Modeling of CollisionsGauthier-Villars, 1998 - 222 من الصفحات |
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الصفحة 154
... Vlasov Equation . As ɛ → 0 , i.e. N → ∞ , we may extract a subsequence still denoted fe , Eg such that : fe Eε f weakly in measure , uniformly in time , → F locally uniformy . Here ƒ C ( R ; M ( R2d ) ) . F € C ( R + × Rd ) and it ...
... Vlasov Equation . As ɛ → 0 , i.e. N → ∞ , we may extract a subsequence still denoted fe , Eg such that : fe Eε f weakly in measure , uniformly in time , → F locally uniformy . Here ƒ C ( R ; M ( R2d ) ) . F € C ( R + × Rd ) and it ...
الصفحة 155
... Vlasov equation ( 13.7 ) . This means that we incorporate from the beginning a statistical description of the particles . Now fN ( t ) is the probability density of finding the N - particles in the configuration ( XN , SN ) . The first ...
... Vlasov equation ( 13.7 ) . This means that we incorporate from the beginning a statistical description of the particles . Now fN ( t ) is the probability density of finding the N - particles in the configuration ( XN , SN ) . The first ...
الصفحة 156
... Equation rather than the Vlasov Equation , the interaction force in ( 13.6 ) should be scaled like Ɛ ( ) . The most classical case is the Hard Sphere gas which dynamics is described by the free transport x ¿ ( t ) = { i ( t ) , 1≤i≤N ...
... Equation rather than the Vlasov Equation , the interaction force in ( 13.6 ) should be scaled like Ɛ ( ) . The most classical case is the Hard Sphere gas which dynamics is described by the free transport x ¿ ( t ) = { i ( t ) , 1≤i≤N ...
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atomic species BBGKY hierarchy Boltzmann Equation Braginskii charge classical collision frequencies collision integrals collision operator collision terms collisional conservation equation Coulomb logarithms defined diffusion distribution function electric field electron-ion energy equation Enskog equal mass ions equation set equilibrium fluid equations Fokker-Planck Galilean invariance heat flux heavy ions hydrodynamic interaction interdiffusion ion species ionic Landau Lemma limit linear magnetic field Maxwellian distributions Maxwellian estimate mean velocity multi-fluid equations neutral plasma obtained Ohm's law particle Perthame perturbation calculation perturbation equations Phys Plasma Physics quantum Quantum Hydrodynamics Raß relative velocity scalar self-collision T₁ T₂ tensor Theorem thermal transport coefficients transport equations vector viscosity Vlasov Equation Wigner αα αβ Μα тв ть მა