Liu, Andrea J
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Publication Interplay of rearrangements, strain, and local structure during avalanche propagation(2021-01-01) Zhang, Ge; Ridout, Sean; Liu, Andrea JJammed soft disks exhibit avalanches of particle rearrangements under quasistatic shear. We introduce a framework for understanding the statistics of the progression of avalanches. We follow the avalanches (simulated using steepest descent energy minimization) to decompose them into individual localized rearrangements. We characterize the local structural environment of each particle by a machine-learned quantity, softness, designed to be highly correlated with rearrangements, and analyze the interplay between softness, rearrangements and strain. Local yield strain has long been incorporated into elastoplastic models; here we show that softness provides a useful proxy for local yield strain. Our findings demonstrate that elastoplastic models must take into account the fully tensorial strain field in order to include the effects of changes in local yield strain due to rearrangements, and introduce the equations underpinning a structuro-elastoplastic model that includes local softness.Publication Finite-Size Scaling at the Jamming Transition(2012-08-27) Goodrich, Carl P; Liu, Andrea J; Nagel, Sidney RWe present an analysis of finite-size effects in jammed packings of N soft, frictionless spheres at zero temperature. There is a 1/N correction to the discrete jump in the contact number at the transition so that jammed packings exist only above isostaticity. As a result, the canonical power-law scalings of the contact number and elastic moduli break down at low pressure. These quantities exhibit scaling collapse with a nontrivial scaling function, demonstrating that the jamming transition can be considered a phase transition. Scaling is achieved as a function of N in both two and three dimensions, indicating an upper critical dimension of 2.Publication Elasticity and Response in Nearly Isostatic Periodic Lattices(2009-11-13) Souslov, Anton; Liu, Andrea J.; Lubensky, Tom C.The square and kagome lattices with nearest-neighbor springs of spring constant k are isostatic with a number of zero-frequency modes that scale with the perimeter. We analytically study the approach to this isostatic limit as the spring constant k' for the next-nearest-neighbor bond vanishes. We identify a characteristic frequency ω* ~ √(k') and length ω* ~ √(k/k' ) for both lattices. The shear modules C44 = k' of the square lattice vanishes with k', but that for the kagome lattice does not.Publication Low-Frequency Vibrations of Soft Colloidal Glasses(2010-07-09) Chen, Ke; Ellenbroek, Wouter G; Zhang, Zexin; Yunker, Peter J; Chen, Daniel T.N.; Henkes, Silke; Brito, Carolina; Dauchot, Oliver; Liu, Andrea J; Van Saarloos, Wim; Yodh, Arjun GWe conduct experiments on two-dimensional packings of colloidal thermosensitive hydrogel particles whose packing fraction can be tuned above the jamming transition by varying the temperature. By measuring displacement correlations between particles, we extract the vibrational properties of a corresponding ‘‘shadow’’ system with the same configuration and interactions, but for which the dynamics of the particles are undamped. The vibrational properties are very similar to those predicted for zerotemperature sphere packings and found in atomic and molecular glasses; there is a boson peak at low frequency that shifts to higher frequency as the system is compressed above the jamming transition.Publication Equivalence of Glass Transition and Colloidal Glass Transition in the Hard-Sphere Limit(2009-12-10) Xu, Ning; Haxton, Thomas K.; Liu, Andrea J.; Nagel, Sidney R.We show that the slowing of the dynamics in simulations of several model glass-forming liquids is equivalent to the hard-sphere glass transition in the low-pressure limit. In this limit, we find universal behavior of the relaxation time by collapsing molecular-dynamics data for all systems studied onto a single curve as a function of T/p, the ratio of the temperature to the pressure. At higher pressures, there are deviations from this universal behavior that depend on the interparticle potential, implying that additional physical processes must enter into the dynamics of glass formation.Publication Vibrational Modes Identify Soft Spots in a Sheared Disordered Packing(2011-08-31) Manning, M. Lisa; Liu, Andrea JWe analyze low-frequency vibrational modes in a two-dimensional, zero-temperature, quasistatically sheared model glass to identify a population of structural ‘‘soft spots’’ where particle rearrangements are initiated. The population of spots evolves slowly compared to the interval between particle rearrangements, and the soft spots are structurally different from the rest of the system. Our results suggest that disordered solids flow via localized rearrangements that tend to occur at soft spots, which are analogous to dislocations in crystalline solids.Publication Temperature-Pressure Scaling for Air-Fluidized Grains near Jamming(2012-03-30) Daniels, L. J.; Haxton, T. K.; Liu, Andrea J; Xu, N.; Durian, Douglas J.We present experiments on a monolayer of air-fluidized beads in which a jamming transition is approached by increasing pressure, increasing packing fraction, and decreasing kinetic energy. This is accomplished, along with a noninvasive measurement of pressure, by tilting the system and examining behavior versus depth. We construct an equation of state and analyze relaxation time versus effective temperature. By making time and effective temperature dimensionless using factors of pressure, bead size, and bead mass, we obtain a good collapse of the data but to a functional form that differs from that of thermal hard-sphere systems. The relaxation time appears to diverge only as the effective temperature to pressure ratio goes to zero.Publication Why is Random Close Packing Reproducible?(2007-10-09) Kamien, Randal D.; Liu, Andrea JWe link the thermodynamics of colloidal suspensions to the statistics of regular and random packings. Random close packing has defied a rigorous definition yet, in three dimensions, there is near universal agreement on the volume fraction at which it occurs.We conjecture that the common value of фrcp ≈ 0.64 arises from a divergence in the rate at which accessible states disappear.We relate this rate to the equation of state for a hard-sphere fluid on a metastable, noncrystalline branch.Publication Branching, Capping, and Severing in Dynamic Actin Structures(2007-08-07) Gopinathan, Anjay; Lee, Kun-Chun; Schwarz, Jennifer; Liu, Andrea JBranched actin networks at the leading edge of a crawling cell evolve via protein-regulated processes such as polymerization, depolymerization, capping, branching, and severing. A formulation of these processes is presented and analyzed to study steady-state network morphology. In bulk, we identify several scaling regimes in severing and branching protein concentrations and find that the coupling between severing and branching is optimally exploited for conditions in vivo. Near the leading edge, we find qualitative agreement with the in vivo morphology.Publication Energy Transport in Jammed Sphere Packings(2009-01-21) Xu, Ning; Vitelli, Vincenzo; Wyart, Matthieu; Liu, Andrea J.; Nagel, Sidney R.We calculate the normal modes of vibration in jammed sphere packings to obtain the energy diffusivity, a spectral measure of transport. At the boson peak frequency, we find an Ioffe-Regel crossover from a diffusivity that drops rapidly with frequency to one that is nearly frequency independent. This crossover frequency shifts to zero as the system is decompressed towards the jamming transition, providing unambiguous evidence of a regime in frequency of nearly constant diffusivity. Such a regime, postulated to exist in glasses to explain the temperature dependence of the thermal conductivity, therefore appears to arise from properties of the jamming transition.