Liu, Andrea J
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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 Heat Transport in Model Jammed Solids(2010-02-03) Xu, Ning; Vitelli, Vincenzo; Liu, Andrea J; Wyart, Matthieu; Nagel, Sidney RWe calculate numerically the normal modes of vibrations in three-dimensional jammed packings of soft spheres as a function of the packing fraction and obtain the energy diffusivity, a spectral measure of transport that controls sound propagation and thermal conductivity. The crossover frequency between weak and strong phonon scattering is controlled by the coordination and shifts to zero as the system is decompressed toward the critical packing fraction at which rigidity is lost. We present a scaling analysis that relates the packing fraction dependence of the crossover frequency to the anomalous scaling of the shear modulus with compression. Below the crossover, the diffusivity displays a power-law divergence with inverse frequency consistent with Rayleigh law, which suggests that the vibrational modes are primarily transverse waves, weakly scattered by disorder. Above it, a large number of modes appear whose diffusivity plateaus at a nearly constant value before dropping to zero above the localization frequency. The thermal conductivity of a marginally jammed solid just above the rigidity threshold is calculated and related to the one measured experimentally at room temperature for most glasses.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 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 Direct Determination of the Size of Basins of Attraction of Jammed Solids(2011-06-17) Xu, Ning; Frenkel, Daan; Liu, Andrea JWe propose a free-energy-based Monte Carlo method to measure the volume of potential-energy basins in configuration space. Using this approach we can estimate the number of distinct potential-energy minima, even when this number is much too large to be sampled directly. We validate our approach by comparing our results with the direct enumeration of distinct jammed states in small packings of frictionless spheres. We find that the entropy of distinct packings is extensive and that the entropy of distinct hard-sphere packings must have a maximum as a function of packing fraction.Publication Measurement of Correlations between Low-Frequency Vibrational Modes and Particle Rearrangements in Quasi-Two-Dimensional Colloidal Glasses(2011-08-31) Chen, Ke; Manning, M. L.; Yunker, Peter J.; Ellenbroek, Wouter G.; Liu, Andrea J; Zhang, Zexin; Yodh, Arjun G.We investigate correlations between low-frequency vibrational modes and rearrangements in two-dimensional colloidal glasses composed of thermosensitive microgel particles, which readily permit variation of the sample packing fraction. At each packing fraction, the particle displacement covariance matrix is measured and used to extract the vibrational spectrum of the "shadow" colloidal glass (i.e., the particle network with the same geometry and interactions as the sample colloid but absent damping). Rearrangements are induced by successive, small reductions in the packing fraction. The experimental results suggest that low-frequency quasilocalized phonon modes in colloidal glasses, i.e., modes that present low energy barriers for system rearrangements, are spatially correlated with rearrangements in this thermal system.Publication Excess Vibrational Modes and the Boson Peak in Model Glasses(2007-04-24) Xu, Ning; Liu, Andrea J; Wyart, Matthieu; Nagel, Sidney R.The excess low-frequency normal modes for two widely used models of glasses are studied at zero temperature. The onset frequencies for the anomalous modes for both systems agree well with predictions of a variational argument, which is based on analyzing the vibrational energy originating from the excess contacts per particle over the minimum number needed for mechanical stability. Even though both glasses studied have a high coordination number, most of the additional contacts can be considered to be weak.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.