Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation

2019 ◽  
Vol 34 (3) ◽  
pp. 143-150
Author(s):  
Sergey V. Rogasinsky
Keyword(s):  
Boltzmann Equation ◽  
Projection Method ◽  
Orthonormal Basis ◽  
Statistical Modelling ◽  
Hermite Functions ◽  
Nonlinear Boltzmann Equation ◽  
Kinetic Boltzmann Equation ◽  
Relaxation Problem ◽  
Nonlinear Kinetic ◽  
Approximation Of A Function

Abstract The paper is focused on justification of a statistical modelling algorithm for solution of the nonlinear kinetic Boltzmann equation on the base of a projection method. Hermite functions are used as an orthonormal basis. The error of approximation of a function by a partial sum of Hermite functions series is estimated in the L2 norm. The estimates are compared for two variants of the projection method in the case of solutions to the homogeneous gas relaxation problem with a known solution.

scholarly journals Classical Size Effects in Films of n-PbTe

2015 ◽  
Vol 16 (4) ◽  
pp. 661-666
Author(s):  
M.A. Ruvinskii ◽  
B.S. Dzundza ◽  
O.B. Kostyuk
Keyword(s):  
Experimental Data ◽  
Boltzmann Equation ◽  
Seebeck Coefficient ◽  
Cross Section ◽  
Size Effects ◽  
Theoretical Calculations ◽  
Rectangular Cross Section ◽  
Charge Carriers ◽  
Kinetic Boltzmann Equation ◽  
Classical Size

Based on kinetic Boltzmann equation the boundary problem of calculating the conductivity and Seebeck coefficient for a film with a rectangular cross section is solved. Mirror- diffuse mechanism of reflection of the charge carriers from the surfaces of the film is considered. Calculations were performed for different thicknesses nondegenerate semiconductor n-PbTe. A comparison of theoretical calculations with obtained experimental data for vapor-phase condensates based on PbTe is made.

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