Describe movement of particles with one equation?

In summary: The question is about mathematically describing the movement of air particles towards a specific point in a box. There is a potential for a pressure difference, but it is not certain that all particles will reach that point. The concept of a single equation for the entire system is challenged as the particles have random motion and there is no deterministic equation of motion. It is suggested to look into the Random Walk problem for more understanding. However, the idea of all particles moving towards the point is discussed without a clear explanation of what is causing this movement. The question is ultimately deemed more of a mathematical question than a physics one. In summary, the conversation revolves around finding a way to
  • #1
meyol99
25
1
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.
Untitled.jpg
 
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  • #2
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).
 
  • #3
mfb said:
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.
 
  • #4
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.
 
  • #5
Mevludin Licina said:
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.
 
  • #6
ZapperZ said:
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.
 
  • #7
Mevludin Licina said:
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.
 
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  • #8
ZapperZ said:
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
 

1. What is the equation used to describe the movement of particles?

The equation used to describe the movement of particles is the Newton's Second Law of Motion, which is F=ma (force equals mass times acceleration).

2. How does this equation explain the movement of particles?

This equation explains that the movement of particles is directly proportional to the force applied to them and inversely proportional to their mass. In other words, the greater the force applied, the greater the acceleration of the particles, and the greater the mass of the particles, the slower their acceleration will be.

3. What factors can affect the movement of particles according to this equation?

The movement of particles can be affected by the force applied to them, their mass, and their acceleration. Additionally, external factors such as friction, air resistance, and gravity can also affect the movement of particles.

4. Can this equation be applied to all types of particles?

Yes, this equation can be applied to all types of particles as long as they have mass and are subject to external forces. It is a fundamental law of physics that applies to both macroscopic and microscopic particles.

5. Are there any limitations to using this equation to describe particle movement?

While this equation is very useful in describing the movement of particles, it does have some limitations. For example, it does not take into account the effects of quantum mechanics on subatomic particles. It also assumes that the particles are moving in a straight line, without any rotational motion.

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