?
Ice-water phase transition on a substrate
Russian Journal of Mathematical Physics. 2023. Vol. 30. No. 2. P. 165–175.
In this paper, we construct and study a model of a phase transition in a system of two
phases (liquid and ice) and three media — water, a piece of ice, and some nonmeltable
solid substrate. Namely, the melting-crystallization process is considered in the problem
of water flow along a small ice irregularity (such as a frozen drop) on a flat substrate for
large Reynolds numbers. The results of numerical simulation are presented.
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
Lerman L. M., Turaev D. V., Regular and Chaotic Dynamics 2026 Vol. 31 No. 3 P. 349–369
We show that bifurcations of four-dimensional symplectic diffeomorphisms with a quadratic homoclinic tangency to a saddle periodic orbit with real multipliers produce 2-elliptic periodic orbits if the tangency is not partially hyperbolic. We show that a normal form for the rescaled first-return maps near such tangency is given by a four-dimensional symplectic H´enonlike map and study bifurcations of the ...
Added: May 15, 2026
Aleskerov F. T., Yakuba V. I., Khutorskaya O. et al., Springer, 2026.
The book contains new models of bibliometric analysis based on centrality measures in network analysis, pattern analysis and stability analysis. A distinctive feature of these centrality measures is that they account for the parameters of vertices and group influence of vertices to a vertex. This reveals specific groups of publications, authors, terms, journals and affiliations ...
Added: May 15, 2026
Kuptsov P., Panyushev A., Stankevich N., Chaos 2026 Vol. 36 No. 5 Article 053138
We develop a machine-learning approach to reproduce the behavior of two versions of the van der Pol oscillator exhibiting a subcritical Andronov–Hopf bifurcation, with or without a codimension-2 Bautin point. We construct a neural-network model that functions as a recur rent map and train it on short segments of oscillator trajectories. The results show that, ...
Added: May 15, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Lebedev V., Journal of Mathematical Analysis and Applications 2026 Vol. 563 No. 2 Article 130787
It is known that for every continuous real-valued
function $f$ on the circle $\mathbb T=\mathbb R/2\pi\mathbb Z$ there exists a
change of variable, i.e., a self-homeomorphism $h$ of $\mathbb T$, such that
the superposition $f\circ h$ is in the Sobolev space $W_2^{1/2}(\mathbb T)$.
We obtain new results on simultaneous improvement of functions by a single
change of variable in relation ...
Added: May 14, 2026
Blokh A., Oversteegen L., Selinger N. et al., Arnold Mathematical Journal 2025 Vol. 12 No. 1 P. 1–40
We describe a model for the boundary of the connectedness locus of the parameter space of cubic symmetric polynomials. We show that there exists a monotone continuous function from the connectedness locus to the model which is a homeomorphism if the former is locally connected. ...
Added: May 13, 2026
Petrov I., Автоматика и телемеханика 2026 № 6 С. 82–118
Системам связанных агентов и сетевому управлению посвящено большое число отечественных и зарубежных исследований. Исторически, наибольший интерес в теории управления возникал к усредняющим системам и, в частности, к задаче консенсуса. Однако сетевое взаимодействие может характеризоваться более специфическими функциями, отражающими зависимость от действий соседей по сети, что особенно явно проявляется в моделях стратегического взаимодействия на сети, которое ...
Added: May 12, 2026
М.: ООО «Макс Пресс», 2026.
В настоящем сборнике представлены тезисы докладов участников семинара "Интеграция основного и дополнительного физико-математического образования", проходившего 11 февраля 2026 года в ГБОУ Школа №2007 ФМШ г. москвы, а также другие публикации, посвящённые вопросам дополнительного физико-математического образования. ...
Added: May 11, 2026
Novikov R., Sivkin V., Inverse Problems 2026 Vol. 42 No. 4 Article 045009
We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for
the Helmholtz equation in an exterior region in Rd, d ⩾ 2. In this region, we consider a hyperplane X with sufficiently large distance s from the origin in Rd. We give two-point local formulas
for approximate recovering the radiation ...
Added: May 11, 2026
Hecht M., Hofmann P., Wicaksono D. et al., IMA Journal of Numerical Analysis 2026 Vol. 00 P. 1–30
Recent advances in Bernstein—Walsh theory have extended Bernstein’s Theorem to multiple dimensions, stating that a multivariate function can be approximated with a geometric rate in a downward-closed polynomial space if and only if it is analytic in a generalized Bernstein polyellipse. To compute approximations of this class of functions—which we term Bos–Levenberg–Trefethen–(BLT) functions—we extend the ...
Added: May 11, 2026
Kelbert M., Kalimulina E. Y., Entropy 2026 Vol. 28 Article 536
We study binary hypothesis testing for i.i.d. observations under a multiplicative context
weight. For the optimal weighted total loss, defined as the sum of weighted type-I and typeII losses, we prove the logarithmic asymptotic L∗n = exp{−nDwC (P,Q) + o(n)}, n →∞, where Dw
C is the weighted Chernoff information. The single-letter form of the exponent
relies on ...
Added: May 7, 2026
Белоусов Н. М., Черепанов Л. К., Деркачов С. Э. et al., Selecta Mathematica, New Series 2026 Vol. 32 Article 44
We prove equivalence of two integral representations for the wave functions of hyperbolic Calogero–Sutherland system. For this we study two families of Baxter operators related to hyperbolic Calogero–Sutherland and rational Ruijsenaars models; the first one as a limit from hyperbolic Ruijsenaars system, while the second one independently. Besides, computing asymptotics of integral representations and also ...
Added: May 6, 2026
Муравьев М. Ю., Annales Mathematiques du Quebec 2025
Recently Rohleder proposed a new variational approach to an inequality between the Neumann and Dirichlet eigenvalues in the simply connected planar case using the language of classical vector analysis. Interpreting his approach in terms of differential forms permits to generalize these results to a much broader context. The spectrum of the absolute boundary problem for ...
Added: May 6, 2026
Цыганов А. В., Порубов Е. О., Теоретическая и математическая физика 2026 Т. 227 № 2 С. 336–355
Теория тензорных инвариантов обыкновенных дифференциальных уравнений и классификация Картана простых алгебр Ли используется для установления изоморфизма задачи Козлова о движении ферромагнетика в магнитном поле и задачи Шоттки о движении четырехмерного твердого тела. Найдены новые полиномиальные и рациональные бивекторы Пуассона, инвариантные либо относительно пары коммутирующих фазовых потоков, либо относительно одного из пары потоков. ...
Added: May 5, 2026
Dmitriev A., Lebedev A., Kornilov V. et al., Frontiers in Physics 2025 Vol. 12 Article 1508465
Our study is based on the hypothesis that stock exchanges, being nonlinear, open and dissipative systems, are capable of self-organization to the edge of a phase transition. To empirically support the hypothesis, we find segments in hourly stock volume series for 3,000 stocks of publicly traded companies, corresponding to the time of stock exchange’s stay ...
Added: January 23, 2025
Gaydukov R., Russian Journal of Mathematical Physics 2025 Vol. 32 No. 3 P. 458–463
Equations of the double-deck boundary layer structure
are obtained in the problem of a flow of a viscous incompressible fluid
around a small irregularity on a curved surface at high Reynolds numbers.
It is shown that due to the chosen coordinate system,
the form of the equations of the double-deck structure
coincides with the previously studied case of a ...
Added: November 2, 2024
Artem A. Krylov, Kovachev S., Radiuk E. et al., Applied Sciences (Switzerland) 2022 Vol. 12 No. 9 Article 4614
The paper is devoted to the problem of numerical modeling of earthquake response of porous saturated soil deposits to seismic waves propagation. Site-specific earthquake response analysis is a necessary and important component of seismic hazard assessment. Accounting for the complex structure of porous saturated soils, i.e., the content in them, in addition to the solid ...
Added: September 30, 2024
Sukhoverkhova D., Shchur L., Письма в Журнал экспериментальной и теоретической физики 2024 Т. 120 № 8 С. 644–649
In this paper, we applied a deep neural network to study the issue of knowledge transferability between statistical mechanics models. The following computer experiment was conducted. A convolutional neural network was trained to solve the problem of binary classification of snapshots of snapshots of the location of spins of the Ising model on a two-dimensional ...
Added: September 25, 2024
Gaydukov R. K., Indian Journal of Pure and Applied Mathematics 2024 P. 1–18
The paper is deals with the heat transfer in the laminar flow of a viscous incompressible fluid along a plate with a small heated localized irregularity. It is well known that double- and triple-deck structures of the boundary layer arise in such flow problems. These structures make it possible, among other things, to describe the phenomenon of ...
Added: May 21, 2024
R. K. Gaydukov, Russian Journal of Mathematical Physics 2024 Vol. 31 No. 2 P. 209–217
The problem of a uniformly rotating disk with slightly perturbed surface immersed in a viscous fluid is considered for large Reynolds numbers. The asymptotic solutions with double-deck structure of the boundary layer are constructed for a non-symmetric irregularity localized on the disk surface. The results of numerical simulation of the flow near the surface are presented. The differences ...
Added: April 18, 2024
Gaydukov R., Сибирские электронные математические известия 2024 Т. 21 № 1 С. 178–187
In this paper we study a Rayleigh-type equation on a semi-infinite cylinder with a Coulomb-type potential.
This equation arises in the double-deck boundary layer structure in the problem of flow induced by a uniformly rotating disk with small periodic irregularities on its surface for large Reynolds numbers. Using combined numerical and analytical approach, the existence of ...
Added: February 17, 2024
R. K. Gaydukov, V. G. Danilov, Computational Mathematics and Mathematical Physics 2024 Vol. 64 No. 6 P. 1317–1325
Mathematical modeling of the ice–water phase transition during liquid flow inside a pipe
with a small ice buildup on the wall at high Reynolds numbers is considered. As a mathematical model
describing the dynamics of the phase transition, a double-deck boundary layer model and a phase field
system are used. Results of numerical simulation are presented. ...
Added: February 17, 2024
Gaydukov R., Russian Journal of Nonlinear Dynamics 2024 Vol. 20 No. 1 P. 113–125
The problem of flow of a non-Newtonian viscous fluid with power-law rheological properties
along a semi-infinite plate with a small localized irregularity on the surface is considered for large
Reynolds numbers. The asymptotic solution with double-deck structure of the boundary layer is
constructed. The numerical simulation of the flow in the region near the surface was performed
for different ...
Added: December 26, 2023