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Plenary Lecture

Nonlinear Boundary Value Problem of the Meniscus for the Capillarity Problems in Crystal Growth Processes



Associate Professor Liliana Braescu
Department of Computer Science
Faculty of Mathematics and Computer Science
West University of Timisoara
Blv. V. Parvan 4, 300223 Timisoara
Romania
E-mail: braesculiliana@yahoo.com

Abstract: The major problem to which crystal growth researchers have been confronted was the development of techniques capable to monitor and control the external shape of melt-grown crystals, and simultaneously to improve the crystal structures. In many crystal growth processes, the shape and the dimensions of the crystal are determined by the liquid meniscus and by the heat transfer at the melt-crystal interface. In addition, the meniscus is also of great practical use for techniques of diameter control: in the weighing method the weight of the melt enclosed by the meniscus appears as an essential parameter; when using video observation the crystal diameter and the interface height have to be measured exactly.
In order to understand the process which leads to a crystal with a constant radius, the static stability of menisci is analyzed. For this aim, starting from the Young-Laplace equation of a capillary surface in equilibrium in the presence of gas pressure, the corresponding nonlinear boundary value problems (BVP) having boundary conditions depending on the chosen configuration are considered. The menisci are computed, and the conditions for which solutions of BVP minimize the total energy functional of the melt column are searched. Necessary or sufficient conditions for the existence of the statically stable convex (or concave, convex-concave, concave-convex) solutions of the considered BVP are established, and numerical illustrations are performed for different configurations of the crystal growth processes.


Brief Biography of the Speaker:
LILIANA BRAESCU obtained her PhD in Mathematics in 2002, and is currently an Associate Professor at the Faculty of Mathematics and Computer Science of the West University of Timisoara, Romania.
Her research interests include control theory, ordinary and partial differential equations, stability and domains of attractions with applicability in modelling of the crystal growth processes, blood coagulation, and dental endosteal implantation. The research accomplishments are reflected through publications in an authored book (Nova Scientific Publishers), 6 chapters in books (Cambridge Scientific Publishers, Wiley & Sons and Springer), 26 peer-reviewed journal articles (Journal of Crystal Growth, Materials Science and Engineering B, Journal of Colloid and Interface Sciences, Optical Materials, International Journal of Theoretical Physics, Nonlinear Studies, Computational Materials Science), and scientific communications at international conferences including the International Workshop in Modeling in Crystal Growth, International Conference on Crystal Growth, European Materials Research Society, International Conference on Nonlinear Problems in Aviation and Aerospace, various conferences of the Society of Photo-Optical Instrumentation Engineers and World Scientific and Engineering Academy and Society.
Liliana Braescu is a member of the following professional societes and organizations: Society of Photo-Optical Instrumentation Engineers (SPIE), European Materials Research Society (E-MRS), World Scientific and Engineering Academy and Society (WSEAS), Sigma Xi, AdAstra Association Romanian Scientific Community, and Romanian Mathematical Society.

 
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