fractals

I attach a Letter I sent to the Editor of a tribology journal, concerning adhesion of rough surfaces. 

I contend that some "criteria" that have been proposed based on extrapolation of numerical results are due to the limitations in present numerical sophisticated rough contact simulations, which only span at most 3 orders of magnitude of wavelengths, so typically people simulate from nanometer to micrometer scale.

Y. S. Chen, W. Choi, S. Papanikolaou, M. Bierbaum, J. P. Sethna

Dear Yavari

I have promised more replies on Mandelbrot, fractals, strongly emotive discussions in journals, and here is a coincise statement, which I take from a Nobel prize, prematurely passed away last year.  I think it has a lot to teach (including the kind of attitude that leads to Nobel prize, i.e. close to no human weakness), you will recognize the real name of the "Caesar" in this book is somebody with a 58 pages CV on his web site, most likely.

For a better idea of fractals, read please the other attachment.

Regards

Mike

A recent string of papers originated from Persson's paper in the physics literature contain a number of interesting new ideas, but compare, of the many theories for randomly rough surfaces, only Persson's and Bush et al, BGT. These papers often assume the original Greenwood and Williamson (GW) theory [1] to be inaccurate, but unfortunately do not test it, assuming BGT to be its better version. The original GW however is, I will show below, still the best paper and method today (not surprisingly, as not many papers have the level of 1300 citations), containing generally less assumptions than any other model, including the constitutive equation which does not need to be elastic! I just submitted this Letter to the Editor: On "Contact mechanics of real vs. randomly rough surfaces: A Green's function molecular dynamics study" by C. Campaña and M. H. Müser, EPL, 77 (2007) 38005. C. Campaña and M. H. Müser also make several questionable statements, including a dubious interpretation of their own results, and do not even cite the original GW paper; hence, we find useful to make some comments.