Friday, 27 July 2012

Stability, Feedback and Tipping Points (Part 1)...

Be it climate change, economic situation, politics, society, relationships - we hear a lot about stability, equilibrium, feedback and these days the term tipping point is used frequently.

We, the homo sapiens,  are comfortable when things are going as expected and we can predict what is going to happen, at least, in the near future.  It just makes planning easier, there is more time do other interesting things - a state of equilibrium (stability) is sought.

Stability is defined as a state in which a system tends to return to its original state after being disturbed. 
A good example of such stable equilibrium is a bowl with a marble in it. If we disturb the marble by moving it up the side of the bowl and let go then after a few oscillations, the marble returns to its original position of stability.

If the bowl was upside down and the marble balanced at the top of the bowl then a disturbance in its position will lead it to fall off, never to terun to its original postion.  That is unstable equilibrium.

The question is what gives rise to stability? - why should a system return to its original position when disturbed? 
It does so because a disturbance causes the system to generate some sort of restoring force which operates to cancel the direction of change.
Gravitational forces pull the marble back towards it original position.  However, the marble oscillates for a while before settling down. 

When you disturb something, you need to do work which is stored in the system as energy (potential energy or I shall call it latent or hidden energy) which has to be eliminated before stability is regained.  This is achieved by dissipative forces or friction in the system. 
Friction converts energy to heat - kind of wasted energy.

For the marble, the new displaced position gave it a higher potential energy.  Oscillations about the lowest point in the bowl, cause loss of energy due to friction and gradually the marble returns to stability.  If the bowl and the marble were completely smooth with no friction present then the marble will oscillate for ever.

We have described above, what in physics is called
negative feedback in which stability is regained after the system has been disturbed.

A familiar example of negative feedback at work is the thermostat of your central heating system.  You set a temperature and the boiler comes on to heat the room to this temperature.  But the boiler doesn't cut-off at the exact temperature chosen on the thermostat.  If it did so, then as soon as the temperature drops by the smallest amount the boiler will have to come back on again.  What the actual systems do is to have a small acceptable range of say about 0.5 degrees on either side of the thermostat setting. The boiler heats the room to the setting plus 0.5 degrees and cuts off and only comes back on when the temperature in the room falls to the setting minus 0.5 degrees.
Refrigerators, ovens, fan heaters, air conditioning systems all work on this basis.  These are examples of what we call Linear Control Systems.  Wiki has a diagram to explain how they work

Global climate regulates itself through feedback mechanisms.
Economic activity, our personal relationships all seem to operate on the basis of feedbacks and responses. 

File:Ideal feedback model.svg

In part 2, we shall look at Positive Feedback...
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