Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Statistical Fractal-Diffusive Avalanche Model of a Slowly-Driven
  Self-Organized Criticality System   We develop a statistical analytical model that predicts the occurrence
frequency distributions and parameter correlations of avalanches in nonlinear
dissipative systems in the state of a slowly-driven self-organized criticality
(SOC) system. This model, called the fractal-diffusive SOC model, is based on
the following four assumptions: (i) The avalanche size $L$ grows as a diffusive
random walk with time $T$, following $L \propto T^{1/2}$; (ii) The
instantaneous energy dissipation rate $f(t)$ occupies a fractal volume with
dimension $D_S$, which predicts the relationships $F = f(t=T) \propto L^{D_S}
\propto T^{D_S/2}$, $P \propto L^{S} \propto T^{S/2}$ for the peak energy
dissipation rate, and $E \propto F T \propto T^{1+D_S/2}$ for the total
dissipated energy; (iii) The mean fractal dimension of avalanches in Euclidean
space $S=1,2,3$ is $D_S \approx (1+S)/2$; and (iv) The occurrence frequency
distributions $N(x) \propto x^{-\alpha_x}$ based on spatially uniform
probabilities in a SOC system are given by $N(L) \propto L^{-S}$, which
predicts powerlaw distributions for all parameters, with the slopes
$\alpha_T=(1+S)/2$, $\alpha_F=1+(S-1)/D_S$, $\alpha_P=2-1/S$, and
$\alpha_E=1+(S-1)/(D_S+2)$. We test the predicted fractal dimensions,
occurrence frequency distributions, and correlations with numerical simulations
of cellular automaton models in three dimensions $S=1,2,3$ and find
satisfactory agreement within $\approx 10%$. One profound prediction of this
universal SOC model is that the energy distribution has a powerlaw slope in the
range of $\alpha_E=1.40-1.67$, and the peak energy distribution has a slope of
$\alpha_P=1.67$ (for any fractal dimension $D_S=1,...,3$ in Euclidean space
S=3), and thus predicts that the bulk energy is always contained in the largest
events, which rules out significant nanoflare heating in the case of solar
flares.

26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol