/sci/ - Science & Math

[Anonymous No.6683426]

Is a lightning characterized by a "random walk"?

[Anonymous No.6683441]

more like a path of least resistance

[Anonymous No.6683442]

The process is highly complicated, but we can make some identifications.

The motion of charged particles making up the lightning is described by a Boltzmann equation (with chemical coupling for the ionization) and I think if you look at the situation more statically* you can in first order reduce it to a Fokker Planck-like expression.
By the Feynman–Kac formula, you have a broad relation between stochastic processes and differential equations, so you can identify the second order constant (often "D") with random motion.

http://en.wikipedia.org/wiki/Feynman%E2%80%93Kac_formula

Note however, that it's not a free random walk as in babbies first simulation. Im particlular, the motion is directed and the first order term corresponds to the drift arising from the field generated by the charged cloud.

http://en.wikipedia.org/wiki/Fokker%E2%80%93Planck_equation#One_dimension
http://en.wikipedia.org/wiki/Electron_mobility

*If you're interested in the actual breakdown (which is nonlinear and what you describe via Fokker Planck), look at the Townsend model first

http://en.wikipedia.org/wiki/Townsend_discharge#General_description_of_the_phenomenon

and for actual lightning models you need Boltzmann and then streamer theory for the photons.

[Anonymous No.6683444]

The process is highly complicated, but we can make some identifications.
The motion of charged particles making up the lightning is described by a Boltzmann equation (with chemical coupling for the ionization) and I think if you look at the situation statically* you can in first order reduce it to a Fokker Planck-like expression.
Note however, that it's not a free random walk as in the first simulations you usually make. In particular, the motion is directed and the first order term corresponds to the drift arising from the field generated by the charged cloud.
By the Feynman–Kac formula, you have a broad relation between stochastic processes and differential equations, so you can identify the second order constant (often "D") with random motion.

http://en.wikipedia.org/wiki/Fokker%E2%80%93Planck_equation#One_dimension
http://en.wikipedia.org/wiki/Electron_mobility
http://en.wikipedia.org/wiki/Feynman%E2%80%93Kac_formula

*If you're interested in the actual breakdown (which is nonlinear and what you describe via Fokker Planck), look at the Townsend model first. And for actual lightning models you need Boltzmann and then "streamer theory" for the photons.