Fun With Polynomials

UPDATE:  The mother of all polynomial fits from the Canadian Medical Association Journal.

Here, we discuss how the outcomes of clinical trials may be affected by the extinction of all mankind and recommend appropriate changes to their conduct. In addition, we use computer modelling to show the effect of the apocalypse on a sample clinical trial. 
 

It looks like Roy Spencer may finally have given up using his third order polynomial fit for the UAH TLT record

September 2012

November 2012

Some, not Eli to be sure, might speculate because the  temperature was going up while the curve was going down, but just to join the party, Eli was looking at an interesting development in Graetzel cells (dye sensitized solar cells) in Science.  Briefly put some characters (Lee, Teuscher, Miyasaka, Murakami and Snaith) took the cell apart and put it together from scratch.  The original cells, first described in the 1990s had thin layers of light absorbing dye coated on an electrode coated with titania. A photocurrent then flows between the electrode and a counter electrode across an electrolyte.  Folks have been working on this cell for about 20 years and efficiencies have gotten up to 12% or so, about half of the best silicon cell, but a lot cheaper to build.  The new twist is to replace all the parts keeping the smile.  Time for a rebuild say Lee and friends, and they substitute the dye with an inorganic perovskite, the titania with alumina and the electrolyte with an organic conductor.  They get 11% efficiency, but it is early days.

Eli, reading the perspective by Norris and Aydil came across a figure showing that since 1975 the cummulative photocell electrical capacity doubles roughly every  2.45 years, but the fit is not quite linear.  Taking Dr. Roy's advice, why use two parameters when you can use four, Eli had a fit

 No problem by 2016:)  More conservatively, fitting a straight line on the semi-log plot which assumes the continued exponential growth, it is all OK by 2030.