Talk:Reaction–diffusion system

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[edit] This is an important concept which needs work

Reaction-diffusion systems, reaction-diffusion models, and the reaction-diffusion equation are very important concepts. We definitely need a good article about these. For now, I redirected reaction-diffusion system and reaction-diffusion equation to reaction-diffusion, as I think this article can explain them all. Oleg Alexandrov (talk) 00:34, 28 January 2007 (UTC)

[edit] Extension of the article

I made a large number of changes and extensions to the article.

Some important points are the following:

From a systematic point of view, it seems more reasonable to distinguish between the number of components of the reaction-diffusion system rather than the spatial dimension although the latter also plays a role for the existence of certain phenomena.

Concerning one-component systems, I added some mathematical details on the existence of a Liapunov functional as well as on stability considerations. Maybe I could plot an image of the mechanical analogue of one-component 1d systems.

Two-component systems, in particular the important Turing instability, are now treated in more detail. I had to adapt the original formulae a bit to match the new ones, but there are no drastic changes. The two new galleries for the Turing instability and other patterns should hopefully make the results more illustrative. Should I give the parameters for the calculation?

I also extended the Applications section. In the part Experiments I added comments on "real life" reaction-diffusion systems. I am not entirely sure whether the sentence "Simple reaction–diffusion-like patterns can be generated in many image editing programs by repeated applications of sharpening and blurring" is not misleading, so I took it out. The described procedure of repeated Fourier filtering and potentially other operations (diffusion = multiplication with -k^2) will probably not lead to a true reaction-diffusion-like process, but maybe some expert can comment on this point.

Last but not least, a number of reference was given, it would certainly be nice if additional ones could be added.

Dr. Hendrik U. Boedeker 13:50, 6 July 2007 (UTC)

That's excellent, well done. Yes, I do think that you should give the parameters. It should be possible for others to reproduce the picture. Personally, I'm curious about the details of the computation because I'm evaluating different methods for simulating RD systems: what numerical method did you use? What grid size? (Very roughly) how long did the computation take and up to which t did you integrate?

But most importantly, thanks very much for your contribution. -- Jitse Niesen (talk) 21:45, 6 July 2007 (UTC)

Alright, I will add the parameters at the beginning of next week when I am back at my institute. I used Comsol 3.3 to produce data for the figures. The program has an adaptive time step selection such that the calculations in 2d take about 2 to 30 minutes on a 3GHz Xeon processor with 4 GB RAM, depending on whether the system converges to a stationary state or not. I used about 20000 nodes for the finite element discretisation. In addition, I also checked the results by comparing with self-written C code using a finite-difference scheme and code I wrote in Matlab (basically, I only exploited the functions for the inversion of tridiagonal matrices). As I did not yet have time to implement an adaptive time step control into my code in either case, the calculation naturally took significantly longer, in particular in Matlab. An implicit time stepping method brought an improvement by about a factor of 3, but Comsol is still faster. I found however that a great advantage of the self-written finite-difference scheme is that spatio-temporal fluctuations are much easier to implement, in particular if one is interested in quantitative results depending on their properties. In this case, I was forced to use an explicit time step procedure for stochastic integration. I hope that could help you a bit. Best,

Dr. Hendrik U. Boedeker 15:06, 7 July 2007 (UTC)

Jitse Niesen reverted my addition of a reaction-diffusion-like image, with the comment: "just because the pictures look similar does not mean that there is a connection (also see talk page); if there is a connection, then please provide a reference)"

Sorry about that Jitse, I thought that looking similar was all that was required to be an example of "reaction-diffusion-like"?

I don't think there is any academic literature about this out there (it's just something I figured out myself) so maybe it will have to stay off the RD page. I wonder if I might instead add it to the 'pattern formation' page though?

Danwills 08:46, 5 September 2007 (UTC)

The main reason why I removed it is that Hendrik removed a similar text before, as he says above (by the way, I wanted to remove both the picture and the text). I think that the Gaussian blur can be considered as diffusion, but the sharpening does not seem to have the form of a reaction term. I guess you could put it in pattern formation, though I would be happier if there were actually a source to go with it (and I think it's quite likely there is a paper on this, though I cannot find one quickly). -- Jitse Niesen (talk) 12:30, 5 September 2007 (UTC)

Ah no worries.. you're certainly correct that sharpening is different from reaction in RD, though obviously that isn't very important in terms of pattern formation because it still generates the same kind of "turing pattern". I will put a 'computer graphics' section on pattern formation and link the image there instead. Thanks for your rigor Jitse! -- Danwills 06:34, 6 September 2007 (UTC)

[edit] Underline or bold?

I am a molecular biologist so I may be wrong but in the intro the diagonal matrix is underlined and I was under the impression when you write on paper and pen you underline as making the character bold would require a thicker pen, which is instead done when typed. --Squidonius (talk) 17:09, 19 May 2008 (UTC)