Modeling of CollisionsGauthier-Villars, 1998 - 222 من الصفحات |
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الصفحة 150
... satisfies the estimate ( 12.29 ) and Q ( f ) 1 + f € L∞ ( R + ; L1 ( R4 × K ) ) ( 12.31 ) for any compact set K of Rd . and + · V2 ) B ( f ) = B ′ ( ƒ ) Q ( ƒ ) in E. ( + + ) B ( 5 ) B ′ ( ƒ ) Q ( ƒ ) in D ' ( R2d × R + ) ( 12.32 ) for ...
... satisfies the estimate ( 12.29 ) and Q ( f ) 1 + f € L∞ ( R + ; L1 ( R4 × K ) ) ( 12.31 ) for any compact set K of Rd . and + · V2 ) B ( f ) = B ′ ( ƒ ) Q ( ƒ ) in E. ( + + ) B ( 5 ) B ′ ( ƒ ) Q ( ƒ ) in D ' ( R2d × R + ) ( 12.32 ) for ...
الصفحة 154
... satisfies , in the distribution sense , მ § afe + E. V2fe + Ee · Våƒe = 0 , N ( 13.10 ) 1 Ee ( t , x ) = Σε ( π - π ; ( t ) ) = N j = 1 = √zdxza E ( x − y ) fe ( t , y , E ) dy dɛ . ( 13.11 ) This is exactly the Vlasov Equation . As ...
... satisfies , in the distribution sense , მ § afe + E. V2fe + Ee · Våƒe = 0 , N ( 13.10 ) 1 Ee ( t , x ) = Σε ( π - π ; ( t ) ) = N j = 1 = √zdxza E ( x − y ) fe ( t , y , E ) dy dɛ . ( 13.11 ) This is exactly the Vlasov Equation . As ...
الصفحة 155
... satisfies ( 13.13 ) and N N + Σ§i · Vx9N + ΣF ( t , xi ) · V§ , 9N = 0 . agN at i = 1 i = 1 ( 13.14 ) The reason why ( 13.12 ) and ( 13.14 ) are close , which means in principle ƒÑ ~ 9N , is that , as N → ∞ , - Xi N √2ve | E ( M ) ...
... satisfies ( 13.13 ) and N N + Σ§i · Vx9N + ΣF ( t , xi ) · V§ , 9N = 0 . agN at i = 1 i = 1 ( 13.14 ) The reason why ( 13.12 ) and ( 13.14 ) are close , which means in principle ƒÑ ~ 9N , is that , as N → ∞ , - Xi N √2ve | E ( M ) ...
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appear approximation assumed atomic average Boltzmann Equation calculation chapter charge classical close collision frequencies collision terms collisional computed conservation consider correct Coulomb logarithms coupled defined density depend developed diffusion distribution function effect electrons energy equal equilibrium estimate existence expressions finally fluid flux formula frame given gives heat heavy hydrodynamic integrals interaction ion species ionic kinetic light limit linear mass Maxwellian mean mean velocity momentum multi-fluid neutral Note numerical obtained operator parameter particle particular perturbation perturbation equations Phys physics plasma pressure problem properties quantities quantum quantum mechanical reduced reference relations relative satisfies scalar single solution solved temperature tensor theory thermal transport coefficients transport equations vector αβ Μα