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 Oct 1st 2016, 04:09 AM #1 Junior Member   Join Date: Oct 2016 Posts: 8 Could anyone please help me with dimensional analysis http://cdsads.u-strasbg.fr/cgi-bin/n...;filetype=.pdf equation no. 2b is used to calculate acceleration of particles. I am trying to solve it in hypothetical situation and want to know if following parameters taken are correct. (I am looking to get particle acceleration in meters per second) Unperturbed velocity: some basic assumption in meters per second Larmor frequency:In angular frequency s Wave frequency: In angular frequency s X3 : assumed random number since it is a position along a coordinate axis. c= speed of light in meters per second t= time taken for gravity waves to reach particles Now since α and a are dimensionless, what should I take them as for calculation? Last edited by ab1994; Oct 4th 2016 at 08:31 PM. Reason: mistake
 Oct 1st 2016, 06:12 AM #2 Senior Member   Join Date: Aug 2010 Posts: 281 As far as "dimensional analysis" is concerned, since $\displaystyle \alpha$ and a are "dimensionless" they can be ignored. topsquark likes this.
Oct 1st 2016, 06:39 AM   #3
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 Originally Posted by HallsofIvy As far as "dimensional analysis" is concerned, since $\displaystyle \alpha$ and a are "dimensionless" they can be ignored.
ok. but if I actually was looking for answer in hypothetical situation wouldnt the amplitude and i (I think is for intensity of wave) would be required?

 Oct 4th 2016, 12:42 PM #4 Physics Team     Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,272 Your link is not working, so it's difficult to provide any help. But the dimension of frequency is s^-1, not s. Not sure what you mean by $\displaystyle \alpha$ and 'a' - if $\displaystyle \alpha$ is radial acceleration then its units are s^-2, and if 'a' means linear acceleration its units are m/s^2. topsquark likes this.
 Oct 4th 2016, 08:28 PM #5 Junior Member   Join Date: Oct 2016 Posts: 8
Oct 4th 2016, 09:17 PM   #6

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 Originally Posted by ab1994 http://cdsads.u-strasbg.fr/cgi-bin/n...;filetype=.pdf equation no. 2b is used to calculate acceleration of particles. I am trying to solve it in hypothetical situation and want to know if following parameters taken are correct. (I am looking to get particle acceleration in meters per second) Unperturbed velocity: some basic assumption in meters per second Larmor frequency:In angular frequency s Wave frequency: In angular frequency s X3 : assumed random number since it is a position along a coordinate axis. c= speed of light in meters per second t= time taken for gravity waves to reach particles Now since α and a are dimensionless, what should I take them as for calculation?
I'm not going to analyze the equations, though there are a number of small errors, like missing brackets. However I can answer your dimensional problems.

As ChipB has stated angular frequencies are measured in Hz = 1/s, $\displaystyle x^3$ is indeed a coordinate and therefore is measured in m, c is in m/s, and t is (obviously) in s.

$\displaystyle \alpha$ appears here as a phase shift so it has units of rad. And, as you stated, a is unitless.

The paper doesn't really explain what a might represent. It is clearly not an acceleration. The paper is using a perturbative method...is it possible that a is a variation parameter?

-Dan
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Oct 5th 2016, 03:48 AM   #7
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 Originally Posted by topsquark I'm not going to analyze the equations, though there are a number of small errors, like missing brackets. However I can answer your dimensional problems. As ChipB has stated angular frequencies are measured in Hz = 1/s, $\displaystyle x^3$ is indeed a coordinate and therefore is measured in m, c is in m/s, and t is (obviously) in s. $\displaystyle \alpha$ appears here as a phase shift so it has units of rad. And, as you stated, a is unitless. The paper doesn't really explain what a might represent. It is clearly not an acceleration. The paper is using a perturbative method...is it possible that a is a variation parameter? -Dan
So if α is in radian is there any way to calculate radian of gravity waves.Also could amplitude be in decibels? Yes, even I think a is a variation parameter and might be taken in m/s

Last edited by ab1994; Oct 5th 2016 at 04:40 AM. Reason: missed out something

 Oct 5th 2016, 05:30 AM #8 Physics Team     Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,272 Now that I can see the paper, 'a' appears to be dimensionless even though it is described as "amplitude." If 'a' is in decibels it must be based on some fundamental value, which is not given. I think you'd have to look up the paper cited that these equations come from to fully understand just what 'a' is. As for calculating alpha - obviously you would need all the other values in order to do so. topsquark likes this.
Oct 5th 2016, 06:43 AM   #9
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 Originally Posted by ChipB Now that I can see the paper, 'a' appears to be dimensionless even though it is described as "amplitude." If 'a' is in decibels it must be based on some fundamental value, which is not given. I think you'd have to look up the paper cited that these equations come from to fully understand just what 'a' is. As for calculating alpha - obviously you would need all the other values in order to do so.
@ChipB & @topsquark

I have researched some more and found the paper they mention : http://articles.adsabs.harvard.edu/c...;filetype=.pdf

Even the paper mentioned does not give much about parameters. Also could alpha actually be attenuation constant in decibels?

Last edited by ab1994; Oct 19th 2016 at 02:39 AM. Reason: mistake

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