Mod-01 Lec-32 Turing patterns: Instability in reaction-diffusion systems

Multiphase flows:Analytical solutions and Stability Analysis by Prof. S.Pushpavanam,Department of Chemical Engineering,IIT Madras.For more details on NPTEL visit nptel.ac.in

[@celle678]

Great video, thanks for recording and uploading!

[@gonzalofdc3151]

Great lecture. Thanks for uploading

[@iitphd]

thanks

[@mohitoness]

Thanks for the great video. I didn't get why the solution u tilde(x, t) = u*exp(sigma*t)sin(alpha*x)?

[@Eldooodarino]

+mohitoness He does two things. (1) linearize, (2) Fourier expand the linear system. Then you compute the growth rate as a function of wave number. ("alpha" is the wave number.) If he had motivated the Fourier transform more clearly it would have been clear that the form of the linearized equations demands the form chosen but he sort of sloughed over a lot of details. He kind of knew where he was going but I don't think he did a great job of describing what he was doing. He could have derived a pair of linear 1st order ordinary differential equations for each wave number. The solutions of each of the linear ordinary differential equations will either grow or decay exponentially for each wave number. He is looking for a wave number for which the solution will grow while it decays for all other wave numbers. Then presumably the growing "mode" would result in nonuniform solution which is often called a "pattern."

[@irbinb.llanqui2423]

+Eldooodarino Could you give me some references to understand the Fourier Expand for this sort of solution. Actually I am interested in solution of form exp(ikx + sigma*t). Thanks

[@laurette1717]

A linear constant-coefficient ODE in t has a set of basic solutions exp(sigma t), where sigma can be real or imaginary or complex. Similarly, a linear constant-coefficient PDE in x and t has solutions exp(sigma t + ikx). Constants sigma and k can be real or imaginary or complex and this is determined by boundary/initial conditions. For example, if one requires solutions that are bounded for all x, then k must be real (so that ik is imaginary).

[@Teknotronik7]

Gracias

[@sujitkumarpradhan6076]

can you explain why instability leads turing pattern? Does it work on human or not? if not then ehy?

[@jonathannaffrichoux5399]

If You do not have instability everything homogenized and turns to look the same. Whereas instability can produce oscillatory reactions, etc

[@shilpakhetan498]

Plz can anyone tell me? These two species u and v are from one animals body

[@krishnaraoragavendran7592]

Finger prints of human beings should also be a consequence of Turing Pattern.

[@gleleylo]

What a pronunciation? I almost unable to understand it.

[@dexterdev]

We speak english like this. For common indians, we dont understand foreigner's english.

[@vasishtapolisetty639]

Use the subtitles!

[@marianonicolini8119]

I am from Argentina and I understood perfectly