Re: Streamer simulation

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

Original poster: "Jim Lux" <jimlux-at-earthlink-dot-net> 

But is it really fractal, in that it has self similarity at all scales, or
is it just reflective of a cellular automata?  I'll grant it's fractal-like
or fractal-appearing, but isn't the core of fractal-ness that there's some
generator that keeps getting applied at successively smaller scales.  I'm
not sure that spark/streamer growth fits in that category.  For instance,
trees or roots can be modeled at some scales very effectively by fractals,
but that doesn't mean that the underlying physics is fractal.  For dendritic
stream drainages, which are very well represented by fractals, there is some
physics (at the macro level) that is self similar.

Hmmm.. I suppose then, just like crystal dendrites, the process is self
similar at a fairly fine scale (much finer than the eventual product...)

Must go read up on this..

----- Original Message -----
From: "Tesla list" <tesla-at-pupman-dot-com>
To: <tesla-at-pupman-dot-com>
Sent: Wednesday, September 24, 2003 4:46 PM
Subject: Re: Streamer simulation


 > 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 --
 > --
 > --------------------------------------------------------------------
 > We specialize in UNIQUE items! Coins shrunk by Ultrastrong Fields,
 > Lichtenberg Figures (electrical discharges in acrylic), & Scarce OOP
 > Technical Books. Stoneridge Engineering -- http://www.teslamania-dot-com
 > --------------------------------------------------------------------
 >
 > 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)
 > >
 > >.
 >
 >
 >
 >