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## DETERMINING THE LENGMUR COEFFICIENT OF THE FILTRATION PROBLEM

International Journal for Computational Civil and Structural Engineering. 2020. Vol. 16. No. 4. P. 50-56.

Kuzmina L., Osipov Y. V.

Filtration of suspension in a porous medium is actual in the construction of tunnels and underground structures.

A model of deep bed filtration with size-exclusion mechanism of particle capture is considered. The inverse filtration

problem – finding the Langmuir coefficient from a given concentration of suspended particles at the porous medium outlet is solved using the asymptotic solution near the concentrations front. The Langmuir coefficient constants are obtained by the least squares method from the condition of best approximation of the asymptotics to exact solution. It is shown that the calculated parameters are close to the coefficients of the model, and the asymptotics well approximates the exact solution.

Kuzmina L., Osipov Y. V., Vetoshkin N. V., International Journal for Computational Civil and Structural Engineering 2018 Vol. 14 No. 1 P. 92-101

The filtration problem in a porous medium is an important part of underground hydromechanics. Filtration of suspensions and colloids determines the processes of strengthening the soil and creating waterproof walls in the ground while building the foundations of buildings and underground structures. It is assumed that the formation of a deposit is dominated by the ...

Added: July 1, 2018

Kuzmina L., Osipov Y., MATEC Web of Conferences 2016 Vol. 86 No. 01005 P. 1-5

The problem of filtering the suspension in a porous medium is considered. The proposed model for the transport of particles of different sizes is a generalization of deep bed filtration model for a monodisperse suspension with size-exclusion particle capture mechanism. Exact and asymptotic solutions are constructed at the filter inlet and on the concentration front ...

Added: November 28, 2016

Kuzmina L., Osipov Y. V., Zheglova Y. G., International Journal for Computational Civil and Structural Engineering 2019 Vol. 15 No. 2 P. 77-85

Filtration of the suspension in a porous medium is important when strengthening the soil and creating
watertight partitions for the construction of tunnels and underground structures. A model of deep bed filtration
with variable porosity and fractional flow, and a size-exclusion mechanism of particle retention are considered.
A global asymptotic solution is constructed in the entire domain in ...

Added: July 7, 2019

Kuzmina L., Osipov, Y. V., Gorbunova, T., Applied Mathematics and Mechanics (English Edition) 2021 Vol. 42 No. 1 P. 109-126

A model for deep bed filtration of a polydisperse suspension with small
impurities in a porous medium is considered. Different suspended particles move with
the same velocity as the carrier water and get blocked in the pore throats due to the
size-exclusion mechanism of particle retention. A solution of the model in the form of a
traveling wave is ...

Added: January 7, 2021

Galaguz Y. P., Kuzmina L., Osipov Y. V., Fluid Dynamics (РФ) 2019 Vol. 54 No. 1 P. 85-97

The macroscopic model of long-term deep-bed filtration flow of a monodisperse suspension through a porous medium with size-exclusion particle-capture mechanism and without retained-particle mobilization is considered. It is assumed that the pore accessibility and the fractional particle flux depend on the deposit concentration and at the initial time the porous medium contains a nonuniformly distributed ...

Added: June 7, 2019

Protasov V., Mathematics of Computation 2017 Vol. 86 No. 305 P. 1499-1524

For an arbitrary set of nonnegative integers, we consider the Euler binary partition function which equals the total number of binary expansions of an integer with ``digits'' from . By applying the theory of subdivision schemes and refinement equations, the asymptotic behaviour of as is characterized. For all finite , we compute the lower and upper exponents of growth of , find when ...

Added: May 11, 2017

Grushin V. V., Наноструктуры. Математическая физика и моделирование 2012 Т. 7 № 2 С. 17-44

В работе получено асимптотическое разложение собственных значений оператора Лапласа с нулевыми данными Дирихле в бесконечных трубках, т. е. в бесконечных изогнутых цилиндрах с внутренним кручением при равномерном сжатии поперечных сечений, по малому параметру, характеризующему поперечные размеры трубки. Аналогичное разложение получено для оператора Шредингера с учетом магнитного поля для конечных изогнутых трубок. Предложен метод сведения задачи ...

Added: December 24, 2012

Kuzmina L., Osipov Y. V., International Journal for Computational Civil and Structural Engineering 2016 Vol. 12 No. 3 P. 145-150

Filtration problem of suspension with identical particles in a porous medium is considered. Physical and mathematical models for size-exclusion capture mechanism of suspended particles at the inlet of filter pores are presented. An exact solution is constructed for the forward and back flow of suspension in a porous medium in case of linear filtration coefficient. ...

Added: December 26, 2016

Gaydukov R., European Journal of Mechanics - B/Fluids 2021 Vol. 89 P. 401-410

An asymptotic solution with double-deck boundary layer structure is constructed for the problem of an incompressible fluid flow along a semi-infinite plate with small localized or periodic (fast-oscillating) irregularities on the surface whose shape depends on time. Numerical simulation of flow in the near-plate region is presented for two types of the shape change: oscillations of the ...

Added: January 4, 2021

Grushin V. V., Математические заметки 2017 Т. 102 № 6 С. 816-827

Asymptotic formulas are obtained for a class of integrals that are Fourier transforms of rapidly oscillating functions. These formulas contain special functions and generalize the well-known method of stationary phase. ...

Added: January 13, 2018

V'yugin V., М.: МЦНМО, 2013

Книга предназначена для первоначлаьного знакомства с математическими основами современной теории машинного обучения (Machine Learning) и теории игр на предсказания. В первой части излагаются основы статистической теории машинного обучения, рассматриваются задачи классификации и регрессии с опорными векторами, теория обобщения и алгоритмы построения разделяющих гиперплоскостей. Во второй и третьей частях рассматриваются задачи адаптивного прогнозирования в нестохастических теоретико-игровой ...

Added: July 9, 2014

Madera A. G., Journal of Engineering and Applied Sciences 2019 Vol. 14 No. 23 P. 8786-8796

Thermal processes in electronic systems are stochastic and nonlinear. The stochasticity of thermal processes in electronic systems can be caused by both external stochastic environmental factors and internal stochastic factors of the electronic systems. Methods existing in the literature allow modeling thermal processes caused only by external stochastic factors. At the same time, there are ...

Added: November 6, 2019

Inverse problems in Pareto’s demand theory and their applications to analysis of stock market crises

Klemashev N., Shananin A. A., Zhang S., Journal of Inverse and Ill-posed problems 2016 Vol. 26 No. 1 P. 95-108

We develop an approach to analysis of stock market crises based on the generalized nonparametric method. The generalized nonparametric method is based on solvability and regularization of ill-posed inverse problem in Pareto's demand theory. Our approach allows one to select a few companies that may be considered as the main reason for the crisis. We ...

Added: March 5, 2019

Ziyadin S., Streltsova E., Borodin A. I. et al., Sustainability 2019 No. 11(9) P. 1-16

This article is devoted to the creation of intelligent modelling tools for decision support in the evaluation of intellectual projects submitted for financing, as based on qualitatively defined characteristics. The economic and mathematical models that form the basis of the toolkit are constructed using the mathematical apparatus of fuzzy logic, which allows for the description ...

Added: May 15, 2019

Utenkov V. M., Shirshov A. G., Bykov P. et al., Journal of Machinery Manufacture and Reliability 2017 Vol. 46 No. 6 P. 589-595

A procedure for the computer-aided modeling of the side surface of a milled groove is presented. The procedure is based on dissecting the groove surface with parallel planes and building 2D sections in each of these planes. The mathematical model used for the purpose makes it possible to separately account for the shifts and tilts ...

Added: November 29, 2019

Korotyaev E., Functional Analysis and Its Applications 2019 Vol. 53 No. 3 P. 174-181

We give a complete solution to the inverse problem for finite Jacobi operators with matrix-valued coefficients. ...

Added: February 5, 2021

Chernyshev V. L., Minenkov D., Nazaikinskii V., Functional Analysis and Its Applications 2016 Vol. 50 No. 4 P. 291-307

We find the asymptotics of the element counting function for an additive arithmetic semigroup with exponential growth of the counting function of prime generators. ...

Added: October 18, 2015

Isozaki H., Korotyaev E., Journal of Geometric Analysis 2020 Vol. 30 P. 4427-4452

We consider an inverse problem for Laplacians on rotationally
symmetric manifolds, which are finite for the transversal
direction and periodic with respect to the axis of the manifold,
i.e., Laplacians on tori. We construct an infinite dimensional
analytic isomorphism between the space of profiles (the radius of
the rotation) of the torus and the spectral data as well as the
stability ...

Added: February 5, 2021

Fonaryova A., Gaydukov R., Russian Journal of Mathematical Physics 2021 Vol. 28 No. 2 P. 224-243

A subsonic flow of a viscous compressible fluid in a two-dimensional channel with small periodic or localized irregularities on the walls for large Reynolds numbers is considered. A formal asymptotic solution with double-deck structure of the boundary layer is constructed. A nontrivial time hierarchy is discovered in the decks. An analysis of the scales of irregularities at ...

Added: March 22, 2021

Kuzmina L., Осипов Ю., Вестник Московского государственного строительного университета 2014 № 7 С. 34-40

A classic pursuit problem is studied in which two material points - a Pursuer and a Pursued - move in a plane at constant speeds. The velocity vector of the Pursued does not change its direction and the velocity vector of the Pursuer turns and always aims at the Pursued. If the Pursuer moves at ...

Added: August 3, 2014

Kuzmina L., Осипов Ю., International Journal for Computational Civil and Structural Engineering 2017 Т. 13 № 1 С. 63-68

Filtration of the suspension in a porous medium with a geometric particle capture mechanism is considered. The porous medium has an initial deposit unevenly distributed across the filter. The nonlinear model of deep bed filtration suggests that the porosity and permeability of the porous medium depend on the deposit. The asymptotics of the movable boundary ...

Added: January 6, 2018

Kuzmina L., Osipov Y., MATEC Web of Conferences 2017 Vol. 117 No. 00097 P. 1-6

The study of filtration of the suspension in a porous medium is a vital problem in the design and construction of tunnels and hydraulic structures. An exact solution is constructed for an unsteady flow of a monodisperse suspension in a homogeneous porous medium with sizeexclusion mechanism for particle retention. The concentrations of suspended and precipitated ...

Added: September 7, 2017

Kuzmina L., Osipov Y. V., Вестник Московского государственного строительного университета 2017 No. 11 P. 1278-1283

Subject: a groundwater filtration affects the strength and stability of underground and hydro-technical constructions. Research objectives: the study of one-dimensional problem of displacement of suspension by the flow of pure water in a porous medium. Materials and methods: when filtering a suspension some particles pass through the porous medium, and some of them are stuck ...

Added: January 6, 2018

Kuzmina L., Osipov Y. V., Tzariova V., , in: IOP Conference Series: Materials Science and Engineering 1030 (2021) VII International Scientific Conference "Integration, Partnership and Innovation in Construction Science and Education" (IPICSE 2020) 11th-14th November 2020, Tashkent, Uzbekistan. Vol. 1030: VII International Scientific Conference "Integration, Partnership and Innovation in Construction Science and Education" (IPICSE 2020) 11th-14th November 2020, Tashkent, Uzbekistan.: IOP Publishing, 2021.. Ch. 012109. P. 1-7.

Filtration problems arise in the design of tunnels and underground structures. A onedimensional
filtration model of a monodisperse suspension in a homogeneous porous medium
is considered. For a general nonlinear filtration function, an asymptotic solution is constructed
behind the concentrations front of suspended and retained particles. It is shown that the
asymptotics is close to the numerical solution. Comparison ...

Added: July 3, 2021