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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.
Осипов Д.В., Математический сборник 2026 Т. 217 № 9 С. 130–146
Изучаются законы взаимности, связанные с комплексными линейными расслоениями на расслоениях на ориентируемые окружности. В частности, доказывается следующий закон взаимности. Пусть B – комплексное многообразие и πi:Mi→B – расслоение на ориентируемые окружности, где индекс i пробегает конечное множество. Пусть Li и Ni – комплексные линейные расслоения на каждом многообразии Mi. Закон взаимности утверждает, что сумма всех элементов (πi)∗(c1(Li)∪c1(Ni)), где (πi)∗ – ...
Added: September 3, 2026
Budkov Y., Journal of Chemical Physics 2026 Vol. 165 No. 9 Article 094902
We derive the stress tensor of a flexible polymer solution within the Gaussian-chain self-consistent field theory (SCFT) without invoking the ground-state dominance (GSD) approximation. Starting from a covariant formulation of the single-chain partition function in a background metric, we obtain the symmetric stress tensor expressed through the full Edwards propagators. The result contains the local ...
Added: September 2, 2026
Pikina E., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 113 No. 5
In this work, we investigate the elastic properties of deflated vesicles and their shape dynamics in uniaxial extensional flow. By analyzing the Helfrich bending energy and viscous flow stresses in the limit of highly elongated shapes, we demonstrate that all stable vesicle configurations are metastable. For vesicles with small reduced volume, we identify the type ...
Added: September 1, 2026
Basalaev A., Rarovskii A., Journal of Singularities 2026 Vol. 30 P. 61–80
Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau-Ginzburg orbifolds. Namely, for the pairs (f,G), where f defines an isolated singularity of A and D type and G is a group of symmetries of ...
Added: September 1, 2026
Rybakov M., Shkatov D., Journal of Logic and Computation 2026 Vol. 36 No. 6 Article exag026
We prove Pi-1-1-hardness, and thus lack of recursive axiomatizability, of constant-domain modal predicate logics defined by a class of Dedekind complete linear Kripke frames containing a frame with an infinitely increasing chain of worlds. The result holds even for the language with one unary predicate letter, one propositional letter, and two individual variables. ...
Added: September 1, 2026
Селянин Ф. И., Moscow Mathematical Journal 2026 Vol. 26 No. 2 P. 167–187
Minkowski mixed volume of n subpolytopes D1,…,Dn of a polytope P⊂Rn clearly does not exceed the normalized volume n!Vol(P). Equality holds if and only if the subpolytopes are interlaced, i.e., each proper face F⊊P intersects at least dim(F)+1 of the polytopes Di. Efficiently computing mixed volumes for more general collections of subpolytopes is crucial for estimating the complexity of numerically solving polynomial systems.
Motivated by relaxing the bound dim(F)+1 to dim(F), we ...
Added: August 31, 2026
Chernyshov A., Padokhin A. M., Grach S. M. et al., Geophysical Research Letters 2026 Vol. 53 P. 1–11
This paper presents the first results of a coordinated experiment on the ionospheric plasma response to high-frequency (HF) overdense heating, conducted using the SURA heating facility and the Ionosfera-M satellite. The experiment combined ground-based observations with in situ satellite measurements, enabling a comprehensive study of artificial ionospheric disturbances. During the experiment, the SURA facility transmitted ...
Added: August 31, 2026
D. A. Dorofeev, A. A. Chernyshov, Mogilevsky M. M. et al., JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS 2025 Vol. 130 Article e2025JA033900
This study analyzes data from the ERG (Arase) satellite over a period of nearly 7 years (2017–2023). During this time, about 1,000 cases of hectometric continuum (HMC) radiation in near‐Earth space were detected, which made it possible to identify characteristic features on different time scales. On a daily scale, it was established that HMC is ...
Added: August 31, 2026
Mogilevsky M. M., Shaposhnikov V., Chernyshov A. et al., Physics of Plasmas 2025 Vol. 32 P. 1–10
The ERG (Arase) satellite recently discovered a non-thermal hectometric continuum with a narrowband frequency structure. The mechanism behind the generation of this type of emission in the near-Earth plasma is still unknown. This study examines the potential use of electron cyclotron harmonics instability to explain the line structure of hectometric radio emissions for the first ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., International Mathematics Research Notices 2026 Vol. 14 Article rnag146
We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and materialization analysis of the spin Gromov–Witten theory of the projective line and is dictated by Z 2 -equivariant ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Communications in Mathematical Physics 2026 Vol. 407 No. 69
We prove that for any initial data on a genus zero spectral curve the cor responding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the r-th roots of the twisted powers of the log canonical bundles ...
Added: August 31, 2026
Gromov V., Переслегин С. Б., Переслегина Е. Б. et al., СПб.: Полакс, 2026.
Механизм происходящих в мире изменений носит эволюционный, а не экологический характер. Иначе говоря, Человечество столкнулось с кризисом развития, который имеет три независимые составляющие: кризис индустриального общества (фазовый кризис), кризис научного мышления (эпистемный кризис) и кризис формата существования разума (социосистемный кризис). Доклад посвящён аспектам этого триединого кризиса и возможным путям его преодоления, не сводящимся к первичному ...
Added: August 31, 2026
Devyatov R. A., Mathematical notes 2026 Vol. 119 No. 3 P. 782–786
Let G/B be a flag variety over ℂ, where G is a simple algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity free if it is possible to multiply it by a Schubert class ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Journal fuer die reine und angewandte Mathematik 2026 Vol. 2026 No. 836 P. 111–162
We give a self-contained and simplified proof of Mukai’s classification of prime Fano threefolds of index 1 and genus g ≥ 6 with at most factorial terminal singularities, and of its extension to higher dimension. ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Compositio Mathematica 2026 Vol. 162 No. 1 P. 59–99
We give a proof of Mukai’s theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literature. The result is essential for Mukai’s biregular classification of prime Fano threefolds, and for the existence of semiorthogonal decompositions in their derived categories. Our ...
Added: August 30, 2026
Guseva L., Novikov A., Advances in Mathematics 2026 Vol. 503 Article 111211
We prove that the Kuznetsov–Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups Sp(2n,C) are full and consist of vector bundles. To achieve this, we construct several classes of complexes, which we call generalized staircase complexes, symplectic staircase complexes and secondary staircase complexes — each of which may be of independent interest. ...
Added: August 30, 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