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@ARTICLE{Brener:22906,
      author       = {Brener, E.A. and Temkin, D.E.},
      title        = {{O}nsager approach to the one-dimensional solidification
                      problem and its relation to the phase-field description},
      journal      = {Physical review / E},
      volume       = {85},
      number       = {3},
      issn         = {1539-3755},
      address      = {College Park, Md.},
      publisher    = {APS},
      reportid     = {PreJuSER-22906},
      pages        = {031601},
      year         = {2012},
      note         = {We thank M. Plapp for useful discussions. We acknowledge
                      the support of the Deutsche Forschungs-gemeinschaft under
                      Project No. SFB 917.},
      abstract     = {We give a general phenomenological description of the
                      steady-state 1D front propagation problem in two cases: the
                      solidification of a pure material and the isothermal
                      solidification of two-component dilute alloys. The
                      solidification of a pure material is controlled by the heat
                      transport in the bulk and the interface kinetics. The
                      isothermal solidification of two-component alloys is
                      controlled by the diffusion in the bulk and the interface
                      kinetics. We find that the condition of
                      positive-definiteness of the symmetric Onsager matrix of
                      interface kinetic coefficients still allows an arbitrary
                      sign of the slope of the velocity-concentration line near
                      the solidus in the alloy problem or of the
                      velocity-temperature line in the case of solidification of a
                      pure material. This result offers a very simple and elegant
                      way to describe the interesting phenomenon of a possible
                      non-single-value behavior of velocity versus concentration
                      that has previously been discussed by different approaches.
                      We also discuss the relation of this Onsager approach to the
                      thin-interface limit of the phase-field description.},
      keywords     = {J (WoSType)},
      cin          = {PGI-2},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-2-20110106},
      pnm          = {Grundlagen für zukünftige Informationstechnologien},
      pid          = {G:(DE-Juel1)FUEK412},
      shelfmark    = {Physics, Fluids $\&$ Plasmas / Physics, Mathematical},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000301844200007},
      doi          = {10.1103/PhysRevE.85.031601},
      url          = {https://juser.fz-juelich.de/record/22906},
}