Concluding Remarks: The Long-Time Tails Story
I am going to make some general remarks about computers and numerical work and what one, in favorable cases, might learn from such computer experiments. The computer can be basically used in two ways: one is to support theory and the other one is doing engineering type of calculations. We have had a number of examples here where people are checking numerical experiments against the existing theory. That’s what I am trying to emphasize here. People studying polymers were checking against the Rouse-Zimm’s theory or people were studying suspensions and seeing whether Batchelor’s predictions were true, and so on. The point here is to try to look for deviations from existing theory. This is of course what experiments try to do continuously and the process can’t be really planned. One has some theoretical structure, one does some numerical experiments and then one tries to see whether existing theory is right, and most of the time, of course, it is, but once in a while, one gets a surprise. Just like the experimentalist finds a new effect, so can a numerical experimentalist. This applies particularly in the theory of turbulence, strongly developed turbulence, where there is really a very weak theoretical structure. The scaling laws are basically not working. People are not saying it. You will hear a lot about scaling, but Ken Wilson for example, is giving up on scaling in turbulence, very early. This is the reason why I would like to urge people to go to this impossible difficult regime of fully developed turbulence to see whether for real questionslike the validity of the renormalization, numerical experiments can give us some insights and any hints for theoretical developments.
KeywordsMolecular Dynamic Kinetic Theory Dimensional Analysis Period Doubling Triple Collision
Unable to display preview. Download preview PDF.