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We perform numerical experiments of damped quasi-dynamic fault slip that include a rate-and-state behavior at steady state to simulate earthquakes and a plastic rheology to model permanent strain. The model shear zone has a finite width which represents a natural fault zone. Here we reproduce fast and slow events that follow theoretical and observational scaling relationships for earthquakes and slow slip events (SSEs). We show that the transition between fast and slow slip occurs when the friction drop in the shear zone is equal to a critical value, Δμc. With lower friction drops, SSEs use nearly all of mechanical work to accumulate inelastic strain, while with higher friction drops fast slips use some of the mechanical work to slip frictionally. Our new formulation replaces the state evolution of rate and state by the stress evolution concurrent with accumulation of permanent damage in and around a fault zone. 

A comprehensive study of the local and nonlocal amplitudes contributing to the decayB⁰→K^*0(→K⁺π⁻)μ⁺μ⁻is performed by analysing the phase-space distribution of the decay products. The analysis is based onppcollision data corresponding to an integrated luminosity of 8.4 fb⁻¹collected by the LHCb experiment. This measurement employs for the first time a model of both one-particle and two-particle nonlocal amplitudes, and utilises the complete dimuon mass spectrum without any veto regions around the narrow charmonium resonances. In this way it is possible to explicitly isolate the local and nonlocal contributions and capture the interference between them. The results show that interference with nonlocal contributions, although larger than predicted, only has a minor impact on the Wilson Coefficients determined from the fit to the data. For the local contributions, the Wilson Coefficient$$ {\mathcal{C}}_9 $$$C_9$, responsible for vector dimuon currents, exhibits a 2.1σdeviation from the Standard Model expectation. The Wilson Coefficients$$ {\mathcal{C}}_{10} $$$C_{10}$,$$ {\mathcal{C}}_9^{\prime } $$$C_9^{\prime }$and$$ {\mathcal{C}}_{10}^{\prime } $$$C_{10}^{\prime }$are all in better agreement than$$ {\mathcal{C}}_9 $$$C_9$with the Standard Model and the global significance is at the level of 1.5σ. The model used also accounts for nonlocal contributions fromB⁰→ K^*0[τ⁺τ⁻→ μ⁺μ⁻] rescattering, resulting in the first direct measurement of thebsττvector effective-coupling$$ {\mathcal{C}}_{9\tau } $$$C_{9\tau }$.