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Finding average time to absorb
Yesterday i said how the expectation value of t was not working out well. It turns out what i was comparing it to was incorrect. I wasn't taking enough intervals in the histogram from the simulation. But now i am and that probability density curve i get from the simulation matches exp(Q t). Taking the expectation value from there gives me the hitting times. So it all looks good, and i am feeling pleased about myself.
With this process I can put in any complicated matrix I need for Q which contains the rate constants, and figure out the expectation value of t.
The expected time for completion is 1.26 seconds. This makes k effective .79 1/s. We still don't know what to do with that k since it isn't actually k since it isn't a one step chemical reaction, but it is something like a k effective since it is inverse the average time it takes to complete the process.