[Hans Blom, 960222c]

(Bill Powers (960220.1130 MST))

Your proposed [Brownian] control system makes r depend on d. You

don't mention any reference level for d, but I presume there is one

in your simulation (even if it's just zero). The reference level of

d is defined for your situation as that value of d at which there is

no tendency to increase or decrease r.

No, I didn't set my system up as a control system. I did the

following:

1. define the chemical's concentration c as position dependent:

c = f (x, y) if in two-space

2. define the particle's radius as concentration dependent:

r = g (c)

3. compute the particle's next position change d based on Einstein's

formula: d = k / sqrt (r) with a suitably chosen k; note that this

disregards that in Einstein's formula d is an _average_ value

only; since I do not know d's probability density function, I

cannot simulate how it would vary

4. make the particle move a distance d in a randomly chosen direction

yielding new x and y coordinates.

5. loop to 1.

My observations showed that the simulated particle's movements depend

upon the choice of the functions f and g. In particular, if f is

constant (no concentration gradient) or if g is constant (no change

of the particle's radius) we have the standard Brownian movement. But

with suitably chosen f and g we observe that the particle's position

tends to remain in the vicinity of the maximum concentration. This

led me to the hypothesis that we might have something resembling a

control system here, where the particle's radius functions both as

the sensor _and_ as the actuator. Kind of funny, maybe, and certainly

different from the standard control setups that we normally consider.

On the other hand, the explanation might be that the particle cannot

escape from a gravitation-like "field", which would indicate that we

have an equilibrium system. Now, which is the "better" explanation?

I didn't program a control system; I iterated a number of (more or

less realistic) physics-like equations in order to see what kind of

movement ("behavior") would result for the particle.

So basically we want to see if the partial derivative of (d^2) with

respect to T is less when your control system is acting than when it

is not acting. And of course it is of interest to see _how much

less_ the effect is when control is present.

This statement indicates that the description of my experiment was

unclear. Sorry. In my simulation, I cannot discriminate between "a

control system acting" or not, because the simulation wasn't set up

that way. I hope the above makes clearer why I cannot do The Test as

you propose it.

Greetings,

Hans

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Eindhoven University of Technology Eindhoven, the Netherlands

Dept. of Electrical Engineering Medical Engineering Group

email: j.a.blom@ele.tue.nl

Great man achieves harmony by maintaining differences; small man

achieves harmony by maintaining the commonality. Confucius