Some exact results for the trapping of subdiffusive particles in one dimension

We study a generalization of the standard trapping problem of random walk theory in which particles move subdiffusively on a one-dimensional lattice. We consider the cases in which the lattice is filled with a one-sided and a two-sided random distribution of static absorbing traps with concentration c. The survival probability Phi(t) that the random walker is not trapped by time t is obtained exactly in both versions of the problem through a fractional diffusion approach. Comparison with simulation results is madeComment: 15 pages, 2 figure

Fault-zone healing effectiveness and the structural evolution of strike-slip fault systems

Numerical simulations of long-term crustal deformation reveal the important role that damage healing (i.e. fault-zone strengthening) plays in the structural evolution of strike-slip fault systems. We explore the sensitivity of simulated fault zone structure and evolution patterns to reasonable variations in the healing-rate parameters in a continuum damage rheology model. Healing effectiveness, defined herein as a function of the healing rate parameters, describes the post-seismic healing process in terms of the characteristic inter-seismic damage level expected along fault segments in our simulations. Healing effectiveness is shown to control the spatial extent of damage zones and the long-term geometrical complexity of strike-slip fault systems in our 3-D simulations. Specifically, simulations with highly effective healing form interseismically shallow fault cores bracketed by wide zones of off-fault damage. Ineffective healing yields deeper fault cores that persist throughout the interseismic interval, and narrower zones of off-fault damage. Furthermore, highly effective healing leads to a rapid evolution of an initially segmented fault system to a simpler through-going fault, while ineffective healing along a segmented fault preserves complexities such as stepovers and fault jogs. Healing effectiveness and its role in fault evolution in our model may be generalized to describe how heat, fluid-flow and stress conditions (that contribute to fault-zone healing) affect fault-zone structure and fault system evolution patterns

Upper limit on damage zone thickness controlled by seismogenic depth

The thickness of fault damage zones, a characteristic length of the cross‐fault distribution of secondary fractures, significantly affects fault stress, earthquake rupture, ground motions, and crustal fluid transport. Field observations indicate that damage zone thickness scales with accumulated fault displacement at short displacements but saturates at a few hundred meters for displacements larger than a few kilometers. To explain this transition of scaling behavior, we conduct 3D numerical simulations of dynamic rupture with off‐fault inelastic deformation on long strike‐slip faults. We find that the distribution of coseismic inelastic strain is controlled by the transition from crack‐like to pulse‐like rupture propagation associated with saturation of the seismogenic depth. The yielding zone reaches its maximum thickness when the rupture becomes a stable pulse‐like rupture. Considering fracture mechanics theory, we show that seismogenic depth controls the upper bound of damage zone thickness on mature faults by limiting the efficiency of stress concentration near earthquake rupture fronts. We obtain a quantitative relation between limiting damage zone thickness, background stress, dynamic fault strength, off‐fault yield strength, and seismogenic depth, which agrees with first‐order field observations. Our results help link dynamic rupture processes with field observations and contribute to a fundamental understanding of damage zone properties

Earthquakes: from chemical alteration to mechanical rupture

In the standard rebound theory of earthquakes, elastic deformation energy is progressively stored in the crust until a threshold is reached at which it is suddenly released in an earthquake. We review three important paradoxes, the strain paradox, the stress paradox and the heat flow paradox, that are difficult to account for in this picture, either individually or when taken together. Resolutions of these paradoxes usually call for additional assumptions on the nature of the rupture process (such as novel modes of deformations and ruptures) prior to and/or during an earthquake, on the nature of the fault and on the effect of trapped fluids within the crust at seismogenic depths. We review the evidence for the essential importance of water and its interaction with the modes of deformations. Water is usually seen to have mainly the mechanical effect of decreasing the normal lithostatic stress in the fault core on one hand and to weaken rock materials via hydrolytic weakening and stress corrosion on the other hand. We also review the evidences that water plays a major role in the alteration of minerals subjected to finite strains into other structures in out-of-equilibrium conditions. This suggests novel exciting routes to understand what is an earthquake, that requires to develop a truly multidisciplinary approach involving mineral chemistry, geology, rupture mechanics and statistical physics.Comment: 44 pages, 1 figures, submitted to Physics Report

Quantum transport in ultracold atoms

Ultracold atoms confined by engineered magnetic or optical potentials are ideal systems for studying phenomena otherwise difficult to realize or probe in the solid state because their atomic interaction strength, number of species, density, and geometry can be independently controlled. This review focuses on quantum transport phenomena in atomic gases that mirror and oftentimes either better elucidate or show fundamental differences with those observed in mesoscopic and nanoscopic systems. We discuss significant progress in performing transport experiments in atomic gases, contrast similarities and differences between transport in cold atoms and in condensed matter systems, and survey inspiring theoretical predictions that are difficult to verify in conventional setups. These results further demonstrate the versatility offered by atomic systems in the study of nonequilibrium phenomena and their promise for novel applications.Comment: 24 pages, 7 figures. A revie

A Physics‐Based Rock Friction Constitutive Law: Steady State Friction

Experiments measuring friction over a wide range of sliding velocities find that the value of the friction coefficient varies widely: friction is high and behaves according to the rate and state constitutive law during slow sliding, yet markedly weakens as the sliding velocity approaches seismic slip speeds. We introduce a physics‐based theory to explain this behavior. Using conventional microphysics of creep, we calculate the velocity and temperature dependence of contact stresses during sliding, including the thermal effects of shear heating. Contacts are assumed to reach a coupled thermal and mechanical steady state, and friction is calculated for steady sliding. Results from theory provide good quantitative agreement with reported experimental results for quartz and granite friction over 11 orders of magnitude in velocity. The new model elucidates the physics of friction and predicts the connection between friction laws to independently determined material parameters. It predicts four frictional regimes as function of slip rate: at slow velocity friction is either velocity strengthening or weakening, depending on material parameters, and follows the rate and state friction law. Differences between surface and volume activation energies are the main control on velocity dependence. At intermediate velocity, for some material parameters, a distinct velocity strengthening regime emerges. At fast sliding, shear heating produces thermal softening of friction. At the fastest sliding, melting causes further weakening. This theory, with its four frictional regimes, fits well previously published experimental results under low temperature and normal stress

The role of the peripheral and central nervous systems in rotator cuff disease

Rotator cuff (RC) disease is an extremely common condition associated with shoulder pain, reduced functional capacities and impaired quality of life. It primarily involves alterations in tendon health and mechanical properties that can ultimately lead to tendon failure. RC tendon tears induce progressive muscular changes that negatively impact surgical reparability of the RC tendons and clinical outcomes. At the same time, a significant base of clinical data suggests a relatively weak relationship between RC integrity and clinical presentation, emphasizing the multifactorial aspects of RC disease. This review aims to summarize the potential contribution of peripheral, spinal and supraspinal neural factors that may: (i) exacerbate structural and functional muscle changes induced by tendon tear, (ii) compromise the reversal of these changes during surgery and rehabilitation, (iii) contribute to pain generation and persistence of pain, iv) impair shoulder function through reduced proprioception, kinematics and muscle recruitment, and iv) help to explain interindividual differences and response to treatment. Given the current clinical and scientific interest in peripheral nerve injury in the context of RC disease and surgery, we carefully reviewed this body of literature with a particular emphasis for suprascapular neuropathy that has generated a large number of studies in the past decade. Within this process, we highlight the gaps in current knowledge and suggest research avenues for scientists and clinicians