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conservation condition for rate equations (PDE)

Posted 2011年2月17日 GMT-5 01:54 Modeling Tools & Definitions, Parameters, Variables, & Functions Version 4.1 1 Reply

Michael Mrejen
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I'm trying to model a structure with the RF module (time dependent) coupled with a system of differential equations that describes the rate equations of atoms populations in different energy levels (similar to the rate equations of a laser).

it's a 4 energy levels system (4 populations to be computed with time N0...N3) so I've 4 eq. diff defined through the Coefficient form PDE interface. I'm now facing difficulties in adding a conservation equation that states that at any given time the total population in the whole system remains equal to the initial population of the ground energy level (N0+....+N4=N0_t0).

Can you tell where I could add such a conservation equation. It's important to emphasize that this conservation is at any time and over all the simulation domain where the system is defined.

I'm looking forward for your help.

Best Regards,

Michael
1 Reply Last Post 2013年4月8日 GMT-4 16:48
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Hello Michael Mrejen

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Dan McLean
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Posted: 1 decade ago 2013年4月8日 GMT-4 16:48
If you have the population equations, the easiet way to hangle the conservation equation for electronic excited states is to use the conservation equation to eliminate one of the populations. for example if the total population is normalized to be 1 so that N0+N1+N2+N3=1 then N3 can be eliminated and the remain 3 popoulations will conserve the total.

I am trying to solve a similar problem. I have done it in other codes. I am having problem even introducing the rate equations. What module or equation did you use?
If you have the population equations, the easiet way to hangle the conservation equation for electronic excited states is to use the conservation equation to eliminate one of the populations. for example if the total population is normalized to be 1 so that N0+N1+N2+N3=1 then N3 can be eliminated and the remain 3 popoulations will conserve the total. I am trying to solve a similar problem. I have done it in other codes. I am having problem even introducing the rate equations. What module or equation did you use?

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