• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • Mathematical Modeling of Field Emission From a Microscale-Size Cathode to a Vacuum
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
May 25, 2026
HSE Scientists Train Neural Network to 'Hear' Faults in Electric Motors
Researchers at the AI and Digital Science Institute of the HSE Faculty of Computer Science have developed a new method—the Signature-Guided Data Augmentation (SGDA) framework—that achieves 99% accuracy in motor fault detection and 86% accuracy in fault classification. The application of this approach can reduce industrial equipment repair costs, minimise downtime, and improve production safety. The study results have been published in Engineering Applications of Artificial Intelligence.
May 25, 2026
'The Humanities Serve as a Conscience'
Maria Mizernaia studies Soviet literature and the history of book publishing. In this interview for the HSE Young Scientists project, she discusses plans to publish a novel about besieged Leningrad, AI-provoked reflections on what it means to be human, and how novels can help satisfy our dopamine hunger.
May 25, 2026
Is It Possible to Predict a Citys Life Based on the Shape of Its Neighbourhoods?
Is it possible to predict, based on the configuration of streets and buildings, where a café will open or where traffic congestion will occur? Participants in the Spatial Analysis and Modelling of Urban Processes research and study group use open data and machine learning to identify universal patterns. Alexander Sheludkov and Eduard Somov discuss the purpose of comparing cities, the need for new forms of urban statistics, and how open data is transforming approaches to urban studies.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Mathematical Modeling of Field Emission From a Microscale-Size Cathode to a Vacuum

IEEE Transactions on Electron Devices. 2025. Vol. 72. No. 3. P. 1462–1468.
Danilov V., Borisov V.

In this article, we propose a numerical method for calculating solutions of the PDE (the heat equation for the cathode temperature and the continuity equation for the current density inside and outside the cathode) with discontinuous flux at the emission surface of a cathode placed in a vacuum. The discontinuity of the flux appears because of the Nottingham effect and tunneling of emitting electrons. In the present article, this approach is applied to mathematical modeling of field emission from a conic silicon cathode of small size (about ten micrometers) to a vacuum, but can be used in other problems with similar types of flux jumps.

Research target: Physics
Language: English
Full text
DOI
Keywords: numerical simulationчисленное моделированиеуравнение теплопроводностиfield emissionНеявная схемаgeneralized solutionполевая эмиссияexplicit numerical schemeheat conduction equationimplicit numerical schemeобобщенное решение
Publication based on the results of:
Advanced materials and technologies (2025)
Similar publications
Электростатически управляемый контроль диссипации в двумерном наноэлектромеханическом резонаторе через напряжение-амплитудный антагонизм с рекордной 928% подстройкой добротности.
Arutyunov K., JIANG1 Q., FANG J. et al., Science China Information Sciences 2026 Vol. 69 No. 6 P. 1–11
Resonators based on nanoelectromechanical systems (NEMS) using two-dimensional (2D) materials with high-quality factors and excellent electrical control are critical for tunable coherent phonon dynamics, resonant sensors and wireless communications. However, their performance is fundamentally limited by the lack of a unified framework governing energy dissipation mechanisms and their electrical tunability. Here, we synergistically modulate both ...
Added: May 28, 2026
Enhanced Terahertz Thermoelectricity Via Engineered Van Hove Singularities and Nernst Effect in Moiré Superlattices
Gayduchenko I., Advanced Functional Materials 2026 P. 1–10
Thermoelectric materials, long explored for energy harvesting and thermal sensing, convert heat directly into electrical signals. Extending their application to the terahertz (THz) frequency range opens opportunities for low-noise, bias-free THz detection, yet conventional thermoelectrics lack the sensitivity required for practical devices. Thermoelectric coefficients can be strongly enhanced near van Hove singularities (VHS), though these ...
Added: May 28, 2026
Non-linear in-band interference cancellation on base of conjugate gradients method
Degtyarev A., Bakhurin S., Yudin N., DSPA 2026 P. 1–6
This paper investigates one possible solution to the problem of self-interference cancellation (SIC) arising in the design of in-band full-duplex (IBFD) communication systems. Self-interference cancellation is performed in the digital domain using multilayer nonlinear models adapted via gradient-based optimization. The presence of local minima and saddle points during the adaptation of multilayer models limits the ...
Added: May 26, 2026
Ising models on the hydrogen peroxide and other lattices
Qian X., Deng Y., Shchur L. et al., Physica A: Statistical Mechanics and its Applications 2026 Vol. 696 P. 1–13
We perform a Monte Carlo analysis of the Ising model on many three-dimensional lattices. By means of finite-size scaling we obtain the critical points and determine the scaling dimensions. As expected, the critical exponents agree with the three-dimensional Ising universality class for all models. The irrelevant field, as revealed by the correction-to-scaling amplitudes, appears to ...
Added: May 24, 2026
Оптические методы детектирования единичных биомолекул: визуализация, сенсорика, секвенирование молекул ДНК
Melentiev P. N., Калмыков А. С., Гритченко А. С. et al., Успехи физических наук 2024 Т. 194 № 11 С. 1130–1145
Представлен краткий обзор достигнутого уровня оптических методов детектирования единичных молекул в биомедицинских приложениях. Показано, что регистрация флуоресценции единичных молекул красителей, ковалентно связанных с антителами (биомолекулами), совместно с использованием современных методов нанофотоники может быть применена для решения различных задач в биологии и медицине: визуализации биомолекул, токсинов, вирусных частиц, определения ультранизких концентраций аналитов напрямую во взятой пробе, ...
Added: May 21, 2026
VACUUM DISCHARGE DRIVEN BY STRIPE LINE STORAGE AS A SOURCE OF EUV RADIATION
Antsiferov P.S., Stepanov L.V., Matiukhin N. D., Review of Scientific Instruments 2025 Vol. 96 No. 12 Article 123506
The article presents the discharge plasma based source of extreme ultraviolet (EUV) radiation. The discharge circuit has been driven by means of stripe line storage with working voltage 10.5 kV. The main feature of the proposed source is that plasma electrons acquire the energy, necessary for the production of multiply charged ions with ionization potentials ...
Added: May 20, 2026
Регистрация спектров на 6.65 метровом ВУФ-УФ спектрометре с помощью многоканального детектора
Анциферов П. С., Степанов Л. В., Матюхин Н. Д., Оптика и спектроскопия 2026 Т. 134 № 2 С. 214–218
Сообщено о разработке системы регистрации спектров на ПЗС-линейке для уникального ВУФ спектрометра, построенного на основе сферической дифракционной решетки с радиусом 6.65 m. Была использована линейка HAMAMATSU S11156-2048-02, которая устанавливалась по касательной к окружности Роуланда с возможностью механического перемещения для сканирования спектра. Были получены спектрограммы в диапазоне длин волн 2130-2270 Angstrem. Описана методика сшивки регистрируемых спектральных ...
Added: May 20, 2026
ML-based Fast Simulation of FARICH Responses
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
On a Possible Method for Separating CO Lines from the Spectrum of the Cosmic Microwave Background
Malinovsky A. M., Пилипенко С. В., Mikhalchenko A. O. et al., Astronomy Reports 2026 Vol. 70 P. 1–6
Radiation from rotational transitions of CO molecules in distant galaxies creates a chaotic background with an intensity reaching 1000 Jy/sr at a wavelength of approximately 1 mm. This background will pose a serious problem, when measuring spectral distortions of the cosmic microwave background, in particular, the mu-distortion, which presumably has an intensity of less than ...
Added: May 19, 2026
Broadband photoluminescence of epitaxial bismuth nanowires and planar nanostructures
Kaveev A. K., Fedorov V. V., Pavlov A. V. et al., Journal of Materials Chemistry C 2026 Vol. 14 No. 7 P. 2697–2705
Bismuth nanostructures represent a promising material platform for semiconductor nanooptoelectronics and colorimetry owing to the multi-colored light reflection and quantum confinement. In this work, we study the photoluminescent properties of bismuth nanostructures grown using molecular beam epitaxy on the planar CaF2/Si(111) surface. We demonstrate the different surface morphologies of Bi, ranging from planar films obtained ...
Added: May 19, 2026
STM study of single phosphorus incorporation into silicon by heating PBr3 on Si(100)
Pavlova T., V.M. Shevlyuga (Шевлюга В. М., Applied Surface Science 2026 Vol. 736 P. 166813–166813
The objective of miniaturizing doped areas in silicon, with the ultimate goal of achieving atomic-precision doping, requires a fundamental understanding of the dopant incorporation process at the atomic level. We present a combined scanning tunneling microscopy (STM) and density functional theory (DFT) investigation of single phosphorus atom incorporation into the Si(100) surface. Phosphorus was supplied ...
Added: May 19, 2026
Single-photon diamond sources created by nature
Pasternak D., Romshin A., Khmelnitsky Р. et al., Carbon 2026 Vol. 256 Article 121655
A single-photon source (SPS) is a key component required for quantum communication devices. We report the discovery of bright diamond-based SPS created by nature. It is shown that narrow (≤2 nm) lines observed in the 500-800 nm range in photoluminescence (PL) spectra of the surface layer of untreated Yakut diamonds rich in nitrogen and hydrogen are linked to ...
Added: May 19, 2026
Optical features of nanoplatelets modified with chiral ligands
A.M. Smirnov, Kurtina D. A., Saitov S. R. et al., Optical Materials: X 2026 Vol. 30 Article 100441
Chiral semiconductor nanostructures and nanoparticles are promising materials for applications in biological sensing, enantioselective separation, photonics, and spin-polarized devices. Here we performed a detailed analysis of optical properties of chiral CdSe nanoplatelets with thickness of 2 and 3 monolayers (ML) with Nacetyl-L-cysteine ligands. We studied the absorption spectra peculiarities, analyzed time-resolved photoluminescence and investigated circular ...
Added: May 18, 2026
Temperature-driven charge transport in annealed CdSe/CdS nanoplatelets film
Saitov S. R., Saidzhonov B. M., Vasiliev R. B. et al., Journal of Applied Physics 2026 Vol. 139 No. 18 Article 185702
This work presents a comprehensive investigation into the temperature-dependent thermally stimulated conductivity and photoconductivity of vacuum-annealed thin films based on core–shell CdSe/CdS nanoplatelets passivated with oleic acid ligands. Controlled thermal annealing under vacuum conditions leads to a substantial increase in both dark and photoinduced conductivity, which is primarily attributed to partial desorption of the ligands. ...
Added: May 18, 2026
Направленность вывода излучения из кольцевых микролазеров с нарушенной вращательной симметрией
Масютин Д. А., Moiseev E., Komarov S. et al., Письма в Журнал технической физики 2026 Т. 52 № 7 С. 27–30
Исследованы инжекционные полупроводниковые микролазеры с кольцевым резонатором радиусом 15 мкм с несимметричным расположением внутреннего отверстия резонатора. Показано, что асимметрия обеспечивает формирование в диаграмме направленности двух лепестков излучения, разориентированных на 50° относительно оси смещения внутреннего отверстия. Измеренная добротность резонаторов сопоставима с добротностью дисковых резонаторов и находится на уровне ∼ 10^6. ...
Added: May 18, 2026
Plasmonic Au-Assisted g-C3N4/CeO2 Heterojunction for Enhanced Photocatalytic Breakdown of Organic Pollutants
Rathish S., Andrey S. Vasenko, Thazhathenair A. et al., The Journal of Physical Chemistry Letters 2026 Vol. 17 No. 18 P. 5386–5394
We demonstrate and rationalize the effect of Au nanoparticles (NPs) on the hierarchical g-C3N4/CeO2 heterojunction. g-C3N4/CeO2 decorated with monodispersed plasmonic Au NPs was synthesized. Detailed analyses showed that CeO2 nanocubes and monodispersed Au NPs were evenly distributed over the 2D g-C3N4 surface, forming a robust interface enriched with abundant active sites. The structure enabled efficient separation of photogenerated charge ...
Added: May 16, 2026
The origin of enhanced photocatalytic performance in titanium dioxide via niobium doping: From experimental assessments to DFT insights
Paul R., Das A., Sharma N. et al., Colloids and Surfaces A: Physicochemical and Engineering Aspects 2026 Vol. 728 Article 138830
Niobium-doped TiO2 (Nb-TiO2), demonstrates dual functionality as an efficient photocatalyst for dye degradation and a promising photoelectrocatalyst for water oxidation. Nb incorporation via a facile hydrothermal method was confirmed by XRD (Rietveld refinement), XPS, TEM, FT-IR, Raman, and BET analyses, indicating successful lattice doping and structural modification. Photocatalytic dye degradation experiments were conducted using a model ...
Added: May 16, 2026
Perturbation theory for phase correlations of a light wave propagating in a turbulent medium
I. V. Kolokolov, V. V. Lebedev, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 113 No. 5 Article 054117
We theoretically investigate the correlation functions of the phase of a light wave propagating through a turbulent medium. We use an equation for the logarithm of a wave packet envelope, which includes a secondorder nonlinear term. Based on this equation, we develop a diagrammatic technique to calculate corrections to the correlation function obtained in the linear approximation. We ...
Added: May 15, 2026
KdV-like soliton gas: similarity and difference in integrable and non-integrable models
Didenkulova E., Flamarion M., Pelinovsky E., Physica D: Nonlinear Phenomena 2025 Vol. 481 Article 134815
A comparison of the statistical characteristics of a rarefied soliton gas is carried out within the framework of integrable and non-integrable equations from the Korteweg-de Vries (KdV) hierarchy. As examples, multi-soliton solutions of the modified KdV equation, and the modular Schamel equation are considered. A common property of the dynamics of bipolar solitons is the ...
Added: March 11, 2026
Fundamental hydrodynamic breathers on standing waves
He Y., Slunyaev A., Mori N. et al., Physica D: Nonlinear Phenomena 2026 Vol. 488 Article 135098
Extreme wave localizations in nonlinear dispersive media, arising from modulation instability in weakly nonlinear wave interactions, can be effectively modeled by breather solutions. These breathers are exact solutions of the nonlinear Schrödinger equation and provide accurate models for understanding and controlling unidirectional rogue wave dynamics in numerical simulations or laboratory settings. A recent study by Y. He et ...
Added: February 12, 2026
Planning Problem for Continuous-Time Finite State Mean Field Game with Compact Action Space
Averboukh Y., Volkov A., Dynamic Games and Applications 2024 Vol. 14 P. 285–303
The planning problem for the mean field game implies that one tries to transfer the system of infinitely many identical rational agents from the given distribution to the final one using the choice of the terminal payoff. It can be formulated as the mean field game system with the boundary condition only on the distribution. ...
Added: June 27, 2025
Numerical simulation of lightning channel reactivation in recoil leader process
D.I. Iudin, N.L. Aleksandrov, Syssoev A. A. et al., Atmospheric Research 2025 Vol. 323 Article 108187
Lightning development involves transient events that produce non-stationary, abrupt changes in lightning structure. The most prominent (and most studied) examples of reactivation of lightning side branches are recoil leaders that are initiated near the tips of previously decayed positive leader channels. This study proposes a numerical model that, among other things, takes into account evolution ...
Added: May 8, 2025
Dynamics of Irregular Wave Fields in the Schamel Equation Framework
Flamarion M. V., E. Pelinovsky, E. Didenkulova, Physics of Wave Phenomena 2025 Vol. 33 No. 1 P. 9–19
The present paper is devoted to the study of the dynamics of narrowband wave fields within the nonintegrable Schamel equation, which plays an important role in plasma physics, wave dynamics in metamaterials, and electrical circuits. A Monte Carlo approach is used to obtain a large number of random independent realizations of the wave fields, allowing for an investigation ...
Added: March 23, 2025
Моделирование микрополосковой антенной решетки с использованием пакета CST MWS
Уткин М. В., Grachev N. N., Utkin B. et al., В кн.: Инновационные, информационные и коммуникационные технологии. Сборник трудов XХ Международной научно-практической конференции.: Ассоциация выпускников и сотрудников ВВИА им. проф. Жуковского, 2024. С. 237–242.
The paper focuses on the numerical simulation of an antenna array using the CST MWS package. Special attention is given to the selection of the array elements' constructive parameters, such as dielectric permittivity, emitter radius, and spacing between elements, as well as the computation of the radiation pattern. The analysis emphasizes the width of the ...
Added: February 17, 2025
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit