Itamar Procaccia

Dissipation, or the loss of energy conservation, is necessarily related to symmetry breaking. Here we study the symmetry breaking that is responsible for dissipation in the mechanical response of amorphous solids to quasi-static strains. To this aim we consider carefully just one cycle of strain, to reveal the source of dissipation. In general the response can be conservative or dissipative, with a sharp transition between these options as a function of preparation parameters, accompanied by translation and rotational symmetry breaking and the onset of screening. We choose an example for which the mesoscopic theory can be solved exactly, and the microscopic physics can be revealed by numerical simulations. The mechanism of energy dissipation (when it exists) is explored in detail, showing that in this case it is due to the breaking of rotational symmetry.

A careful examination of the Quasi-Localized Modes (QLMs) that exist in a generic atomistic model of a glass former reveals at least two types of them, each exhibiting a different density of states, one depending on the frequency as and the other as . The properties of the glassy energy landscape that is responsible for the two types of modes is examined here, explaining the analytic feature responsible for the creations of (at least) two families of QLMs. It is argued that the QLMs that are revealed by diagonalizing the Hessian matrix are not related to possibly existing Two-Level Systems (TLS).

We revisit the problem of the stress distribution in a frictional sandpile with both normal and tangential (frictional) inter-granular forces, under gravity, equipped with a new numerical method of generating such assemblies.

It is known [H. G. E. Hentschel et al., Phys. Rev. E 83, 061101 (2011)] that amorphous solids at zero temperature do not possess a nonlinear elasticity theory: besides the shear modulus, which exists, none of the higher order coefficients exist in the thermodynamic limit. Here we show that the same phenomenon persists up to temperatures comparable to that of the glass transition. The zero-temperature mechanism due to the prevalence of dangerous plastic modes of the Hessian matrix is replaced by anomalous stress fluctuations that lead to the divergence of the variances of the higher order elastic coefficients. The conclusion is that in amorphous solids elasticity can never be decoupled from plasticity: the nonlinear response is very substantially plastic.

We employ a recently developed model that allows the study of two-dimensional brittle crack propagation under fixed grip boundary conditions. The crack development highlights the importance of voids which appear ahead of the crack as observed in experiments on the nanoscale. The appearance of these voids is responsible for roughening the crack path on small scales, in agreement with theoretical expectations. With increasing speed of propagation one observes the branching instabilities that were reported in experiments. The simulations allow understanding the phenomena by analyzing the elastic stress field that accompanies the crack dynamics. DOI: http://dx.doi.org/10.1103/PhysRevE.87.012801 ©2013 American Physical Society

A free material surface which supports surface diffusion becomes unstable when put under external nonhydrostatic stress. Since the chemical potential on a stressed surface is larger inside an indentation, small shape fluctuations develop because material preferentially diffuses out of indentations. When the bulk of the material is purely elastic one expects this instability to run into a finite-time cusp singularity. It is shown here that this singularity is cured by plastic effects in the material, turning the singular solution to a regular crack.

We address the “additive equivalence” discovered by Virk and co-workers: drag reduction affected by flexible and rigid rodlike polymers added to turbulent wall-bounded flows is limited from above by a very similar maximum drag reduction (MDR) asymptote. Considering the equations of motion of rodlike polymers in wall-bounded turbulent ensembles, we show that although the microscopic mechanism of attaining the MDR is very different, the macroscopic theory is isomorphic, rationalizing the interesting experimental observations.