Nonuniformity of the constitutive law parameters for shear rupture and quasistatic nucleation to dynamic rupture: a physical model of earthquake generation processes.

Based on the recent high-resolution laboratory experiments on propagating shear rupture, the constitutive law that governs shear rupture processes is discussed in view of the physical principles and constraints, and a specific constitutive law is proposed for shear rupture. It is demonstrated that nonuniform distributions of the constitutive law parameters on the fault are necessary for creating the nucleation process, which consists of two phases: (i) a stable, quasistatic phase, and (ii) the subsequent accelerating phase. Physical models of the breakdown zone and the nucleation zone are presented for shear rupture in the brittle regime. The constitutive law for shear rupture explicitly includes a scaling parameter Dc that enables one to give a common interpretation to both small scale rupture in the laboratory and large scale rupture as earthquake source in the Earth. Both the breakdown zone size Xc and the nucleation zone size L are prescribed and scaled by Dc, which in turn is prescribed by a characteristic length lambda c representing geometrical irregularities of the fault. The models presented here make it possible to understand the earthquake generation process from nucleation to unstable, dynamic rupture propagation in terms of physics. Since the nucleation process itself is an immediate earthquake precursor, deep understanding of the nucleation process in terms of physics is crucial for the short-term (or immediate) earthquake prediction.

Diffusion and formation of microtubule asters: physical processes versus biochemical regulation.

Microtubule asters forming the mitotic spindle are assembled around two centrosomes through the process of dynamic instability in which microtubules alternate between growing and shrinking states. By modifying the dynamics of this assembly process, cell cycle enzymes, such as cdc2 cyclin kinases, regulate length distributions in the asters. It is believed that the same enzymes control the number of assembled microtubules by changing the "nucleating activity" of the centrosomes. Here we show that assembly of microtubule asters may be strongly altered by effects connected with diffusion of tubulin monomers. Theoretical analysis of a simple model describing assembly of microtubule asters clearly shows the existence of a region surrounding the centrosome depleted in GTP tubulin. The number of assembled microtubules may in some cases be limited by this depletion effect rather than by the number of available nucleation sites on the centrosome.