[PD] dynamic stochastic synthesis in pd?

[Charles Henry]

It occurs to me that one thing you could do for knowing what the
parameters should be, and how to interpolate with the right finite
sampling frequency is to do dimensional analysis like is done with
non-linear equations in fluid mechanics.

for ex.
If we have the modified van Der Pol equation, by introducing another parameter:

x''(t) + e (x(t)^2 -1) * x'(t) + w^2 * x(t) = s(t)

where s(t) is the signal input and x(t) is the system's output:

we could consider x as having units of Volts, w as having units of
rad/sec, and e as having units of 1/sec*V^2.  Then, we could form
dimensionless groups of variables that make this equation
dimensionless.
fs is the sampling frequency of simulation (the interpolated sampling freq)
and a new variable y could be added that normalizes the signal amplitude, y= 1 V

we could rewrite this equation as:

x''(t) * 1/y*fs^2 +  ((x(t)^2 -1) * x'(t) *e/y*fs^2 + x(t)*
w^2/y*fs^2=s(t)/y*fs^2

Then, we could have two notable dimensionless groups:
pi1=e*y^2/fs^2
and pi2=w^2/fs^2

For two different systems, we can expect the same behavior, if pi1 and
pi2 are the same for the different systems.  You would still have to
determine values of pi1 and pi2 over which different types of system
behavior occur, and that can be an arduous process.  Maybe someone has
already done this?

That's just an example of how this dimensional analysis idea might
work.  I don't rightly know what types of systems you all are looking
at.

--
Charles Zachary Henry

anti.dazed.med
Med student who needs a Mickey's