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)
Обратная задача для линейной функции фильтрации
2020 · ARTICLE · ru
Задачи фильтрации суспензии в пористой среде описывают закачку жидкого раствора в пористую породу для укрепления рыхлого грунта или создания водонепроницаемых перегородок при строительстве туннелей и подземных сооружений. Суспензия впрыскивается под давлением в пустую однородную пористую среду и движется от входа к выходу. Некоторые частицы застревают в порах и образуют неподвижный осадок. Макроскопическая модель фильтрации включает уравнение баланса масс взвешенных и осажденных частиц и кинетическое уравнение роста осадка. Для одномерной модели с линейной функцией фильтрации строится асимптотическое решение вблизи фронта концентраций взвешенных и осажденных частиц. Малым параметром асимптотики служит характеристическая переменная, пропорциональная расстоянию до фронта концентраций. На основе явных асимптотических формул решается обратная задача фильтрации - нахождение функции фильтрации по заданной концентрации взвешенных частиц на выходе пористой среды. Коэффициенты функции фильтрации находятся методом наименьших квадратов из условия наилучшего приближения асимптотики к численному решению. Показано, что вычисленные параметры близки к коэффициентам модели, а найденная асимптотика хорошо приближает численное решение.
A chemical reaction model in a porous medium
2020 · CHAPTER · en
Chemical reactions in a porous medium are found in many natural phenomena and technological processes. Reactive substances dissolved in groundwater can significantly change the soil strength. The precipitate formed as a result of the reaction changes the porous medium structure and affects the porosity and permeability. A one-dimensional model of the reaction of two reagents in a homogeneous porous medium with a linear reaction function is considered. The model includes the mass balance equations of each reagent and precipitate, and the kinetic equation of precipitate growth. It is assumed that the precipitate is stationary and the growth rate of the precipitate is proportional to the reagents’ concentration. A carrier fluid with constant concentration reagents is injected at the empty porous medium entrance. The reaction front moves in a porous medium at a constant speed. The exact solution to the problem is constructed by eliminating the unknown functions and lowering the equations’ order. A Riemann invariant that relates the concentration of sediment and reagents to the system’s characteristics was found. The reaction’s numerical simulation is performed. It is shown that, for a long time, the reagents’ concentrations and the precipitate tend to final limit values. Sediment profiles always decrease monotonously, and the type of the profiles’ convexity changes.
Filtration of a highly concentrated suspension in a porous medium
2020 · CHAPTER · en
The problems of filtration in porous media are in demand when strengthening foundations and building waterproof walls in rocks. Deep bed filtration of a highly concentrated monodisperse suspension in a homogeneous porous medium with size-exclusion particle retention mechanism is considered. When filtering a suspension in a porous medium, some solid particles get stuck on the porous frame and form a deposit. The concentration of suspended particles injected at the porous medium inlet decreases when moving from inlet to outlet. The mathematical model for a highly concentrated suspension in a porous medium assumes a nonlinear dependence of the deposit growth rate on the concentration of suspended particles. The exact solution to the filtration problem in implicit integral form and the Riemann invariant relating the concentrations of suspended and retained particles are obtained. The problem is solved for a linear filtration function and a general nonlinear concentration function. An asymptotic solution is constructed near the concentrations front of suspended and retained particles. It is shown that the asymptotics is close to the exact solution, the error decreases with increasing order of asymptotic expansions. The asymptotic solution explicitly defines the dependence of the solution on model parameters and can be used to solve the inverse filtration problem.
EXACT SOLUTION FOR DEEP BED FILTRATION WITH FINITE BLOCKING TIME
2020 · ARTICLE · en
An initial-boundary value problem for a quasilinear system describing deep bed ltra- tion of a monodisperse suspension in a medium with pores of various sizes is investigated analytically. The ltration function is assumed to have power-law type while tending to zero with the power index lower than one. We found that this assumption has two consequences: (i) the blocking time is nite, and (ii) the characteristics issuing from the points where the retained particle concentration reaches its maximum are not uniquely determined. The exact solution is constructed by a modi ed method of characteristics, which removes the ambiguity by using an additional blocking line equation derived from the original problem. The weak singularity of the solution on the blocking line is described. A simple sucient coecient condition for the unique solvability of the problem is derived.
DETERMINING THE LENGMUR COEFFICIENT OF THE FILTRATION PROBLEM
2020 · ARTICLE · en
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.
Exact upscaling for transport of size distributed colloids
2019 · ARTICLE · en
The article investigates one‐dimensional (1D) suspension‐colloidal transport of size distributed particles with particle attachment. A population balance approach is presented for computing the particle transport and capture by porous media. The occupied area of each attached particle is particle‐size dependent. The main model assumption is the retention‐rate dependency of the overall vacancy concentration for all particle sizes. For the first time, we derive an exact averaging (upscaling) procedure resulting in a closed system of large‐scale equations for average concentrations of suspended and retained particles, and of occupied rock surface area. The resulting large‐scale 3x3 system significantly differs from the traditional 2x2 deep bed filtration model. However, the traditional model becomes a particular case that corresponds to an equal occupied area for all particles. The averaging yields the appearance of two empirical suspension and site‐occupation functions, which govern the kinetics of particle retention and site occupation, respectively. 1D flow problems for the averaged equations are essentially non‐linear. However, they allow for exact solutions. We derive novel exact solutions for three 1D problems: continuous injection of particulate colloidal suspension, injection of colloidal suspension bank with particle‐free chase drive, and fines migration induced by high‐rate flows. The analytical model for continuous injection closely matches three series of laboratory tests on nano‐fluid transport.
Задача фильтрации суспензии в пористой среде с осадком
2019 · ARTICLE · ru
Рассматривается макроскопическая модель долговременной глубинной фильтрации моно- дисперсной суспензии в пористой среде с механико-геометрическим механизмом захвата взвешенных частиц при отсутствии мобилизации осажденных частиц. Предполагается, что доступность пор и фракционный поток частиц зависят от концентрации осадка, и в началь- ный момент пористая среда содержит неравномерно распределенный осадок. Результатом работы является нахождение аналитического решения вблизи подвижной криволинейной границы – фронта концентрации взвешенных частиц суспензии. Доказана знакоопределен- ность решения. Точное решение задачи фильтрации на криволинейной границе найдено в явном виде. Получено достаточное условие существования решения на фронте концентра- ции. В окрестности границы построено асимптотическое решение. Временной интервал применимости асимптотики определяется на основе численного расчета задачи.
On a Deep Bed Filtration Problem with Finite Blocking Time
2019 · ARTICLE · en
We consider an initial{boundary value problem for a simple semilinear ltration equation with nonunique characteristics and prove that uniqueness nevertheless holds for the solution of this problem. The solution is then constructed by quadratures.
Problem of Deep Bed Filtration in a Porous Medium with the Initial Deposit
2019 · ARTICLE · en
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 deposit. The aim of the study is to find the analytical solution in the neighborhood of a mobile curvilinear boundary, namely, of the suspended-particle concentration front. The property of having fixed sign is proved for the solution. The exact solution of the filtration problem on the curvilinear front is found in explicit form. The sufficient condition of existence of the solution on the concentration front is obtained. An asymptotic solution is constructed in the neighborhood of the front. The time interval of applicability of asymptotics is determined from the numerical solution.
Global asymptotics of filtration in porous media
2019 · CHAPTER · en
Filtration problems are actual for the design of underground structures and foundations, strengthening of loose soil and construction of watertight walls in the porous rock. A liquid grout pumped under pressure penetrates deep into the porous rock. Solid particles of the suspension retained in the pores, strengthen the loose soil and create watertight partitions. The aim of the study is to construct an explicit analytical solution of the filtration problem. A one-dimensional model of deep bed filtration of a monodisperse suspension in a homogeneous porous medium with size-exclusion mechanism of particles retention is considered. Solid particles are freely transferred by the carrier fluid through large pores and get stuck in the throats of small pores. The mathematical model of deep bed filtration includes the mass balance equation for suspended and retained particles and the kinetic equation for the deposit growth. The model describes the movement of concentrations front of suspended and retained particles in an empty porous medium. Behind the concentrations front, solid particles are transported by a carrier fluid, accompanied by the formation of a deposit. The complex model has no explicit exact solution. To construct the asymptotic solution in explicit form, methods of nonlinear asymptotic analysis are used. The new coordinate transformation allows to obtain a parameter that is small at all points of the porous sample at any time. In this paper, a global asymptotic solution of the filtration problem is constructed using a new small parameter. Numerical calculations are performed for a nonlinear filtration coefficient found experimentally. Calculations confirm the closeness of the asymptotics to the solution in the entire filtration domain. For a nonlinear filtration coefficient, the asymptotics is closer to the numerical solution than the exact solution of the problem with a linear coefficient. The analytical solution obtained in the paper can be used to analyze solutions of problems of underground fluid mechanics and fine-tune laboratory experiments.
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