PSN-L Email List Message

Subject: important subtlety
From: Randall Peters PETERS_RD@..........
Date: Thu, 18 Aug 2011 20:02:27 -0400


With the attention being given to acoustic emission ('pops'), I need to say=
 more concerning what I believe to be the 'heart' of the problem.  It is tr=
ue that such emissions point graphically to the discrete nature of changes =
that begin to happen as one moves in energy toward the mesodynamic range.  =
But I don't see them as necessarily the crux of the problem in my postulate=
 that spring anelasticity should limit performance.  Remember that I previo=
usly mentioned how the potential energy curve is not the smooth parabola re=
quired to yield Hooke's law behavior.  Rather, at low energies it has local=
ized metastable components.  In other words, like the potential (though inv=
erted) of the system my brother discovered (suspension effect).  In that su=
perconductor case, there is absolutely no question but that localized posit=
ions of stable equilibrium exist, superposed on an overall inverted (to fir=
st order, harmonic approximation) parabola.  It is the only way the superco=
nducting sample can hang at rest beneath the magnet in seeming violation of=
 Earnshaw's theorem.  These localized stable points can be visualized as sm=
all 'depressions' in the parabola.  In the case of the spring, such a 'depr=
ession' (that is not fixed in time) causes the inertial mass, when sitting =
at rest in one, to be interacting with an effectively 'harder' spring-until=
 it is dithered out of that depression.  I have even wondered if the reason=
 for static friction being greater than kinetic friction is this very mecha=
nism.  We know hardly anything concerning friction from first principles; s=
o that everything is empirical, starting with Coulomb.  One theorist who ha=
s done some modelling of hypothesized dislocation lattices that could be re=
levant is Prof. Michael Marder at the University of Texas.

With the attenti= on being given to acoustic emission (‘pops’), I need to say mor= e concerning what I believe to be the ‘heart’ of the problem.&n= bsp; It is true that such emissions point graphically to the discrete natur= e of changes that begin to happen as one moves in energy toward the mesodyn= amic range.  But I don’t see them as necessarily the crux of the= problem in my postulate that spring anelasticity should limit performance.=   Remember that I previously mentioned how the potential energy curve = is not the smooth parabola required to yield Hooke’s law behavior.&nb= sp; Rather, at low energies it has localized metastable components.  I= n other words, like the potential (though inverted) of the system my brothe= r discovered (suspension effect).  In that superconductor case, there = is absolutely no question but that localized positions of stable equilibriu= m exist, superposed on an overall inverted (to first order, harmonic approx= imation) parabola.  It is the only way the superconducting sample can = hang at rest beneath the magnet in seeming violation of Earnshaw’s th= eorem.  These localized stable points can be visualized as small ̵= 6;depressions’ in the parabola.  In the case of the spring, such= a ‘depression’ (that is not fixed in time) causes the inertial= mass, when sitting at rest in one, to be interacting with an effectively &= #8216;harder’ spring—until it is dithered out of that depressio= n.  I have even wondered if the reason for static friction being great= er than kinetic friction is this very mechanism.  We know hardly anyth= ing concerning friction from first principles; so that everything is empiri= cal, starting with Coulomb.  One theorist who has done some modelling = of hypothesized dislocation lattices that could be relevant is Prof. Michae= l Marder at the University of Texas.    

=

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