Кузьмина Людмила Ивановна
Московский институт электроники и математики им. А.Н. Тихонова
Профессиональные интересы
Должности
- Доцент — Московский институт электроники и математики им. А.Н. Тихонова, Департамент прикладной математики
Био
- · Начала работать в НИУ ВШЭ в 2012 году.
- · Научно-педагогический стаж: 49 лет.
Образование
- 1994 · Ученое звание: Доцент
- 1986 · Кандидат физико-математических наук: Ленинградский государственный университет им. А.А. Жданова, специальность 01.00.00 «Физико-математические науки», тема диссертации: Дифракция поверхностных волн на вертикальных преградах
- 1980 · Аспирантура: Ленинградский государственный университет им. А.А. Жданова, специальность «дифференциальные уравнения и математическая физика»
- 1976 · Специалитет: Ленинградский государственный университет им. А.А. Жданова, специальность «Прикладная математика», квалификация «Математик»
- 1976 · Специалитет: Ленинградский государственный университет им. А.А. Жданова, факультет: прикладной математики-процессов управления, специальность «прикладная математика»
Опыт работы
- · 2012: НИУ ВШЭ с года
Награды и поощрения
- · Почетная грамота Министерства науки и высшего образования Российской Федерации (декабрь 2024)
- · Благодарственное письмо первого проректора НИУ ВШЭ (январь 2021)
- · Почетная грамота Высшей школы экономики (декабрь 2017)
- · Благодарность Высшей школы экономики (июнь 2014)
- · Надбавка за публикацию в международном рецензируемом научном издании (2022–2023, 2020–2022, 2019–2020, 2018–2020)
- · Надбавка за регулярные публикации в международных рецензируемых научных изданиях (2025–2030, 2023–2028, 2021–2022)
- · Надбавка за статью в зарубежном рецензируемом журнале (2014–2016)
- · Надбавка за статью в зарубежном рецензируемом научном издании (2016–2018)
- · Лучший преподаватель — 2022, 2015–2017
Конференции (15)
Показать все
- · 2021: Innovations and Technologies in Construction (BUILDINTECH BIT 2021) (Белгород). Доклад: Filtration of 2-particles suspension in a porous medium
- · 2020: VII International Scientific Conference "Integration, Partnership and Innovation in Construction Science and Education" (IPICSE 2020) (Ташкент). Доклад: Asymptotics of inverse filtration problem in porous media
- · 2020: XXIII International Scientific Conference on Advance in Civil Engineering: "CONSTRUCTION - THE FORMATION OF LIVING ENVIRONMENT" (FORM-2020) (Ханой). Доклад: Filtration of a highly concentrated suspension in a porous medium
- · 2019: XXII International Scientific Conference “Construction the Formation of Living Environment” (FORM-2019) (Ташкент). Доклад: Global asymptotics of filtration in porous media
- · 2019: XXVIII R-S-P Seminar «Theoretical Foundation of Civil Engineering» (Жилина). Доклад: Particle Capture in Porous Medium
- · 2018: XXVII R-S-P Seminar, Theoretical Foundation of Civil Engineering (27RSP) (Ростов-на-Дону). Доклад: Deep bed filtration with multiple pore-blocking mechanisms
- · 2018: XXI International Scientific Conference on Advanced in Civil Engineering (FORM 2018) (Москва). Доклад: Particle transport in a porous medium with initial deposit
- · 2018: VII International Symposium Actual Problems of Computational Simulation in Civil Engineering (Новосибирск). Доклад: Modelling uniform asymptotics of the filtration problem in a porous medium
- · 2017: XXVI R-S-P Seminar 2017 Theoretical Foundation of Civil Engineerin (Варшава). Доклад: Filtration model of the unsteady suspension flow in a porous medium
- · 2016: XXV Russian-Slovak-Polish seminar «Theoretical Foundation of Civil Engineering» (Жилина). Доклад: Deep Bed Filtration Asymptotics at the Filter Inlet
- · 2016: 5th International Scientific Conference “Integration, Partnership and Innovation in Construction Science and Education” (Москва). Доклад: Calculation of filtration of polydisperse suspension in a porous medium
- · 2015: XXIV Russian-Slovak-Polish seminar (24RSP) «Theoretical Foundation of Civil Engineering» (Самара). Доклад: Asymptotic solution for deep bed filtration with small deposit
- · 2014: 3rd International scientific-practical conference «Innovative Information Technologies» (Прага). Доклад: Learning Management System Lms In Mathematical University Courses
- · 2013: Х Международная научная конференция "Новые информационные технологии и менеджмент качества" (Белек). Доклад: Система управления обучением LMS в преподавании математических дисциплин
- · 2013: XX Всероссийская научно-методическая конференция "Телематика 2013" (Санкт-Петербург). Доклад: Использование системы LMS для контроля знаний по математическим дисциплинам: возможности и проблемы
Идентификаторы исследователя
- ORCID:
0000-0002-6551-733X - ResearcherID:
K-5547-2015 - SPIN РИНЦ:
6746-8613 - Google Scholar: https://scholar.google.ru/citations?user=QhVshaMAAAAJ&hl=ru&citsig=AMstHGT9sENG2XgE0QEZidveOuaIfuutIA
- Scopus AuthorID:
56104145400
Публикации (82)
GLOBAL ASYMPTOTICS OF THE FILTRATION PROBLEM IN A POROUS MEDIUM
2019 · ARTICLE · en
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 which the filtering process takes place. The obtained asymptotics is close to the numerical solution.
Particle Capture in Porous Medium
2019 · CHAPTER · en
Filtration problems in porous media are important for studying the movement of groundwater in porous formations and the spreading of liquid concrete injected into porous soil. Deep bed filtration of a monodisperse suspension in a homogeneous porous medium with two simultaneously acting particle capture mechanisms is considered. A mathematical model of suspension flow through porous medium with pore blocking by size-exclusion and arched bridging is developed. Exact solutions are obtained on the concentration front and at the porous medium inlet. For the linear filtration function, exact and asymptotic solutions are constructed.
Calculation of Long-Term Filtration in a Porous Medium
2018 · ARTICLE · en
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 size-exclusion mechanism of pore blocking: solid particles pass freely through large pores and get stuck at the inlet of pores smaller than the diameter of the particles. A one-dimensional mathematical model for the filtration of a monodisperse suspension includes the equation for the mass balance of suspended and retained particles and the kinetic equation for the growth of the deposit. For the blocking filtration coefficient with a double root, the exact solution is given implicitly. The asymptotics of the filtration problem is constructed for large time. The numerical calculation of the problem is carried out by the finite differences method. It is shown that asymptotic approximations rapidly converge to a solution with the increase of the expansion order.
Analytical model for deep bed filtration with multiple mechanisms of particle capture
2018 · ARTICLE · en
model for deep bed filtration of a monodisperse suspension in a porous medium with multiple geometric particle capture mechanisms is considered. It is assumed that identical suspended particles can block pores of different sizes. The pores smaller than the particle size are clogged by single particles; if the pore size exceeds the diameter of the particles, it can be blocked by bridging— several particles forming various stable structures. An exact solution is obtained for constant filtration coefficients. Exact solutions for non-constant filtration functions are obtained on the concentrations front of the suspended and retained particles and at the porous medium inlet. Asymptotic solutions are constructed near these lines. For small and close to constant filtration functions, global asymptotic solutions are obtained. A basic model with two mechanisms of particle capture is studied in detail. Asymptotic solutions are compared to the results of numerical simulation. The applicability of various types of asymptotics is analyzed.
Deep bed filtration with multiple pore-blocking mechanisms
2018 · CHAPTER · en
A one-dimensional model for the deep bed filtration of a monodisperse suspension in a porous medium with variable porosity and permeability and multiple pore-blocking mechanisms is considered. It is assumed that the small pores are clogged by separate particles; pores of medium size, exceeding the diameter of the particles, can be blocked by arched bridges, forming stable structures at the pore throats. These poreblocking mechanisms - size-exclusion and different types of bridging act simultaneously. Exact solutions are obtained for constant coefficients, on the concentrations front and at the porous medium inlet.
Particle transport in a porous medium with initial deposit
2018 · CHAPTER · en
Modelling of the suspended particles transport in a porous medium is used in the analysis of methods for strengthening foundations. To strengthen the porous soil, a low concentration cement-based grout is pumped into it under pressure. The suspension is filtered in a porous medium and fills the cavity of the soil. Grains of the grout are distributed along the network structure of the porous medium and strengthen the soil. The transfer of particles by a flow of a carrier fluid is accompanied by an uneven formation of a deposit on the porous medium frame. The purpose of the paper is to determine the mobile two-phase boundary between water and the particles during the injection of a suspension into a porous medium and to obtain an analytical solution of the nonlinear filtration problem for a general case of variable porosity and permeability. The mathematical model of one-dimensional deep bed filtration with size-exclusion particles retention includes the equations of mass balance and kinetic rate of a deposit and unsteady boundary conditions with unknown dimensionless concentrations of suspended and retained particles. Methods of non-linear asymptotic analysis are used to obtain the analytical solution and to construct an asymptotics near the porous medium inlet. The asymptotics is determined on the basis of a local exact solution of the problem. It is shown that the mobile two-phase boundary moves with variable speed. At the boundary of two phases, the concentration of suspended particles is discontinuous, and the concentration of retained particles is continuous and loses its smoothness. The exact explicit formula for the two-phase boundary and its asymptotics in a form convenient for calculations are obtained. An exact solution is obtained on the boundary of the porous medium and the asymptotics of the filtration problem is constructed near the porous medium inlet. Numerical calculation of the asymptotic solution is performed; graphs of the dependence of concentrations on time and coordinate are presented. In contrast to the numerical solution, analytical methods make it possible to determine the dependence of the solution of the filtration problem on the controlled external parameters. This allows the construction engineers to choose the best size of injected grout grains and the properties of the carrier fluid, optimize the filtration process and form a grouted porous soil of the required strength and density.
Modelling uniform asymptotics of the filtration problem in a porous medium
2018 · CHAPTER · en
The solution of the filtration problem allows calculating the injection of the grout into a loose ground to create a solid foundation. The basic deep bed filtration model of a monodisperse suspension in a porous medium is considered. Based on the synthesis of the standard asymptotic solution for a short time and the asymptotics of the filtration problem for a long time, a uniform asymptotic solution is constructed. A numerical calculation shows that the asymptotics is close to the solution for any time.
Calculation of two-size particles filtration in a porous medium
2018 · CHAPTER · en
Filtration describes a variety of the construction complex problems: strengthening loose soil to create a solid foundation, the movement of groundwater with solid impurities near underground structures, and many others. A model of two-sized deep bed filtration particles moving with different velocities in a porous medium with three-size pores is considered. The competition of pores and various size particles for deposit formation is modeled. Solutions are constructed at the porous medium inlet and on the concentrations front of the fast particles. For constant filtration coefficients, a global exact solution is obtained. Numerical calculation illustrates the evolution of the filtration process.
Расчёт фильтрации с двумя механизмами захвата частиц
2017 · ARTICLE · ru
Рассматривается модель фильтрации суспензии в пористой среде с двумя механизмами захвата частиц. Отдельные частицы задерживаются порами малых размеров, на крупных порах осаждаются группы частиц, образующие устойчивые конструкции в виде сводовых перемычек. В предположении линейности коэффициентов фильтрации построено точное и асимптотическое решение задачи и выполнен численный расчет асимптотики на выходе пористой среды.
A Model of Two-Velocity Particles Transport in a Porous Medium
2017 · ARTICLE · en
A one-dimensional flow of suspension with two types of solid particles moving with different velocities in a porous medium is considered. A mathematical model of deep bed filtration which generalizes the known equations of mass balance and particle capture kinetics for a flow of fluid with identical particles is developed. The exact solution is evaluated at the filter inlet and on the concentration front of fast suspended and retained particles, asymptotic solutions are provided in certain vicinities of these lines. A global asymptotic solution to the problem with a small limit deposit is constructed. The asymptotics rapidly converges to the numerical solution.
Курсы (3)
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Математический анализ · 5 раза
2025/2026, 2024/2025, 2023/2024, 2022/2023, 2021/2022 · Бакалавриат / Специалитет · рус
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Дифференциальные уравнения · 2 раза
2024/2025, 2022/2023 · Бакалавриат · рус
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Теория функций комплексного переменного
2022/2023 · Бакалавриат · рус