Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Domain Patterns in Incommensurate Systems with the Uniaxial Real Order
  Parameter   The basic Landau model for the incommensurate-commensurate transition to the
uniform or dimerized uniaxial ordering is critically reexamined. The previous
analyses identified only sinusoidal and homogeneous solutions as
thermodynamically stable and proposed a simple phase diagram with the first
order phase transition between these configurations. By performing the
numerical analysis of the free energy and the Euler-Lagrange equation we show
that the phase diagram is more complex. It also contains a set of metastable
solutions present in the range of coexistence of homogeneous and sinusoidal
solutions. These new configurations are periodic patterns of homogeneous
domains connected by sinusoidal segments. They are Lyapunov unstable, very
probably due to the nonintegrability of the free energy functional. We also
discuss some other mathematical aspects of the model, and compare it with the
essentially simpler sine-Gordon model for the transitions to the states with
higher commensurabilities. The present results might be a basis for the
explanation of phenomena like thermal hystereses, cascades of phase
transitions, and memory effects, observed in materials exhibiting the
transitions to uniform or dimerized state.
  Some particular examples are discussed in detail.

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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: math
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys