By S. Joseph Antony, W. Hoyle, Yulong Ding

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The purpose of this section is to 44 Snapshots on Some States of Granular Matter show that flows generated in vibrated beds can often be interpreted within this scheme. On the other hand, many recent s t ~ d i e s ~ have ~ - ~been ~ investigating the dynamics of dry granular media with a free surface and subject to vertical or horizontal vibrations. Many of them consider the flow to result from the dynamic character of the excitation, which enhance some “thermal excitation”. Indeed, if the grains are “thermally” agitated in a inhomogeneous way, the diffusion coefficient of the grains varies with space, which forces flowing.

In the case of vertical vibration, the same approach should be valid if some horizontal component remains; but when the horizontal component becomes too small, or when the amplitude is too large, the modelling needs to also include fluid inside the pores to get the correct answer. That defines a scale of difficulty for computer scientists. The last part studies the propagation of sonic and ultrasonic waves in a granular medium, since it has been argued that it can reveal the “fragile” nature of the material.

Is quite small. We have also observed in this case that h remains constant close to the threshold. Then h grows using a mechanism of period doubling, l 2 Lastly, much further above the threshold, one observes that h scales as the relief amplitude a,. The explanation of these last three phenomena is as follows: when the system is close to the threshold, the capillary length lcapillar = {a/[g(p2 - P ~ ) ] ] ” plays ~ a significant role, because it fixes the wavelength h of the relief according to Equation lb): h = 27c lcapillar.

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