Mathematical Modeling of Emission in Small-Size Cathode

1. Front Matter

   Pages i-xii

   PDF

2. Introduction

   • Vladimir Danilov, Roman Gaydukov, Vadim Kretov

   Pages 1-10

3. Physical Basis for Field Emission

   • Vladimir Danilov, Roman Gaydukov, Vadim Kretov

   Pages 11-58

4. Mathematical Model

   • Vladimir Danilov, Roman Gaydukov, Vadim Kretov

   Pages 59-130

5. Numerical Simulation and its Results

   • Vladimir Danilov, Roman Gaydukov, Vadim Kretov

   Pages 131-194

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.​

• 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

“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)

• National Research University Higher School of Economics, Moscow, Russia

  Vladimir Danilov, Roman Gaydukov, Vadim Kretov

Vladimir G. Danilov 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.

Roman K. Gaydukov 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.

Vadim I. Kretov 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.  His current research interests include mathematical simulation, field emission, and numerical solution of PDE.

Policies and ethics