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- ItemTransient numerical study of termperature gradients during sublimation growth of SiC: Dependence on apparatus design(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2005) Geiser, Jürgen; Klein, Olaf; Philip, PeterUsing a transient mathematical heat transfer model including heat conduction, radiation, and radio frequency (RF) induction heating, we numerically investigate the time evolution of temperature gradients in axisymmetric growth apparatus during sublimation growth of silicon carbide (SiC) bulk single crystals by physical vapor transport (PVT) (modified Lely method). Temperature gradients on the growing crystal's surface can cause defects. Here, the evolution of these gradients is studied numerically during the heating process, varying the apparatus design, namely the amount of the source powder charge as well as the size of the upper blind hole used for cooling of the seed. Our results show that a smaller upper blind hole can reduce the temperature gradients on the surface of the seed crystal without reducing the surface temperature itself.
- ItemNoncompactness of integral operators modeling diffuse-gray radiation in polyhedral and transient settings(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Druet, Pierre-Étienne; Philip, PeterWhile it is well-known that the standard integral operator K of (stationary) diffuse-gray radiation, as it occurs in the radiosity equation, is compact if the domain of radiative interaction is sufficiently regular, we show noncompactness of the operator if the domain is polyhedral. We also show that a stationary operator is never compact when reinterpreted in a transient setting. Moreover, we provide new proofs, which do not use the compactness of K, for 1 being a simple eigenvalue of K for connected enclosures, and for I-(1-e)K being invertible, provided the emissivity e does not vanish identically