arXiv subjects

Andrea J. Liu

Publications and source records attributed to Andrea J. Liu.

At least 73 records · Page 4Linked to original sources

arXiv2016

Disconnecting structure and dynamics in glassy thin films

Nanometrically thin glassy films depart strikingly from the behavior of their bulk counterparts. We investigate whether the dynamical differences between bulk and thin film glasses can be understood by differences in local microscopic structure. We employ machine-learning methods that have previously identified strong correlations between local structure and particle rearrangement dynamics in bulk systems. We show that these methods completely fail to detect key aspects of thin-film glassy dynamics. Furthermore, we show that no combination of local structural features drawn from a very general set of two- and multi-point functions is able to distinguish between particles at the center of film and those in intermediate layers where the dynamics are strongly perturbed.

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arXiv2016

Designing allostery-inspired response in mechanical networks

Recent advances in designing meta-materials have demonstrated that global mechanical properties of disordered spring networks can be tuned by selectively modifying only a small subset of bonds. Here, using a computationally-efficient approach, we extend this idea in order to tune more general properties of networks. With nearly complete success, we are able to produce a strain between any pair of target nodes in a network in response to an applied source strain on any other pair of nodes by removing only ~1% of the bonds. We are also able to control multiple pairs of target nodes, each with a different individual response, from a single source, and to tune multiple independent source/target responses simultaneously into a network. We have fabricated physical networks in macroscopic two- and three-dimensional systems that exhibit these responses. This targeted behavior is reminiscent of the long-range coupled conformational changes that often occur during allostery in proteins. The ease with which we create these responses may give insight into why allostery is a common means for the regulation of activity in biological molecules.

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arXiv2016

The Relationship Between Local Structure and Relaxation in Out-of-Equilibrium Glassy Systems

The dynamical glass transition is typically taken to be the temperature at which a glassy liquid is no longer able to equilibrate on experimental timescales. Consequently, the physical properties of these systems just above or below the dynamical glass transition, such as viscosity, can change by many orders of magnitude over long periods of time following external perturbation. During this progress towards equilibrium, glassy systems exhibit a history dependence that has complicated their study. In previous work, we bridged the gap between structure and dynamics in glassy liquids above their dynamical glass transition temperatures by introducing a scalar field called "softness", a quantity obtained using machine learning methods. Softness is designed to capture the hidden patterns in relative particle positions that correlate strongly with dynamical rearrangements of particle positions. Here we show that the out-of-equilibrium behavior of a model glassforming system can be understood in terms of softness. To do this we first demonstrate that the evolution of behavior following a temperature quench is a primarily structural phenomenon: the structure changes considerably, but the relationship between structure and dynamics remains invariant. We then show that the history-dependent relaxation time can be robustly computed from structure as quantified by softness. Together, these results motivate the use of softness to characterize the history dependence of glasses.

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arXiv2016

Pinning Susceptibility: The effect of dilute, quenched disorder on jamming

We study the effect of dilute pinning on the jamming transition. Pinning reduces the average contact number needed to jam unpinned particles and shifts the jamming threshold to lower densities, leading to a pinning susceptibility, $χ_p$. Our main results are that this susceptibility obeys scaling form and diverges in the thermodynamic limit as $χ_p \propto |ϕ- ϕ_c^\infty|^{-γ_p}$ where $ϕ_c^\infty$ is the jamming threshold in the absence of pins. Finite-size scaling arguments yield these values with associated statistical (systematic) errors $γ_p = 1.018 \pm 0.026 (0.291) $ in $d=2$ and $γ_p =1.534 \pm 0.120 (0.822)$ in $d=3$. Logarithmic corrections raise the exponent in $d=2$ to close to the $d=3$ value, although the systematic errors are very large.

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arXiv2016

Spatial structure of states of self stress in jammed systems

States of self stress, organizations of internal forces in many-body systems that are in equilibrium with an absence of external forces, can be thought of as the constitutive building blocks of the elastic response of a material. In overconstrained disordered packings they have a natural mathematical correspondence with the zero-energy vibrational modes in underconstrained systems. While substantial attention in the literature has been paid to diverging length scales associated with zero- and finite-energy vibrational modes in jammed systems, less is known about the spatial structure of the states of self stress. In this work we define a natural way in which a unique state of self stress can be associated with each bond in a disordered spring network derived from a jammed packing, and then investigate the spatial structure of these bond-localized states of self stress. This allows for an understanding of how the elastic properties of a system would change upon changing the strength or even existence of any bond in the system.

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arXiv2015

Divergence of Voronoi cell anisotropy vector: A threshold-free characterization of local structure in amorphous materials

Characterizing structural inhomogeneity is an essential step in understanding the mechanical response of amorphous materials. We introduce a threshold-free measure based on the field of vectors pointing from the center of each particle to the centroid of the Voronoi cell in which the particle resides. These vectors tend to point in toward regions of high free volume and away from regions of low free volume, reminiscent of sinks and sources in a vector field. We compute the local divergence of these vectors, for which positive values correspond to overpacked regions and negative values identify underpacked regions within the material. Distributions of this divergence are nearly Gaussian with zero mean, allowing for structural characterization using only the moments of the distribution. We explore how the standard deviation and skewness vary with packing fraction for simulations of bidisperse systems and find a kink in these moments that coincides with the jamming transition.

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arXiv2015

Scaling theory for the jamming transition

We propose a scaling ansatz for the elastic energy of a system near the critical jamming transition in terms of three relevant fields: the compressive strain $Δϕ$ relative to the critical jammed state, the shear strain $ε$, and the inverse system size $1/N$. We also use $ΔZ$, the number of contacts relative to the minimum required at jamming, as an underlying control parameter. Our scaling theory predicts new exponents, exponent equalities and scaling collapses for energy, pressure and shear stress that we verify with numerical simulations of jammed packings of soft spheres. It also yields new insight into why the shear and bulk moduli exhibit different scalings; the difference arises because the shear stress vanishes as $1/\sqrt{N}$ while the pressure approaches a constant in the thermodynamic limit. The success of the scaling ansatz implies that the jamming transition exhibits an emergent scale invariance, and that it should be possible to develop a renormalization-group theory for jamming.

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arXiv2015

Strain fluctuations and elastic moduli in disordered solids

Recently there has been a surge in interest in using video-microscopy techniques to infer the local mechanical properties of disordered solids. One common approach is to minimize the difference between particle vibrational displacements in a local coarse-graining volume and the displacements that would result from a best-fit affine deformation. Effective moduli are then be inferred under the assumption that the components of this best-fit affine deformation tensor have a Boltzmann distribution. In this paper, we combine theoretical arguments with experimental and simulation data to demonstrate that the above does not reveal information about the true elastic moduli of jammed packings and colloidal glasses.

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arXiv2015

A random matrix definition of the boson peak

The density of vibrational states for glasses and jammed solids exhibits universal features, including an excess of modes above the Debye prediction known as the boson peak located at a frequency $ω^*$ . We show that the eigenvector statistics for boson peak modes are universal, and develop a new definition of the boson peak based on this universality that displays the previously observed characteristic scaling $ω^*\sim p^{-1/2}$ . We identify a large new class of random matrices that obey a generalized global tranlational invariance constraint and demonstrate that members of this class also have a boson peak with precisely the same universal eigenvector statistics. We denote this class as boson peak random matrices, and conjecture it comprises a new universality class. We characterize the eigenvector statistics as a function of coordination number, and find that one member of this new class reproduces the scaling of $ω^{*}$ with coordination number that is observed near the jamming transition.

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arXiv2015

Tuning by pruning: exploiting disorder for global response and the principle of bond-level independence

We exploit the intrinsic difference between disordered and crystalline solids to create systems with unusual and exquisitely tuned mechanical properties. To demonstrate the power of this approach, we design materials that are either virtually incompressible or completely auxetic. Disordered networks can be efficiently driven to these extreme limits by removing a very small fraction of bonds via a selected-bond removal procedure that is both simple and experimentally relevant. The procedure relies on the nearly complete absence of any correlation between the contributions of an individual bond to different elastic moduli. A new principle unique to disordered solids underlies this lack of correlation: independence of bond-level response.

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arXiv2015

Deformation-Driven Diffusion and Plastic Flow in Two-Dimensional Amorphous Granular Pillars

We report a combined experimental and simulation study of deformation-induced diffusion in compacted two-dimensional amorphous granular pillars, in which thermal fluctuations play negligible role. The pillars, consisting of bidisperse cylindrical acetal plastic particles standing upright on a substrate, are deformed uniaxially and quasistatically by a rigid bar moving at a constant speed. The plastic flow and particle rearrangements in the pillars are characterized by computing the best-fit affine transformation strain and non-affine displacement associated with each particle between two stages of deformation. The non-affine displacement exhibits exponential crossover from ballistic to diffusive behavior with respect to the cumulative deviatoric strain, indicating that in athermal granular packings, the cumulative deviatoric strain plays the role of time in thermal systems and drives effective particle diffusion. We further study the size-dependent deformation of the granular pillars by simulation, and find that different-sized pillars follow self-similar shape evolution during deformation. In addition, the yield stress of the pillars increases linearly with pillar size. Formation of transient shear lines in the pillars during deformation becomes more evident as pillar size increases. The width of these elementary shear bands is about twice the diameter of a particle, and does not vary with pillar size.

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arXiv2014

Jamming in finite systems: stability, anisotropy, fluctuations and scaling

Athermal packings of soft repulsive spheres exhibit a sharp jamming transition in the thermodynamic limit. Upon further compression, various structural and mechanical properties display clean power-law behavior over many decades in pressure. As with any phase transition, the rounding of such behavior in finite systems close to the transition plays an important role in understanding the nature of the transition itself. The situation for jamming is surprisingly rich: the assumption that jammed packings are isotropic is only strictly true in the large-size limit, and finite-size has a profound effect on the very meaning of jamming. Here, we provide a comprehensive numerical study of finite-size effects in sphere packings above the jamming transition, focusing on stability as well as the scaling of the contact number and the elastic response.

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arXiv2014

Contact nonlinearities and linear response in jammed particulate packings

Packings of frictionless athermal particles that interact only when they overlap experience a jamming transition as a function of packing density. Such packings provide the foundation for the theory of jamming. This theory rests on the observation that, despite the multitude of disordered configurations, the mechanical response to linear order depends only on the distance to the transition. We investigate the validity and utility of such measurements that invoke the harmonic approximation and show that, despite particles coming in and out of contact, there is a well-defined linear regime in the thermodynamic limit.

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arXiv2014

Comment on 'Repulsive Contact Interactions Make Jammed Particulate Systems Inherently Nonharmonic'

In their Letter, Schreck, Bertrand, O'Hern and Shattuck [Phys. Rev. Lett. 107, 078301 (2011)] study nonlinearities in jammed particulate systems that arise when contacts are altered. They conclude that there is "no harmonic regime in the large system limit for all compressions" and "at jamming onset for any system size." Their argument rests on the claim that for finite-range repulsive potentials, of the form used in studies of jamming, the breaking or forming of a single contact is sufficient to destroy the linear regime. We dispute these conclusions and argue that linear response is both justified and essential for understanding the nature of the jammed solid.

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arXiv2014

Disordered surface vibrations in jammed sphere packings

We study the vibrational properties near a free surface of disordered spring networks derived from jammed sphere packings. In bulk systems, without surfaces, it is well understood that such systems have a plateau in the density of vibrational modes extending down to a frequency scale $ω^*$. This frequency is controlled by $ΔZ = \langle Z \rangle - 2d$, the difference between the average coordination of the spheres and twice the spatial dimension, $d$, of the system, which vanishes at the jamming transition. In the presence of a free surface we find that there is a density of disordered vibrational modes associated with the surface that extends far below $ω^*$. The total number of these low-frequency surface modes is controlled by $ΔZ$, and the profile of their decay into the bulk has two characteristic length scales, which diverge as $ΔZ^{-1/2}$ and $ΔZ^{-1}$ as the jamming transition is approached.

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arXiv2014

Identifying structural flow defects in disordered solids using machine learning methods

We use machine learning methods on local structure to identify flow defects - or regions susceptible to rearrangement - in jammed and glassy systems. We apply this method successfully to two disparate systems: a two dimensional experimental realization of a granular pillar under compression, and a Lennard-Jones glass in both two and three dimensions above and below its glass transition temperature. We also identify characteristics of flow defects that differentiate them from the rest of the sample. Our results show it is possible to discern subtle structural features responsible for heterogeneous dynamics observed across a broad range of disordered materials.

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arXiv2014

Understanding plastic deformation in thermal glasses from single-soft-spot dynamics

By considering the low-frequency vibrational modes of amorphous solids, Manning and Liu [Phys. Rev. Lett. 107, 108302 (2011)] showed that a population of "soft spots" can be identified that are intimately related to plasticity at zero temperature under quasistatic shear. In this work we track individual soft spots with time in a two-dimensional sheared thermal Lennard Jones glass at temperatures ranging from deep in the glassy regime to above the glass transition temperature. We show that the lifetimes of individual soft spots are correlated with the timescale for structural relaxation. We additionally calculate the number of rearrangements required to destroy soft spots, and show that most soft spots can survive many rearrangements. Finally, we show that soft spots are robust predictors of rearrangements at temperatures well into the super-cooled regime. Altogether, these results pave the way for mesoscopic theories of plasticity of amorphous solids based on dynamical behavior of individual soft spots.

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arXiv2014

Predicting plasticity with soft vibrational modes: from dislocations to glasses

We show that quasi localized low-frequency modes in the vibrational spectrum can be used to construct soft spots, or regions vulnerable to rearrangement, which serve as a universal tool for the identification of flow defects in solids. We show that soft spots not only encode spatial information, via their location, but also directional information, via directors for particles within each soft spot. Single crystals with isolated dislocations exhibit low-frequency phonon modes that localize at the core, and their polarization pattern predicts the motion of atoms during elementary dislocation glide in exquisite detail. Even in polycrystals and disordered solids, we find that the directors associated with particles in soft spots are highly correlated with the direction of particle displacements in rearrangements.

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