Andrea J. Liu

Random Packings of Frictionless Particles

We conduct numerical simulations of random packings of frictionless particles at T = 0. The packing fraction where the pressure becomes nonzero is the same as the jamming threshold, where the static shear modulus becomes nonzero. The distribution of threshold packing fractions narrows, and its peak approaches random close packing as the system size increases. For packing fractions within the peak, there is no self-averaging, leading to exponential decay of the interparticle force distribution.

Spotted vesicles, striped micelles and Janus assemblies induced by ligand binding

Selective binding of multivalent ligands within a mixture of polyvalent amphiphiles provides, in principle, a mechanism to drive domain formation in self-assemblies. Divalent cations are shown here to crossbridge polyanionic amphiphiles that thereby demix from neutral amphiphiles and form spots or rafts within vesicles as well as stripes within cylindrical micelles. Calcium and copper crossbridged domains of synthetic block copolymers or natural lipid (PIP2, phosphatidylinositol-4,5-bisphosphate) possess tunable sizes, shapes, and/or spacings that can last for years. Lateral segregation in these ‘responsive Janus assemblies’ couples weakly to curvature and proves restricted within phase diagrams to narrow regimes of pH and cation concentration that are centered near the characteristic binding constants for polyacid interactions. Remixing at high pH is surprising, but a theory for Strong Lateral Segregation (SLS) shows that counterion entropy dominates electrostatic crossbridges, thus illustrating the insights gained into ligand induced pattern formation within self-assemblies.

Generalized Levy walks and the role of chemokines in migration of effector CD8+ T cells

Chemokines have a central role in regulating processes essential to the immune function of T cells, such as their migration within lymphoid tissues and targeting of pathogens in sites of inflammation. Here we track T cells using multi-photon microscopy to demonstrate that the chemokine CXCL10 enhances the ability of CD8+ T cells to control the pathogen Toxoplasma gondii in the brains of chronically infected mice. This chemokine boosts T-cell function in two different ways: it maintains the effector T-cell population in the brain and speeds up the average migration speed without changing the nature of the walk statistics. Notably, these statistics are not Brownian; rather, CD8+ T-cell motility in the brain is well described by a generalized Lévy walk. According to our model, this unexpected feature enables T cells to find rare targets with more than an order of magnitude more efficiency than Brownian random walkers. Thus, CD8+ T-cell behaviour is similar to Lévy strategies reported in organisms ranging from mussels to marine predators and monkeys, and CXCL10 aids T cells in shortening the average time taken to find rare targets.

The three-dimensional Ising model revisited numerically

Several basic universal amplitude ratios are studied afresh for three-dimensional nearest-neighbor Ising models. In revising earlier work, modern estimates of the critical temperature and exponents are used in conjunction with biased inhomogeneous differential approximants to extrapolate the longest available series expansions to find the critical amplitudes: C± for the susceptibility χ; ƒ1± for the correlation length ζ1; A± for the specific heat C(T); and B for the spontaneous magnetization M0. We find C+C- = 4.95±0.15, ƒ1+ƒ1- = 1.960±0.01, A+A- = 0.523±0.009, αA+C+B+ = 0.0581±0.0010, while αA+ (ƒ1+)3 verifies hyperuniversality to within ±0.8%. A method for calculating amplitude ratios which allows for corrections to scaling yields estimates for C+C- and ƒ1+ƒ1- in excellent agreement with those derived from the individual amplitudes. Finally, explicit formulae are given for the numerical evaluation of χ(T), ζ1(T), C(T) and M0(T) over the full temperature range from criticality to T=0 and ∞; corresponding plots and convenient near-critical representations are also presented.

Force Distributions near Jamming and Glass Transitions

We calculate the distribution of interparticle normal forces P(F) near the glass and jamming transitions in model supercooled liquids and foams, respectively. P(F) develops a peak that appears near the glass or jamming transitions, whose height increases with decreasing temperature, decreasing shear stress and increasing packing density. A similar shape of P(F) was observed in experiments on static granular packings. We propose that the appearance of this peak signals the development of a yield stress. The sensitivity of the peak to temperature, shear stress, and density lends credence to the recently proposed generalized jamming phase diagram.

Vibrations and Diverging Length Scales Near the Unjamming Transition

We numerically study the vibrations of jammed packings of particles interacting with finite-range, repulsive potentials at zero temperature. As the packing fraction phi is lowered towards the onset of unjamming at phi(c), the density of vibrational states approaches a nonzero value in the limit of zero frequency. For phi >phi(c), there is a crossover frequency, omega* below which the density of states drops towards zero. This crossover frequency obeys power-law scaling with phi-phi(c). Characteristic length scales, determined from the dominant wave vector contributing to the eigenmode at omega*, diverge as power laws at the unjamming transition.

Thermal vestige of the zero-temperature jamming transition

When the packing fraction is increased sufficiently, loose particulates jam to form a rigid solid in which the constituents are no longer free to move. In typical granular materials and foams, the thermal energy is too small to produce structural rearrangements. In this zero-temperature (T = 0) limit, multiple diverging and vanishing length scales characterize the approach to a sharp jamming transition. However, because thermal motion becomes relevant when the particles are small enough, it is imperative to understand how these length scales evolve as the temperature is increased. Here we used both colloidal experiments and computer simulations to progress beyond the zero-temperature limit to track one of the key parameters—the overlap distance between neighbouring particles—which vanishes at the T = 0 jamming transition. We find that this structural feature retains a vestige of its T = 0 behaviour and evolves in an unusual manner, which has masked its appearance until now. It is evident as a function of packing fraction at fixed temperature, but not as a function of temperature at fixed packing fraction or pressure. Our results conclusively demonstrate that length scales associated with the T = 0 jamming transition persist in thermal systems, not only in simulations but also in laboratory experiments.

Why is random close packing reproducible

We 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 phi{rcp} approximately 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.

Effective Temperatures of a Driven System Near Jamming

Fluctuations in a model of a sheared, zero-temperature foam are studied numerically. Five different quantities that independently reduce to the true temperature in an equilibrium thermal system are calculated. One of the quantities is calculated up to an unknown coefficient. The other four quantities have the same value and all five have the same shear-rate dependence. These results imply that statistical mechanics is useful for the system even though it is far from thermal equilibrium.

Heart-Specific Stiffening in Early Embryos Parallels Matrix and Myosin Expression to Optimize Beating

In development and differentiation, morphological changes often accompany mechanical changes [1], but it is unclear whether or when cells in embryos sense tissue elasticity. The earliest embryo is uniformly pliable, while adult tissues vary widely in mechanics from soft brain and stiff heart to rigid bone [2]. However, cell sensitivity to microenvironment elasticity is debated based in part on results from complex three-dimensional culture models [3]. Regenerative cardiology provides strong motivation to clarify any cell-level sensitivities to tissue elasticity because rigid postinfarct regions limit pumping by the adult heart [4]. Here, we focus on the spontaneously beating embryonic heart and sparsely cultured cardiomyocytes, including cells derived from pluripotent stem cells. Tissue elasticity, Et, increases daily for heart to 1-2 kPa by embryonic day 4 (E4), and although this is ~10-fold softer than adult heart, the beating contractions of E4 cardiomyocytes prove optimal at ~Et,E4 both in vivo and in vitro. Proteomics reveals daily increases in a small subset of proteins, namely collagen plus cardiac-specific excitation-contraction proteins. Rapid softening of the hearts matrix with collagenase or stiffening it with enzymatic crosslinking suppresses beating. Sparsely cultured E4 cardiomyocytes on collagen-coated gels likewise show maximal contraction on matrices with native E4 stiffness, highlighting cell-intrinsic mechanosensitivity. While an optimal elasticity for striation proves consistent with the mathematics of force-driven sarcomere registration, contraction wave speed is linear in Et as theorized for excitation-contraction coupled to matrix elasticity. Pluripotent stem cell-derived cardiomyocytes also prove to be mechanosensitive to matrix and thus generalize the main observation that myosin II organization and contractile function are optimally matched to the load contributed by matrix elasticity.