... unstable equilibrium ...

[FEBAUSA]

Hello everybody.

Please to inform me some examples of permanent or almost permanent unstable equilibrium on the planet earth.

[GAHD]

errrr...what, exactly, are you talking about?

Either way, we're glad to have you here at hypography, I hope this leads to some interesing discussion.

[Aquagem]

Originally Posted by FEBAUSA

Please to inform me some examples of permanent or almost permanent unstable equilibrium on the planet earth.

An unstable equilibrium is a situation in which all forces on an object resolve to zero, but if any one of the forces is changed slightly, the object will fall over, dash off in some direction, etc., and come to rest in a different place. A "pure" example from my physics book is shows a hollow hemishpherical bowl and a marble. In one configuration, the bowl is placed with its open side upward (like a U) and the marble is inside the bowl at rest at the geometric center of the bottom. Any force displacing the marble from center, then released, will result in the marble returning to the center. That's a stable equlibrium. Turn the bowl over and balance the marble on the very top, and you have an unstable equilibrium, in which the slightest displacement from center results in a catastrophic disequlibrium and marble lost in your shag carpet (where it's stable again).

Using the bowl explanation as a metaphor, you can see that a playground swing at rest is a stable equlibrium situation. Unstable equilibriums, in the pure sense, would not last long enough, generally, to be detected in the chaotic Earth environment. A wind, earthquake, temperature change, snow accumulation, etc., would produce an acceleration in some direction and upset the delicate balance. Many natural phenomena approach a position of unstable equilibrium for a while. Big boulders balanced precariously atop slender columns of eroding sandstone in the ancient seabed areas of the American West come to mind; trees (high center of gravity, small cross-section, limited root systems; skyscrapers (same logic); towering thunderstorms (really brief lifetime); etc.

But there's a hybrid situation of stable/unstable equilibriums that is to me the most interesting. Picture the bowl again, placed with rounded side up, and a small indentation in the very top. Now the marble sits in the indent with good stability, and will stay there until a perturbing force exceeds the restorative force of the marbles mass and gravitational field holding it in place. At that point, the system goes unstable, just like before.

Nature if full of examples of this kind of conditionally unstable systems, in which a relatively gentle, or small, sharp input of energy kicks off an avalanche-like reaction. Moving a pebble can send a boulder down an incline; hot air convecting upward off a runway can touch off a thunderstorm; a single match lights a forest fire. Two more examples: chlorophyll stores sunlight in glucose, a conditionally unstable molecule, which can be cracked to release the energy again by catalyzed reactions in a cell, or in a forest fire, or a termites gut. And explosives, which store huge amounts of energy, including the oxygen necessary to combine with other chemicals to burn even underwater. The first (glucose) is an unstable equilibrium that powers all of life. Explosives are a human value-added product, putting a very powerful genie in a bottle for later use and abuse.


Is this what you wanted to know?

[Fishteacher73]

Originally Posted by FEBAUSA

permanent or almost permanent unstable equilibrium .

I think it is contadictory to have a permanantly unstaible equilibrium. Many of the natural processes are unstable and are "searching" for equilibrium, but is a continual change of stresses that are shifting the equilibrium, hardly what one could consider permanent. If I understand what you are asking about, I may be off the mark for your question though...

[paultrr]

One good example of the bowl idea is inflation and how our vacuum state came about. In general we consider our present state as stable. At one time, far in the past, the vacuum was what we term a false vacuum state that decayed into its present stable one. However, at a quantum level, while overall globally it seems that our vacuum is stable, we also have the zero point field out of quantum theory where the vacuum is composed mostly of virtual particles coming into and going out of existance all the time in a fraction of an instant. Here, we generally consider the vacuum to be constantly ballanced out to a zero. Yet, we also have observational evidence that things are not exactly ballanced to zero due to the accelerated expansion of the cosmos. So, at some levels things can seem ballanced at the center of the bowl and also, at other levels, be not so ballanced as one would think.

[Turtle]

Aqua said: "Nature if full of examples of this kind of conditionally unstable systems, in which a relatively gentle, or small, sharp input of energy kicks off an avalanche-like reaction". This sounds like the butterfly effect of chaos theory. So how about this thought; the Butterfly Effect then is itself a permanent instability.

[Aquagem]

Originally Posted by Turtle

Aqua said: "Nature if full of examples of this kind of conditionally unstable systems, in which a relatively gentle, or small, sharp input of energy kicks off an avalanche-like reaction". This sounds like the butterfly effect of chaos theory. So how about this thought; the Butterfly Effect then is itself a permanent instability.

Good catch! I almost mentioned the butterfly effect, but hadn't thought about the basic principle being the instability itself. Hmmm... but we see the BE everywhere -- so it seems to be stable...

[sanctus]

If I rember right glass (when it's trnsparent) is in unstable equilibrium, but it seems to be permant. If for example try to heat up glass in a fire and then you let it cool down slowly (for example letting it in the fire and when fire goes out letting it in the brace), it will be broken eventually. Chemically speaking the cristalline structure of glass is unstable.

I guess that the earths orbit can as well be seen as in a unstable equilibrium, simply because mathematically already the problem of three bodies interacting is not solvable, therefore taking in account all the planets and their moons.... But I don't know if analytically unsolvable really implies unstable.

[lindagarrette]

Originally Posted by Turtle

Aqua said: "Nature if full of examples of this kind of conditionally unstable systems, in which a relatively gentle, or small, sharp input of energy kicks off an avalanche-like reaction". This sounds like the butterfly effect of chaos theory. So how about this thought; the Butterfly Effect then is itself a permanent instability.

The "butterfly effect" is an analogy for chaos theory. It has nothing to do with instability, if by that you mean randomness. Chaos theory proposes that if there were no changes to a system, i.e. all variables remained constant, then every event within it would be completely predictable. In reality, everything is stable within our universe which is (supposedly) a closed system.

[Turtle]

May I recharacterize the Butterfly Effect; it reflects that small changes in initial conditons can have enormous effects/results down the iterative chain. Yes, once you start down the chain, it plays out the same each time;at least in a symbolic algorthmic sense.
The implication for the real world however, is that instability is just around the corner, & it takes no more than the flap of a butterfly's wing to set it off. Or a belch at table, or, dare I say, a "break of wind".