In the following section, we outline the main steps required to perform a linear stability analysis (LSA) in elliptical geometry, emphasising the major differences relative to the well-known stability analysis in planar system geometries with no bulk-boundary coupling (see e.g., a didactic derivation of linear stability analysis written by Cross and Greenside43). A detailed derivation of LSA in elliptical geometry can be found in the Supplementary Information of Halatek et al.24.
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