Maybe they are creating fractals...:) More precisely, the Mandelbrot set is the set of values of *c* in the complex plane <http://en.m.wikipedia.org/wiki/Complex_plane> for which the orbit<http://en.m.wikipedia.org/wiki/Orbit_(dynamics)> of 0 under iteration <http://en.m.wikipedia.org/wiki/Iterated_function> of thecomplex quadratic polynomial<http://en.m.wikipedia.org/wiki/Complex_quadratic_polynomial> *z**n*+1 = *z**n*2 +*c* remains bounded<http://en.m.wikipedia.org/wiki/Bounded_sequence> .[1] <http://en.m.wikipedia.org/wiki/Mandelbrot_set#cite_note-1> That is, a complex number *c* is part of the Mandelbrot set if, when starting with *z*0 = 0 and applying the iteration repeatedly, the absolute value<http://en.m.wikipedia.org/wiki/Absolute_value> of*z**n* remains bounded however large *n* gets.
Stewart Darkmattersalot.com On Sunday, November 18, 2012, David Roberson wrote: > I have been following the fine work of the MFMP team and analyzing the > data. These guys are doing excellent work and I congratulate them for > sharing their data on a real time basis for everyone to view. I wish that > we had the same cooperation from the other experimenters, but I understand > why they are reluctant. > > The purpose for this post is to see if anyone among us can explain the > unusual power output as a function of the outer glass temperature of the > test cylinder. I believe that it has been the assumption that the outer > glass surface should behave as a radiation source in a more or less black > body manner. This implies that the radiation should be proportional to the > 4th power of the temperature at that surface according to the > Stefan-Boltzmann equation. I began my analysis assuming that this would > be likely, but find that it does not seem to be true. > > I performed a curve fitting operation on some of the recent data that > the guys submitted on line and found that the power leaving the cell very > much matches a second order equation over a wide range of input values. My > actual function is as follows: P(Out) = .001656 * T * T - .6284 * T + > 40.3. Here P(Out) is in units of watts and T is Kelvin degrees. This > function does a good job of matching the point pairs from 0 watts to 100 > watts of output. The temperature varies from approximately 300 to 450 > Kelvin over that output range. > > It is apparent that the function that I am posting does not work over a > much larger range than that in actual use since an entry of 0 degrees > Kelvin would result in an output of 40.3 watts which is nonsense. > > I started my review by assuming the forth order function. I thought of > a cute trick of taking the derivative of the expected function to eliminate > the fixed incoming radiation that must be subtracted to obtain accurate > output radiation power calculations. Then I took the ratio of the > derivatives for each adjacent pair of power points to eliminate the > proportional constant. My procedure was a bit tricky to perform, but > eventually I got the bugs worked out of my results. At that point I was > expecting to see the ratio of adjacent derivatives follow a cubic function > of their temperature ratios. This expectation was not demonstrated to my > satisfaction. > > I was seeking useful results so I plotted the derivative of the power > output versus temperature and saw that the curve followed a linear path > instead of third order. With this result as a reference I performed a > curve fit of power out versus temperature using a second order function and > got very reasonable results. > > Am I missing something here? Why does the temperature on the surface of > the glass cylinder not obey the Stefan-Boltzmann relationship? Does this > suggest that the major heat transport mechanism is convection into the air > instead of radiation? Is it possible that the IR radiation is escaping > the demonstration device and the calibrations are mainly derived from the > direct gas heating of the glass? > > Dave >
