Earthquake magnitude distribution and aftershocks: A statistical geometry explanation.

The emergence of a power-law distribution for the energy released during an earthquake is investigated in several models. Generic features are identified which are based on the self-affine behavior of the stress field prior to an event. This field behaves at large scale as a random trajectory in one dimension of space and a random surface in two dimensions.

Modeling crack propagation in heterogeneous materials: Griffith's law, intrinsic crack resistance, and avalanches.

Various kinds of heterogeneity in solids, including atomistic discreteness, affect the fracture strength as well as the failure dynamics remarkably. Here we study the effects of an initial crack in a discrete model for fracture in heterogeneous materials, known as the fiber bundle model. We find three distinct regimes for fracture dynamics depending on the initial crack size.

Model for tectonic tremors: Enduring events, moment rate spectrum, and moment-duration scaling.

Numerous attempts have been made to obtain earthquake statistics from a theoretical-physics perspective, but these studies mostly involve regular earthquakes. In recent years, a new category of earthquakes, referred to as slow earthquakes, has been discovered. Slow earthquakes emit only weak or no seismic signals and have different statistics than regular earthquakes.

Failure processes of cemented granular materials.

The mechanics of cohesive or cemented granular materials is complex, combining the heterogeneous responses of granular media, like force chains, with clearly defined material properties. Here we use a discrete element model simulation, consisting of an assemblage of elastic particles connected by softer but breakable elastic bonds, to explore how this class of material deforms and fails under uniaxial compression. We are particularly interested in the connection between the microscopic interactions among the grains or particles and the macroscopic material response.

Unique universal scaling in nanoindentation pop-ins.

Power laws are omnipresent and actively studied in many scientific fields, including plasticity of materials. Here, we report the power-law statistics in the second and subsequent pop-in magnitudes during load-controlled nanoindentation testing, whereas the first pop-in is characterized by Gaussian-like statistics with a well-defined average value. The transition from Gaussian-like to power-law is due to the change in the deformation mechanism from dislocation nucleation to dislocation network evolution in the sharp-indenter induced abruptly decaying stress and dislocation density fields.

Stress Relaxation above and below the Jamming Transition.

We numerically investigate stress relaxation in soft athermal disks to reveal critical slowing down when the system approaches the jamming point. The exponents describing the divergence of the relaxation time differ dramatically depending on whether the transition is approached from the jammed or unjammed phase. This contrasts sharply with conventional dynamic critical scaling scenarios, where a single exponent characterizes both sides.

Universal Relaxation Dynamics of Sphere Packings below Jamming.

We show that non-Brownian suspensions of repulsive spheres below jamming display a slow relaxational dynamics with a characteristic timescale that diverges at jamming. This slow timescale is fully encoded in the structure of the unjammed packing and can be readily measured via the vibrational density of states. We show that the corresponding dynamic critical exponent is the same for randomly generated and sheared packings.

Geological implication of grain-size segregation in dense granular matter.

To the current common belief, grain size segregation in granular matter requires sufficient porosity. Therefore, grain size segregation found in a natural fault gouge could imply elevated fluid pressure and the reduced normal stress on fault, possibly caused by the frictional heat during an earthquake. To clarify whether fluidization is essential to grain size segregation, we conduct numerical simulation on a simple model of fault gouge in a plane shear geometry under constant volume condition: the volume fraction is fixed at 0.

Creeplike behavior in athermal threshold dynamics: Effects of disorder and stress.

We study the dynamical aspects of a statistical-mechanical model for fracture of heterogeneous media: the fiber bundle model with various interaction ranges. Although the model does not include any nontrivial elementary processes such as nonlinear rheology or stochasticity, the system exhibits creeplike behaviors under a constant load being slightly above the critical value. These creeplike behaviors comprise three stages: primary, secondary, and tertiary.

Common dependence on stress for the statistics of granular avalanches and earthquakes.

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.

Growing length and time scales in a suspension of athermal particles.

We simulate a relaxation process of non-Brownian particles in a sheared viscous medium; the system is subject to the small shear strain and then undergoes relaxation. We estimate the exponents with which the relaxation time and the correlation length diverge as the density approaches the jamming density from below. In particular, the dynamic critical exponent is estimated as 4.

Power-law friction in closely packed granular materials.

In order to understand the nature of friction in dense granular materials, a discrete element simulation on granular layers subjected to isobaric plain shear is performed. It is found that the friction coefficient increases as the power of the shear rate, the exponent of which does not depend on the material constants. Using a nondimensional parameter that is known as the inertial number, the power law can be cast in a generalized form so that the friction coefficients at different confining pressures collapse on the same curve.

Dislocation nucleation in shocked fcc solids: effects of temperature and preexisting voids.

Quantitative behaviors of shock-induced dislocation nucleation are investigated by means of molecular dynamics simulations on fcc Lennard-Jones solids: a model argon. In perfect crystals, it is found that the Hugoniot elastic limit (HEL) is a linearly decreasing function of temperature: from near-zero to melting temperatures. In a defective crystal with a void, dislocations are found to nucleate on the void surface.

Spatiotemporal behavior of void collapse in shocked solids.

Molecular dynamics simulations on a three-dimensional defective Lennard-Jones solid containing a void are performed in order to investigate detailed properties of hot spot generation. In addition to the temperature, I monitor the number of energetically colliding particles which characterizes the intensity of shock-enhanced chemistry. This quantity normalized by void volume is found to saturate for nanoscale voids and to be maximized after voids have completely collapsed.

Measuring nonequilibrium temperature of forced oscillators.

The meaning of temperature in nonequilibrium thermodynamics is considered by using a forced harmonic oscillator in a heat bath, where we have two effective temperatures for the position and the momentum, respectively. We propose a concrete model of a thermometer to testify the validity of these different temperatures from the operational point of view. It is found that the measured temperature depends on a specific form of interaction between the system and a thermometer, which means that the zeroth law of thermodynamics cannot be immediately extended to nonequilibrium cases.