Timeline for Starting from an expression of E(V) and P(V) for the Birch-Murnaghan's equation of state, is there a way of obtaining an expression for E(P)?
Current License: CC BY-SA 3.0
20 events
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| Jun 19, 2016 at 18:10 | comment | added | DavidC. |
@LubošMotl the function exists and is obtained by elimination of V which is a purely mathematical task. That is what I am looking for, the analytical expression of $E(P)$, but I can't find the way for that purely mathematical task
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| Jun 19, 2016 at 11:35 | history | edited | Bosoneando | CC BY-SA 3.0 |
changed title to make it more specific
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| Jun 19, 2016 at 11:26 | answer | added | auxsvr | timeline score: 2 | |
| Jun 19, 2016 at 3:49 | comment | added | Luboš Motl | The function may be ill-defined for some values of $P$ - it may be legalized by saying that the range of $P$ is limited - and the function may have several values of $E$ for a given argument $P$ - however, only one of them is right in certain circumstances. With these disclaimers, the function exists and is obtained by elimination of $V$ which is a purely mathematical task. You can always do it numerically, can't you? For each value of $P$ you're interested in (e.g. all), find the value of $V$ from eq 3 and substitute this $V$ to eq 1 to get $E$. What the hell is the problem? | |
| Jun 18, 2016 at 18:54 | comment | added | DavidC. | @LubošMotl See the EDIT | |
| Jun 18, 2016 at 18:53 | history | edited | DavidC. | CC BY-SA 3.0 |
I need the expression of $E(P)$ because I need to fit the data
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| Jun 18, 2016 at 18:19 | comment | added | DavidC. |
@LubošMotl a function that solves it obviously exists Really? do you know what is that function?
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| Jun 18, 2016 at 17:45 | comment | added | Luboš Motl | @DavidC - the problem to eliminate V may be mathematically hard and the solution may fail to be analytic but a function that solves it obviously exists. | |
| Jun 18, 2016 at 17:36 | comment | added | dmckee --- ex-moderator kitten |
BTW, the mark-up \tag{tag text} is the usual way to number equations in MathJax (and the way to force the numbering in LaTeX, though forcing it is usually discouraged in favor of automatic schemes). I've done yours.
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| Jun 18, 2016 at 17:35 | history | edited | dmckee --- ex-moderator kitten | CC BY-SA 3.0 |
fix equation taging; add tag
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| Jun 18, 2016 at 15:50 | comment | added | DavidC. | @LubošMotl There is no possible way to describe a combination of Equations 1,3 that have no $V$ | |
| Jun 18, 2016 at 15:09 | comment | added | Luboš Motl | @DavidC - you misunderstood Karlo's obvious recipe. You clearly can't eliminate $V$ just from equation 1. You need to elimininate $V$ from the set of equations 1,3. These are two equations involving $E,P,V$, if you eliminate $V$, i.e. find a combination of 1,3 that has no $V$, you will have an equation with $E,P$ only which is an implicit (or explicit, if you are lucky) prescription for $E=E(P)$. | |
| Jun 18, 2016 at 14:37 | history | edited | DavidC. |
edited tags
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| Jun 18, 2016 at 13:52 | comment | added | DavidC. | @Karlo In the hypothetical case you were to eliminate $V$ from Eq. 1, you would not end up with an expression of $E(P)$ | |
| Jun 18, 2016 at 13:50 | history | edited | DavidC. | CC BY-SA 3.0 |
added 119 characters in body
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| Jun 18, 2016 at 13:08 | comment | added | garyp | Whoops ... comment deleted. | |
| Jun 18, 2016 at 12:54 | comment | added | Karlo | You could try to manually eliminate $V$. | |
| Jun 18, 2016 at 12:51 | review | First posts | |||
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| Jun 18, 2016 at 12:51 | history | edited | ACuriousMind♦ |
edited tags
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| Jun 18, 2016 at 12:47 | history | asked | DavidC. | CC BY-SA 3.0 |