Quadrat Analysis_RW_Thomas

Quadrat Analysis_RW_Thomas

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Unformatted text preview: h any one meso-state description. Indeed, it can easily be proved (see Gray, 1967, p.97) that the total number of micro-states asso- Fig. 6: State descriptions and their properties 31 Further, the total number of micro-states associated with a meso-state description is given by the multinomial coefficient (62) Consequently, if we wish to find the probability that a specified cell contains exactly x points when all micro-states associated with n and r are assumed to be equally likely, then the probability x = m is given by (65) This is probability distribution known as Bose-Einstein statistics. It follows by conjecture that, because this distribution assumes all micro-states associated with the macro-state description to be equally likely, then, if we multiply the successive probabilities in (65) through by n, we will obtain the meso-state description of the pattern that maximises the value of (62) subject to (1) and (2 ). Similarly, the probabilities themselves will maximise the value of (63) subject to (7) and 8). Simulated verification of these conjectures...
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This note was uploaded on 02/15/2012 for the course GEO 6938 taught by Professor Staff during the Summer '08 term at University of Florida.

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