arXiv subjects

Samuel S. Schoenholz

Publications and source records attributed to Samuel S. Schoenholz.

44 records · Page 3Linked to original sources

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.

cond-mat.soft↗

arXiv2015

A structural approach to relaxation in glassy liquids

When a liquid freezes, a change in the local atomic structure marks the transition to the crystal. When a liquid is cooled to form a glass, however, no noticeable structural change marks the glass transition. Indeed, characteristic features of glassy dynamics that appear below an onset temperature, T_0, are qualitatively captured by mean field theory, which assumes uniform local structure at all temperatures. Even studies of more realistic systems have found only weak correlations between structure and dynamics. This raises the question: is structure important to glassy dynamics in three dimensions? Here, we answer this question affirmatively by using machine learning methods to identify a new field, that we call softness, which characterizes local structure and is strongly correlated with rearrangement dynamics. We find that the onset of glassy dynamics at T_0 is marked by the onset of correlations between softness (i.e. structure) and dynamics. Moreover, we use softness to construct a simple model of slow glassy relaxation that is in excellent agreement with our simulation results, showing that a theory of the evolution of softness in time would constitute a theory of glassy dynamics.

cond-mat.soft↗

arXiv2015

Nonlinear Sigma Models with Compact Hyperbolic Target Spaces

We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the $O(2)$ model. Unlike in the $O(2)$ case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.

hep-th↗

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.

cond-mat.soft↗

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.

cond-mat.soft↗

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.

cond-mat.soft↗

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.

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↗