Determining Time for Explosions to Fill a Given Volume

[romeo6]

Hi Folks,

I'm working on a paper at the moment and need to use some kind of statistic but I'm not too great at stats.

Here is the set up.

1) I have some volume.

2) Within this volume there is an even distribution of objects.

3) These objects 'explode' with a known frequency and their explosion sweeps out a known volume, which is much smaller than the total volume.

I want to figure out how long it would take for explosions to have 'filled' the entire volume.

I hope this question is clear. If you could give me some idea on how to start I would be grateful. Sorry if its not clear.

PS - this is an astrophysics problem, not a weapons design problem!

 

[Valkarie]

Thanks!The best way to approach this problem is to use the Poisson distribution. The Poisson distribution describes the probability of a given number of events (in this case explosions) occurring in a given time frame. You can then use this to calculate the expected time it will take for the entire volume to be filled, given the frequency and size of the explosions.

 

[tacman]

Hi there,

Thank you for reaching out with your question. It sounds like you are trying to determine the time it would take for explosions to fill a given volume, given an even distribution of objects and a known frequency and volume of the explosions. This is definitely an interesting problem and it can be approached using some basic statistics.

One way to approach this problem is to use the concept of probability. Since the objects are evenly distributed within the volume, the probability of an explosion occurring at any given point is the same. Let's say the total volume is V and the volume of the explosions is v. The probability of an explosion occurring at any given point in the volume is v/V.

Now, since we know the frequency of the explosions, let's call it f, we can say that the probability of an explosion occurring in a given time interval is f times the probability of an explosion occurring at any given point. In other words, the probability of an explosion occurring in a time interval is f(v/V).

To determine how long it would take for the entire volume to be filled, we can use the concept of expected value. The expected value is the average of all possible outcomes, weighted by their probabilities. In this case, the expected value would be the average time it takes for an explosion to occur in the entire volume. We can calculate this by dividing the total volume by the probability of an explosion occurring in a given time interval. So, the expected value in this case would be V/(f(v/V)). This would give us the approximate time it would take for the entire volume to be filled with explosions.

I hope this helps you get started on your paper. Good luck with your research! And no worries, I understand this is an astrophysics problem and not a weapons design problem. Keep up the good work!