Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ferroelastic Dynamics and Strain Compatibility   We derive underdamped evolution equations for the order-parameter (OP)
strains of a ferroelastic material undergoing a structural transition, using
Lagrangian variations with Rayleigh dissipation, and a free energy as a
polynomial expansion in the $N=n+N_{op}$ symmetry-adapted strains. The $N_{op}$
strain equations are structurally similar in form to the Lagrange-Rayleigh 1D
strain dynamics of Bales and Gooding (BG), with `strain accelerations'
proportional to a Laplacian acting on a sum of the free energy strain
derivative and frictional strain force. The tensorial St. Venant's elastic
compatibility constraints that forbid defects, are used to determine the n
non-order-parameter strains in terms of the OP strains, generating anisotropic
and long-range OP contributions to the free energy, friction and noise. The
{\it same} OP equations are obtained by either varying the displacement vector
components, or by varying the N strains subject to the $N_c$ compatibility
constraints. A Fokker-Planck equation, based on the BG dynamics with noise
terms, is set up. The BG dynamics corresponds to a set of nonidentical
nonlinear (strain) oscillators labeled by wavevector $\vec{k}$, with competing
short- and long-range couplings. The oscillators have different `strain-mass'
densities $\rho (k) \sim 1/k^2$ and dampings $\sim 1/\rho (k) \sim k^2$, so the
lighter large-k oscillators equilibrate first, corresponding to earlier
formation of smaller-scale oriented textures. This produces a sequential-scale
scenario for post-quench nucleation, elastic patterning, and hierarchical
growth. (Continued ...)

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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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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: math
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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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: econ