Escape probability of a particle in a sphere

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Discussion Overview

The discussion revolves around determining the probability of a particle escaping from a sphere through a hole on its surface, specifically using concepts from statistical mechanics and other approaches. The focus includes theoretical considerations and mathematical reasoning related to particle motion and geometry.

Discussion Character

  • Exploratory, Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant inquires about using statistical mechanics to calculate the escape probability of a particle from a sphere.
  • Another participant suggests looking into Brownian Motion as a relevant concept.
  • A different viewpoint argues that the problem may not be rooted in statistical mechanics and proposes a simpler comparison of the area of the hole to the sphere's surface area, along with the particle's speed.
  • Another contribution outlines a formula for the probability of a particle escaping based on its speed, the aperture area, and the volume of the sphere, while noting uncertainty about the multiplicative constant involved.

Areas of Agreement / Disagreement

Participants express differing opinions on whether statistical mechanics is applicable to the problem, with some proposing alternative methods for calculating escape probability. No consensus is reached on the best approach.

Contextual Notes

The discussion includes assumptions about particle motion and geometry, as well as the potential influence of factors like speed and area, which remain unresolved.

Who May Find This Useful

Individuals interested in statistical mechanics, particle dynamics, and mathematical modeling of physical systems may find this discussion relevant.

anon_man
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how can we use statistical mechanics to find the probability of a particle inside a sphere to escape through a hole on the surface (no potential energy) ? any ideas ??
 
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Look up Brownian Motion.

Cheers.Roman.
 
I don't think this is statistical mechanics. Just compare the area of the hole to the area of the sphere, and consider how fast the particle is moving.
 
Probability of particle traveling at speed U escaping from volume V through aperture area A in time period dT will be proportional to U.A.dT/V. Don't know what the multiplicative constant would be - perhaps depends on geometry.
 

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