  Critically understanding the `standard candle'-like behavior of Type Ia
supernovae requires understanding their explosion mechanism. One family of
models for Type Ia Supernovae begins with a deflagration in a Carbon-Oxygen
white dwarf which greatly accelerates through wrinkling and flame
instabilities. While the planar speed and behavior of astrophysically-relevant
flames is increasingly well understood, more complex behavior, such as the
flame's response to stretch and curvature, has not been extensively explored in
the astrophysical literature; this behavior can greatly enhance or suppress
instabilities and local flame-wrinkling, which in turn can increase or decrease
the bulk burning rate. In this paper, we explore the effects of curvature on
both nuclear flames and simpler model flames to understand the effect of
curvature on the flame structure and speed.
