3. Contributions to the theory for granular media
Granular media is a challenging topic for scientific investigation, which can be approached from a great variety of aspects. G.A. has considered some geometric properties of "sand piles" and, in particular, finite collections of growing "sand cones". The basic idea is that, under certain conditions, these sand cones interact via a mechanism of taking pointwise maximum of cone functions. A nonlinear system of ordinary differential equations can be derived. It turns out to have good properties. This theory was presented in
- A mathematical model in sand mechanics, SIAM J. Appl. Math. 22:3(1972), 437-458.
Actually, supporting physical experiments with sand were carried out at the department of physical geography, Uppsala University in 1981. Results were reported in
- A deposition problem in the theory of granular media, Technical report 1984:04, Luleå University, Luleå, Sweden.
The mechanism at the micro level was explained in
- On the formation of compound cones for non-cohesive powders, unpublished manuscript, Linköping 1990.
Besides the above papers, G.A. wrote three more departmental reports in Göteborg around 1975 on further geometric aspects of cones, including talus cones.
Please recall the unexpected relation between sand cone systems and the p-parabolic equation for big p, explained above in 2.
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