Re: Streamer simulation

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

Original poster: Peter Lawrence <Peter.Lawrence-at-Sun.COM> 


Jim,
     fractal is a mathematical concept that involves the infinitely small,
in the real world as we know it this is impossible, once you get down to
the scale of molecules and atoms whatever macroscopic structure you were
originally looking at disappears. When people talk about fractals in
nature they really mean when observed at some limited number of scales
things look similar.

Most of the mathematical fractal objects we think we've "seen" are actually
the limit of an infinite sequence of objects, each with finer detail than its
predecessor, and there is no way to actually "see" the limit.

Lightening can appear fractal, and we can describe it as such, even though
we know that electrons themselve cannot be divided down into finer structure.

I suspect that off-topic posts have a fractal nature too, but now thats
"really" getting off-topic :-)))))

-Pete Lawrence.




 >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)
 > > >
 > > >.
 > >
 > >
 > >
 > >
 >
 >