Brett,
I have done a lot of computer modeling myself through the years, and i=
t is for that reason I am struggling just what to try and tell you from my =
own experiences - as relates to the 'numbers' you would like and mention be=
low:
"If anyone could suggest what is the magnitude of the effect on the
spring characteristics, I could at least model the instrument
response to such stepwise force changes. Someone must have studied
this and come up with some real numbers."
If there are indeed others beside myself who have done experiments along=
these lines-that relate directly to the specific challenges of seismometer=
construction-then I would love to know who they are.
What befuddles me in this matter derives from my exposure to the failed =
attempt years ago to understand chaos by means of 'perturbation analysis'. =
Those of us holding advanced degrees in physics 'cut our teeth' on perturb=
ation methods (beginning with astronomy and orbit calculations), because it=
was at that time almost the only way to try and wring out something of val=
ue from nonlinear equations of motion (before the computer became user frie=
ndly). But fact is, perturbation analysis just plain 'misses the mark' whe=
n it comes to trying to model chaotic systems. I say this from a position =
of more personal experience than many-having in fact written one of the cha=
os articles for the 10th ed. of the McGraw Hill Encyclopedia of Science and=
Technology ("math methods of physics used in chaos"-you can see some of th=
e figures from my article by typing "period doubling route to chaos access =
science"-the last five of the 11 figures mentioned in the 2nd citation). A=
nother of the contributors to that chaos section is the legendary Ed Lorenz=
(1917-2008), whose paper "Predictability: Does the flap of a butterfly's =
wings in Brazil set off a tornado in Texas". It made Ed a legend in his ow=
n time.
Mesoanelastic complexity is much more difficult to try and model than i=
s chaos, which is frequently described by the seeming misnomer "determinist=
ic chaos'. It is deterministic because the equations are, for many cases, =
quite well known in their detailed, adequate mathematical form. With compl=
ex systems we don't have that luxury.
There is some similarity to the present problem and the matter of influ=
ence differences between the static and kinetic coefficients of friction (g=
iven to us by Charles Augustus Coulomb). 'Stiction' features that derive f=
rom the static value exceeding the kinetic one, gives rise to 'curse-worthy=
' features when it comes to modeling mechanical oscillators. I've had some=
success, as documented in the paper that I wrote with a colleague while at=
West Point, titled "The not-so-simple harmonic oscillator", that was publi=
shed in the American Journal of Physics in 1997. You can readily read the =
abstract by googling it. If you want to read it I may be able to get one o=
f the Mercer librarians to send me a copy.
Randall
Brett,
I have done a lot of comp=
uter modeling myself through the years, and it is for that reason I am stru=
ggling just what to try and tell you from my own experiences – as rel=
ates to the ‘numbers’ you would like and mention below:
“If anyone could suggest what is the m=
agnitude of the effect on the
spring=
characteristics, I could at least model the instrument response to such stepwise force changes. Someone =
must have studied
this and come up w=
ith some real numbers.”
&=
nbsp; If there are indeed others beside myself who have done experiments al=
ong these lines—that relate directly to the specific challenges of se=
ismometer construction—then I would love to know who they are.
What befuddles me in this matt=
er derives from my exposure to the failed attempt years ago to understand c=
haos by means of ‘perturbation analysis’. Those of us hol=
ding advanced degrees in physics ‘cut our teeth’ on perturbatio=
n methods (beginning with astronomy and orbit calculations), because it was=
at that time almost the only way to try and wring out something of value f=
rom nonlinear equations of motion (before the computer became user friendly=
). But fact is, perturbation analysis just plain ‘misses the ma=
rk’ when it comes to trying to model chaotic systems. I say thi=
s from a position of more personal experience than many—having in fac=
t written one of the chaos articles for the 10th ed. of the McGr=
aw Hill Encyclopedia of Science and Technology (“math methods of phys=
ics used in chaos”—you can see some of the figures from my arti=
cle by typing “period doubling route to chaos access science”&#=
8212;the last five of the 11 figures mentioned in the 2nd citati=
on). Another of the contributors to that chaos section is the legenda=
ry Ed Lorenz (1917-2008), whose paper “Predictability: Does the=
flap of a butterfly’s wings in Brazil set off a tornado in TexasR=
21;. It made Ed a legend in his own time.
Mesoanelastic complexity is much =
more difficult to try and model than is chaos, which is frequently describe=
d by the seeming misnomer “deterministic chaos’. It is de=
terministic because the equations are, for many cases, quite well known in =
their detailed, adequate mathematical form. With complex systems we d=
on’t have that luxury.
There is some similarity to the present proble=
m and the matter of influence differences between the static and kinetic co=
efficients of friction (given to us by Charles Augustus Coulomb). =
216;Stiction’ features that derive from the static value exceeding th=
e kinetic one, gives rise to ‘curse-worthy’ features when it co=
mes to modeling mechanical oscillators. I’ve had some success, =
as documented in the paper that I wrote with a colleague while at West Poin=
t, titled “The not-so-simple harmonic oscillator”, that was pub=
lished in the American Journal of Physics in 1997. You can readily re=
ad the abstract by googling it. If you want to read it I may be able =
to get one of the Mercer librarians to send me a copy.
=
Randall
=