“…Modern numerical studies of mantle convection have addressed many of the unexplored complexities from the earlier studies including: non-linear temperature-dependent rheology (Torrence and Parmentier et al, 1976); compressibility (Jarvis and McKenzie, 1980;Leng and Zhong, 2008;King et al, 2010); three-dimensional geometry (c.f., Gable et al, 1991;Tackley et al, 1993;Lowman et al, 2001;2003;2004), self-consistent equations of state (Ita and King, 1994;1998;Nakagawa et al, 2009); spherical geometry (Schubert and Zebib, 1980;Hager and O'Connell, 1981;Bercovici et al, 1989;Tackley et al, 1993;Bunge et al, 1997;Anderson, 1997a, 1997b;Zhong et al, 2000); the role of plates and slabs (Gurnis and Hager, 1988;Gurnis and Zhong, 1991;Zhong and Gurnis, 1992;King and Hager, 1994;Bercovici, 1995;Chen and King, 1998;Trompert and Hansen, 1998;Tackley, 2000;Billen and Gurnis, 2003;Billen and Hirth, 2007;Tackley, 2008, 2011;Billen, 2008Billen, , 2010Coltice et al, 2013Coltice et al, ,2014.…”