Aging and Failure of a Polymer Chain under Tension.

The rupture of a polymer chain maintained at temperature T under fixed tension is prototypical to a wide array of systems failing under constant external stress and random perturbations. Past research focused on analytic and numerical studies of the mean rate of collapse of such a chain. Surprisingly, an analytic calculation of the probability distribution function (PDF) of collapse rates appears to be lacking. Since rare events of rapid collapse can be important and even catastrophic, we present here a theory of this distribution, with a stress on its tail of fast rates. We show that the tail of the PDF is a power law with a universal exponent that is theoretically determined. Extensive numerics validate the offered theory. Lessons pertaining to other problems of the same type are drawn.

Transition from Static to Dynamic Friction in an Array of Frictional Disks.

The nature of an instability that controls the transition from static to dynamical friction is studied in the context of an array of frictional disks that are pressed from above on a substrate. In this case the forces are all explicit and Newtonian dynamics can be employed without any phenomenological assumptions. We show that an oscillatory instability that had been discovered recently is responsible for the transition, allowing individual disks to spontaneously reach the Coulomb limit and slide with dynamic friction. The transparency of the model allows a full understanding of the phenomenon, including the speeds of the waves that travel from the trailing to the leading edge and vice versa.

Anomalous elasticity and emergent dipole screening in three-dimensional amorphous solids.

In recent work, we developed a screening theory for describing the effect of plastic events in amorphous solids on its emergent mechanics. The suggested theory uncovered an anomalous mechanical response of amorphous solids where plastic events collectively induce distributed dipoles that are analogous to dislocations in crystalline solids. The theory was tested against various models of amorphous solids in two dimensions, including frictional and frictionless granular media and numerical models of amorphous glass. Here we extend our theory to screening in three-dimensional amorphous solids and predict the existence of anomalous mechanics similar to the one observed in two-dimensional systems. We conclude by interpreting the mechanical response as the formation of nontopological distributed dipoles that have no analog in the crystalline defects literature. Having in mind that the onset of dipole screening is reminiscent of Kosterlitz-Thouless and hexatic transitions, the finding of dipole screening in three dimensions is surprising.

Generic mechanism for remote triggering of earthquakes.

"Remote triggering" refers to the inducement of earthquakes by weak perturbations that emanate from faraway sources, typically intense earthquakes that happen at much larger distances than their nearby aftershocks, sometimes even around the globe. Here, we propose a mechanism for this phenomenon; the proposed mechanism is generic, resulting from the breaking of Hamiltonian symmetry due to the existence of friction. We allow a transition from static to dynamic friction. Linearly stable stressed systems display giant sensitivity to small perturbations of arbitrary frequency (without a need for resonance), which trigger an instability with exponential oscillatory growth. Once nonlinear effects kick in, the blow up in mean-square displacements can reach 15-20 orders of magnitude. Analytic and numerical results of the proposed model are presented and discussed.

Giant amplification of small perturbations in frictional amorphous solids.

Catastrophic events in nature can be often triggered by small perturbations, with "remote triggering" of earthquakes being an important example. Here we present a mechanism for the giant amplification of small perturbations that is expected to be generic in systems whose dynamics is not derivable from a Hamiltonian. We offer a general discussion of the typical instabilities involved (being oscillatory with an exponential increase of noise) and examine in detail the normal forms that determine the relevant dynamics. The high sensitivity to external perturbations is explained for systems with and without dissipation. Numerical examples are provided using the dynamics of frictional granular matter. Finally, we point out the relationship of the presently discussed phenomenon to the highly topical issue of "exceptional points" in quantum models with non-Hermitian Hamiltonians.