On flushed partitions and concave compositions

In this work, we give combinatorial proofs for generating functions of two problems, i.e., flushed partitions and concave compositions of even length. We also give combinatorial interpretation of one problem posed by Sylvester involving flushed partitions and then prove it. For these purposes, we first describe an involution and use it to prove core identities. Using this involution with modifications, we prove several problems of different nature, including Andrews' partition identities involving initial repetitions and partition theoretical interpretations of three mock theta functions of third order $f(q)$, $\phi(q)$ and $\psi(q)$. An identity of Ramanujan is proved combinatorially. Several new identities are also established.Comment: 19 page

Liquid phase diffusion growth of SiGe single crystals under magnetic fields

The manuscript presents the results of a combined experimental and modeling study on the Liquid Phase Diffusion (LPD) growth of single crystal SixGe1-x on Germanium with and with the application of magnetic fields. Although the LPD process is mainly diffusion driven through out the growth period, strong natural thermosolutal convection occurs in the first five hours of growth, and the growth interface is concave to the melt. Applied rotating and static magnetic fields were considered to examine the growth and silicon dissolution processes in the LPD system. Results show that the application of a combined applied magnetic is beneficial