Hopf bifurcation and solution multiplicity in a model for destabilized Bridgman crystal growth

Three-dimensional bifurcations in a cubic cavity due to buoyancy-driven natural convection

“…The resulting onset of convective instability and its subsequent transition to periodic, non-periodic, and chaotic states in a threedimensional (3-D) thermally driven cavity are relevant to crystal growth processes. One major issue that continues to challenge the crystal growth processing engineers is to clarify the occurrence of layers of impurity, which can normally destroy the crystal homogeneity [1]. Characterization of different thresholds and flow regimes of different physical natures becomes thus an essential issue in the design of a proper crystal growth process.…”

Improved radial segregation via the destabilizing vertical Bridgman configuration

“…For brevity, the detailed equations and boundary conditions are not listed; the interested reader is referred to Refs. [16,18] for a more complete description.…”

“…Details of this study are available in our previous work [16]. The computational mesh, shown in Fig.…”

“…Details of this modeling approach, as well as a more complete discussion of the nonlinear dynamical aspects of this system, are presented in Ref. [16]. A one-parameter bifurcation diagram for the model is shown in Fig.…”

“…[16,17]). At sufficiently high Rayleigh numbers, stable, time-periodic flow behavior was shown to exist.…”