brihaspati wrote:Ah! amazing and amusing!
But anyway, it is good to know that "power law decays" are contrary to "physics"! This is good. Anyway, perhaps people who still continue to use unrelated adjectives or phrases - like "Hindu rate of growth" or "fans" or "uber nationalists" and pretend that these words are most relevant, and think all "decays" are exponential in "nature" perhaps should consider whether "decay heat" should always be "exponential" and anything contrary to this is contrary to "physics". As for me, it does not matter whether it is the "decay rate" or "prostitution rate". I treated it simply as a given equation in a paper jointly authored by someone whose 2008 paper is supposed to have busted another author's perfidy - and therefore must be showing acceptable standards of scientific "rounding off" and "error percentage/uncertainties".
Brihaspati, I believe GP is correct. (Read his message carefully to get the fine points and context)
Of course, quite often, even the exponential decay can, and usually, approximated by a polynomial (or even linear) function --- as long as one has narrow range of time.
One example is decay heat in spent fuel rods. If you saw GP's posts (in the other thread)
one can approximate ( I did that for Fukushima's case to calculate/estimate the decay heat etc) the sum of various exponential decays into simpler formula which may look
similar to (but not exactly same) your formula.
(GP - correct me, if I am wrong)
I used P=P_0*0.07*((T-T')^(-.2) - T^(-.2))
For more technical detail see, for example:
http://www.nuceng.ca/papers/decayhe1b.pdf
Bottom line, the decay heat is exponential in nature. Above formula can be used, as long as T is less than, about 100 days, to give meaningful result.
(In fact, for higher value of T, a simple exponential curve, would give a better approximation)
Amber G,
my question was rather simple. If you have such an equation, where the two constants are given up to 4th place of decimal, and the time count does not start at +infinity and 0 is not excluded - would you be satisfied, with an additional 20% uncertainty added on to this - as "scientifically" okay?
I will not even go into "theoretical" implications of adding uncertainties to parameters or results of equations which themselves appear as parameters/variables/inputs into other equations.
But, rather the question is whether 4 places after decimal, is acceptable to you, and 20% "uncertainties" added on top of interim calculations are also okay. I will proceed on the premise that 3 places of decimal is unscientific and to be rejected, but 4 places is scientific. Moreover, if it is 3 places of decimal then 20-30% uncertainties are unacceptable and unscientific, whereas if it is 4 places of decimal then 20-30% uncertainties are acceptable and scientific. I have no problems with this "hypothesis". As you must be realizing, we can carry out the explicit set of equations given in the paper I quoted in details, and test them for robustness for "neglecting" the 4th place of decimal.
Whatever it turns out should be illustrative. It could reveal the seriousness of that paper's neglect of 4th place of decimal and sticking to 3. It could be inconclusive. Let us see. If you want you can also disagree with the set of difference equations used or the parameter values. Let me know. Since if you disagree with the structural equations or differecne scheme - there is no point in implementing them. Seriously, if that paper is such a huge hatchet job, you could show the problems and the results should be submitted to Energy Policy as a rebuttal.
I made quite a few passes reading above but still, honestly, can not understand what exactly is your point.
I gave the explicit formula for to just plug in..
( Obviously, you can forget about uncertainty in "a", as you just add relative error in a for its contribution .. IOW if (relative uncertainty in "a" is .0001, just add that in the final result )
For example, if b=0.2000 (uncertainty here, say .00005)
When t=1 , the contribution due to this will be zero. (ln 1 = 0)
When t = 100, the contribution would be .0002
You get the idea.
Rest of your post, makes no sense to me (and I have tried to read it many times).. may be some one else can comment.
As to:
But, rather the question is whether 4 places after decimal, is acceptable to you, and 20% "uncertainties" added on top of interim calculations are also okay. I will proceed on the premise that 3 places of decimal is unscientific and to be rejected, but 4 places is scientific. Moreover, if it is 3 places of decimal then 20-30% uncertainties are unacceptable and unscientific, whereas if it is 4 places of decimal then 20-30% uncertainties are acceptable and scientific.
I don't even know (and you don't tell)
what exactly is described? And what has uncertainty as 20%?