Cellular interface morphologies in directional solidification. The one-sided model

摘要: Results of the shape and stability finite-amplitude cellular interfaces arising in directional solidification are reported for a binary alloy described by "one-sided" model which an imposed temperature gradient is unaffected changes interface shape. Asymptotic results valid slightly deformed melt-solid shapes describe both smooth sudden transitions to terms supercritical subcritical bifurcations with decreasing gradient. Computer-implemented perturbation methods combined finite-element approximations concentration field verify asymptotic small-amplitude cells extend analysis highly interfaces. Numerical predict that at large amplitudes, families first evolved unstably toward increased reverse direction regain stability. A discontinuous change stable morphology effective halving its spatial wavelength predicted occur secondary bifurcation between two neighboring familes related existence second-order critical points onset forms.