the evolutionary game dynamics we make use of the stochastic Moran process, as well as the Monte Carlo method to sample game trajectories. Mutual synchronization is defined by the appropriately generalized criteria of frequency and phase locking. Results. It is shown that the system of coupled evolutionary games «Battle of the Sexes» demonstrates mutual synchronization of oscillations under sufficiently strong coupling. In particular, oscillation frequencies of two communities get adjusted to each other and begin to coincide at some interaction parameter, while the oscillations themselves become almost identical. A similar result was also observed for an ensemble of more than two communities. Conclusion. The dependence of the average frequencies of community oscillations on the coupling strength was determined, the adjustment of oscillations with an increase in the coupling strength was demonstrated, thereby showing the possibility of mutual synchronization in the model of coupled evolutionary games «Battle of the Sexes». The region of frequency synchronization was numerically found.
{"title":"Mutual synchronization of oscillations in a system of coupled evolutionary games","authors":"Olga Vershinina, Mihail Ivanchenko","doi":"10.18500/0869-6632-003056","DOIUrl":"https://doi.org/10.18500/0869-6632-003056","url":null,"abstract":"The purpose of this study is to investigate collective dynamics of coupled communities that evolve according to the population game «Battle of the Sexes». A separate community includes two interacting populations of players of opposite sex, where each player has one of two possible competing behavior strategies. It is necessary to determine the possibility of mutual synchronization of oscillations in the number of players adhering to a particular strategy, build a synchronization region, and also evaluate the dependence of the properties of oscillations on the coupling strength. Methods. In this paper, we study the system of evolutionary games «Battle of the Sexes» interacting through migration. To simulate the evolutionary game dynamics we make use of the stochastic Moran process, as well as the Monte Carlo method to sample game trajectories. Mutual synchronization is defined by the appropriately generalized criteria of frequency and phase locking. Results. It is shown that the system of coupled evolutionary games «Battle of the Sexes» demonstrates mutual synchronization of oscillations under sufficiently strong coupling. In particular, oscillation frequencies of two communities get adjusted to each other and begin to coincide at some interaction parameter, while the oscillations themselves become almost identical. A similar result was also observed for an ensemble of more than two communities. Conclusion. The dependence of the average frequencies of community oscillations on the coupling strength was determined, the adjustment of oscillations with an increase in the coupling strength was demonstrated, thereby showing the possibility of mutual synchronization in the model of coupled evolutionary games «Battle of the Sexes». The region of frequency synchronization was numerically found.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85394789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.18500/0869-6632-003047
G. Vishnyakov, A. Yurin, V. Minaev, Alexander Golopolosov
The purpose of this work is to analyze the effect of the polarimeter signal processing algorithm on the results of measurements of the optical rotation angle of the polarization plane to improve the accuracy of measurements in differential polarimetry. Methods. The paper considers the methods of polarimetry used for the analysis of optically active substances, based on the methods of phase measurements used to calculate the optical rotation angle. The expediency of using the Fourier transform to calculate the phase difference of differential polarimeter signals is noted. To analyze the error of the algorithm, mathematical modeling of the measurement information processing for various signal parameters is applied. Results. The results of the study of the effect of the bit depth of the analog-to-digital converter, the number of samples over the period of the signal and the accumulation time on the accuracy of restoring the phase difference are presented. The influence of the ratio of signal amplitudes and the level of amplitude and phase noise caused by the imperfection of the measuring system has also been investigated. Conclusion. The obtained results make it possible to optimize the operating mode and improve the accuracy of the optical rotation angle measurements using a differential phase polarimeter based on the Fourier transform.
{"title":"Analysis of the accuracy of the signal processing algorithm of the differential phase polarimeter","authors":"G. Vishnyakov, A. Yurin, V. Minaev, Alexander Golopolosov","doi":"10.18500/0869-6632-003047","DOIUrl":"https://doi.org/10.18500/0869-6632-003047","url":null,"abstract":"The purpose of this work is to analyze the effect of the polarimeter signal processing algorithm on the results of measurements of the optical rotation angle of the polarization plane to improve the accuracy of measurements in differential polarimetry. Methods. The paper considers the methods of polarimetry used for the analysis of optically active substances, based on the methods of phase measurements used to calculate the optical rotation angle. The expediency of using the Fourier transform to calculate the phase difference of differential polarimeter signals is noted. To analyze the error of the algorithm, mathematical modeling of the measurement information processing for various signal parameters is applied. Results. The results of the study of the effect of the bit depth of the analog-to-digital converter, the number of samples over the period of the signal and the accumulation time on the accuracy of restoring the phase difference are presented. The influence of the ratio of signal amplitudes and the level of amplitude and phase noise caused by the imperfection of the measuring system has also been investigated. Conclusion. The obtained results make it possible to optimize the operating mode and improve the accuracy of the optical rotation angle measurements using a differential phase polarimeter based on the Fourier transform.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88057338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.18500/0869-6632-003039
V. Govorukhin
Purpose of this article is to study the transport of passive particles in the velocity field of a vortex tripole with a change in the parameter that determines the speed of the configuration movement. A structure consisting of a central vortex and satellite vortices rotating around it with the opposite vorticity is understood as a tripole. We employ a system of three point vortices, the most simple mathematical representation of a vortex tripole, which may be expressed as a system of nonlinear ordinary differential equations with a parameter. Consideration is limited to a particular case of a tripole with zero total vorticity. The influence of the speed values of vortex configuration movement on the processes of passive particle transport has been studied. Methods. The study was carried out numerically using algorithms based on the dynamical systems approaches including the construction of the Poincare map and the analysis of the dynamics of marker particles. Were carried out long ´ times calculations, corresponding to hundreds and thousands of turns around the tripole center. Integrators of high orders of accuracy were used to solve the Cauchy problems, which made it possible to adequacy of the calculation result control. Results. We found that transferring passive particles is fundamentally different depending on the speed of the tripole. A vast zone of chaotic dynamics forms in the neighborhood of the vortices when the velocity is low. This zone slowly shifts along with the tripole. There are subregions of active and slow mixing inside the chaos region. The possible stages of particle dynamics are: transfer from the region to the right of the tripole to the area to the left, vigorous mixing near the vortices, and slowly drifting to the region to the left of the tripole. At a high speed of vortex configuration in the entire chaotic region, the particles are strongly mixed. The vortex tripole removes particles from the vicinity of its initial position over long distances and practically does not capture new particles along its path. In intermediate situations, both processes can be realized at varying degrees. Conclusion. Non-trivial scenarios for the transport of passive particles by a vortex tripole, which can also occur in real vortex configurations of fluids, have been discovered and described.
{"title":"Transfer of passive particles in the velocity field of vortex tripole moving on a plane","authors":"V. Govorukhin","doi":"10.18500/0869-6632-003039","DOIUrl":"https://doi.org/10.18500/0869-6632-003039","url":null,"abstract":"Purpose of this article is to study the transport of passive particles in the velocity field of a vortex tripole with a change in the parameter that determines the speed of the configuration movement. A structure consisting of a central vortex and satellite vortices rotating around it with the opposite vorticity is understood as a tripole. We employ a system of three point vortices, the most simple mathematical representation of a vortex tripole, which may be expressed as a system of nonlinear ordinary differential equations with a parameter. Consideration is limited to a particular case of a tripole with zero total vorticity. The influence of the speed values of vortex configuration movement on the processes of passive particle transport has been studied. Methods. The study was carried out numerically using algorithms based on the dynamical systems approaches including the construction of the Poincare map and the analysis of the dynamics of marker particles. Were carried out long ´ times calculations, corresponding to hundreds and thousands of turns around the tripole center. Integrators of high orders of accuracy were used to solve the Cauchy problems, which made it possible to adequacy of the calculation result control. Results. We found that transferring passive particles is fundamentally different depending on the speed of the tripole. A vast zone of chaotic dynamics forms in the neighborhood of the vortices when the velocity is low. This zone slowly shifts along with the tripole. There are subregions of active and slow mixing inside the chaos region. The possible stages of particle dynamics are: transfer from the region to the right of the tripole to the area to the left, vigorous mixing near the vortices, and slowly drifting to the region to the left of the tripole. At a high speed of vortex configuration in the entire chaotic region, the particles are strongly mixed. The vortex tripole removes particles from the vicinity of its initial position over long distances and practically does not capture new particles along its path. In intermediate situations, both processes can be realized at varying degrees. Conclusion. Non-trivial scenarios for the transport of passive particles by a vortex tripole, which can also occur in real vortex configurations of fluids, have been discovered and described.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89418986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-29DOI: 10.18500/0869-6632-003027
A. Koronovskii, M. Kurovskaya, O. Moskalenko
Purpose of this study is to investigate the problem of how typical (or, conversely, unique) is the phenomenon of explosive synchronization in networks of nonlinear oscillators with topologies of links such as “ring” and “small world”, and, in turn, how the partial frequencies of the interacting oscillators must correlate with each other for the phenomenon of explosive synchronization in these networks can be possible. Methods. In this paper, we use an analytical description of the synchronous behavior of networks of nonlinear elements with “ring” and “small world” link topologies. To confirm the obtained results the numerical simulation is used. Results. It is shown that in networks of nonlinear oscillators with topologies of links such as “ring” and “small world”, the phenomenon of explosive synchronization can be observed for the different distributions of partial frequencies of network oscillators. Conclusion. The paper considers an analytical description of the behavior of network oscillators with “ring” and “small world” topologies of links and shows that the phenomenon of explosive synchronization in such networks is atypical, but not unique.
{"title":"On the typicity of the explosive synchronization phenomenon in oscillator networks with the link topology of the “ring” and “small world” types","authors":"A. Koronovskii, M. Kurovskaya, O. Moskalenko","doi":"10.18500/0869-6632-003027","DOIUrl":"https://doi.org/10.18500/0869-6632-003027","url":null,"abstract":"Purpose of this study is to investigate the problem of how typical (or, conversely, unique) is the phenomenon of explosive synchronization in networks of nonlinear oscillators with topologies of links such as “ring” and “small world”, and, in turn, how the partial frequencies of the interacting oscillators must correlate with each other for the phenomenon of explosive synchronization in these networks can be possible. Methods. In this paper, we use an analytical description of the synchronous behavior of networks of nonlinear elements with “ring” and “small world” link topologies. To confirm the obtained results the numerical simulation is used. Results. It is shown that in networks of nonlinear oscillators with topologies of links such as “ring” and “small world”, the phenomenon of explosive synchronization can be observed for the different distributions of partial frequencies of network oscillators. Conclusion. The paper considers an analytical description of the behavior of network oscillators with “ring” and “small world” topologies of links and shows that the phenomenon of explosive synchronization in such networks is atypical, but not unique.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83933544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-29DOI: 10.18500/0869-6632-003020
Roman Belenkov, Eugene Postnicov
The nonlinearity parameter B/A is a characteristic of liquids and soft matter, which gains growing attention due to its sensibility to the composition of materials. This makes it a prospective indicator for nondestructive testing applications based on the ultrasound sounding suitable for a variety of applications from physic chemistry to biomedical studies. At the same time, the thermodynamic definition of the nonlinearity parameter requires extensive measurements at elevated pressures that are not always available; in addition, there are known certain contradiction of such data with the data obtained by methods of nonlinear acoustics. Objective. In this work, we consider a recently proposed approach to the prediction of the speed of sound at high pressures, which uses the property of invariance of the reduced pressure fluctuations and the data obtained at normal ambient pressure only. The method generalises the classic Nomoto model, which however gives only a qualitative picture, and results in the quantitative correspondence to the experimental values within their range of uncertainty. Methods. Analytical methods of the theory of thermodynamic fluctuations applied to the parameters of equations of nonlinear acoustics as well as numerical simulation in the COMSOL Multiphysics® environment. Results. Expressions for calculating the nonlinearity parameter with acceptable accuracy were obtained using thermodynamic data obtained only at atmospheric pressure. Numerical calculations were performed for toluene. In addition, the discrepancy between values of the nonlinear parameter obtained via the thermodynamic and nonlinear acoustic routes is analysed based on the numerical solution of the Westervelt equation; it is revealed that this deviation emerges when the effects of absorption of finite-amplitude waves were not properly taken into account.
{"title":"Approach to nonlinearity parameter in liquids calculation based on the scaling theory of thermodynamic fluctuations","authors":"Roman Belenkov, Eugene Postnicov","doi":"10.18500/0869-6632-003020","DOIUrl":"https://doi.org/10.18500/0869-6632-003020","url":null,"abstract":"The nonlinearity parameter B/A is a characteristic of liquids and soft matter, which gains growing attention due to its sensibility to the composition of materials. This makes it a prospective indicator for nondestructive testing applications based on the ultrasound sounding suitable for a variety of applications from physic chemistry to biomedical studies. At the same time, the thermodynamic definition of the nonlinearity parameter requires extensive measurements at elevated pressures that are not always available; in addition, there are known certain contradiction of such data with the data obtained by methods of nonlinear acoustics. Objective. In this work, we consider a recently proposed approach to the prediction of the speed of sound at high pressures, which uses the property of invariance of the reduced pressure fluctuations and the data obtained at normal ambient pressure only. The method generalises the classic Nomoto model, which however gives only a qualitative picture, and results in the quantitative correspondence to the experimental values within their range of uncertainty. Methods. Analytical methods of the theory of thermodynamic fluctuations applied to the parameters of equations of nonlinear acoustics as well as numerical simulation in the COMSOL Multiphysics® environment. Results. Expressions for calculating the nonlinearity parameter with acceptable accuracy were obtained using thermodynamic data obtained only at atmospheric pressure. Numerical calculations were performed for toluene. In addition, the discrepancy between values of the nonlinear parameter obtained via the thermodynamic and nonlinear acoustic routes is analysed based on the numerical solution of the Westervelt equation; it is revealed that this deviation emerges when the effects of absorption of finite-amplitude waves were not properly taken into account.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86038493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-19DOI: 10.18500/0869-6632-003012
D. Eshmamatova, M. Tadzhieva, R. Ganikhodzhaev
Purpose of the work is to study the dynamics of the asymptotic behavior of trajectories of discrete Lotka–Volterra dynamical systems with homogeneous tournaments operating in an arbitrary (𝑚 − 1)-dimensional simplex. It is known that a dynamic system is an object or a process for which the concept of a state is uniquely defined as a set of certain quantities at a given time, and a law describing the evolution of initial state over time is given. Mainly in questions of population genetics, biology, ecology, epidemiology and economics, systems of nonlinear differential equations describing the evolution of the process under study often arise. Since the Lotka–Volterra equations often arise in life phenomena, the main purpose of the work is to study the trajectories of discrete dynamical Lotka–Volterra systems using elements of graph theory. Methods. In the paper cards of fixed points are constructed for quadratic Lotka–Volterra mappings, that allow describing the dynamics of the systems under consideration. Results. Using cards of fixed points of a discrete dynamical system, criteria for the existence of fixed points with odd nonzero coordinates are given in a particular case, and these results on the location of fixed points of Lotka–Volterra systems are generalized accordingly in the case of an arbitrary simplex. The main results are theorems 5–9, which allow us to describe the dynamics of these systems arising in a number of genetic, epidemiological and ecological models. Conclusion. The results obtained in the paper give a detailed description of the dynamics of the trajectories of Lotka–Volterra maps with homogeneous tournaments. The map of fixed points highlights a specific area in the simplex that is most important and interesting for studying the dynamics of these maps. The results obtained are applicable in environmental problems, for example, to describe and study the cycle of biogens.
{"title":"Criteria for internal fixed points existence of discrete dynamic Lotka–Volterra systems with homogeneous tournaments","authors":"D. Eshmamatova, M. Tadzhieva, R. Ganikhodzhaev","doi":"10.18500/0869-6632-003012","DOIUrl":"https://doi.org/10.18500/0869-6632-003012","url":null,"abstract":"Purpose of the work is to study the dynamics of the asymptotic behavior of trajectories of discrete Lotka–Volterra dynamical systems with homogeneous tournaments operating in an arbitrary (𝑚 − 1)-dimensional simplex. It is known that a dynamic system is an object or a process for which the concept of a state is uniquely defined as a set of certain quantities at a given time, and a law describing the evolution of initial state over time is given. Mainly in questions of population genetics, biology, ecology, epidemiology and economics, systems of nonlinear differential equations describing the evolution of the process under study often arise. Since the Lotka–Volterra equations often arise in life phenomena, the main purpose of the work is to study the trajectories of discrete dynamical Lotka–Volterra systems using elements of graph theory. Methods. In the paper cards of fixed points are constructed for quadratic Lotka–Volterra mappings, that allow describing the dynamics of the systems under consideration. Results. Using cards of fixed points of a discrete dynamical system, criteria for the existence of fixed points with odd nonzero coordinates are given in a particular case, and these results on the location of fixed points of Lotka–Volterra systems are generalized accordingly in the case of an arbitrary simplex. The main results are theorems 5–9, which allow us to describe the dynamics of these systems arising in a number of genetic, epidemiological and ecological models. Conclusion. The results obtained in the paper give a detailed description of the dynamics of the trajectories of Lotka–Volterra maps with homogeneous tournaments. The map of fixed points highlights a specific area in the simplex that is most important and interesting for studying the dynamics of these maps. The results obtained are applicable in environmental problems, for example, to describe and study the cycle of biogens.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84849989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-14DOI: 10.18500/0869-6632-003013
O. Moskalenko, E. Evstifeev
Aim of this work is to study the possibility of existence of multistability near the boundary of generalized synchronization in systems with complex attractor topology. Unidirectionally coupled Lorentz systems have been chosen as an object of study, and a modified auxiliary system method has been used to detect the presence of the synchronous regime. Result of the work is a proof of the presence of multistability near the boundary of generalized synchronization in unidirectionally coupled systems with a complex topology of attractor. For this purpose, the basins of attraction of the synchronous and asynchronous states of interacting Lorenz systems have been obtained for the value of the coupling parameter corresponding to the realization of the intermittent generalized synchronization regime in the system under study, and the dependence of the multistability measure on the value of the coupling parameter has also been calculated. It is shown that in the regime of intermittent generalized synchronization the measure of multistability turns out to be positive, which is an additional confirmation of the presence of multistability in this case.
{"title":"On existence of multistability near the boundary of generalized synchronization in unidirectionally coupled systems with complex topology of attractor","authors":"O. Moskalenko, E. Evstifeev","doi":"10.18500/0869-6632-003013","DOIUrl":"https://doi.org/10.18500/0869-6632-003013","url":null,"abstract":"Aim of this work is to study the possibility of existence of multistability near the boundary of generalized synchronization in systems with complex attractor topology. Unidirectionally coupled Lorentz systems have been chosen as an object of study, and a modified auxiliary system method has been used to detect the presence of the synchronous regime. Result of the work is a proof of the presence of multistability near the boundary of generalized synchronization in unidirectionally coupled systems with a complex topology of attractor. For this purpose, the basins of attraction of the synchronous and asynchronous states of interacting Lorenz systems have been obtained for the value of the coupling parameter corresponding to the realization of the intermittent generalized synchronization regime in the system under study, and the dependence of the multistability measure on the value of the coupling parameter has also been calculated. It is shown that in the regime of intermittent generalized synchronization the measure of multistability turns out to be positive, which is an additional confirmation of the presence of multistability in this case.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79891297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-05DOI: 10.18500/0869-6632-003011
E. Ekomasov, K. Samsonov, A. Gumerov, R. Kudryavtsev
Purpose of this work is to use analytical and numerical methods to consider the problem of the structure and dynamics of coupled localized nonlinear waves in the sine-Gordon model with impurities (or spatial inhomogeneity of the periodic potential). Methods. Using the analytical method of collective coordinates for the case of the arbitrary number the same point impurities on the same distance each other, differential equation system was got for localized waves amplitudes as the functions on time. We used the finite difference method with explicit scheme for the numerical solution of the modified sine-Gordon equation. We used a discrete Fourier transform to perform a frequency analysis of the oscillations of localized waves calculate numerically. Results. We found of the differential equation system for three harmonic oscillators with the elastic connection for describe related oscillations of nonlinear waves localized on the three same impurity. The solutions obtained from this system of equations for the frequencies of related oscillation well approximate the results of direct numerical modeling of a nonlinear system. Conclusion. In the article shows that the related oscillation of nonlinear waves localized on three identical impurities located at the same distance from each other represent the sum of three harmonic oscillations: in-phase, in-phase-antiphase and antiphase type. The analysis of the influence of system parameters and initial conditions on the frequency and type of associated oscillations is carried out.
{"title":"Nonlinear waves of the sine-Gordon equation in the model with three attracting impurities","authors":"E. Ekomasov, K. Samsonov, A. Gumerov, R. Kudryavtsev","doi":"10.18500/0869-6632-003011","DOIUrl":"https://doi.org/10.18500/0869-6632-003011","url":null,"abstract":"Purpose of this work is to use analytical and numerical methods to consider the problem of the structure and dynamics of coupled localized nonlinear waves in the sine-Gordon model with impurities (or spatial inhomogeneity of the periodic potential). Methods. Using the analytical method of collective coordinates for the case of the arbitrary number the same point impurities on the same distance each other, differential equation system was got for localized waves amplitudes as the functions on time. We used the finite difference method with explicit scheme for the numerical solution of the modified sine-Gordon equation. We used a discrete Fourier transform to perform a frequency analysis of the oscillations of localized waves calculate numerically. Results. We found of the differential equation system for three harmonic oscillators with the elastic connection for describe related oscillations of nonlinear waves localized on the three same impurity. The solutions obtained from this system of equations for the frequencies of related oscillation well approximate the results of direct numerical modeling of a nonlinear system. Conclusion. In the article shows that the related oscillation of nonlinear waves localized on three identical impurities located at the same distance from each other represent the sum of three harmonic oscillations: in-phase, in-phase-antiphase and antiphase type. The analysis of the influence of system parameters and initial conditions on the frequency and type of associated oscillations is carried out.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75581149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-30DOI: 10.18500/0869-6632-003006
A. Nikitin, Andrey Y. Komlev, A. Nikitin, Aleksej Ustinov
One of the key elements for modern microwave circuits is a delay line, which is widely utilized for the signal generation as well as processing. Spin-wave delay lines based on ferrite films provide a high delay time and small dimensions. Typically, the performance characteristics of such lines are tuned by the variation of an externally applied magnetic field characterized by some drawbacks. The phenomenon of a metal–insulator transition (MIT) in the phase change materials permits to improve the performance characteristics of the spin-wave delay lines. In particular, this concept allows to reduce the power consumption and improve the control speed of a delay time. Aim. Development of a tunable spin-wave delay line based on ferrite and vanadium dioxide films, as well as the study of its performance characteristics. Methods. Experimental investigations were carried out for the delay line composed of the yttrium iron garnet (YIG) and vanadium dioxide (VO2) films. The ferrite waveguide was fabricated from a single-crystal YIG film grown on a gallium gadolinium garnet substrate. A vanadium dioxide film was formed on a silicon dioxide substrate by DC reactive magnetron sputtering. The microwave measurements were carried out using the vector network analyzer R&S®R ZVA40. Results. It was shown that heating of the VO2 film induces a sufficient drop of its resistance that causes the transformation of the spin-wave dispersion characteristic. This leads to the decrease in the group velocity of the propagating waves providing a growth of a delay time. Namely, experimental structure of 5-mm length offers a tunable time delay range from 130 up to 150 ns at the operating frequency of 4.33 GHz. Conclusion. A proof-of-principle for the MIT control of the delay time composed on the YIG-VO2 structure has been presented. It was shown that a switch of VO2 film from the isolating into conducting state produces a 15% change in the delay time. The considered microwave delay lines look favorable for applications as a complimentary part to the traditional approach for general computing and microwave signal processing.
{"title":"Tunable spin-wave delay line based on ferrite and vanadium dioxide","authors":"A. Nikitin, Andrey Y. Komlev, A. Nikitin, Aleksej Ustinov","doi":"10.18500/0869-6632-003006","DOIUrl":"https://doi.org/10.18500/0869-6632-003006","url":null,"abstract":"One of the key elements for modern microwave circuits is a delay line, which is widely utilized for the signal generation as well as processing. Spin-wave delay lines based on ferrite films provide a high delay time and small dimensions. Typically, the performance characteristics of such lines are tuned by the variation of an externally applied magnetic field characterized by some drawbacks. The phenomenon of a metal–insulator transition (MIT) in the phase change materials permits to improve the performance characteristics of the spin-wave delay lines. In particular, this concept allows to reduce the power consumption and improve the control speed of a delay time. Aim. Development of a tunable spin-wave delay line based on ferrite and vanadium dioxide films, as well as the study of its performance characteristics. Methods. Experimental investigations were carried out for the delay line composed of the yttrium iron garnet (YIG) and vanadium dioxide (VO2) films. The ferrite waveguide was fabricated from a single-crystal YIG film grown on a gallium gadolinium garnet substrate. A vanadium dioxide film was formed on a silicon dioxide substrate by DC reactive magnetron sputtering. The microwave measurements were carried out using the vector network analyzer R&S®R ZVA40. Results. It was shown that heating of the VO2 film induces a sufficient drop of its resistance that causes the transformation of the spin-wave dispersion characteristic. This leads to the decrease in the group velocity of the propagating waves providing a growth of a delay time. Namely, experimental structure of 5-mm length offers a tunable time delay range from 130 up to 150 ns at the operating frequency of 4.33 GHz. Conclusion. A proof-of-principle for the MIT control of the delay time composed on the YIG-VO2 structure has been presented. It was shown that a switch of VO2 film from the isolating into conducting state produces a 15% change in the delay time. The considered microwave delay lines look favorable for applications as a complimentary part to the traditional approach for general computing and microwave signal processing.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76494605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-30DOI: 10.18500/0869-6632-003007
M. Amel'chenko, A. Bir, F. Ogrin, Sergej Odintsov, D. Romanenko, A. Sadovnikov, Sergej Nikitov, Sergej Grishin
Purpose of this paper is the development and creation of the magnetic metasurfaces with metallic inclusions operating both in the microwave and terahertz frequency ranges. Methods. The Maxwell’s equations and the expressions for the effective medium parameters are used to build the analytical models of the magnetic metasurfaces based on either a ferromagnetic (FM) or antiferromagnetic (AFM) dielectric matrix, containing a two-dimensional periodic structure of thin metal (non-magnetic) wires surrounded by insulators. Numerical simulation of such structures operating in the microwave range is carried out using the MaxLLG software package. The magnetron sputtering, liquid etching, optical lithography, and lift-off photolithography are used to create bicomponent magnetic metasurfaces, consisting of two magnetic materials with very different values of magnetization. The study of linear and nonlinear characteristics of the bicomponent magnetic metasurfaces is carried out using the methods of microwave and Brillouin spectroscopy. Results. Based on the developed analytical model of the magnetic metasurface with metallic (nonmagnetic) inclusions it is shown that the FM metasurface possesses properties of a left-handed medium in a microwave range and the AFM metasurface possesses similar properties in a terahertz range. In the last case, the material parameters of the AFM metasurface are twice negative in two frequency bands. For the magnetic metasurfaces with metallic magnetic inclusions, the formation of absorption bands in the spectrum of a traveling magnetostatic surface spin wave due to the resonant properties of the inclusions has been established. In the nonlinear regime, the effect of nonreciprocal parametric three-wave resonance was obtained. Conclusion. The results presented in the paper demonstrate a number of physical phenomena that are observed only in the magnetic metasurfaces with metallic (nonmagnetic and magnetic) inclusions.
{"title":"Magnetic metasurfaces with metallic inclusions","authors":"M. Amel'chenko, A. Bir, F. Ogrin, Sergej Odintsov, D. Romanenko, A. Sadovnikov, Sergej Nikitov, Sergej Grishin","doi":"10.18500/0869-6632-003007","DOIUrl":"https://doi.org/10.18500/0869-6632-003007","url":null,"abstract":"Purpose of this paper is the development and creation of the magnetic metasurfaces with metallic inclusions operating both in the microwave and terahertz frequency ranges. Methods. The Maxwell’s equations and the expressions for the effective medium parameters are used to build the analytical models of the magnetic metasurfaces based on either a ferromagnetic (FM) or antiferromagnetic (AFM) dielectric matrix, containing a two-dimensional periodic structure of thin metal (non-magnetic) wires surrounded by insulators. Numerical simulation of such structures operating in the microwave range is carried out using the MaxLLG software package. The magnetron sputtering, liquid etching, optical lithography, and lift-off photolithography are used to create bicomponent magnetic metasurfaces, consisting of two magnetic materials with very different values of magnetization. The study of linear and nonlinear characteristics of the bicomponent magnetic metasurfaces is carried out using the methods of microwave and Brillouin spectroscopy. Results. Based on the developed analytical model of the magnetic metasurface with metallic (nonmagnetic) inclusions it is shown that the FM metasurface possesses properties of a left-handed medium in a microwave range and the AFM metasurface possesses similar properties in a terahertz range. In the last case, the material parameters of the AFM metasurface are twice negative in two frequency bands. For the magnetic metasurfaces with metallic magnetic inclusions, the formation of absorption bands in the spectrum of a traveling magnetostatic surface spin wave due to the resonant properties of the inclusions has been established. In the nonlinear regime, the effect of nonreciprocal parametric three-wave resonance was obtained. Conclusion. The results presented in the paper demonstrate a number of physical phenomena that are observed only in the magnetic metasurfaces with metallic (nonmagnetic and magnetic) inclusions.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88483964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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