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Stationary and nonstationary nonlinear dynamics of the finite sine-lattice
Nonlinear Dynamics. 2022. P. 1819–1837.
We present the results of the analytical as well as numerical study of the stationary and nonstationary dynamics of the sine-lattice. The latter is the discrete constitutive model used in various fields of physics, in particular, for the description of flexible polymers, quasi-one-dimensional spin chains, biopolymers, etc. To analyze the sine-lattice dynamics, we introduce the complex functions that allow us to determine the nonlinear normalmodes as the stationary solutions to the equations in the wide range of the oscillation amplitudes and the wavenumbers. We present the dispersion relations in the analytical form. Analysis of the slow nonstationary processes allows us to determine the conditions of energy localization in the chain. We observe a good agreement between the analytical
and numerical values of the localization thresholds for the chains of different lengths. In the longwavelength approximation, the sine-lattice is equivalent to the Frenkel–Kontorova model. We demonstrate in the continuum limit that the equation is reduced to the nonlinear Schrödinger equation instead of the wellknown sine-Gordon equation.We reveal the conditions of the existence of a breather-like solution and reduce the analytical representation for the small-amplitude approximation. We consider nonstationary dynamics of the forced oscillations for the undamped system in terms of the limiting phase trajectory; its bifurcations determine the change of the oscillatory regimes.
We discuss the effect of damping on the slow system dynamics.We also present the generalized equation for the stationary amplitude of the forced oscillations in the presence of the damping.
Aleksei Samarin, Nazarenko A., Nazarenko D. et al., Machine Learning and Knowledge Extraction 2026 Vol. 8 No. 10 Article 330
Automated microscopic image analysis is essential for quantitative microbiology, yet manual acquisition and generic recognition models struggle with morphological variability and scene artifacts. We address both ends of this pipeline. First, we present a low-cost, open-source acquisition system, based on an Arduino UNO R3 microcontroller and NEMA 17 stepper motors, that automates focusing, magnification, and ...
Added: October 14, 2026
Parkhomenko V., Kulikova S., Buzmakov A. V., Lobachevskii Journal of Mathematics 2026 Vol. 47 No. 6 P. 2979–2992
The stability of formal concepts and its generalization as robustness are considered in the paper. We use an approximation of stability in the form of Δ-measure for fast calculations. A computationally efficient method for calculating robustness based on subcontexts is presented. We also present a new method to analytically evaluate the number of preimages for ...
Added: October 14, 2026
Kuznetsov A. P., Sedova Y. V., Sataev I. R. et al., Mathematics and Computers in Simulation 2027 Vol. 2 P. 574–592
Universal bifurcation structures on the parameter plane of nonlinear systems, known as shrimps, are discussed. An overview of numerous examples from various fields of science is given. Shrimps are typical for both maps of different dimensions and flows. The varieties of shrimp are discussed and relevant examples are given. The similarity property on the parameter ...
Added: October 14, 2026
Dmitriev A., Kornilov V., Batienkov R., Lecture Notes in Civil Engineering 2026 Vol. 886 P. 249–255
Numerous studies have provided compelling evidence that the probability distribution of avalanche sizes follows a power law, and that 1/f noise is present in the stochastic dynamics of landslides. We present a theoretical explanation of these phenomena within the framework of self-organized criticality theory, proposing a discrete-time model in the form of a sandpile cellular ...
Added: October 13, 2026
Dmitriev A., Shulman I., Lebedev A., Studies in Computational Intelligence 2026 Vol. 1265 P. 266–273
A discrete-time model is presented for the self-organization of the X/Twitter social network to the edge of a phase transition, characterized by avalanche-like propagation of information in the network. The model is based on the analogy between the critical dynamics of the X social network and sandpile cellular automata with Manna rule on the Chung-Lu ...
Added: October 13, 2026
Arutyunov K., Kharitonov I. A., Petrosyants K. O., JETP Letters 2026 Vol. 124 No. 6 P. 1–16
Superconducting properties of metallic micro- and nanowires can be entirely different from those of bulk superconductors. Of particular interest is the nonequilibrium current-induced state of a quasi-one-dimensional superconducting channel. The most interesting phenomenon here is the stepped I–V characteristic, explained by a process known as phase slip center activation. If the origin of such step-like ...
Added: October 13, 2026
Makarov D. M., Kalikin N., Fashchevsky K. A. et al., Electrochimica Acta 2026 Vol. 579 Article 150159
Machine learning (ML) has become a powerful tool for accelerating the development of carbon-based supercapacitors;
however, most published models assume that a single predictive framework can describe both conventional
porous carbons and hybrid carbon electrodes. Here, we test this assumption using a comprehensive
benchmark dataset and an extended literature-curated dataset enriched with synthesis- and electrolyte-related
descriptors. Three ML algorithms ...
Added: October 13, 2026
Gusein-Zade S., Campillo A., Delgado F., Mathematische Zeitschrift 2026 Vol. 314 No. 1 P. 1–22
For a subfield $\K$ of the field $\C$ of complex numbers, we consider curve and divisorial valuations on the algebra $\K[[x,y]]$ of formal power series in two variables with the coefficients in $\K$. We compute the semigroup Poincar\'e series and the classical Poincar\'e series of a (discrete, rank one) valuation on it. ...
Added: October 13, 2026
Махлуф М., Ozhegov R., Elezov M. et al., Фотоника 2026 Vol. 20 No. 6 P. 414–423
This paper compares the ranging precision of direct time-of-flight (dToF) and non-line-of-sight (NLOS) LiDAR architectures, both using a superconducting nanowire single-photon detector (SNSPD). Both systems operate at 1550 nm with a 50 ps pulsed laser and time-correlated single-photon counting (TCSPC). The dToF configuration achieved approximately 100 µm precision at 10 m, while the NLOS configuration achieved 500 µm precision for ...
Added: October 12, 2026
Ivanova A., Polikovskiy T., Victoria E. Gontcharenko et al., Sensors and Actuators, A: Physical 2024 Vol. 379 Article 115969
Luminescence thermometry, leveraging the temperature-dependent luminescent properties of coordination compounds, offers precise and remote temperature measurement. However, many existing luminescent thermometers exhibit a narrow peak in temperature sensitivity, restricting their effective operating range. In this study, we synthesized new complexes [LnL2(NO3)(TPPO)2], where Ln = Eu (1), Tb (2), Gd (3), Tb0.94Eu0.06 (4), (HL - 4,4,4-trifluoro-1-(furan-2-yl) ...
Added: November 22, 2024
Alimov O., Doroshenko M., Egorysheva A. et al., Optical Materials 2022 Vol. 128 Article 112330
The optical properties of a highly dispersed bismuth orthogermanate powder (HDP_BGO) were studied at 300 K. The fluorescence of undoped HDP_BGO under ultraviolet (UV) excitation (266nm) was shown to result from Frenkel excitons. The HDP_BGO fluorescence decay kinetics under UV excitation had a complex decay form similar to that of BGO single crystal and was a ...
Added: October 23, 2022
Kovaleva M., Manevitch L. I., Physica Scripta 2021 Vol. 96 No. 12 Article 125035
In this report we consider two weakly coupled Schrödinger equations as a reduced model of interchain energy transport in the DNA double-helix torsional model. We employ a reduction of the Yakushevich-type model that considers the torsional dynamics of the DNA as effective chains of pendula. In previous works, only small amplitude excitations and stationary dynamics ...
Added: February 14, 2022
Tumanov M., Абдуллин С. Р., Серебренников П. С., Вестник Московского государственного университета леса - Лесной вестник 2020 № 1 С. 20–30
В статье исследованы нелинейные колебательные процессы, возникающие в системах с переменными параметрами c запаздыванием. На практике часто встречаются системы, в которых происходит переключение параметров в зависимости от некоторых условий работы, при этом при каждом значении параметров система остаётся линейной, но в целом, конечно, она нелинейная и имеет запаздывание. Известно, что такие системы могут как терять ...
Added: February 27, 2020
Victor K., Kovaleva M., Jayaprakash K. et al., Chaos 2016 Vol. 26 No. 073102 P. 1–12
In the present paper, we study the mechanism of formation and bifurcations of highly nonstationary
regimes manifested by different energy transport intensities, emerging in an anharmonic trimer
model. The basic model under investigation comprises a chain of three coupled anharmonic
oscillators subject to localized excitation, where the initial energy is imparted to the first oscillator
only. We report the ...
Added: February 28, 2019
Kovaleva Margarita, Pilipchuk V., Manevitch L. I., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2016 Vol. 94 No. 032223 P. 032223-1–032223-10
The present work follows our previous study dealing with a new type of synchronization in a system of two
weakly coupled generalized van der Pol–Duffing autogenerators. The essence of the effect revealed is that the
synchronized oscillations are not stationary but accompanied by the most intensive energy exchange between
the oscillators. The phase shift between the generators remains ...
Added: February 28, 2019
Kovaleva Margarita, Smirnov V., Manevitch L. I., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2019 Vol. 99 No. 012209 P. 012209-1–012209-12
The low- and high-amplitude oscillations in the system of three nonlinear coupled pendula (trimer) are analyzed beyond the quasilinear approximation. The considered oscillations are fundamental for many models of the energy exchange processes in physical, mechanical, and biological systems, in particular, for the torsional vibrations of flexible polymers or DNA's double strands. We obtained the ...
Added: February 1, 2019
Vorotnikov K., Kovaleva Margarita, Starosvetsky Y., Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 2018 Vol. 376 No. 20170134 P. 1–21
In the present paper we give a selective review of some very recent works concerning the non-stationary regimes emerging in various one- and two- dimensional models incorporating internal rotators. In one-dimensional models, these regimes are characterized by the intense energy transfer from the outer element subject to initial or harmonic loading to the internal rotator. ...
Added: January 22, 2019
D.R. Shklyar, JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS 2017 Vol. 122 P. 640–655
We study the problem of energy exchange between waves and particles, which leads to energization of the latter, in an unstable plasma typical of the radiation belts. The ongoing Van Allen Probes space mission brought this problem among the most discussed in space physics. A free energy which is present in an unstable plasma provides ...
Added: November 26, 2017
Chistyakov A., Zvaigzne M., Nikitenko V. et al., The Journal of Physical Chemistry Letters 2017 Vol. 8 No. 17 P. 4129–4139
Quantum dot (QD) solids represent a new type of condensed matter drawing high fundamental and applied interest. Quantum confinement in individual QDs, combined with macroscopic scale whole materials, leads to novel exciton and charge transfer features that are particularly relevant to optoelectronic applications. This Perspective discusses the structure of semiconductor QD solids, optical and spectral ...
Added: October 7, 2017
Timofeev A., Semyonov V., Journal of Physics: Conference Series 2016 Vol. 774 No. 012171 P. 1–5
Dust particles under certain conditions can acquire kinetic energy of the order of
10 eV and higher, far above the temperature of gas and temperatures of ions and electrons in the
discharge. Such heating can be explained by the energy transfer between degrees of freedom of
a dusty plasma system. One of the mechanisms of such energy transfer ...
Added: February 17, 2017
Markov N., Dmitriev V., Maltseva S. V. et al., Financial Assets and Investing 2016 Vol. 7 No. 3 P. 5–19
The research deals with the construction, implementation and analysis of the model of the non-equilibrium financial market using econophysical approach and the theory of nonlinear oscillations. We used the scaled variation of supply and demand prices and elasticity of these two variables as dynamic variables in the simulation of the non-equilibrium financial market. View of ...
Added: December 1, 2016
Markov N., Dmitriev V., Maltseva S. V. et al., , in: European Financial Systems 2015. Proceedings of the 12th International Scientific Conference.: Brno: Masarykova univerzita, 2015. P. 375–381.
The research deals with the construction, implementation and analysis of the model of non-equilibrium financial market using econophysical approach and the theory of nonlinear oscillations. We used scaled variation of supply and demand prices and elasticity of these two variables as dynamic variables in the simulation of the nonequilibrium financial market. View of the dynamical ...
Added: September 21, 2015