Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Feedback control of surface roughness in a one-dimensional KPZ growth
  process   Control of generically scale-invariant systems, i.e., targeting specific
cooperative features in non-linear stochastic interacting systems with many
degrees of freedom subject to strong fluctuations and correlations that are
characterized by power laws, remains an important open problem. We study the
control of surface roughness during a growth process described by the
Kardar--Parisi--Zhang (KPZ) equation in $(1+1)$ dimensions. We achieve the
saturation of the mean surface roughness to a prescribed value using non-linear
feedback control. Numerical integration is performed by means of the
pseudospectral method, and the results are used to investigate the coupling
effects of controlled (linear) and uncontrolled (non-linear) KPZ dynamics
during the control process. While the intermediate time kinetics is governed by
KPZ scaling, at later times a linear regime prevails, namely the relaxation
towards the desired surface roughness. The temporal crossover region between
these two distinct regimes displays intriguing scaling behavior that is
characterized by non-trivial exponents and involves the number of controlled
Fourier modes. Due to the control, the height probability distribution becomes
negatively skewed, which affects the value of the saturation width.

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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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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: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: math
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph