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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.
Potanin B., Dolgikh S., Statistics and Probability Letters 2026 Article 110984
We derive bounds on the gradient and Hessian of the log-CDF, ln F(x), of the multivariate normal distribution. These bounds scale linearly and quadratically in ‖x‖ , respectively, with constants depending only on the covariance matrix. We demonstrate the usefulness of these bounds by proving asymptotic normality of the maximum-likelihood estimator of the multivariate probit ...
Added: October 1, 2026
A. V. Pereskokov, Journal of Mathematical Sciences 2026 Vol. 302 No. 4 P. 531–545
We consider the Zeeman effect problem for the hydrogen atom in a magnetic field using
irreducible representations of the Karasev–Novikova algebra with quadratic commutation
relations. We find the asymptotics of a series of eigenvalues and the corresponding
asymptotic eigenfunctions near the upper boundaries of spectral clusters. ...
Added: October 1, 2026
Yakovlev K., Puchkin N., Journal of Complexity 2026 Vol. 97
We present a theory for simultaneous approximation of the score function and its derivatives, enabling the handling of data distributions with low-dimensional structure and unbounded support. Our approximation error bounds match those in the literature while relying on assumptions that relax the usual bounded support requirement. Crucially, our bounds are free from the curse of ...
Added: September 30, 2026
Zlotnik A., Mathematical notes 2026 Vol. 120 No. 6 P. 1005–1009
Numerical methods for solving systems of gas dynamic equations are the subject of a vast literature. A special family of spatially symmetric conservative difference methods based on preliminary kinetic, or quasi-gasdynamic (QGD), regularization of these equations was constructed and successfully tested. A pressing issue is the construction of numerical methods that are not only conservative ...
Added: September 30, 2026
Obraztsova Anna, Fominykh Nikita, Komarov Sergey et al., Applied Physics Letters 2026 Vol. 129 Article 132110
Miniaturization of edge-emitting quantum-dot lasers is hampered by increased mirror losses in ultra-short Fabry–Perot cavities and limited modal gain of quantum dots (QDs). Here, we demonstrate electrically injected InGaAs/GaAs quantum-dot stripe lasers with an 8-lm stripe width and focused-ion-beam (FIB)-etched mirrors defining cavity lengths from 300 to 77 lm. The laser cavities were fabricated using ...
Added: September 30, 2026
Beldiev I., Тимашёв Д. А., Алгебра и анализ 2026 Т. 38 № 5 С. 1–10
An algebraic variety X is called a homogeneous space if there exists a transitive regular action of an algebraic group on X. We prove inequalities between the dimension of a homogeneous space of a linear algebraic group and its Picard number. ...
Added: September 30, 2026
Planche L., Ilina A., Jay F. et al., Molecular Biology and Evolution 2026 Article 235
Admixture between populations is a common feature of human history. Admixture events introduce new genetic variation that can fuel evolution. Characterizing the significance of admixture events on the evolution of populations across various species is of great interest to evolutionary geneticists. Local Ancestry Inference (LAI) methods infer genetic ancestry of an individual at a particular ...
Added: September 30, 2026
Glutsyuk A., Ilyashenko Y., Izvestiya. Mathematics 2026 Vol. 90 No. 1 P. 73–89
We show that a completely non-degenerate B-group is uniquely determined by its factor: two such groups with conformally equivalent factors are Möbius conjugate. A similar property is inherent to the quasi-Fuchsian groups but not to degenerate B-groups. We also study the factor of a B-group as a triple: the main factor, the marked characteristic complex, and a homotopy class of ...
Added: September 30, 2026
Tuzhilin M., Автоматика и телемеханика 2026 № 11 С. 84–97
Предлагается обобщение двух известных инвариантов реальных сетей: степени и кси-центральности. Строится серия центральностей, основанная на матрице Лапласа сети и параметризованная параметром j со следующими свойствами: во-первых, при j = 0, 1 эти центральности совпадают со степенью и ксицентральностью; во-вторых, их распределение хорошо приближается распределением Вейбулла; в-третьих, для реальных сетей они имеют правостороннюю асимметрию, а для ...
Added: September 29, 2026
Melnikov I., Pelinovsky E., Доклады Российской академии наук. Физика, технические науки (ранее - Доклады Академии Наук. Физика) 2026 Т. 529 С. 29–36
Conditions for the emergence of pyramidal solitary waves (solitary waves possessing more than two inflection points) are presented for a family of generalized Korteweg – de Vries (KdV) equations. For the generalized Gardner equation, it is shown that pyramidal solitons are unstable. The decay of initial perturbations close to pyramidal solitary waves is demonstrated numerically. ...
Added: September 29, 2026
Merkulov S., Journal of Pure and Applied Algebra 2026 Vol. 230 P. 1–19
We study the dual cyclic Hochschild complex $Cyc(A,\K)$ of a
(possibly, infinite-dimensional) $A_\infty$-algebra $(A,\mu)$ and prove
that any pre-Calabi-Yau extension $\pi$ of the given $A_\infty$ structure $\mu$ in $A$
induces on the cyclic cohomology of $(A,\mu)$ a representation of a new dg properad of {\em oriented}\, ribbon graphs. We compute the cohomology of that properad in terms of ...
Added: September 29, 2026
Kartsev A., Васильев Д. А., Kushchuk L. et al., Materials Today Communications 2026
Amorphous carbon coatings, including diamond-like carbon (DLC), exhibit a wide range of structural and mechanical properties governed by the local bonding topology (the sp2/sp3 ratio), as well as by deposition conditions and substrate material. Recently, machine-learning interatomic potentials trained predominantly on density functional theory (DFT) reference data have significantly advanced multiscale modeling of amorphous carbon ...
Added: September 28, 2026
Хрыстик М. А., European Journal of Combinatorics 2026 Vol. 136 P. 104393–104393
Let 𝑓𝑊(𝑛) be the number of different factors of length 𝑛 appearing in a word 𝑊. In a classical result by Morse and Hedlund, a characterization is given for infinite words satisfying the condition 𝑓𝑊(𝑛)≤𝑛 for some 𝑛∈ℕ. In this paper, we describe the form of finite words that satisfy the condition 𝑓𝑊(𝑛)≤𝑛. We study ...
Added: September 28, 2026
The Search of the Process e+e−→(ω, ρ)→ηe+e− at 680–820 MeV c.m. Energy Range with the CMD-3 Detector
A. K. Narvatkina, Physics of Atomic Nuclei 2025 Vol. 88 No. 4 P. 386–393
We report a search for the rare Dalitz decays ω → ηe+e− and ρ → ηe+e− using data from the CMD-3 detector at the VEPP-2000 e+e− collider. These decays probe the electromagnetic structure of vector mesons and test the Vector Dominance Model (VDM) in low-energy QCD. A blind analysis technique, combined with kinematic constraints and ...
Added: September 28, 2026
Fominykh N., Stegailov V., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 Article 115132
The enigmatic puzzle of the Verwey transition in magnetite Fe3O4 has been unresolved for almost a century. We present an ab initio-based model of the polaron transport combining kinetic Monte Carlo and molecular dynamics calculations to directly describe the coupling of polarons with lattice vibrations. Contrary to the Ihle-Lorenz small-polaron model, we find no significant ...
Added: September 28, 2026
Piliugin L., Antropov A., Lobashev E. et al., Journal of Nuclear Materials 2026 Vol. 632 Article 156876
The effects of dislocations on the mobility of gas nanobubbles pinned to them are considered as novel unex- plored mechanisms of accelerated fission gas release and investigated using classical molecular dynamics of helium bubbles in FCC aluminum. Non-equilibrium methods are developed to calculate the mobility of a pinned bubble both along and across the dislocation ...
Added: September 28, 2026
Teregulov T., Loubenets E. R., / Series Quantum Physics "arXiv". 2026. No. 2609.31472.
We develop a new three-party quantum secret-sharing (QSS) protocol based on a three-qubit W state. This protocol encodes the secret-sequence bits using X gates and employs randomly selected Hadamard operations and measurement bases to generate information and security-test rounds. We evaluate the efficiency of the proposed protocol and analyze its security against an internal adversary ...
Added: September 28, 2026
Щербинин С. А., Корзникова Е. А., Дмитриев С. В. et al., Physics Letters A 2026 Vol. 591 Article 131884
In this work, a simple genetic algorithm (GA) is used to find and characterize different QBs in a 𝛽-FPUT chain. By considering the space of initial particle displacements as a global optimization landscape, GA maximizes the energy localization function by automatically evolving candidate states toward highly localized long-lived solutions without a priori symmetry assumptions. 200 ...
Added: September 28, 2026
Копьев А., JETP Letters 2026 Vol. 123 No. 5 P. 310–316
The incompressible three-dimensional Euler equations develop very thin pancake-like regions of exponen tially increasing vorticity. The characteristic thickness of such regions decreases exponentially with time, while the other two dimensions do not change considerably, making the flow near each pancake strongly anisotropic. The pancakes emerge in increasing number with time, which may enhance the anisotropy ...
Added: September 18, 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
Leon L. Ogorodnikov, Vergeles S. S., Physics of Fluids 2022 Vol. 34 No. 12 Article 125111
We consider analytically velocity pair structure function of turbulent pulsations on the background of a coherent geostrophic vortex in a fast rotating fluid. The statistics of the turbulent pulsations is determined by their dynamics that is the dynamics of inertial waves affected by the differential rotation in the vortex and weak viscous damping. Our consideration ...
Added: December 14, 2022
Копьев А., Zybin K., Сирота В. А. et al., Physics of Fluids 2021 Vol. 33 No. 3 P. 031703–031704
The paper [Djenidi et al., Phys. Fluids 33(3), 031703 (2021)] considers a classical issue of an anomalous scaling of velocity structure functions in a high-Reynolds number turbulent flow. The paper offers a mathematical proof of the ground-breaking result: the intermittency is an artifact of the Reynolds number finiteness. However, the proof contains a technical error that makes ...
Added: November 5, 2021