Existence and static stability of a capillary free surface appearing in a dewetted Bridgman process. I

This paper present six theoretical results concerning the existence and static stability of a capillary free surface appearing in a dewetted Bridgman crystal growth technique. The results are obtained in an axis symmetric 2D model for semiconductors for which the sum of wetting angle and growth angle is less than 180. Numerical results are presented in case of InSb semiconductor growth. The reported results can help, the practical crystal growers, in better understanding the dependence of the free surface shape and size on the pressure difference across the free surface and prepare the appropriate seed size, and thermal conditions before seeding the growth process.Comment: This is an extended version of the conference paper TIM 19 of 10pages and 9 figure

Propagation of the initial value perturbation in a cylindrical lined duct carrying a gas flow

For the homogeneous Euler equation linearized around a non-slipping mean flow andboundary conditions corresponding to the mass-spring-damper impedance, smooth initial dataperturbations with compact support are considered. The propagation of this type of initial dataperturbations in a straight cylindrical lined duct is investigated. Such kind of investigations is missingin the existing literature. The mathematical tools are the Fourier transform with respect to the axialspatial variable and the Laplace transform with respect to the time variable. The functionalframework and sufficient conditions are researched that the so problem be well-posed in the sense ofHadamard and the Briggs-Bers stability criteria can be applied

The Concepts of Well-Posedness and Stability in Different Function Spaces for the 1D Linearized Euler Equations

This paper considers the stability of constant solutions to the 1D Euler equation. The idea is to investigate the effect of different function spaces on the well-posedness and stability of the null solution of the 1D linearized Euler equations. It is shown that the mathematical tools and results depend on the meaning of the concepts “perturbation,” “small perturbation,” “solution of the propagation problem,” and “small solution, that is, solution close to zero,” which are specific for each function space