scholarly journals Correction to: The Landau Equation with the Specular Reflection Boundary Condition

2021 ◽  
Vol 240 (1) ◽  
pp. 605-626
Author(s):  
Yan Guo ◽  
Hyung Ju Hwang ◽  
Jin Woo Jang ◽  
Zhimeng Ouyang
Keyword(s):  
Boundary Condition ◽  
Specular Reflection ◽  
Landau Equation ◽  
Reflection Boundary

scholarly journals The Landau Equation with the Specular Reflection Boundary Condition

2020 ◽  
Vol 236 (3) ◽  
pp. 1389-1454
Author(s):  
Yan Guo ◽  
Hyung Ju Hwang ◽  
Jin Woo Jang ◽  
Zhimeng Ouyang
Keyword(s):  
Boundary Condition ◽  
Specular Reflection ◽  
Landau Equation ◽  
Reflection Boundary

An inverse problem for the Vlasov–Poisson system

2015 ◽  
Vol 23 (4) ◽  
Author(s):  
Fikret Gölgeleyen ◽  
Masahiro Yamamoto
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Specular Reflection ◽  
Nauk Sssr ◽  
Poisson System ◽  
Local Uniqueness ◽  
Electrical Field ◽  
Stability Theorems ◽  
Akad Nauk Sssr ◽  
Reflection Boundary

AbstractIn this paper, we discuss an inverse problem for the Vlasov–Poisson system. We prove local uniqueness and stability theorems by using the method in Anikonov and Amirov [Dokl. Akad. Nauk SSSR 272 (1983), 1292–1293] under the specular reflection boundary condition and with a prescribed outward electrical field at the boundary.

scholarly journals The model reduction of the Vlasov-Poisson-Fokker-Planck system to the Poisson-Nernst-Planck system via the Deep Neural Network Approach

2021 ◽  
Author(s):  
Jae Yong Lee ◽  
Jin Woo Jang ◽  
Hyung Ju Hwang
Keyword(s):  
Neural Network ◽  
Boundary Condition ◽  
Model Reduction ◽  
Deep Neural Network ◽  
Specular Reflection ◽  
Classical Solutions ◽  
Diffusion Limit ◽  
Flux Boundary Condition ◽  
Bounded Interval ◽  
Fokker Planck

The model reduction of a mesoscopic kinetic dynamics to a macroscopic continuum dynamics has been one of the fundamental questions in mathematical physics since Hilbert's time. In this paper, we consider a diagram of the diffusion limit from the Vlasov-Poisson-Fokker-Planck (VPFP) system on a bounded interval with the specular reflection boundary condition to the Poisson-Nernst–Planck (PNP) system with the no-flux boundary condition. We provide a Deep Learning algorithm to simulate the VPFP system and the PNP system by computing the time-asymptotic behaviors of the solution and the physical quantities. We analyze the convergence of the neural network solution of the VPFP system to that of the PNP system via the Asymptotic-Preserving (AP) scheme. Also, we provide several theoretical evidence that the Deep Neural Network (DNN) solutions to the VPFP and the PNP systems converge to the a priori classical solutions of each system if the total loss function vanishes.

Stoßbestimmte Grenzschicht in einem schwach ionisierten Plasma

1970 ◽  
Vol 25 (4) ◽  
pp. 525-541
Author(s):  
Karl Gerhard Müller ◽  
Peter Wahle
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Velocity Distribution ◽  
Specular Reflection ◽  
Correction Term ◽  
Charge Carriers ◽  
Macroscopic Models ◽  
Basic Set ◽  
Transfer Equations ◽  
Set Up

Abstract In this work we develop a collision-dominated sheath model which includes the well known macroscopic models as extreme cases. We set up a description of the charge carriers with the help of the velocity distribution. In order to fulfil the microscopic boundary conditions at the wall we split up the velocity distributions into two parts. A basic set of new transport equations arises which differ from the usual equations by a correction term in the momentum transfer equations. Because of this splitting up of the velocity distribution we are able to take into account exactly specular reflection of the electrons at the wall. In a good approximation our results can also be obtained from the usual equations, if a suitably fitted factor is introduced into the electron boundary condition. at the wall.

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