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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.
Gusev I., Maksaev A., Promyslov V., Journal of Mathematical Sciences 2025 Vol. 299 No. 6
The regular graph of the space of n × m matrices over a field F is defined as the undirected graph whose vertices are matrices of rank min(n, m), and distinct matrices A and B are connected by an edge if and only if rk(A + B) < min(n, m). In this paper, for |F| ...
Added: May 25, 2026
Qian X., Deng Y., Shchur L. et al., Physica A: Statistical Mechanics and its Applications 2026 Vol. 696 P. 1–13
We perform a Monte Carlo analysis of the Ising model on many three-dimensional lattices. By means of finite-size scaling we obtain the critical points and determine the scaling dimensions. As expected, the critical exponents agree with the three-dimensional Ising universality class for all models. The irrelevant field, as revealed by the correction-to-scaling amplitudes, appears to ...
Added: May 24, 2026
Tyukin I., Tyukina T., van Helden D. P. et al., Information Sciences 2024 Vol. 678 Article 120856
AI errors pose a significant challenge, hindering real-world applications. This work introduces a novel approach to cope with AI errors using weakly supervised error correctors that guarantee a specific level of error reduction. Our correctors have low computational cost and can be used to decide whether to abstain from making an unsafe classification. We provide ...
Added: May 23, 2026
Zaikin A., Sviridov I., Sosedka A. et al., Technologies 2026 Vol. 14 No. 2 Article 84
High-dimensional tabular data are common in biomedical and clinical research, yet conventional machine learning methods often struggle in such settings due to data scarcity, feature redundancy, and limited generalization. In this study, we systematically evaluate Synolitic Graph Neural Networks (SGNNs), a framework that transforms high-dimensional samples into sample-specific graphs by training ensembles of low-dimensional pairwise ...
Added: May 23, 2026
Kibkalo Vladislav, Chertopolokhov V., Mukhamedov A. et al., IEEE Access 2026 Vol. 14 P. 14369–14392
This study presents on-the-fly identification and multi-step prediction of nonlinear systems with delayed inputs using a dynamic neural network combined with a smooth projection onto ellipsoids. The projection enforces parameter constraints that guarantee stability, while a Lyapunov–Krasovskii analysis yields computable ultimate error bounds. Riccati-type matrix inequalities are derived, providing an efficient vectorization–projection–devectorization implementation suitable for ...
Added: May 22, 2026
Морозов С. В., Calcolo 2026 Vol. 63 No. 2 Article 23
The approximation of tensors in a low-para metric format is a crucial component in many mathematical modelling and data analysis tasks. Among the widely used low-parametric representations, the canonical polyadic (CP) decomposition is known to be very efficient. Nowadays, most algorithms for CP approximation aim to construct the approximation in the Frobenius norm; however, some ...
Added: May 22, 2026
Селянин Ф. И., Journal of Dynamical and Control Systems 2026 Vol. 32 No. 2 P. 1–16
A B-facet is a lattice -dimensional polytope in the positive octant with a positive normal covector, such that every -dimensional simplex with vertices in it is a B-simplex (i.e., a pyramid of height one with base on a coordinate hyperplane). B-facets were introduced in [2] in the context of the monodromy conjecture. In this paper, we complete the ...
Added: May 21, 2026
Melentiev P. N., Калмыков А. С., Гритченко А. С. et al., Успехи физических наук 2024 Т. 194 № 11 С. 1130–1145
Представлен краткий обзор достигнутого уровня оптических методов детектирования единичных молекул в биомедицинских приложениях. Показано, что регистрация флуоресценции единичных молекул красителей, ковалентно связанных с антителами (биомолекулами), совместно с использованием современных методов нанофотоники может быть применена для решения различных задач в биологии и медицине: визуализации биомолекул, токсинов, вирусных частиц, определения ультранизких концентраций аналитов напрямую во взятой пробе, ...
Added: May 21, 2026
Antsiferov P.S., Stepanov L.V., Matiukhin N. D., Review of Scientific Instruments 2025 Vol. 96 No. 12 Article 123506
The article presents the discharge plasma based source of extreme ultraviolet (EUV) radiation. The discharge circuit has been driven by means of stripe line storage with working voltage 10.5 kV. The main feature of the proposed source is that plasma electrons acquire the energy, necessary for the production of multiply charged ions with ionization potentials ...
Added: May 20, 2026
Анциферов П. С., Степанов Л. В., Матюхин Н. Д., Оптика и спектроскопия 2026 Т. 134 № 2 С. 214–218
Сообщено о разработке системы регистрации спектров на ПЗС-линейке для уникального ВУФ спектрометра, построенного на основе сферической дифракционной решетки с радиусом 6.65 m. Была использована линейка HAMAMATSU S11156-2048-02, которая устанавливалась по касательной к окружности Роуланда с возможностью механического перемещения для сканирования спектра. Были получены спектрограммы в диапазоне длин волн 2130-2270 Angstrem. Описана методика сшивки регистрируемых спектральных ...
Added: May 20, 2026
Ausubel L., Baranov O., Journal of Economic Theory 2026 Vol. 235 No. 106192
The Vickrey-Clarke-Groves (VCG) mechanism is one of the most compelling constructs in mechanism design, but the presence of complementary goods creates the possibility of non-core and even zero-revenue outcomes. In this article, we show that joint feasibility constraints on allocations offer a second pathway to ill-behaved outcomes in the VCG mechanism, even when all bidders ...
Added: May 20, 2026
Denis Seliutskii, Russian Journal of Mathematical Physics 2025 Vol. 32 No. 2 P. 399–407
In this paper, we find an upper bound for the first Steklov eigenvalue for a surface of revolution with boundary consisting of two spheres of different radii. Moreover, we prove that, in some cases, this boundary is sharp. ...
Added: May 19, 2026
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
Malinovsky A. M., Пилипенко С. В., Mikhalchenko A. O. et al., Astronomy Reports 2026 Vol. 70 P. 1–6
Radiation from rotational transitions of CO molecules in distant galaxies creates a chaotic background with an intensity reaching 1000 Jy/sr at a wavelength of approximately 1 mm. This background will pose a serious problem, when measuring spectral distortions of the cosmic microwave background, in particular, the mu-distortion, which presumably has an intensity of less than ...
Added: May 19, 2026
Kaveev A. K., Fedorov V. V., Pavlov A. V. et al., Journal of Materials Chemistry C 2026 Vol. 14 No. 7 P. 2697–2705
Bismuth nanostructures represent a promising material platform for semiconductor nanooptoelectronics and colorimetry owing to the multi-colored light reflection and quantum confinement. In this work, we study the photoluminescent properties of bismuth nanostructures grown using molecular beam epitaxy on the planar CaF2/Si(111) surface. We demonstrate the different surface morphologies of Bi, ranging from planar films obtained ...
Added: May 19, 2026
Pavlova T., V.M. Shevlyuga (Шевлюга В. М., Applied Surface Science 2026 Vol. 736 P. 166813–166813
The objective of miniaturizing doped areas in silicon, with the ultimate goal of achieving atomic-precision doping, requires a fundamental understanding of the dopant incorporation process at the atomic level. We present a combined scanning tunneling microscopy (STM) and density functional theory (DFT) investigation of single phosphorus atom incorporation into the Si(100) surface. Phosphorus was supplied ...
Added: May 19, 2026
Pasternak D., Romshin A., Khmelnitsky Р. et al., Carbon 2026 Vol. 256 Article 121655
A single-photon source (SPS) is a key component required for quantum communication devices. We report the
discovery of bright diamond-based SPS created by nature. It is shown that narrow (≤2 nm) lines observed in the
500-800 nm range in photoluminescence (PL) spectra of the surface layer of untreated Yakut diamonds rich in
nitrogen and hydrogen are linked to ...
Added: May 19, 2026
Жакупов О. Б., European Journal of Mathematics 2025 Vol. 11 Article 84
We provide examples of smooth three-dimensional Fano complete intersections of degree 2, 4, 6, and 8 that have absolute coregularity 0. Considering the main theorem of Avilov, Loginov, and Przyjalkowski (CNTP 18:506–577, 2024) on the remaining 101 families of smooth Fano threefolds, our result implies that each family of smooth Fano threefolds has an element of absolute ...
Added: May 18, 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