Probability of Particle Collision on a Closed Surface

In summary, the conclusion is that it is more probable that particles will collide if both are moving, but it is also possible that they will collide if one has a velocity equal to 0.
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Fasso
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Is it more probable that particles will collide if both are moving or if one has velocity equal to 0?
Let's say we don't have any forces between them and they're on a closed surface (for example a square).
 
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  • #2
Fasso said:
Is it more probable that particles will collide if both are moving or if one has velocity equal to 0?
Let's say we don't have any forces between them and they're on a closed surface (for example a square).
There is no such thing as "velocity equal to 0". EVERYTHING is moving in some frame of reference. Since you say "on a closed surface" I assume you mean relative to that surface, yes?

So, what do you think the answer is and why?
 
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Yes, relative to that surface, of course.
I don't know, I think it's more likely that they will collide if both particles are moving, but I don't have the mathematical proof for that opinion.
 
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I assume you mean not only that there is no force between them, but also that no common force is affecting them both. So their motions are independent of each other. And I assume you are talking about the probability of colliding in a fixed amount of time. You can easily say something about the extreme cases: 1) no motion at all; 2) a lot of fast motion.
Draw your own conclusions.
To get a mathematical proof for the general case, you would have to be very specific about the situation.
 
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FactChecker said:
I assume you mean not only that there is no force between them, but also that no common force is affecting them both. So their motions are independent of each other. And I assume you are talking about the probability of colliding in a fixed amount of time. You can easily say something about the extreme cases: 1) no motion at all; 2) a lot of fast motion.
Draw your own conclusions.
To get a mathematical proof for the general case, you would have to be very specific about the situation.

Exactly. Well, I don't have any idea how to set up this problem. Maybe it's more probable that if one of the particles is standing still relative to the surface, they'll collide in the middle due to Gauss's law. But, in my opinion, it's more likely that they'll collide if both particles are moving.
 
  • #6
Fasso said:
Exactly. Well, I don't have any idea how to set up this problem. Maybe it's more probable that if one of the particles is standing still relative to the surface, they'll collide in the middle due to Gauss's law. But, in my opinion, it's more likely that they'll collide if both particles are moving.
It probably depends on the average relative motion. If one point zipps around very fast then it obviously is more likely to collide. A rough conclusion can be obtained from the fact that for independent X and Y, the variance of X+Y is σX+Y2 = σX2 + σY2
So a non-zero separation is more likely to reach zero.
 
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FactChecker said:
It probably depends on the average relative motion. If one point zipps around very fast then it obviously is more likely to collide. A rough conclusion can be obtained from the fact that for independent X and Y, the variance of X+Y is σX+Y2 = σX2 + σY2
So a non-zero separation is more likely to reach zero.

Thank you for answer. What is the conclusion then? Which case is more likely to happen? And how did we get that formula? Is it some definition or?
 
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1. What is the definition of "Probability of Particle Collision on a Closed Surface"?

The probability of particle collision on a closed surface refers to the likelihood that two particles will collide with each other on a surface that is completely enclosed or bounded, with no openings or holes.

2. How is the probability of particle collision calculated on a closed surface?

The probability of particle collision on a closed surface can be calculated by taking into account the number of particles, their velocities and trajectories, and the surface area of the closed surface. This calculation is based on the principles of classical mechanics and statistical mechanics.

3. What factors affect the probability of particle collision on a closed surface?

The probability of particle collision on a closed surface is affected by several factors including the size and shape of the particles, their velocities, the surface area and shape of the closed surface, and any external forces or fields that may be present.

4. How is the probability of particle collision on a closed surface related to the concept of entropy?

The probability of particle collision on a closed surface is related to the concept of entropy, which is a measure of the disorder or randomness of a system. In a closed system, particles tend to move towards more disordered states, which increases the likelihood of collision.

5. Can the probability of particle collision on a closed surface be manipulated or controlled?

Yes, the probability of particle collision on a closed surface can be manipulated or controlled by adjusting the factors that affect it, such as particle size and velocity, surface area, and external forces. This is an important concept in various fields of science, such as physics, chemistry, and materials science.

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