Re: Streamer simulation

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: Bert Hickman <bert.hickman-at-aquila-dot-net> 

Jim and Antonio,

Lightning, Lichtenberg Figures, and streamers all appear to be forms of 
fractals that seem to be characterized by Diffusion Limited Aggregation 
(DLA). For an example of a computer model that uses a DLA algorithm to 
model growth to form a Lichtenberg Figure before your eyes, check out:
http://apricot.ap.polyu.edu.hk/~lam/dla/dla.html

Per the author, the algorithm is very simple: "We start with an immobile 
seed on the plane. A walker is then launched from a random position far 
away and is allowed to diffuse. If it touches the seed, it is immobilized 
instantly and becomes part of the aggregate. We then launch similar walkers 
one-by-one and each of them stops upon hitting the cluster. After launching 
a few hundred particles, a cluster with intricate branch structures results."

You can see the shallow angles (mentioned by Dr. Resonance in a previous 
post) formed between most of the branches in this model as well.

Best regards,

-- Bert --
-- 
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Tesla list wrote:

>Original poster: "Jim Lux" <jimlux-at-earthlink-dot-net>
>----- Original Message -----
>From: "Tesla list" <tesla-at-pupman-dot-com>
>To: <tesla-at-pupman-dot-com>
>Sent: Monday, September 22, 2003 6:29 PM
>Subject: Re: Streamer simulation
>
>  > Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br>
>  >
>  > Tesla list wrote:
>  >  >
>  >  > Original poster: Jim Lux <jimlux-at-earthlink-dot-net>
>  >  >
>  >  > I don't know that a fractal model is optimum (streamer development
>isn't
>  >  > scale independent, like fractals are), but some sort of cellular
>automata
>  >  > model might be...
>  >
>  > Journal of Physics D: Applied Physics 34 (2001) 936-946.
>  > "Simulation of breakdown in air using cellular automata with streamer
>  > to leader transition".
>  > Has nice plots of simulated streamers. The references mention several
>  > papers about the fractal nature of streamers.
>I see that my random thoughts have been anticipated...
>  >
>  >  > Essentially, you've got chunks of air that are in one of three
>states...
>  >  > nothing, streamer growing, and streamer fully formed, and then they get
>  >  > connected in an essentially random (tree structured) way.  The physics
>  >  > going on at the tip of the streamer is pretty much the same, whether
>it's
>  >  > at the end of a 10cm streamer or a 1m streamer.  Likewise, what's going
>on
>  >  > inside the developed streamer is essentially the same regardless of
>where
>  >  > along the streamer it is.
>  >
>  > The idea in the paper appears to be similar.
>I'll have to get it tomorrow at work...
>The cellular automata thing is nifty because it can be made very
>computationally efficient (as opposed to a big FEM grid or a 2.5 D sim)
>
>.