Publications

*Takahiro Hatano,
Friction laws from dimensional-analysis point of view.,
Geophysical Journal International 202, 2159-2162 (2015).

[Summary] Friction laws, which are a key to the understanding of the diversity of earthquakes, are considered theoretically. Using dimensional analysis, the logarithmic dependence of the friction coefficient on the slip velocity and the state variable is derived without any knowledge of the underlying physical processes on the frictional surface. This is based on a simple assumption that the friction coefficient is expressed as the difference from a reference state. Therefore, the functional form of the rate and state dependent friction law itself does not necessarily mean that thermal activation processes dominate friction. It is also shown that if there are two (or more) state variables having the same dimension, we need not assume the logarithmic dependence on the state variables.

Takahiro Hatano, Clément Narteau and Peter Shebalin,
Common dependence on stress for the statistics of granular avalanches and earthquakes,
Scientific Reports 5, 12280 (2015).

[Summary] Both earthquake size-distributions and aftershock decay rates obey power laws. Recent studies have demonstrated the sensibility of their parameters to faulting properties such as focal mechanism, rupture speed or fault complexity. The faulting style dependence may be related to the magnitude of the differential stress, but no model so far has been able to reproduce this behaviour. Here we investigate the statistical properties of avalanches in a dissipative, bimodal particulate system under slow shear. We find that the event size-distribution obeys a power law only in the proximity of a critical volume fraction, whereas power-law aftershock decay rates are observed at all volume fractions accessible in the model. Then, we show that both the exponent of the event size-distribution and the time delay before the onset of the power-law aftershock decay rate are decreasing functions of the shear stress. These results are consistent with recent seismological observations of earthquake size-distribution and aftershock statistics.

Péter Ván, Noa Mitsui, Takahiro Hatano,
Non-equilibrium thermodynamical framework for rate- and state-dependent friction,
Periodica Polytechnica Civil Engineering 59, 583-589 (2015).

[Summary] Rate- and state-dependent friction laws for velocity-step and healing are analysed from a thermodynamic point of view. Assuming a logarithmic deviation from steady-state, a unification of the classical Dieterich and Ruina models of rock friction is proposed.