arXiv subjects

Andrea J. Liu

Publications and source records attributed to Andrea J. Liu.

At least 91 records · Page 5Linked to original sources

arXiv2013

Stability of jammed packings I: the rigidity length scale

In 2005, Wyart et al. (Europhys. Lett., 72 (2005) 486) showed that the low frequency vibrational properties of jammed amorphous sphere packings can be understood in terms of a length scale, called l*, that diverges as the system becomes marginally unstable. Despite the tremendous success of this theory, it has been difficult to connect the counting argument that defines l* to other length scales that diverge near the jamming transition. We present an alternate derivation of l* based on the onset of rigidity. This phenomenological approach reveals the physical mechanism underlying the length scale and is relevant to a range of systems for which the original argument breaks down. It also allows us to present the first direct numerical measurement of l*.

cond-mat.soft↗

arXiv2013

Stability of jammed packings II: the transverse length scale

As a function of packing fraction at zero temperature and applied stress, an amorphous packing of spheres exhibits a jamming transition where the system is sensitive to boundary conditions even in the thermodynamic limit. Upon further compression, the system should become insensitive to boundary conditions provided it is sufficiently large. Here we explore the linear response to a large class of boundary perturbations in 2 and 3 dimensions. We consider each finite packing with periodic-boundary conditions as the basis of an infinite square or cubic lattice and study properties of vibrational modes at arbitrary wave vector. We find that the stability of such modes be understood in terms of a competition between plane waves and the anomalous vibrational modes associated with the jamming transition; infinitesimal boundary perturbations become irrelevant for systems that are larger than a length scale that characterizes the transverse excitations. This previously identified length diverges at the jamming transition.

cond-mat.soft↗

arXiv2013

Phonon Dispersion and Elastic Moduli of Two-Dimensional Disordered Colloidal Packings of Soft Particles with Frictional Interactions

Particle tracking and displacement covariance matrix techniques are employed to investigate the phonon dispersion relations of two-dimensional colloidal glasses composed of soft, thermoresponsive microgel particles whose temperature-sensitive size permits \textit{in situ} variation of particle packing fraction. Bulk, $B$, and shear, $G$, moduli of the colloidal glasses are extracted from the dispersion relations as a function of packing fraction, and variation of the ratio $G/B$ with packing fraction is found to agree quantitatively with predictions for jammed packings of frictional soft particles. In addition, $G$ and $B$ individually agree with numerical predictions for frictional particles. This remarkable level of agreement enabled us to extract an energy scale for the inter-particle interaction from the individual elastic constants and to derive an approximate estimate for the inter-particle friction coefficient.

cond-mat.soft↗

arXiv2013

Phonons in two-dimensional soft colloidal crystals

The vibrational modes of pristine and polycrystalline monolayer colloidal crystals composed of thermosensitive microgel particles are measured using video microscopy and covariance matrix analysis. At low frequencies, the Debye relation for two dimensional harmonic crystals is observed in both crystal types; at higher frequencies, evidence for van Hove singularities in the phonon density of states is significantly smeared out by experimental noise and measurement statistics. The effects of these errors are analyzed using numerical simulations. We introduce methods to correct for these limitations, which can be applied to disordered systems as well as crystalline ones, and we show that application of the error correction procedure to the experimental data leads to more pronounced van Hove singularities in the pristine crystal. Finally, quasi-localized low-frequency modes in polycrystalline two-dimensional colloidal crystals are identified and demonstrated to correlate with structural defects such as dislocations, suggesting that quasi-localized low-frequency phonon modes may be used to identify local regions vulnerable to rearrangements in crystalline as well as amorphous solids.

cond-mat.soft↗

arXiv2013

The syncytial Drosophila embryo as a mechanically excitable medium

Mitosis in the early syncytial Drosophila embryo is highly correlated in space and time, as manifested in mitotic wavefronts that propagate across the embryo. In this paper we investigate the idea that the embryo can be considered a mechanically-excitable medium, and that mitotic wavefronts can be understood as nonlinear wavefronts that propagate through this medium. We study the wavefronts via both image analysis of confocal microscopy videos and theoretical models. We find that the mitotic waves travel across the embryo at a well-defined speed that decreases with replication cycle. We find two markers of the wavefront in each cycle, corresponding to the onsets of metaphase and anaphase. Each of these onsets is followed by displacements of the nuclei that obey the same wavefront pattern. To understand the mitotic wavefronts theoretically we analyze wavefront propagation in excitable media. We study two classes of models, one with biochemical signaling and one with mechanical signaling. We find that the dependence of wavefront speed on cycle number is most naturally explained by mechanical signaling, and that the entire process suggests a scenario in which biochemical and mechanical signaling are coupled.

physics.bio-ph↗

arXiv2013

Mechanical signaling via nonlinear wavefront propagation in a mechanically-excitable medium

Models that invoke nonlinear wavefront propagation in a chemically excitable medium are rife in the biological literature. Indeed, the idea that wavefront propagation can serve as a signaling mechanism has often been invoked to explain synchronization of developmental processes. In this paper we suggest a new kind of signaling based not on diffusion of a chemical species but on the propagation of mechanical stress. We construct a theoretical approach to describe mechanical signaling as a nonlinear wavefront propagation problem and study its dependence on key variables such as the effective elasticity and damping of the medium.

cond-mat.soft↗

arXiv2012

Finite-Size Scaling at the Jamming Transition

We 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 non-trivial scaling function, demonstrating that the jamming transition can be considered a phase transition. Scaling is achieved as a function of N in both 2 and 3 dimensions, indicating an upper critical dimension of 2.

cond-mat.soft↗

arXiv2011

Measurement of correlations between low-frequency vibrational modes and particle rearrangements in quasi-two-dimensional colloidal glasses

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 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 packing fraction. The experimental results suggest that low-frequency quasi-localized 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.

cond-mat.soft↗

arXiv2011

Self-Diffusiophoresis in the Advection Dominated Regime

In both biological and artificial systems, concentration gradients can serve as a convenient mechanism for manipulating particles and generating motility. Particles that interact with a solute will move along its gradient; if they themselves generate the gradient, this mechanism provides a means of self-propulsion. We consider a version of this type of motility appropriate to certain biological systems where polymeric filaments provide the concentration gradient. As the filament diffusion is small, this corresponds to a regime of large Péclet number where the motion is dominated by the effects of fluid advection. The nature of such concentration-gradient-driven motion in the advective regime differs in certain fundamental respects from the same process at low Péclet number. In particular, we show that out of four broad scenarios of steady state motion at low Péclet number, only two remain viable in the strongly advecting limit.

cond-mat.soft↗

arXiv2011

Mapping the glassy dynamics of soft spheres onto hard-sphere behavior

We show that the dynamics of soft-sphere systems with purely repulsive interactions can be described by introducing an effective hard-sphere diameter determined using the Andersen-Weeks-Chandler approximation. We find that this approximation, known to describe static properties of liquids, also gives a good description of a dynamical quantity, the relaxation time, even in the vicinity of the glass transition.

cond-mat.soft↗

arXiv2011

Direct determination of the size of basins of attraction of jammed solids

We 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.

cond-mat.soft↗

arXiv2011

The jamming scenario - an introduction and outlook

The jamming scenario of disordered media, formulated about 10 years ago, has in recent years been advanced by analyzing model systems of granular media. This has led to various new concepts that are increasingly being explored in in a variety of systems. This chapter contains an introductory review of these recent developments and provides an outlook on their applicability to different physical systems and on future directions. The first part of the paper is devoted to an overview of the findings for model systems of frictionless spheres, focussing on the excess of low-frequency modes as the jamming point is approached. Particular attention is paid to a discussion of the cross-over frequency and length scales that govern this approach. We then discuss the effects of particle asphericity and static friction, the applicability to bubble models for wet foams in which the friction is dynamic, the dynamical arrest in colloids, and the implications for molecular glasses.

cond-mat.soft↗

arXiv2010

Vibrational modes identify soft spots in a sheared disordered packing

We 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.

cond-mat.soft↗

arXiv2010

Rotational and Translational Phonon Modes in Glasses Composed of Ellipsoidal Particles

The effects of particle shape on the vibrational properties of colloidal glasses are studied experimentally. 'Ellipsoidal glasses' are created by stretching polystyrene spheres to different aspect ratios and then suspending the resulting ellipsoidal particles in water at high packing fraction. By measuring displacement correlations between particles, we extract vibrational properties of the corresponding "shadow" ellipsoidal glass with the same geometric configuration and interactions as the 'source' suspension but without damping. Low frequency modes in glasses composed of ellipsoidal particles with major/minor axis aspect ratios $\sim$1.1 are observed to have predominantly rotational character. By contrast, low frequency modes in glasses of ellipsoidal particles with larger aspect ratios ($\sim$3.0) exhibit a mix of rotational and translational character. All glass samples were characterized by a distribution of particles with different aspect ratios. Interestingly, even within the same sample it was found that small-aspect-ratio particles participate relatively more in rotational modes, while large-aspect-ratio particles tend to participate relatively more in translational modes.

cond-mat.soft↗

arXiv2010

Universal Jamming Phase Diagram in the Hard-Sphere Limit

We present a new formulation of the jamming phase diagram for a class of glass-forming fluids consisting of spheres interacting via finite-ranged repulsions at temperature $T$, packing fraction $ϕ$ or pressure $p$, and applied shear stress $Σ$. We argue that the natural choice of axes for the phase diagram are the dimensionless quantities $T/pσ^3$, $pσ^3/ε$, and $Σ/p$, where $T$ is the temperature, $p$ is the pressure, $Σ$ is the stress, $σ$ is the sphere diameter, $ε$ is the interaction energy scale, and $m$ is the sphere mass. We demonstrate that the phase diagram is universal at low $pσ^3/ε$; at low pressure, observables such as the relaxation time are insensitive to details of the interaction potential and collapse onto the values for hard spheres, provided the observables are non-dimensionalized by the pressure. We determine the shape of the jamming surface in the jamming phase diagram, organize previous results in relation to the jamming phase diagram, and discuss the significance of various limits.

cond-mat.soft↗

arXiv2010

Far-From-Equilibrium Physics: An Overview

Isolated systems tend to evolve towards equilibrium, a special state that has been the focus of many-body research for a century. Yet much of the richness of the world around us arises from conditions far from equilibrium. Phenomena such as turbulence, earthquakes, fracture, and life itself occur only far from equilibrium. Subjecting materials to conditions far from equilibrium leads to otherwise unattainable properties. For example, rapid cooling is a key process in manufacturing the strongest metallic alloys and toughest plastics. Processes that occur far from equilibrium also create some of the most intricate structures known, from snowflakes to the highly organized structures of life. While much is understood about systems at or near equilibrium, we are just beginning to uncover the basic principles governing systems far from equilibrium.

cond-mat.soft↗

arXiv2010

Jamming Mechanisms and Density Dependence in a Kinetically-Constrained Model

We add relaxation mechanisms that mimic the effect of temperature and non-equilibrium driving to the recently-proposed spiral model which jams at a critical density rho_c < 1. This enables us to explore unjamming by temperature or driving at rho_c < rho < 1. We numerically calculate the relaxation time of the persistence function and its spatial heterogeneity. We disentangle the three different relaxation mechanisms responsible for unjamming when varying density, temperature, and driving strength, respectively. We show that the spatial scale of dynamic heterogeneity depends on density much more strongly than on temperature and driving.

cond-mat.soft↗

arXiv2010

Low-frequency vibrations of soft colloidal glasses

We 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 spectrum and the nature of the modes are very similar to those predicted for zero-temperature idealized sphere models 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.

cond-mat.soft↗