Similarly, by taking moments of the entire Boltzmann equation, any number of arbitrary integro-differential equations may be generated,
32.
He starts with the collisionless Boltzmann equation ( sometimes called the Vlasov equation, anachronistically in this context ), in generalized coordinates:
33.
When combining this result for the charge density with the Poisson equation from electrostatics, a form of the Poisson Boltzmann equation results:
34.
The Poisson Boltzmann equation describes a model proposed independently by Louis George Gouy and David Leonard Chapman in 1910 and 1913, respectively.
35.
Letting g = m w _ i, the momentum of the particle, the integrated Boltzmann equation becomes the conservation of momentum equation:
36.
It is possible to write down relativistic Boltzmann equations for relativistic quantum systems in which the number of particles is not conserved in collisions.
37.
PyMOL uses OpenGL Extension Wrangler Library ( GLEW ) and Freeglut, and can solve Poisson Boltzmann equations using the Adaptive Poisson Boltzmann Solver.
38.
The fusion of Chapman's and Enskog's theories later became known as the Chapman Enskog method for solving the Boltzmann equation.
39.
More efficient ways of solving the linearized Poisson Boltzmann equation have also been developed, relying on Feynman " Kac representations of the solutions.
40.
Using the relaxation time approximation for the Boltzmann equation and assuming steady-state conditions, the phonon thermal conductivity ? L can be determined.
