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$).
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0729105-173104 |
| Date | 29 July 2005 |
| Creators | Yang, Chao-shun |
| Contributors | none, none, none, none, none |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | Cholon |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0729105-173104 |
| Rights | off_campus_withheld, Copyright information available at source archive |
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