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Mathematical Modeling of Emission in Small-Size Cathode


Mathematical Modeling of Emission in Small-Size Cathode


Heat and Mass Transfer

von: Vladimir Danilov, Roman Gaydukov, Vadim Kretov

96,29 €

Verlag: Springer
Format: PDF
Veröffentl.: 17.09.2019
ISBN/EAN: 9789811501951
Sprache: englisch

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Beschreibungen

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.​
1 Introduction.- 2 Physical basis for field emission.- 3 Mathematical model.- 4 Numerical simulation and its results.
<p><b>Vladimir G. Danilov</b> received the Ph.D. degree from the Moscow Institute of Electronics and Mathematics, Moscow, Russia, in 1976, and the D.Sci. degree from Moscow State University, Moscow, in 1990. He is currently a Professor with the National Research University Higher School of Economics, Moscow. His current research interests include linear and nonlinear problems of PDE, asymptotic methods, and mathematical simulation.</p>

<b>Roman K. Gaydukov </b>received the M.S. degree from the Moscow Institute of Electronics and Mathematics, Moscow, Russia, in 2012, and the Ph.D. degree from National Research University Higher School of Economics, Moscow, Russia, in 2016. He is currently an Associate Professor with the National Research University Higher School of Economics, Moscow. His current research interests include asymptotic methods, mathematical and numerical simulation, field emission, fluid mechanics and boundary layer theory.<div><p><b>Vadim I. Kretov</b> received the M.S.degree from the Moscow Institute of Electronics and Mathematics, Moscow, Russia, in 2008, and the Ph.D. degree from National Research University Higher School of Economics, Moscow, Russia, in 2019.&nbsp; His current research interests include mathematical simulation, field emission, and numerical solution of PDE.<br></p><br></div>
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. &nbsp;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

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