Reversible plasticity in amorphous materials

A fundamental assumption in our understanding of material rheology is that when microscopic deformations are reversible, the material responds elastically to external loads. Plasticity, i.e. dissipative and irreversible macroscopic changes in a material, is assumed to be the consequence of irreversible microscopic events. Here we show direct evidence for reversible plastic events at the microscopic scale in both experiments and simulations of two-dimensional foam. In the simulations, we demonstrate a link between reversible plastic rearrangement events and pathways in the potential energy landscape of the system. These findings represent a fundamental change in our understanding of materials--microscopic reversibility does not necessarily imply elasticity.Comment: Revised pape

Viscoplasticity and large-scale chain relaxation in glassy-polymeric strain hardening

A simple theory for glassy polymeric mechanical response which accounts for large scale chain relaxation is presented. It captures the crossover from perfect-plastic response to strong strain hardening as the degree of polymerization $N$ increases, without invoking entanglements. By relating hardening to interactions on the scale of monomers and chain segments, we correctly predict its magnitude. Strain activated relaxation arising from the need to maintain constant chain contour length reduces the $N$ dependence of the characteristic relaxation time by a factor $\sim \dot\epsilon N$ during active deformation at strain rate $\dot\epsilon$. This prediction is consistent with results from recent experiments and simulations, and we suggest how it may be further tested experimentally.Comment: The theoretical treatment of the mechanical response has been significantly revised, and the arguments for coherent relaxation during active deformation made more transparen

Elastic Correlations in Nucleosomal DNA Structure

The structure of DNA in the nucleosome core particle is studied using an elastic model that incorporates anisotropy in the bending energetics and twist-bend coupling. Using the experimentally determined structure of nucleosomal DNA [T.J. Richmond and C.A. Davey, Nature {\bf 423}, 145 (2003)], it is shown that elastic correlations exist between twist, roll, tilt, and stretching of DNA, as well as the distance between phosphate groups. The twist-bend coupling term is shown to be able to capture these correlations to a large extent, and a fit to the experimental data yields a new estimate of G=25 nm for the value of the twist-bend coupling constant

Structural Properties of the Sliding Columnar Phase in Layered Liquid Crystalline Systems

Under appropriate conditions, mixtures of cationic and neutral lipids and DNA in water condense into complexes in which DNA strands form local 2D smectic lattices intercalated between lipid bilayer membranes in a lamellar stack. These lamellar DNA-cationic-lipid complexes can in principle exhibit a variety of equilibrium phases, including a columnar phase in which parallel DNA strands from a 2D lattice, a nematic lamellar phase in which DNA strands align along a common direction but exhibit no long-range positional order, and a possible new intermediate phase, the sliding columnar (SC) phase, characterized by a vanishing shear modulus for relative displacement of DNA lattices but a nonvanishing modulus for compressing these lattices. We develop a model capable of describing all phases and transitions among them and use it to calculate structural properties of the sliding columnar phase. We calculate displacement and density correlation functions and x-ray scattering intensities in this phase and show, in particular, that density correlations within a layer have an unusual $\exp(- {\rm const.} \ln^2 r)$ dependence on separation r. We investigate the stability of the SC phase with respect to shear couplings leading to the columnar phase and dislocation unbinding leading to the lamellar nematic phase. For models with interactions only between nearest neighbor planes, we conclude that the SC phase is not thermodynamically stable. Correlation functions in the nematic lamellar phase, however, exhibit SC behavior over a range of length scalesComment: 28 pages, 4 figure

Geometrical families of mechanically stable granular packings

We enumerate and classify nearly all of the possible mechanically stable (MS) packings of bidipserse mixtures of frictionless disks in small sheared systems. We find that MS packings form continuous geometrical families, where each family is defined by its particular network of particle contacts. We also monitor the dynamics of MS packings along geometrical families by applying quasistatic simple shear strain at zero pressure. For small numbers of particles (N < 16), we find that the dynamics is deterministic and highly contracting. That is, if the system is initialized in a MS packing at a given shear strain, it will quickly lock into a periodic orbit at subsequent shear strain, and therefore sample only a very small fraction of the possible MS packings in steady state. In studies with N>16, we observe an increase in the period and random splittings of the trajectories caused by bifurcations in configuration space. We argue that the ratio of the splitting and contraction rates in large systems will determine the distribution of MS-packing geometrical families visited in steady-state. This work is part of our long-term research program to develop a master-equation formalism to describe macroscopic slowly driven granular systems in terms of collections of small subsystems.Comment: 18 pages, 23 figures, 5 table

Measurements of the Yield Stress in Frictionless Granular Systems

We perform extensive molecular dynamics simulations of 2D frictionless granular materials to determine whether these systems can be characterized by a single static yield shear stress. We consider boundary-driven planar shear at constant volume and either constant shear force or constant shear velocity. Under steady flow conditions, these two ensembles give similar results for the average shear stress versus shear velocity. However, near jamming it is possible that the shear stress required to initiate shear flow can differ substantially from the shear stress required to maintain flow. We perform several measurements of the shear stress near the initiation and cessation of flow. At fixed shear velocity, we measure the average shear stress $\Sigma_{yv}$ in the limit of zero shear velocity. At fixed shear force, we measure the minimum shear stress $\Sigma_{yf}$ required to maintain steady flow at long times. We find that in finite-size systems $\Sigma_{yf} > \Sigma_{yv}$, which implies that there is a jump discontinuity in the shear velocity from zero to a finite value when these systems begin flowing at constant shear force. However, our simulations show that the difference $\Sigma_{yf} - \Sigma_{yv}$, and thus the discontinuity in the shear velocity, tend to zero in the infinite system size limit. Thus, our results indicate that in the large system limit, frictionless granular systems are characterized by a single static yield shear stress. We also monitor the short-time response of these systems to applied shear and show that the packing fraction of the system and shape of the velocity profile can strongly influence whether or not the shear stress at short times overshoots the long-time average value.Comment: 7 pages and 6 figure

Constraint optimization and landscapes

We describe an effective landscape introduced in [1] for the analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring. This geometric construction reexpresses these problems in the more familiar terms of optimization in rugged energy landscapes. In particular, it allows one to understand the puzzling fact that unsophisticated programs are successful well beyond what was considered to be the `hard' transition, and suggests an algorithm defining a new, higher, easy-hard frontier.Comment: Contribution to STATPHYS2

Nonlinear Elasticity of the Sliding Columnar Phase

The sliding columnar phase is a new liquid-crystalline phase of matter composed of two-dimensional smectic lattices stacked one on top of the other. This phase is characterized by strong orientational but weak positional correlations between lattices in neighboring layers and a vanishing shear modulus for sliding lattices relative to each other. A simplified elasticity theory of the phase only allows intralayer fluctuations of the columns and has three important elastic constants: the compression, rotation, and bending moduli, $B$, $K_y$, and $K$. The rotationally invariant theory contains anharmonic terms that lead to long wavelength renormalizations of the elastic constants similar to the Grinstein-Pelcovits renormalization of the elastic constants in smectic liquid crystals. We calculate these renormalizations at the critical dimension $d=3$ and find that $K_y(q) \sim K^{1/2}(q) \sim B^{-1/3}(q) \sim (\ln(1/q))^{1/4}$, where $q$ is a wavenumber. The behavior of $B$, $K_y$, and $K$ in a model that includes fluctuations perpendicular to the layers is identical to that of the simple model with rigid layers. We use dimensional regularization rather than a hard-cutoff renormalization scheme because ambiguities arise in the one-loop integrals with a finite cutoff.Comment: This file contains 18 pages of double column text in REVTEX format and 6 postscript figure

Jamming in Systems Composed of Frictionless Ellipse-Shaped Particles

We study the structural and mechanical properties of jammed ellipse packings, and find that the nature of the jamming transition in these systems is fundamentally different from that for spherical particles. Ellipse packings are generically hypostatic with more degrees of freedom than constraints. The spectra of low energy excitations possess two gaps and three distinct branches over a range of aspect ratios. In the zero compression limit, the energy of the modes in the lowest branch increases {\it quartically} with deformation amplitude, and the density of states possesses a $\delta$-function at zero frequency. We identify scaling relations that collapse the low-frequency part of the spectra for different aspect ratios. Finally, we find that the degree of hypostaticity is determined by the number of quartic modes of the packing.Comment: 4 pages, 4 figure

On the study of jamming percolation

We investigate kinetically constrained models of glassy transitions, and determine which model characteristics are crucial in allowing a rigorous proof that such models have discontinuous transitions with faster than power law diverging length and time scales. The models we investigate have constraints similar to that of the knights model, introduced by Toninelli, Biroli, and Fisher (TBF), but differing neighbor relations. We find that such knights-like models, otherwise known as models of jamming percolation, need a ``No Parallel Crossing'' rule for the TBF proof of a glassy transition to be valid. Furthermore, most knight-like models fail a ``No Perpendicular Crossing'' requirement, and thus need modification to be made rigorous. We also show how the ``No Parallel Crossing'' requirement can be used to evaluate the provable glassiness of other correlated percolation models, by looking at models with more stable directions than the knights model. Finally, we show that the TBF proof does not generalize in any straightforward fashion for three-dimensional versions of the knights-like models.Comment: 13 pages, 18 figures; Spiral model does satisfy property