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Deformation in the Earth is rarely homogeneous and often occurs in narrow regions of concentrated strain referred to as zones of shear localization. Mylonites found in the continental crust are the manifestation of shear localization (White et al. 1980) and, at the largest scale, shear localization is proposed to be crucial for the generation of tectonic plates from a convecting mantle (Bercovici 1993, 1995b,Bercovici a, 1996, 1998; Bercovici et al. 2000; Trompert and Hansen 1998; Tackley 1998, 2000a, Tackley b,c,d). Shear localization is apparent in many field of physics, including, for example, metallurgy (Lemonds and Needleman 1986), rock mechanics (Poirier 1980; Jin et al. 1998), granular dynamics (Scott 1996; Géminard et al. 1999, e.g.) and glaciology (Yuen and Schubert 1979). However, basic solid-state rheologies, such as elasticity, visco-elasticity, viscous flow and even steady-state non-Newtonian viscous flow, are insufficient by themselves to generate shear-localization; this is because in all such rheologies an increase in deformation or rate of deformation results in greater resistance (i.e., stress) instead of self-weakening and loss of strength. Shear-localization tends to require dynamic feedback mechanisms wherein self-weakening is controlled by a macroscopic variable (such as temperature) or microscopic structure (grain size or microcrack density) whose evolution and concentration are themselves determined by deformation; in this way deformation can induce weakening, which subsequently causes deformation to concentrate on the weak zone (being most easily deformed), causing further weakening, and thus more focusing of deformation, and so on.
One of the most fundamental manifestations of such feedback mechanisms arises from the coupling of viscous heating and temperature-dependent viscosity wherein the zone of dissipative heating weakens and thus focuses deformation, leading to further heating and weakening; this mechanism is thought applicable to problems …