Distribution function of random strains in an elastically anisotropic continuum and defect strengths of Tm3+ impurity ions in crystals with zircon structure

2017 ◽  
Vol 96 (1) ◽  
Author(s):  
B. Z. Malkin ◽  
N. M. Abishev ◽  
E. I. Baibekov ◽  
D. S. Pytalev ◽  
K. N. Boldyrev ◽  
...  
Keyword(s):  
Distribution Function ◽  
Zircon Structure ◽  
Impurity Ions

scholarly journals Study of up–down poloidal density asymmetry of high- impurities with the new impurity version of XGCa

2019 ◽  
Vol 85 (5) ◽  
Author(s):  
J. Dominski ◽  
C. S. Chang ◽  
R. Hager ◽  
P. Helander ◽  
S. Ku ◽  
...  
Keyword(s):  
Distribution Function ◽  
Friction Force ◽  
Balance Equation ◽  
Numerical Data ◽  
Force Balance ◽  
Viscous Force ◽  
Plasma Transport ◽  
Particle In Cell ◽  
Impurity Ions ◽  
Force Balance Equation

Addition of multispecies impurity ions to the total-f gyrokinetic particle-in-cell code XGCa is reported, including a cross-verification of neoclassical physics against the NEO code. This new version of the neoclassical gyrokinetic code XGCa is used to benchmark and confirm the previous reduced-equation-based prediction that high- $Z$ impurity particles in the Pfirsch–Schlüter regime can exhibit a significant level of up–down poloidal asymmetry, through the large parallel friction force, and thus influence the radial plasma transport significantly. The study is performed in a plasma with weak toroidal rotation. In comparison, when the impurity particles are in the plateau regime, the up–down poloidal asymmetry becomes weak, with the parallel friction force becoming weaker than the parallel viscous force. It is also found that the linearization of the perturbed distribution function, based on the small poloidal asymmetry assumption, can become invalid. Using the numerical data from XGCa, each term in the parallel fluid force-balance equation have been analysed to find that both the main ions and the electrons respond to the poloidal potential variation adiabatically when the high- $Z$ tungsten possesses large poloidal variation.

Influence of extinction phenomenon on determination of the orientation distribution function

2006 ◽  
Vol 2006 (suppl_23_2006) ◽  
pp. 175-180
Author(s):  
G. Gómez-Gasga ◽  
T. Kryshtab ◽  
J. Palacios-Gómez ◽  
A. de Ita de la Torre
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Orientation Distribution

The Approximation of Sum of Independent Distributions by the Erlang Distribution Function

2002 ◽  
Vol 7 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Antanas Karoblis
Keyword(s):  
Distribution Function ◽  
Exponential Distribution ◽  
Queueing Theory ◽  
Erlang Distribution ◽  
Estimation Of Error

The exponential distribution and the Erlang distribution function are been used in numerous areas of mathematics, and specifically in the queueing theory. Such and similar applications emphasize the importance of estimation of error of approximation by the Erlang distribution function. The article gives an analysis and technique of error’s estimation of an accuracy of such approximation, especially in some specific cases.

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