Mathematical Modeling of Emission in Small-Size Cathode

Beschreibung

This book deals with mathematical modeling, namely, it describes the mathematical model of heat transfer in a silicon cathode of small (nano) dimensions with the possibility of partial melting taken into account.  This mathematical model is based on the phase field system, i.e., on a contemporary generalization of Stefan-type free boundary problems. The approach used is not purely mathematical but is based on the understanding of the solution structure (construction and study of asymptotic solutions) and computer calculations. The book presents an algorithm for numerical solution of the equations of the mathematical model including its parallel implementation. The results of numerical simulation concludes the book. The book is intended for specialists in the field of heat transfer and field emission processes and can be useful for senior students and postgraduates.
This book deals with mathematical modeling, namely, it describes the mathematical model of heat transfer in a silicon cathode of small (nano) dimensions with the possibility of partial melting taken into account.  This mathematical model is based on the phase field system, i.e., on a contemporary generalization of Stefan-type free boundary problems. The approach used is not purely mathematical but is based on the understanding of the solution structure (construction and study of asymptotic solutions) and computer calculations. The book presents an algorithm for numerical solution of the equations of the mathematical model including its parallel implementation. The results of numerical simulation concludes the book. The book is intended for specialists in the field of heat transfer and field emission processes and can be useful for senior students and postgraduates.
Describes a mathematical model of heat transfer in a silicon cathode of small (nano) dimensions Presents an algorithm for numerical solution of the equations of the mathematical model including its parallel implementation Intended for specialists in the field of heat transfer and field emission processes

Autor*in

Vladimir Danilov

Themen in »Mathematical Modeling of Emission in Small-Size Cathode«

Thermo-field emission Heat transfer Melting and solidification Phase-field system Numerical simulation Nottingham effect Stefan-Gibbs-Thomson problem Specific conductance Electron heat conductivity Support function in metals Electron tunneling Hugoniot-type conditions Heat conduction equation

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“The intended audience for this book includes researchers and specialists working in the field of electron emission processes and heat transfer, but this book also contains many details from the point of view of modeling and the corresponding mathematical architecture that may be useful for advanced students and postgraduates.” (Federico Zullo, Mathematical Reviews, March, 2021)

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