Describe movement of particles with one equation?

[meyol99]

Hello everybody,

I have a new thread to post,it is very important to find a solution for this :
-Imagine a box full of air particles.The particles are forced to move to a point A on the edge of the box.My question is now,how can I mathematicly describe the movement of these particles toward point A using one generalised equation ?

(See picture.)

Thank you for your time.

 

[mfb]

What do you mean with "one generalised equation"?
How are the particles forced to move towards A? A potential with a minimum at A will lead to a pressure difference in the box, but you won't get all particles moving all the way to A (unless you make a black hole there).

 

[meyol99]

What do you mean with "one generalised equation"?
How are the particles forced to move towards A? A potential with a minimum at A will lead to a pressure difference in the box, but you won't get all particles moving all the way to A (unless you make a black hole there).

By saying "one generalised equation" I mean a single equation that will work for the whole "system" of particles.
It doesn't matter how the particles are forced to move towards A. A is a point where a particle can get out of the box.

 

[mfb]

You can write down a Lagrangian, but I doubt that's what you are looking for.

Can you give an example of "a single equation" in any system? Just to see what that is supposed to mean.

 

[ZapperZ]

By saying "one generalised equation" I mean a single equation that will work for the whole "system" of particles.
It doesn't matter how the particles are forced to move towards A. A is a point where a particle can get out of the box.

One can write the Hamiltonian, or the Lagrangian of the system, as mfb stated, but one cannot solve for the equation of motion.

The problem here is that you have a system that essentially has a random motion of all the particles. So you cannot write a deterministic equation of motion of ANY of the particles. You can talk about the probability of a particle from one location reaching another particular location, but you cannot determine the motion definitely. That is why we have Statistical Mechanics! If we can write such a deterministic equation of motion, we won't need any statistical treatment.

Look up "Random Walk" problem, and you'll understand why there isn't "one generalized equation" here.

Zz.

 

[meyol99]

One can write the Hamiltonian, or the Lagrangian of the system, as mfb stated, but one cannot solve for the equation of motion.

The problem here is that you have a system that essentially has a random motion of all the particles. So you cannot write a deterministic equation of motion of ANY of the particles. You can talk about the probability of a particle from one location reaching another particular location, but you cannot determine the motion definitely. That is why we have Statistical Mechanics! If we can write such a deterministic equation of motion, we won't need any statistical treatment.

Look up "Random Walk" problem, and you'll understand why there isn't "one generalized equation" here.

Zz.

Yeah,but there is one common characteristic for all particles : that is there all moving towards point A.

 

[ZapperZ]

Yeah,but there is one common characteristic for all particles : that is there all moving towards point A.

Why? What's compelling them to move towards that point? Is there a universal vortex that is sucking all the air particles in that box? You never did explain what is meant by "...The particles are forced to move to a point A on the edge of the box..."

If all you want is the "line equation describing the edge of the box", then this is not a physics physics question, but rather, a mathematics question.

Zz.

 

[meyol99]

Why? What's compelling them to move towards that point? Is there a universal vortex that is sucking all the air particles in that box? You never did explain what is meant by "...The particles are forced to move to a point A on the edge of the box..."

If all you want is the "line equation describing the edge of the box", then this is not a physics physics question, but rather, a mathematics question.

Zz.

Yes