Estimating the fraction of ejecta travelling between velocity limitsby deltapants Tags: ejecta, estimating, fraction, gaussian, impacts, integration, spallation, velocity 

#1
Nov713, 06:31 AM

P: 5

First of all,
THIS IS NOT HOMEWORK. It's related to my research. And forgive me if this is rather elementary (sadly, I was something of an underachiever at school, which has left some gaps in my maths education that I've been working on since I returned to education) but I have a question about estimating the fraction of spalled impact ejecta that occupies a given velocity range. I have a reasonable estimate for the total number of particles ejected, and a minimum and maximum velocity (11.2 and 15). I'm assuming that the ejecta follows a Gaussian distribution, and I'm assuming a variance of 1 and a mean of 13.1. My question is  how would I actually integrate this, so I can estimate how many particles are travelling between 11.7 and 12.7 km/s? I've been approaching the problem conceptually like I might with a QM problem, by considering the function as a probability distribution such that the integral between ∞ and +∞ = 1, except in this case it's between 11.2 and 15 as my limits. Does this make sense? How would I then go about integrating between the 11.7 and 12.7 limits? Do I set 11.2 = 0 and 15 = 1 or something? Again, sorry if this is all very elementary, but some guidance would be appreciated! 



#2
Nov713, 08:41 AM

Mentor
P: 10,864

Ejecta where?
Gaussian distribution for the velocity in 3D, or for the speed? A Gaussian distribution has no minimal and maximal values. 



#3
Nov713, 11:24 AM

P: 5

Hi, thanks for getting back to me.
Sorry, It's the speed distribution I'm interested in. And the ejecta is travelling through a vacuum. I know the lower limit of the speed is 11.2 km/s, and the upper is 15. And I want to estimate what fraction of the total is travelling betweem around 11.7 and 12.7 km/s. Is this easily doable? What do you mean the Gaussian doesn't have a min and max value? Does that mean I'm wrong to assume a Gaussian/normal distribution here? Thanks in advance. 



#4
Nov713, 11:42 AM

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P: 10,864

Estimating the fraction of ejecta travelling between velocity limits 



#5
Nov713, 11:56 AM

P: 5

It's just the speed I need to be concerned with.
So, would I restrict the Gaussian as you suggested, by setting 10 km/s to equal 0 while 15 equals 1. Then integrate between 11.7 and 12.7? Would a top hat distribution be appropriate perhaps? It really is an estimation  a high degree of accuracy is not necessary. 



#6
Nov713, 11:58 AM

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P: 10,864

A symmetric speed distribution with a minimal and maximal value looks really unrealistic to me. 



#7
Nov713, 03:55 PM

P: 5

Ahh, so integrate between 11.2 and 15 first, to get a value that is normalised to 1... THEN integrate between 11.7 and 12.7 to obtain the fraction of that value that I'm looking for?
Thanks so much for your help! 



#8
Nov813, 08:30 AM

Mentor
P: 10,864





#9
Nov813, 09:16 AM

P: 5

Perfect, thanks a lot for your help.



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