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Mathematical Modeling of Emission in Small-Size Cathode [electronic resource] / by Vladimir Danilov, Roman Gaydukov, Vadim Kretov.

By: Danilov, Vladimir [author.].
Contributor(s): Gaydukov, Roman [author.] | Kretov, Vadim [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Heat and Mass Transfer: Publisher: Singapore : Springer Nature Singapore : Imprint: Springer, 2020Edition: 1st ed. 2020.Description: XII, 194 p. 77 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9789811501951.Subject(s): Mathematical physics | Thermodynamics | Heat engineering | Heat transfer | Mass transfer | Optical materials | Semiconductors | Microtechnology | Microelectromechanical systems | Theoretical, Mathematical and Computational Physics | Engineering Thermodynamics, Heat and Mass Transfer | Optical Materials | Semiconductors | Microsystems and MEMSAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 530.1 Online resources: Click here to access online
Contents:
1 Introduction -- 2 Physical basis for field emission -- 3 Mathematical model -- 4 Numerical simulation and its results.
In: Springer Nature eBookSummary: 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.
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1 Introduction -- 2 Physical basis for field emission -- 3 Mathematical model -- 4 Numerical simulation and its results.

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.

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