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Subject: nature of the mesoscopic nonlinearity
From: Randall Peters PETERS_RD@..........
Date: Sun, 10 Feb 2008 09:14:18 -0500

    I've been able now to give enough thought to your comments about "potholes" to
provide the following response.
Chris 'hit the nail on the head' with his statement "... to cope with discrete steps in
the zero level".  In other words, if the term is at all appropriate, it is not your
'average' pothole as found in northern climate highways where temperatures are at times
routinely below freezing.  The 'potholes of seismic type' are 'diffusive' in terms of
both temperature and stress.
    There is a paper of mine at
titled "Harmonic oscillator potential to describe internal dissipation".  As discussed
there, the potential function is not fixed.  As the seismometer mass moves back and
forth, the equilibrium position, to which it would go if motion were suppressed, shifts
back and forth.  This is the basis for hysteresis--reason the term 'hysteretic damping'
is appropriate.
    The problem with this hysteresis is that the mesoanelastic steps associated with it
are not themselves fixed.  My study of creep mentioned earlier is proof positive of that
fact.  What happens is the strain energy that accumulates at polycrystalline grain
boundaries causes a rearrangement of the atoms (redistribution of the defect structures)
when various thresholds are exceeded.  Such is the nature of work-hardening.  In primary
creep (exponential variation), the material is trying to arrest the changes brought about
by the external forcing.  'Success' in so doing results in a conversion to secondary
(linear variation) creep.  If the temperature were zero--end of story.  But temperature
serves to undo the hardening and so a 'balance' results between hardening and softening.
If the stress levels become large enough, the defect structural reorganizations become
much bigger, resulting in cracks and eventual fatigue failure.  Truly, what I'm
discussing is one of the most important and yet still mysterious of scientific
phenomena.  Its complexity has so far prohibited  understanding of the processes from
first principles.
    Perhaps another analogy is of some related value--that of a non-Newtonian liquid.
Maybe you've seen the Mythbusters episode in which they filled a 'small swimming pool'
with such a liquid (huge amount of corn starch with water).  One of the team was able to
easily 'walk on water' across the surface of this mix as long as he moved quickly.  But
if he tried to do so slowly, he sank all the way to his neck.  The more natural example
of the same phenomenon is that of quicksand.
    Still another fascinating example of such complexity is ordinary sea sand mixed with
ocean water.  If the sand is too dry, it is hard to walk on.  Same if the sand is too
wet.  Get the amount of water just right and you can drive tanks on it!
    What we're dealing with are the yet-unknown properties of granular materials, which
is an advancing frontier of science and engineering.  One of my favorite examples is a
can of nuts.  If you briskly shake a can of mixed nuts the larger ones will migrate
toward the upper surface, in seeming defiance of the influence of gravity--because of
their interaction with smaller nuts responsible for 'symmetry breaking'.

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