Correlation and shear bands in a plastically deformed granular medium

Recent experiments (Le Bouil et al., Phys. Rev. Lett., 2014, 112, 246001) have analyzed the statistics of local deformation in a granular solid undergoing plastic deformation. Experiments report strongly anisotropic correlation between events, with a characteristic angle that was interpreted using elasticity theory and the concept of Eshelby transformations with dilation; interestingly, the shear bands that characterize macroscopic failure occur at an angle that is different from the one observed in microscopic correlations. Here, we interpret this behavior using a mesoscale elastoplastic model of solid flow that incorporates a local Mohr-Coulomb failure criterion. We show that the angle observed in the microscopic correlations can be understood by combining the elastic interactions associated with Eshelby transformation with the local failure criterion. At large strains, we also induce permanent shear bands at an angle that is different from the one observed in the correlation pattern. We interpret this angle as the one that leads to the maximal instability of slip lines

Robust Parameter Selection for Parallel Tempering

This paper describes an algorithm for selecting parameter values (e.g. temperature values) at which to measure equilibrium properties with Parallel Tempering Monte Carlo simulation. Simple approaches to choosing parameter values can lead to poor equilibration of the simulation, especially for Ising spin systems that undergo $1^st$-order phase transitions. However, starting from an initial set of parameter values, the careful, iterative respacing of these values based on results with the previous set of values greatly improves equilibration. Example spin systems presented here appear in the context of Quantum Monte Carlo.Comment: Accepted in International Journal of Modern Physics C 2010, http://www.worldscinet.com/ijmp

Multiscale modeling of kinetic sluggishness in equiatomic NiCoCr and NiCoCrFeMn single-phase solid solutions

Complex, concentrated, multi-component alloys have been shown to display outstanding thermo-mechanical properties, that have been typically attributed to sluggish diffusion, entropic, and lattice distortion effects. Here, we investigate two metal alloys with such exemplary properties, the equiatomic, single-phase, face-centered-cubic (FCC) alloys NiCoCr and NiCoCrFeMn, and we compare their microstructural kinetics to the behaviors in a pure-Ni FCC metal. We perform long-time, kinetic Monte Carlo (kMC) simulations, and we analyze in detail the kinetics of atomic vacancies. We find that vacancies in both concentrated alloys exhibit subdiffusive thermally driven dynamics, in direct contrast to the diffusive dynamics of pure Ni. Subdiffusive dynamics shall be attributed to dynamical sluggishness, that is modeled by a fractional Brownian random walk. Furthermore, we analyze the statistics of waiting times, and we interpret long power-law-distributed rest periods as a direct consequence of barriers' energy-scales and lattice distortions

Induced representations of Hilbert modules over locally C*-algebras and the imprimitivity theorem

We study induced representations of Hilbert modules over locally C*-algebras and their non-degeneracy. We show that if V and W are Morita equivalent Hilbert modules over locally C*-algebras A and B, respectively, then there exists a bijective correspondence between equivalence classes of non-degenerate representations of V and W

Emergent lengthscales in the quenched stresses and elastic response of soft particle packings near jamming

We study stress correlations and elastic response in large-scale computer simulations of two-dimensional particle packings near jamming. We show that there are characteristic lengths in both the stresses and elastic response that diverge in similar ways as the confining pressure approaches zero from above. For the case of the stress field, we show that the power spectrum of the hydrostatic pressure and shear stress agrees with a field-theoretic framework proposed by Henkes and Chakraborty at short to intermediate wavelengths (where the power is flat in Fourier space), but contains significant excess power at wavelengths larger than ~ 50‑100 particle diameters, with the specific crossover point going to larger wavelength at decreasing pressure, consistent with a divergence at p = 0. For the case of the elastic response, we probe the system in three ways: (i) point forcing; (ii) “constrained” homogeneous deformation where the system is driven with no-slip boundary conditions; and (iii) “free periodic” homogeneous deformation. For the point force, we see distinct characteristic lengths for longitudinal and transverse modes each of which diverges in a different way with decreasing pressure with ξT ~ P –0.25 and ξL ~ P –0.4 respectively. For the constrained homogeneous deformation we see a scaling of the local shear modulus with the size of the probing region consistent with ξ ~ P –0.5 similar to the ξL ~ P –0.4 observed in the longitudinal component of the point-response and in perfect agreement with the rigidity length discussed in recently proposed scenarios for jamming. Finally, we show that the transverse and longitudinal contributions to the strain field in response to unconstrained deformation (either volumetric or shear) have markedly different behavior. The transverse contribution is surprisingly invariant with respect to p with localized shear transformations dominating the response down to surprisingly small pressures. The longitudinal contribution develops a feature at small wavelength that intensifies with decreasing p but does not show any appreciable change in length. We interpret this pressure-invariant length as the characteristic shear zone size