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Перемежаемость в случайных потоках и стохастические интегралы движения
Успехи физических наук. 2025. Т. 195. № 8. С. 794–806.
This review presents recent advances in the study of frozen-in material lines and surfaces evolving in random flows. A remarkable feature of this process is the formation of long lived coherent structures on surfaces, which are associated with certain stochastic integrals of motion. While the exact form of these integrals depends on flow properties, they become univer sal under the condition of local isotropy. We derive these integrals explicitly and discuss the elegant mathematics under lying this phenomenon.
Абызов А. Н., Буутай П. Н., Математика и теоретические компьютерные науки 2026 Т. 4 № 2 С. 4–75
This paper is expository and methodological in nature and is devoted to the development of E.I. Zolotarev’s ideas embedded in his approach to the proof of the quadratic reciprocity law (1872). We consider extensions of Zolotarev’s approach to abstract number rings presented in the work of A. Brunyate and P.L. Clark (2015), and to finite ...
Added: July 30, 2026
Ponomarenko A., / Series Computer Science "arxiv.org". 2025.
This paper addresses the challenge of merging hierarchical navigable small world (HNSW) graphs, a critical operation for distributed systems, incremental indexing, and database compaction. We propose three algorithms for this task: Naive Graph Merge (NGM), Intra Graph Traversal Merge (IGTM), and Cross Graph Traversal Merge (CGTM). These algorithms differ in their approach to vertex selection ...
Added: July 30, 2026
Mikhaylets E. V., Razorenova A. М., Chernyshev V. L. et al., Scientific Reports 2026 Vol. 16 Article 23560
Meditation offers a naturalistic paradigm for studying introspection, yet the neural dynamics of advanced tantric practices remain largely unexplored. Buddhist Highest Yoga Tantra (BHYT) comprises a sequence of eight dissolution stages culminating in the “clear light” state. We recorded EEG during eyes-closed BHYT meditation performed in monasteries and hermitages (51 sessions from 36 male practitioners; ...
Added: July 29, 2026
Попеленский Ф. Ю., Математический сборник 2026 Т. 217 № 2 С. 108–153
In a recent paper Buchstaber and the author introduced a new structure on the cohomology of Hopf algebras in terms of the Buchstaber spectral sequence (Bss). We fully calculate this structure on the cohomology (known for a long time) of the important Hopf subalgebra A(1) of the classical Steenrod algebra A2.
As part of a demonstration ...
Added: July 28, 2026
Metlov K., Andrei B. Bogatyrëv, Annalen der Physik 2026 Vol. 538 No. 6 Article e70234
Thanks to the recent progress in bulk full three-dimensional nanoscale magnetization distribution imaging, there is a growing
interest to three-dimensional (3D) magnetization textures, promising new high information density spintronic applications.
Compared to 1D domain walls or 2D magnetic vortices/skyrmions, they are a much harder challenge to represent, analyze and
reason about. Here we build analytical representation for such ...
Added: July 28, 2026
Menovshchikov A., Ukhlov A., Rendiconti del Circolo Matematico di Palermo 2026 Vol. 75 Article 91
We consider the nonlinear Neumann eigenvalue problem in outward cuspidal domains with a weighted measure. Using composition operators on Sobolev spaces, we establish embeddings of Sobolev spaces into weighted Lebesgue spaces. These embeddings give the solvability of the Neumann spectral problem in this setting and provide estimates for the corresponding weighted Neumann eigenvalues. ...
Added: July 27, 2026
Menovshchikov A., Journal of Mathematical Sciences 2026 Vol. 298 P. 608–618
We study the set of (p, q)-eigenvalues of the p-Laplace operator with no-flux boundary conditions. We show that this set is closed and that its smallest positive element (the first nontrivial eigenvalue) admits a variational characterization. Moreover, we establish lower bounds for this eigenvalue in cuspidal domains. ...
Added: July 27, 2026
Dmitry Vasilyev, Gorev V., Ikhsanov R. et al., Journal of Materials Science 2026 No. 61 P. 25452–25470
The orthorhombic phase of 𝛼-Mo2 C is a key component in electrocatalytic applications, as Mo2C-based catalysts can exhibit catalytic performance comparable to or exceeding that of noble metals. Despite its technological relevance, theoretical understanding of the anisotropy in the thermal expansion and related thermoelastic properties of 𝛼-Mo2 C remains limited. In this work, first-principles calculations ...
Added: July 23, 2026
Edward R. Rzaev, Aleksandr Y. Romanov, Andrey M. Sukhov, IEEE Access 2026 Vol. 14 P. 2169–3536
This work presents a hierarchy of strictly local fault-tolerant routing algorithms for 3D mesh networks-on-chip, culminating in an algorithm that combines a live-neighbor selection rule with a bounded single-hop rollback mechanism. The proposed algorithms operate exclusively on immediate neighbor information, maintain O(1) per hop complexity, and require no global topology knowledge, additional virtual channels, or ...
Added: July 23, 2026
Borovitskaya I. V., Pimenov V. N., Korshunov S. N. et al., Physics of Atomic Nuclei 2026 Vol. 89 No. 1 P. S48–S55
The effect of high-power pulsed laser radiation (LR) generated in the GOS 1001 setup in the
Q-modulated mode (with a flux power density q equal to 1 × 1014 W/m2, pulse duration t = 50 ns, and the
number of pulses N from 1 to 8 in vacuum) on the structure and microhardness of the surface of ...
Added: July 22, 2026
Korogod D., Shapeev A., Ivan S. Novikov, Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 No. 2 Article 024104
We present two models with explicit long-range electrostatics in the form of Coulomb interactions. Both models include point charges depending on their local atomic environments, and the second model also conserves a total charge of an atomic system. We combine the proposed long-range models with the local moment tensor potential (MTP) and demonstrate that they ...
Added: July 22, 2026
Sozykin K., Rybin N., Chertkov A. et al., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 113 No. 22 Article 224111
The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with system size (i.e., the curse of dimensionality). We introduce a framework that overcomes this limitation by exploiting the low-rank structure of potential energy surfaces through tensor train (TT) decomposition. Our ...
Added: July 22, 2026
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
Parfenyev V., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 114 No. 1 Article 015104
Zermelo's navigation problem seeks the trajectory of minimal travel time between two points in a fluid flow. We address this problem for an agent -- such as a floating drone or active particle -- that is advected by a two-dimensional flow, self-propels at a fixed speed smaller than or comparable to the characteristic flow velocity, ...
Added: July 17, 2026
Singapore: Springer, 2024.
Included in the following conference series:
INdAM: INdAM Meeting: Kolmogorov Operators and their Applications Workshop
Conference proceedings info: INdAM 2022
Kolmogorov equations are a fundamental bridge between the theory of partial differential equations and that of stochastic differential equations that arise in several research fields.
This volume collects a selection of the talks given at the Cortona meeting by ...
Added: July 17, 2026
Veretennikov A., Pascucci A., Rondelli A., Stochastic Processes and their Applications 2026 Vol. 199 Article 104978
We present existence results for weak solutions to a broad class of degenerate McKean-Vlasov equations with rough coefficients, expanding upon and refining the techniques recently introduced by the third author. Under certain structural conditions, we also establish results concerning both weak and strong well-posedness. ...
Added: July 17, 2026
Veretennikov A., Ляппиева А. А., Теория вероятностей и ее применения 2026 Т. 71 № 2 С. 295–304
Установлен новый результат о сильной единственности для многомерного СДУ с невырожденной диффузией и частично нерегулярным сносом. Его можно рассматривать как комбинированный вариант на темы Ямада и Ватанабэ (1971), Звонкина (1974) и первого автора настоящей статьи (1980). ...
Added: July 17, 2026
Veretennikov A., Нуриева А. И., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2025 Т. 525 С. 24–30
Предложено новое достаточное условие в задаче о центральной предельной теореме в схеме серий для неоднородных цепей Маркова, с возможностью того, что минимум эргодического коэффициента Маркова–Добрушина может быть ближе к нулю, чем в основном условии Добрушина. ...
Added: July 17, 2026
О частных производных модифицированных полиномов Бернштейна–Станку для функций нескольких переменных
Veretennikov A., Мазутский Н. М., Математический сборник 2025 Т. 216 № 7 С. 3–27
Целью работы является доказательство аппроксимации смешанных производных второго порядка для функции нескольких переменных в норме L1 такими же производными модифицированных полиномов Бернштейна–Станку при минимальной возможной регулярности. ...
Added: July 17, 2026
Ахмярова А. Т., Veretennikov A., Теория вероятностей и ее применения 2025 Т. 70 № 2 С. 211–227
В работе предложены новые версии слабого закона больших чисел (ЗБЧ) для слабо зависимых слагаемых (вообще говоря, разнораспределенных) как при наличии математического ожидания каждого из них, так и без такового. Одним из основных условий в первом из трех рассматриваемых случаев, в котором развиваются идеи из статьи Ю. Ш. Чау 1971 г., является равномерная интегрируемость слагаемых по Чезаро в духе работ по ЗБЧ для ...
Added: July 17, 2026
Veretennikov A., Stochastics and Dynamics 2024
A new weak existence result for degenerate multi-dimensional stochastic McKean–Vlasov equation is established under relaxed regularity conditions. ...
Added: July 17, 2026
Shikanian A., Parfenyev V., Physics of Fluids 2025 Vol. 37 No. 9 Article 095127
We study two-dimensional turbulence in a square no-slip domain without bottom drag using direct numerical simulations. The dynamics are shown to depend strongly on the torque $M$ of the external forcing. When $M$ is relatively large, a long-lived coherent vortex forms at the domain center, establishing a persistent angular momentum. At lower torques, the angular ...
Added: September 6, 2025
Pavlov D., Galigerov V., Kolotinskii D. et al., International Journal of High Performance Computing Applications 2024 Vol. 38 No. 1 P. 34–49
Fluid dynamics is a ubiquitous problem that arises in different branches of science and industry. It is usually tackled by numerically solving differential equations on a finite grid. Molecular dynamics was not a feasible tool to approach fluid dynamics until very recently due to its disproportional computational complexity. In this paper we propose a new ...
Added: July 18, 2023
A. S. Il'yn, Kopyev A. V., Sirota V. A. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2023 Vol. 107 No. 2 Article L023101
We consider the line, surface, and volume elements of fluid in stationary isotropic incompressible stochastic flow in d-dimensional space and investigate the long-time evolution of their statistic properties. We report the discovery of a family of d!−1 stochastical integrals of motion that are universal in the sense that their explicit form does not depend on the statistics of ...
Added: February 23, 2023