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Old Oct 1st 2016, 04:09 AM   #1
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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
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Old Oct 1st 2016, 06:12 AM   #2
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As far as "dimensional analysis" is concerned, since $\displaystyle \alpha$ and a are "dimensionless" they can be ignored.
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Old Oct 1st 2016, 06:39 AM   #3
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Originally Posted by HallsofIvy View Post
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?
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Old Oct 4th 2016, 12:42 PM   #4
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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.
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Old Oct 4th 2016, 08:28 PM   #5
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http://cdsads.u-strasbg.fr/cgi-bin/n...;filetype=.pdf

Try this link
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Old Oct 4th 2016, 09:17 PM   #6
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Originally Posted by ab1994 View Post
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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Old Oct 5th 2016, 03:48 AM   #7
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Originally Posted by topsquark View Post
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
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Old Oct 5th 2016, 05:30 AM   #8
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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.
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Old Oct 5th 2016, 06:43 AM   #9
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Originally Posted by ChipB View Post
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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