Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-similar but not conformally invariant traces obtained by modified
  Loewner forces   The two-dimensional Loewner exploration process is generalized to the case
where the random force is self-similar with positively correlated increments.
We model this random force by a fractional Brownian motion with Hurst exponent
$H\geq \frac{1}{2}\equiv H_{\text{BM}}$, where $H_{\text{BM}}$ stands for the
one-dimensional Brownian motion. By manipulating the deterministic force, we
design a scale-invariant equation describing self-similar traces which lack
conformal invariance. The model is investigated in terms of the "input
diffusivity parameter" $\kappa$, which coincides with the one of the ordinary
Schramm-Loewner evolution (SLE) at $H=H_{\text{BM}}$. In our numerical
investigation, we focus on the scaling properties of the traces generated for
$\kappa=2,3$, $\kappa=4$ and $\kappa=6,8$ as the representatives, respectively,
of the dilute phase, the transition point and the dense phase of the ordinary
SLE. The resulting traces are shown to be scale-invariant. Using two equivalent
schemes, we extract the fractal dimension, $D_f(H)$, of the traces which
decrease monotonically with increasing $H$, reaching $D_f=1$ at $H=1$ for all
$\kappa$ values. The left passage probability (LPP) test demonstrates that, for
$H$ values not far from the uncorrelated case (small $\epsilon_H\equiv
\frac{H-H_{\text{BM}}}{H_{\text{BM}}}$) the prediction of the ordinary SLE is
applicable with an effective diffusivity parameter $\kappa_{\text{eff}}$. Not
surprisingly, the $\kappa_{\text{eff}}$'s do not fulfill the prediction of SLE
for the relation between $D_f(H)$ and the diffusivity parameter.

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The categories of this paper are: math
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat