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3-dimensional random walk question

E

Eeezee

Diamond Member
I've randomly generated 3-d unit vectors. Basically I had to write a computer program that generated 100 point particles which then took 100 steps or 10000 steps randomly. I had to make a histogram illustrating probability versus R^2 for each of these cases. I am then asked the following question

"Use your histograms if possible to determine whatever you can about the following equation. What is this quantity measuring?

sqrt(average[{R^2 - average(R^2)}^2]) / average(R^2)

So it's one over the average of R^2 multiplied by the square root of the average of the square of R squared minus the average of R squared.

I have little idea what this could be measuring or how to obtain it from a strange looking histogram (it almost looks like a gaussian). I know that the average of R^2 is equal to N, the number of steps,for an ensemble system. WTF?
 
Dang, no wonder kids have to pull all nighters in high school now. I remember when a random walk involved getting from the cafeteria to fifth hour class. Damn Geoffrey Taylor!
 
Is ATOT how you did so well on your physics test? :laugh: 😉

OP, by the way, the monster spider with it's babies are no longer threatening my wife and I--we moved. So your sig is officially a fact of the past. 😀
 
the (average[{R^2 - average(R^2)}^2]) seems to be the varience of R^2. The sqtr giver you the Standard Dev. So I guess this is some form of normalized S.D of R^2, which seems strange..... but that's all I can do to help you.

You might want to ask in highly technical, people might me more receptive.

Originally posted by: Eeezee
I've randomly generated 3-d unit vectors. Basically I had to write a computer program that generated 100 point particles which then took 100 steps or 10000 steps randomly. I had to make a histogram illustrating probability versus R^2 for each of these cases. I am then asked the following question

"Use your histograms if possible to determine whatever you can about the following equation. What is this quantity measuring?

sqrt(average[{R^2 - average(R^2)}^2]) / average(R^2)

So it's one over the average of R^2 multiplied by the square root of the average of the square of R squared minus the average of R squared.

I have little idea what this could be measuring or how to obtain it from a strange looking histogram (it almost looks like a gaussian). I know that the average of R^2 is equal to N, the number of steps,for an ensemble system. WTF?
Click to expand...

 
Originally posted by: ironwing
Dang, no wonder kids have to pull all nighters in high school now. I remember when a random walk involved getting from the cafeteria to fifth hour class. Damn Geoffrey Taylor!
Click to expand...

This is a college senior problem, no worries, high school was very easy 4 years ago when I graduated.
 
Originally posted by: Fullmetal Chocobo
Is ATOT how you did so well on your physics test? :laugh: 😉

OP, by the way, the monster spider with it's babies are no longer threatening my wife and I--we moved. So your sig is officially a fact of the past. 😀
Click to expand...

Actually Harvard has a very good website for studying for the Physics GRE, with full solutions to 4 practice exams (ETS service gives you 1 practice exam). Although the problems are easy enough that I'm sure most of ATOT could answer them 😛

And I'll change my sig for you, although I love the quote so much
 
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