Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universality classes for unstable crystal growth   Universality has been a key concept for the classification of equilibrium
critical phenomena, allowing associations among different physical processes
and models. When dealing with non-equilibrium problems, however, the
distinction in universality classes is not as clear and few are the examples,
as phase separation and kinetic roughening, for which universality has allowed
to classify results in a general spirit. Here we focus on an out-of-equilibrium
case, unstable crystal growth, lying in between phase ordering and pattern
formation. We consider a well established 2+1 dimensional family of continuum
nonlinear equations for the local height $h(\mathbf{x},t)$ of a crystal surface
having the general form ${\partial_t h(\mathbf{x},t)} = -\mathbf{\nabla}\cdot
{[\mathbf{j}(\nabla h) + \mathbf{\nabla}(\nabla^2 h)]}$: $\mathbf{j}(\nabla h)$
is an arbitrary function, which is linear for small $\nabla h$, and whose
structure expresses instabilities which lead to the formation of pyramid-like
structures of planar size $L$ and height $H$. Our task is the choice and
calculation of the quantities that can operate as critical exponents, together
with the discussion of what is relevant or not to the definition of our
universality class. These aims are achieved by means of a perturbative,
multiscale analysis of our model, leading to phase diffusion equations whose
diffusion coefficients encapsulate all relevant informations on dynamics. We
identify two critical exponents: i) the coarsening exponent, $n$, controlling
the increase in time of the typical size of the pattern, $L\sim t^n$; ii) the
exponent $\beta$, controlling the increase in time of the typical slope of the
pattern, $M \sim t^{\beta}$ where $M\approx H/L$. Our study reveals that there
are only two different universality classes...

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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
10
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: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn