Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Velocity fluctuations of stochastic reaction fronts propagating into an
  unstable state: strongly pushed fronts   The empirical velocity of a reaction-diffusion front, propagating into an
unstable state, fluctuates because of the shot noises of the reactions and
diffusion. Under certain conditions these fluctuations can be described as a
diffusion process in the reference frame moving with the average velocity of
the front. Here we address pushed fronts, where the front velocity in the
deterministic limit is affected by higher-order reactions and is therefore
larger than the linear spread velocity. For a subclass of these fronts --
strongly pushed fronts -- the effective diffusion constant $D_f\sim 1/N$ of the
front can be calculated, in the leading order, via a perturbation theory in
$1/N \ll 1$, where $N\gg 1$ is the typical number of particles in the
transition region. This perturbation theory, however, overestimates the
contribution of a few fast particles in the leading edge of the front. We
suggest a more consistent calculation by introducing a spatial integration
cutoff at a distance beyond which the average number of particles is of order
1. This leads to a non-perturbative correction to $D_f$ which even becomes
dominant close to the transition point between the strongly and weakly pushed
fronts. At the transition point we obtain a logarithmic correction to the $1/N$
scaling of $D_f$. We also uncover another, and quite surprising, effect of the
fast particles in the leading edge of the front. Because of these particles,
the position fluctuations of the front can be described as a diffusion process
only on very long time intervals with a duration $\Delta t \gg \tau_N$, where
$\tau_N$ scales as $N$. At intermediate times the position fluctuations of the
front are anomalously large and non-diffusive. Our extensive Monte-Carlo
simulations of a particular reacting lattice gas model support these
conclusions.

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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: math
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn