# Theoretical and Numerical Approaches to Critical Natures of A Sandpile

Abstract (Summary)

A self-organized criticality (SOC) system is driven and maintained
by repeatedly adding energy at random, and by dissipating energy in a
specified way. The dissipating way is seldom considered, yet it
plays an important role in the source of a SOC. Here, we use
sandpile models as an example to point out the effects of
dissipation on a SOC. First, we study the dissipation through a
losing probability $f$ during each toppling process. In such a
dissipative system, we find the SOC behavior is broken when $f >
0.1$ and that it is not evident for $0.1>f>0.01$. Numerical
simulations of the toppling size exponents for all ($ au_a$),
dissipative ($ au_d$), and last ($ au_l$) waves have been
investigated for $f le 0.01$. We find that $ au_a=1$ is
independent of $f$ and identical to the original sandpile model
which dissipates energy at the boundary. However, the values of
$ au_d$ and $ au_l$ do indeed depend on $f$. Furthermore, we
derive analytic expressions of the exponents of $ au_d$ and
$ au_l$, and conjecture $ au_l + au_d = frac{11}{8}$ and the
exponent of the dissipative last waves $ au_{ld}=frac{3}{8}$. All of
them are well consistent with the numerical study. We conclude that
dissipation drives a system from being a non-SOC to a SOC.
However, these SOC universality classes consist of three kinds of
exponents: overall ($ au_a$), local ($ au_{ld}$), and detailed
($ au_d$ and $ au_l$).
Bibliographical Information:

Advisor:none; none; none; none; none

School:National Sun Yat-Sen University

School Location:China - Taiwan

Source Type:Master's Thesis

Keywords:sandpile

ISBN:

Date of Publication:07/29/2005