Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Power law tail in the radial growth probability distribution for DLA   Using both analytic and numerical methods, we study the radial growth
probability distribution $P(r,M)$ for large scale off lattice diffusion limited
aggregation (DLA) clusters. If the form of $P(r,M)$ is a Gaussian, we show
analytically that the width $\xi(M)$ of the distribution {\it can not} scale as
the radius of gyration $R_G$ of the cluster. We generate about $1750$ clusters
of masses $M$ up to $500,000$ particles, and calculate the distribution by
sending $10^6$ further random walkers for each cluster. We give strong support
that the calculated distribution has a power law tail in the interior ($r\sim
0$) of the cluster, and can be described by a scaling Ansatz $P(r,M) \propto
{r^\alpha\over\xi}\cdot g\left( {r-r_0}\over \xi \right)$, where $g(x)$ denotes
some scaling function which is centered around zero and has a width of order
unity. The exponent $\alpha$ is determined to be $\approx 2$, which is now
substantially smaller than values measured earlier. We show, by including the
power-law tail, that the width {\it can} scale as $R_G$, if $\alpha > D_f-1$.

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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an