Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How a dissimilar-chain system is splitting. Quasi-static, subsonic and
  supersonic regimes   We consider parallel splitting of a strip composed of two different chains.
As a waveguide, the dissimilar-chain structure radically differs from the
well-studied identical-chain system. It is characterized by three speeds of the
long waves, two for the separate chains, and one for the intact strip where the
chains are connected. Accordingly, there exist three ranges, the subsonic for
both chains, the intersonic and the supersonic. The speed in the latter range
is supersonic for the intact strip and at the same time, it is subsonic for the
separate higher-speed chain. This fact allows the splitting wave to propagate
in the strip supersonically. We derive steady-state analytical solutions and
find that the splitting can propagate steadily only in two of these speed
ranges, the subsonic and the supersonic, whereas the intersonic regime is
forbidden. In the case of considerable difference in the chain stiffness, the
lowest dynamic threshold corresponds to the supersonic regime. The peculiarity
of the supersonic mode is that the supersonic energy delivery channel, being
initially absent, is opening with the moving splitting point. Based on the
discrete and related continuous models we find which regime can be implemented
depending on the structure parameters and loading conditions. The analysis
allows us to represent the characteristics of such processes and to demonstrate
strengths and weaknesses of different formulations, quasi-static, dynamic,
discrete or continuous. Analytical solutions for steady-state regimes are
obtained and analyzed in detail. We find the force-speed relations and show the
difference between the static and dynamic thresholds. The parameters and energy
of waves radiated by the propagating splitting are determined. We calculate the
strain distribution ahead of the transition point and check whether the
steady-state solutions are admissible.

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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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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: alg-geom
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The categories of this paper are: quant-ph