Contact Changes of Sheared Systems: Scaling, Correlations, and Mechanisms

We probe the onset and effect of contact changes in 2D soft harmonic particle packings which are sheared quasistatically under controlled strain. First, we show that in the majority of cases, the first contact changes correspond to the creation or breaking of contacts on a single particle, with contact breaking overwhelmingly likely for low pressures and/or small systems, and contact making and breaking equally likely for large pressures and in the thermodynamic limit. The statistics of the corresponding strains are near-Poissonian. The mean characteristic strains exhibit scaling with the number of particles N and pressure P, and reveal the existence of finite size effects akin to those seen for linear response quantities. Second, we show that linear response accurately predicts the strains of the first contact changes, which allows us to study the scaling of the characteristic strains of making and breaking contacts separately. Both of these show finite size scaling, and we formulate scaling arguments that are consistent with the observed behavior. Third, we probe the effect of the first contact change on the shear modulus G, and show in detail how the variation of G remains smooth and bounded in the large system size limit: even though contact changes occur then at vanishingly small strains, their cumulative effect, even at a fixed value of the strain, are limited, so that effectively, linear response remains well-defined. Fourth, we explore multiple contact changes under shear, and find strong and surprising correlations between alternating making and breaking events. Fifth, we show that by making a link with extremal statistics, our data is consistent with a very slow crossover to self averaging with system size, so that the thermodynamic limit is reached much more slowly than expected based on finite size scaling of elastic quantities or contact breaking strains

Softening and Yielding of Soft Glassy Materials

Solids deform and fluids flow, but soft glassy materials, such as emulsions, foams, suspensions, and pastes, exhibit an intricate mix of solid and liquid-like behavior. While much progress has been made to understand their elastic (small strain) and flow (infinite strain) properties, such understanding is lacking for the softening and yielding phenomena that connect these asymptotic regimes. Here we present a comprehensive framework for softening and yielding of soft glassy materials, based on extensive numerical simulations of oscillatory rheological tests, and show that two distinct scenarios unfold depending on the material's packing density. For dense systems, there is a single, pressure-independent strain where the elastic modulus drops and the particle motion becomes diffusive. In contrast, for weakly jammed systems, a two-step process arises: at an intermediate softening strain, the elastic and loss moduli both drop down and then reach a new plateau value, whereas the particle motion becomes diffusive at the distinctly larger yield strain. We show that softening is associated with an extensive number of microscopic contact changes leading to a non-analytic rheological signature. Moreover, the scaling of the softening strain with pressure suggest the existence of a novel pressure scale above which softening and yielding coincide, and we verify the existence of this crossover scale numerically. Our findings thus evidence the existence of two distinct classes of soft glassy materials -- jamming dominated and dense -- and show how these can be distinguished by their rheological fingerprint.Comment: 9 pages, 11 figures, to appear in Soft Matte

Bose-Einstein Correlations and the Equation of State of Nuclear Matter

Within a relativistic hydrodynamic framework, we use four different equations of state of nuclear matter to compare to experimental spectra from CERN/SPS experiments NA44 and NA49. Freeze-out hypersurfaces and Bose-Einstein correlation functions for identical pion pairs are discussed. We find that two-pion Bose-Einstein interferometry measures the relationship between the temperature and the energy density in the equation of state during the late hadronic stage of the fireball expansion. Little sensitivity of the light-hadron data to a quark-gluon plasma phase-transition is seen.Comment: 4 pages, including 4 figures. You can also download a PostScript file of the manuscript from http://p2hp2.lanl.gov/people/schlei/eprint.htm

Model for the Scaling of Stresses and Fluctuations in Flows near Jamming

We probe flows of soft, viscous spheres near the jamming point, which acts as a critical point for static soft spheres. Starting from energy considerations, we find nontrivial scaling of velocity fluctuations with strain rate. Combining this scaling with insights from jamming, we arrive at an analytical model that predicts four distinct regimes of flow, each characterized by rational-valued scaling exponents. Both the number of regimes and values of the exponents depart from prior results. We validate predictions of the model with simulations.Comment: 4 pages, 5 figures (revised text and one new figure). To appear in Phys. Rev. Let

Stresses in Smooth Flows of Dense Granular Media

The form of the stress tensor is investigated in smooth, dense granular flows which are generated in split-bottom shear geometries. We find that, within a fluctuation fluidized spatial region, the form of the stress tensor is directly dictated by the flow field: The stress and strain-rate tensors are co-linear. The effective friction, defined as the ratio between shear and normal stresses acting on a shearing plane, is found not to be constant but to vary throughout the flowing zone. This variation can not be explained by inertial effects, but appears to be set by the local geometry of the flow field. This is in agreement with a recent prediction, but in contrast with most models for slow grain flows, and points to there being a subtle mechanism that selects the flow profiles.Comment: 5 pages, 4 figure

Contact Changes near Jamming

We probe the onset and effect of contact changes in soft harmonic particle packings which are sheared quasistatically. We find that the first contact changes are the creation or breaking of contacts on a single particle. We characterize the critical strain, statistics of breaking versus making a contact, and ratio of shear modulus before and after such events, and explain their finite size scaling relations. For large systems at finite pressure, the critical strain vanishes but the ratio of shear modulus before and after a contact change approaches one: linear response remains relevant in large systems. For finite systems close to jamming the critical strain also vanishes, but here linear response already breaks down after a single contact change.Comment: 5 pages, 4 figure

Jamming in finite systems: stability, anisotropy, fluctuations and scaling

Athermal packings of soft repulsive spheres exhibit a sharp jamming transition in the thermodynamic limit. Upon further compression, various structural and mechanical properties display clean power-law behavior over many decades in pressure. As with any phase transition, the rounding of such behavior in finite systems close to the transition plays an important role in understanding the nature of the transition itself. The situation for jamming is surprisingly rich: the assumption that jammed packings are isotropic is only strictly true in the large-size limit, and finite-size has a profound effect on the very meaning of jamming. Here, we provide a comprehensive numerical study of finite-size effects in sphere packings above the jamming transition, focusing on stability as well as the scaling of the contact number and the elastic response.Comment: 20 pages, 12 figure

Soft Sphere Packings at Finite Pressure but Unstable to Shear

When are athermal soft sphere packings jammed ? Any experimentally relevant definition must at the very least require a jammed packing to resist shear. We demonstrate that widely used (numerical) protocols in which particles are compressed together, can and do produce packings which are unstable to shear - and that the probability of generating such packings reaches one near jamming. We introduce a new protocol that, by allowing the system to explore different box shapes as it equilibrates, generates truly jammed packings with strictly positive shear moduli G. For these packings, the scaling of the average of G is consistent with earlier results, while the probability distribution P(G) exhibits novel and rich scalingComment: 5 pages, 6 figures. Resubmitted to Physical Review Letters after a few change

Silver(I) triflate-catalyzed protocol for the post-ugi synthesis of spiroindolines

A silver(I) triflate-catalyzed protocol for the post-Ugi synthesis of tetracyclic spiroindolines has been developed. The protocol worked best for indole-3-carbaldehyde-derived Ugi adducts obtained using anilines and 3-aryl propiolic acids. Thus, it is complementary to the previous cationic gold-catalyzed procedure that was developed for analogues Ugi substrates derived from aliphatic amines and 3-alkyl propiolic acids. Furthermore, we have demonstrated that under our new settings this domino Friedel-Crafts ipso cyclization / imine trapping process could be efficiently combined with the preceding four-component Ugi reaction into a two-step one-pot transformation