| Summary: | 碩士 === 國立中正大學 === 物理所 === 93 === The dynamically driven renormalization group (DDRG) approach for a sandpile
is based on the similarity of dynamical part for all relaxation events between
a cell and a site. Follow the idea of DDRG, we classify a relaxation event on a RG
cell being static or dynamical by the toppling number g. Replacing to count a
huge number of dynamical events, we propose a Monte Carlo procedure to simplify
RG calculations. This RG scheme allows us to investigate the effect of g.
In addition, two important dynamics, the grain redistribution and multiple topplings,
are also considered.Our result of avalanche exponent on the 3*3 square
cell shows that the multiple topplings is important and the redistribution
effect can be omitted. Furthermore, through choosing a proper value of g
(~5.7 or 4.6 for considering multiple topplings or not, respectively),
both height probabilities and avalanche exponent arrive at the predicted values
simultaneously
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