| 11. | Nevertheless, the two equations can be combined to produce the Poisson Boltzmann equation.
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| 12. | Villani received the Fields Medal for his work on Landau damping and the Boltzmann equation.
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| 13. | A special form of the Boltzmann equation
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| 14. | The corresponding Boltzmann equation is given by
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| 15. | If the charge density follows a Boltzmann distribution, then the Poisson-Boltzmann equation results.
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| 16. | Keizer also provided fluctuating generalizations of the Boltzmann equation and of hidrodynamics ( fluctuating hydrodynamics ).
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| 17. | In biophysics and certain surface chemistry applications, it is known simply as the Poisson Boltzmann equation.
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| 18. | However, for an ideal gas the standard Chapman Enskog solution of the Boltzmann equation is highly accurate.
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| 19. | As with any approximate model, the Poisson Boltzmann equation is an approximation rather than an exact representation.
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| 20. | The Poisson Boltzmann equation plays a role in the development of the Debye H�ckel theory of dilute electrolyte solutions.
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