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- W2004261734 abstract "A full study of parity-broken states in the directional solidification of lamellar eutectics is performed within the boundary-integral formulation. Symmetric states cease to exist at a wavelength ensuremath{lambda}, which is approximately twice that corresponding to their minimum undercooling, whereas solutions with a broken parity, drifting transversely to the growth front, appear as a forward bifurcation. Our results suggest that if one effectively doubles the wavelength of the initially symmetric state---a situation that can be achieved via a sudden jump of the velocity V by a factor of about 4, since ${ensuremath{lambda}}^{2}$Vensuremath{simeq}const---then tilted lamellae should appear as extended states and not as ``solitons.'' We find here that parity-broken states exist for hypereutectic as well as for hypoeutectic and eutectic compositions. We have extended the derivation of the similarity equation derived previously [K. Kassner and C. Misbah, Phys. Rev. Lett. 66, 445 (1991)] to the present situation. This case involves additional subtleties, due to the loss of reflection symmetry about the growth axis. Among other results, we find that the tilt angle ensuremath{varphi} should depend on ensuremath{sigma}=${mathit{d}}_{0}$l/${ensuremath{lambda}}^{2}$ and ensuremath{chi}=l/${mathit{l}}_{mathit{T}}$ only, where ${mathit{d}}_{0}$, l, and ${mathit{l}}_{mathit{T}}$ are the capillary, diffusion, and thermal lengths, respectively, and ensuremath{lambda} is the wavelength of the pattern. At large enough growth velocities V, ensuremath{varphi}ensuremath{simeq}ensuremath{varphi}(ensuremath{sigma}), while at small V the dependence on ensuremath{chi} is strong. These predictions can be tested experimentally." @default.
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- W2004261734 date "1991-11-01" @default.
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- W2004261734 title "Spontaneous parity-breaking transition in directional growth of lamellar eutectic structures" @default.
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- W2004261734 doi "https://doi.org/10.1103/physreva.44.6533" @default.
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