Glass transitions in one-, two-, three-, and four-dimensional binary Lennard-Jones systems

Ion-Ion Structural Correlation and Dynamics of Water in Aqueous NaCl Solutions with a Wide Range of Concentrations

The behavior of water in concentrated ionic solutions, including supersaturated conditions, is crucial for numerous material and energy conversion processes and fundamental research. All electrolytes whether they "structure-make" or "structure-break" the water structure lead to slower water motion. This study investigates the structure and dynamics of aqueous NaCl solutions across a wide range of concentrations. On the structural side, the primary focus is on ion-ion correlations. In terms of dynamics, we demonstrate that the slowing down of water dynamics continues even beyond the saturated state. We identify three distinct types of dynamics at large concentrations: ballistic, trapped, and diffusive. The van Hove correlation function exhibits no signs of relaxation within a time interval where particle motion is effectively halted. The system displays dynamical heterogeneities, confirmed by evaluating non-Gaussian parameters for the self-part of the van Hove function and identifying the mobile particles. These particles form clusters, with the largest sizes occurring when the non-Gaussian parameters are at their maximum. Additionally, we discuss the relaxation times associated with these systems using the incoherent intermediate scattering function and establish a connection with the mode-coupling theory.

Is the glassy dynamics same in 2D as in 3D? The Adam Gibbs relation test

It has been recognized of late that even amorphous, glass-forming materials in two dimensions (2D) are affected by Mermin-Wagner-type long wavelength thermal fluctuation, which is inconsequential in three dimensions (3D). We consider the question of whether the effect of spatial dimension on dynamics is only limited to such fluctuations or if the nature of glassy dynamics is intrinsically different in 2D. To address it, we study the relationship between dynamics and thermodynamics using the Adam-Gibbs (AG) relation and the random first order transition (RFOT) theory. Using two model glass-forming liquids, we find that even after removing the effect of long wavelength fluctuations, the AG relation breaks down in two dimensions. Next, we consider the effect of anharmonicity of vibrational entropy-a second factor that affects the thermodynamics but not dynamics. Using the potential energy landscape formalism, we explicitly compute the configurational entropy, both with and without the anharmonic correction. We show that even with both the corrections, the AG relation still breaks down in 2D. The extent of deviation from the AG relation crucially depends on the attractive vs repulsive nature of interparticle interactions, choice of representative timescale (diffusion coefficient vs α-relaxation time), and implies that the RFOT scaling exponents also depend on these factors. Thus, our results suggest that some differences in the nature of glassy dynamics between 2D and 3D remain that are not explained by long wavelength fluctuations.

Homogeneous crystallization in four-dimensional Lennard-Jones liquids

We observe homogeneous crystallization in simulated high-dimensional (d>3) liquids that follow physically realistic dynamics and have system sizes that are large enough to eliminate the possibility that crystallization was induced by the periodic boundary conditions. Supercooled four-dimensional (4D) Lennard-Jones (LJ) liquids maintained at zero pressure and constant temperatures 0.59 Collapse

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Robert S Hoy Department of Physics, University of South Florida, Tampa, Florida 33620, USA

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Thawed matrix method for computing local mechanical properties of amorphous solids

We present a method for computing locally varying nonlinear mechanical properties in particle simulations of amorphous solids. Plastic rearrangements outside a probed region are suppressed by introducing an external field that directly penalizes large nonaffine displacements. With increasing strength of the field, plastic deformation can be localized. We characterize the distribution of local plastic yield stresses (residual local stresses to instability) with our approach and assess the correlation of their spatial maps with plastic activity in a model two-dimensional amorphous solid. Our approach reduces artifacts inherent in a previous method known as the "frozen matrix" approach that enforces fully affine deformation and improves the prediction of plastic rearrangements from structural information.

Athermal quasistatic cavitation in amorphous solids: Effect of random pinning

Amorphous solids are known to fail catastrophically via fracture, and cavitation at nano-metric scales is known to play a significant role in such a failure process. Micro-alloying via inclusions is often used as a means to increase the fracture toughness of amorphous solids. Modeling such inclusions as randomly pinned particles that only move affinely and do not participate in plastic relaxations, we study how the pinning influences the process of cavitation-driven fracture in an amorphous solid. Using extensive numerical simulations and probing in the athermal quasistatic limit, we show that just by pinning a very small fraction of particles, the tensile strength is increased, and also the cavitation is delayed. Furthermore, the cavitation that is expected to be spatially heterogeneous becomes spatially homogeneous by forming a large number of small cavities instead of a dominant cavity. The observed behavior is rationalized in terms of screening of plastic activity via the pinning centers, characterized by a screening length extracted from the plastic-eigenmodes.

Enhanced vibrational stability in glass droplets

We show through simulations of amorphous solids prepared in open-boundary conditions that they possess significantly fewer low-frequency vibrational modes compared to their periodic boundary counterparts. Specifically, using measurements of the vibrational density of states, we find that the D ( ω ) ∼ ω 4 law changes to D ( ω ) ∼ ω δ with δ ≈ 5 in two dimensions and δ ≈ 4.5 in three dimensions. Crucially, this enhanced stability is achieved when utilizing slow annealing protocols to generate solid configurations. We perform an anharmonic analysis of the minima corresponding to the lowest frequency modes in such open-boundary systems and discuss their correlation with the density of states. A study of various system sizes further reveals that small systems display a higher degree of localization in vibrations. Lastly, we confine open-boundary solids in order to introduce macroscopic stresses in the system, which are absent in the unconfined system and find that the D ( ω ) ∼ ω 4 behavior is recovered.

Non-phononic density of states of two-dimensional glasses revealed by random pinning

The vibrational density of states of glasses is considerably different from that of crystals. In particular, there exist spatially localized vibrational modes in glasses. The density of states of these non-phononic modes has been observed to follow g(ω) ∝ ω4, where ω is the frequency. However, in two-dimensional systems, the abundance of phonons makes it difficult to accurately determine this non-phononic density of states because they are strongly coupled to non-phononic modes and yield strong system-size and preparation-protocol dependencies. In this article, we utilize the random pinning method to suppress phonons and disentangle their coupling with non-phononic modes and successfully calculate their density of states as g(ω) ∝ ω4. We also study their localization properties and confirm that low-frequency non-phononic modes in pinned systems are truly localized without far-field contributions. We finally discuss the excess density of states over the Debye value that results from the hybridization of phonons and non-phononic modes.

Universal mechanical instabilities in the energy landscape of amorphous solids: Evidence from athermal quasistatic expansion

Using numerical simulations, we study the failure of an amorphous solid under athermal quasistatic expansion starting from a homogeneous high-density state. During the expansion process, plastic instabilities occur, manifested via sudden jumps in pressure and energy, with the largest event happening via cavitation leading to the material's yielding. We demonstrate that all these plastic events are characterized by saddle-node bifurcation, during which the smallest nonzero eigenvalue of the Hessian matrix vanishes via a square-root singularity. We find that after yielding and prior to complete fracture, the statistics of pressure or energy jumps corresponding to the plastic events show subextensive system-size scaling, similar to the case of simple shear but with different exponents. Thus, overall, our paper reveals universal features in the fundamental characteristics during mechanical failure in amorphous solids under any quasistatic deformation protocol.

Unjamming and emergent nonreciprocity in active ploughing through a compressible viscoelastic fluid

A dilute suspension of active Brownian particles in a dense compressible viscoelastic fluid, forms a natural setting to study the emergence of nonreciprocity during a dynamical phase transition. At these densities, the transport of active particles is strongly influenced by the passive medium and shows a dynamical jamming transition as a function of activity and medium density. In the process, the compressible medium is actively churned up - for low activity, the active particle gets self-trapped in a cavity of its own making, while for large activity, the active particle ploughs through the medium, either accompanied by a moving anisotropic wake, or leaving a porous trail. A hydrodynamic approach makes it evident that the active particle generates a long-range density wake which breaks fore-aft symmetry, consistent with the simulations. Accounting for the back-reaction of the compressible medium leads to (i) dynamical jamming of the active particle, and (ii) a dynamical non-reciprocal attraction between two active particles moving along the same direction, with the trailing particle catching up with the leading one in finite time. We emphasize that these nonreciprocal effects appear only when the active particles are moving and so manifest in the vicinity of the jamming-unjamming transition.

Interplay between jamming and motility-induced phase separation in persistent self-propelling particles

In living and engineered systems of active particles, self-propulsion induces an unjamming transition from a solid to a fluid phase and phase separation between a gas and a liquidlike phase. We demonstrate an interplay between these two nonequilibrium transitions in systems of persistent active particles. The coexistence and jamming lines in the activity-density plane meet at the jamming transition point in the limit of hard particles or zero activity. This interplay induces an anomalous dynamic in the liquid phase and hysteresis at the active jamming transition.

Local Plastic Response and Slow Heterogeneous Dynamics of Supercooled Liquids

We demonstrate, via numerical simulations, that the relaxation dynamics of supercooled liquids correlates well with a plastic length scale measuring a particle's response to impulsive localized perturbations and weakly to measures of local elasticity. We find that the particle averaged plastic length scale vanishes linearly in temperature and controls the super-Arrhenius temperature dependence of the relaxation time. Furthermore, we show that the plastic length scale of individual particles correlates with their typical displacement at the relaxation time. In contrast, the local elastic response only correlates with the dynamics on the vibrational timescale.

Efficient d-dimensional molecular dynamics simulations for studies of the glass-jamming transition

We develop an algorithm suitable for parallel molecular dynamics simulations in d spatial dimensions and describe its implementation in C++. All routines work in arbitrary d; the maximum simulated d is limited only by available computing resources. These routines include several that are particularly useful for studies of the glass-jamming transition, such as SWAP Monte Carlo and FIRE energy minimization. The scalings of simulation runtimes with the number of particles N and number of simulation threads n_{threads} are comparable to popular molecular dynamics codes such as LAMMPS. The efficient parallel implementation allows simulation of systems that are much larger than those employed in previous high-dimensional glass-transition studies. As a demonstration of the code's capabilities, we show that supercooled d=6 liquids can possess dynamics that are substantially more heterogeneous and experience a breakdown of the Stokes-Einstein relation that is substantially stronger than previously reported, owing at least in part to the much smaller system sizes employed in earlier simulations.

Low-Frequency Excess Vibrational Modes in Two-Dimensional Glasses

Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes are crucial for the understanding of the low temperature thermal and mechanical properties of glasses, which differ from those of crystalline solids. Recent simulational studies suggest that the density of the excess modes scales with their frequency ω as ω^{4} in two and higher dimensions. Here, we present extensive numerical studies of two-dimensional model glass formers over a large range of glass stabilities. We find that the density of the excess modes follows D_{exc}(ω)∼ω^{2} up to around the boson peak, regardless of the glass stability. The stability dependence of the overall scale of D_{exc}(ω) correlates with the stability dependence of low-frequency sound attenuation. However, we also find that, in small systems, where the first sound mode is pushed to higher frequencies, at frequencies below the first sound mode, there are excess modes with a system size independent density of states that scales as ω^{3}.

Shear-induced orientational ordering in an active glass former

Dense assemblies of self-propelled particles that can form solid-like states also known as active or living glasses are abundant around us, covering a broad range of length scales and timescales: from the cytoplasm to tissues, from bacterial biofilms to vehicular traffic jams, and from Janus colloids to animal herds. Being structurally disordered as well as strongly out of equilibrium, these systems show fascinating dynamical and mechanical properties. Using extensive molecular dynamics simulation and a number of distinct dynamical and mechanical order parameters, we differentiate three dynamical steady states in a sheared model active glassy system: 1) a disordered state, 2) a propulsion-induced ordered state, and 3) a shear-induced ordered state. We supplement these observations with an analytical theory based on an effective single-particle Fokker-Planck description to rationalize the existence of the shear-induced orientational ordering behavior in an active glassy system without explicit aligning interactions of, for example, Vicsek type. This ordering phenomenon occurs in the large persistence time limit and is made possible only by the applied steady shear. Using a Fokker-Planck description with parameters that can be measured independently, we make testable predictions for the joint distribution of single-particle position and orientation. These predictions match well with the joint distribution measured from direct numerical simulation. Our results are of relevance for experiments exploring the rheological response of dense active colloids and jammed active granular matter systems.

How to study a persistent active glassy system

We explore glassy dynamics of dense assemblies of soft particles that are self-propelled by active forces. These forces have a fixed amplitude and a propulsion direction that varies on a timescaleτ_p, the persistence timescale. Numerical simulations of such active glasses are computationally challenging when the dynamics is governed by large persistence times. We describe in detail a recently proposed scheme that allows one to study directly the dynamics in the large persistence time limit, on timescales around and well above the persistence time. We discuss the idea behind the proposed scheme, which we call 'activity-driven dynamics', as well as its numerical implementation. We establish that our prescription faithfully reproduces all dynamical quantities in the appropriate limitτ_p→ ∞. We deploy the approach to explore in detail the statistics of Eshelby-like plastic events in the steady state dynamics of a dense and intermittent active glass.

MD simulations of charged binary mixtures reveal a generic relation between high- and low-temperature behavior

Experimental studies of the glassy slowdown in molecular liquids indicate that the high-temperature activation energy E_∞ of glass-forming liquids is directly related to their glass transition temperature T_g. To further investigate such a possible relation between high- and low-temperature dynamics in glass-forming liquids, we analyze the glassy dynamics of binary mixtures using molecular dynamics simulations. We consider a binary mixture of charged Lennard-Jones particles and vary the partial charges of the particles and, thus, the high-temperature activation energy and the glass transition temperature of the system. Based on previous results, we introduce a phenomenological model describing relaxation times over the whole temperature regime from high temperatures to temperatures well inside the supercooled regime. By investigating the dynamics of both particle species on molecular and diffusive length scales along isochoric and isobaric pathways, we find a quadratic charge dependence of both E_∞ and T_g, resulting in an approximately constant ratio of both quantities independent of the underlying observable, the thermodynamic ensemble, and the particle species, and this result is robust against the actual definition of T_g. This generic relation between the activation energy and the glass transition temperature indicates that high-temperature dynamics and the glassy slowdown are related phenomena, and the knowledge of E_∞ may allow us to approximately predict T_g.

Multiple Types of Aging in Active Glasses

Recent experiments and simulations have revealed glassy features in, e.g., cytoplasm, living tissues and dense assemblies of self-propelled colloids. This leads to a fundamental question: how do these nonequilibrium (active) amorphous materials differ from conventional passive glasses, created by lowering temperature or increasing density? To address this we investigate the aging after a quench to an almost arrested state of a model active glass former, a Kob-Andersen glass in two dimensions. Each constituent particle is driven by a constant propulsion force whose direction diffuses over time. Using extensive molecular dynamics simulations we reveal rich aging behavior of this dense active matter system: short persistence times of the active forcing give effective thermal aging; in the opposite limit we find a two-step aging process with active athermal aging at short times and activity-driven aging at late times. We develop a dedicated simulation method that gives access to this longtime scaling regime for highly persistent active forces.

Coarse-graining strategy for modeling effective, highly diffusive fluids with reduced polydispersity: A dynamical study

We present a coarse-graining strategy for reducing the number of particle species in mixtures to achieve a simpler system with higher diffusion while preserving the total particle number and characteristic dynamic features. As a system of application, we chose the bidisperse Lennard-Jones-like mixture, discovered by Kob and Andersen [Phys. Rev. Lett. 73, 1376 (1994)], possessing a slow dynamics due to the fluid's multi-component character with its apparently unconventional choice for the pair potential of the type-A-type-B arrangement. We further established in a so-formed coarse-grained and temperature-independent monodisperse system an equilibrium structure with a radial distribution function resembling its mixture counterpart. This one-component system further possesses similar dynamic features such as glass transition temperature and critical exponents while subjected to Newtonian mechanics. This strategy may finally lead to the manufacturing of new nanoparticle/colloidal fluids by experimentally modeling only the outcoming effective pair potential(s) and no other macroscopic quantity.

Extreme active matter at high densities

We study the remarkable behaviour of dense active matter comprising self-propelled particles at large Péclet numbers, over a range of persistence times, from τ_p → 0, when the active fluid undergoes a slowing down of density relaxations leading to a glass transition as the active propulsion force f reduces, to τ_p → ∞, when as f reduces, the fluid jams at a critical point, with stresses along force-chains. For intermediate τ_p, a decrease in f drives the fluid through an intermittent phase before dynamical arrest at low f. This intermittency is a consequence of periods of jamming followed by bursts of plastic yielding associated with Eshelby deformations. On the other hand, an increase in f leads to an increase in the burst frequency; the correlated plastic events result in large scale vorticity and turbulence. Dense extreme active matter brings together the physics of glass, jamming, plasticity and turbulence, in a new state of driven classical matter.

While active matter exhibits unusual dynamics at low density, high density behavior has not been explored. Mandal et al. show that extreme dense active matter, shows a rich spectrum of behaviour from intermittent plastic bursts and turbulence, to glassy states and jamming in the limit of infinite persistence time.

Systems with Size and Energy Polydispersity: From Glasses to Mosaic Crystals

We use Langevin dynamics simulations to study dense 2d systems of particles with both size and energy polydispersity. We compare two types of bidisperse systems which differ in the correlation between particle size and interaction parameters: in one system big particles have high interaction parameters and small particles have low interaction parameters, while in the other system the situation is reversed. We study the different phases of the two systems and compare them to those of a system with size but not energy bidispersity. We show that, depending on the strength of interaction between big and small particles, cooling to low temperatures yields either homogeneous glasses or mosaic crystals. We find that systems with low mixing interaction, undergo partial freezing of one of the components at intermediate temperatures, and that while this phenomenon is energy-driven in both size and energy bidisperse systems, it is controlled by entropic effects in systems with size bidispersity only.

Long-wavelength fluctuations and anomalous dynamics in 2-dimensional liquids

In 2-dimensional systems at finite temperature, long-wavelength Mermin-Wagner fluctuations prevent the existence of translational long-range order. Their dynamical signature, which is the divergence of the vibrational amplitude with the system size, also affects disordered solids, and it washes out the transient solid-like response generally exhibited by liquids cooled below their melting temperatures. Through a combined numerical and experimental investigation, here we show that long-wavelength fluctuations are also relevant at high temperature, where the liquid dynamics do not reveal a transient solid-like response. In this regime, these fluctuations induce an unusual but ubiquitous decoupling between long-time diffusion coefficient D and structural relaxation time τ, where [Formula: see text], with [Formula: see text] Long-wavelength fluctuations have a negligible influence on the relaxation dynamics only at extremely high temperatures in molecular liquids or at extremely low densities in colloidal systems.

Effect of Pinning on the Yielding Transition of Amorphous Solids

Using numerical simulations, we have studied the yielding response, in the athermal quasistatic limit, of a model amorphous material having inclusions in the form of randomly pinned particles. We show that, with increasing pinning concentration, the plastic activity becomes more spatially localized, resulting in smaller stress drops, and a corresponding increase in the magnitude of strain where yielding occurs. We demonstrate that, unlike the spatially heterogeneous and avalanche led yielding in the case of the unpinned glass, for the case of large pinning concentration, yielding takes place via a spatially homogeneous proliferation of localized events.

Effective forces in thermal amorphous solids with generic interactions

In thermal glasses at temperatures sufficiently lower than the glass transition, the constituent particles are trapped in their cages for a sufficiently long time such that their time-averaged positions can be determined before diffusion and structural relaxation takes place. The effective forces are those that hold these average positions in place. In numerical simulations the effective forces F_{ij} between any pair of particles can be measured as a time average of the bare forces f_{ij}(r_{ij}(t)). In general, even if the bare forces come from two-body interactions, thermal dynamics dress the effective forces to contain many-body interactions. Here, we develop the effective theory for systems with generic interactions, where the effective forces are derivable from an effective potential and in turn they give rise to an effective Hessian whose eigenvalues are all positive when the system is stable. In this Rapid Communication, we offer analytic expressions for the effective theory, and demonstrate the usefulness and the predictive power of the approach.

Phase Diagram of Kob-Andersen-Type Binary Lennard-Jones Mixtures

The binary Kob-Andersen (KA) Lennard-Jones mixture is the standard model for computational studies of viscous liquids and the glass transition. For very long simulations, the viscous KA system crystallizes, however, by phase separating into a pure A particle phase forming a fcc crystal. We present the thermodynamic phase diagram for KA-type mixtures consisting of up to 50% small (B) particles showing, in particular, that the melting temperature of the standard KA system at liquid density 1.2 is 1.028(3) in A particle Lennard-Jones units. At large B particle concentrations, the system crystallizes into the CsCl crystal structure. The eutectic corresponding to the fcc and CsCl structures is cutoff in a narrow interval of B particle concentrations around 26% at which the bipyramidal orthorhombic PuBr_{3} structure is the thermodynamically stable phase. The melting temperature's variation with B particle concentration at two constant pressures, as well as at the constant density 1.2, is estimated from simulations at pressure 10.19 using isomorph theory. Our data demonstrate approximate identity between the melting temperature and the onset temperature below which viscous dynamics appears. Finally, the nature of the solid-liquid interface is briefly discussed.

Ultra-long-range dynamic correlations in a microscopic model for aging gels

We use large-scale computer simulations to explore the nonequilibrium aging dynamics in a microscopic model for colloidal gels. We find that gelation resulting from a kinetically arrested phase separation is accompanied by "anomalous" particle dynamics revealed by superdiffusive particle motion and compressed exponential relaxation of time correlation functions. Spatiotemporal analysis of the dynamics reveals intermittent heterogeneities producing spatial correlations over extremely large length scales. Our study is a microscopically resolved model reproducing all features of the spontaneous aging dynamics observed experimentally in soft materials.

Breakdown of nonlinear elasticity in stress-controlled thermal amorphous solids

In recent work it was clarified that amorphous solids under strain control do not possess nonlinear elastic theory in the sense that the shear modulus exists but nonlinear moduli exhibit sample-to-sample fluctuations that grow without bound with the system size. More relevant, however, for experiments are the conditions of stress control. In the present Rapid Communication we show that also under stress control the shear modulus exists, but higher-order moduli show unbounded sample-to-sample fluctuation. The unavoidable consequence is that the characterization of stress-strain curves in experiments should be done with a stress-dependent shear modulus rather than with nonlinear expansions.

Role of structure in the α and β dynamics of a simple glass-forming liquid

The elusive connection between dynamics and local structure in supercooled liquids is an important piece of the puzzle in the unsolved problem of the glass transition. The Johari-Goldstein β relaxation, ubiquitous in glass-forming liquids, exhibits mean properties that are strongly correlated to the long-time α dynamics. However, the former comprises simpler, more localized motion, and thus has perhaps a more straightforward connection to structure. Molecular dynamics simulations were carried out on a two-dimensional, rigid diatomic molecule (the simplest structure exhibiting a distinct β process) to assess the role of the local liquid structure on both the Johari-Goldstein β and the α relaxation. Although the average properties for these two relaxations are correlated, there is no connection between the β and α properties of a given (single) molecule. The propensity for motion at long times is independent of the rate or strength of a molecule's β relaxation. The mobility of a molecule averaged over many initial energies, a measure of the influence of structure, was found to be heterogeneous, with clustering at both the β and α time scales. This heterogeneity is less extended spatially for the β than for the α dynamics, as expected; however, the local structure is the more dominant control parameter for the β process. In the glassy state, the arrangement of neighboring molecules determines entirely the relaxation properties, with no discernible effect from the particle momenta.

Plastic response and correlations in athermally sheared amorphous solids

The onset of irreversible deformation in low-temperature amorphous solids is due to the accumulation of elementary events, consisting of spatially and temporally localized atomic rearrangements involving only a few tens of atoms. Recently, numerical and experimental work addressed the issue of spatiotemporal correlations between these plastic events. Here, we provide further insight into these correlations by investigating, via molecular dynamics (MD) simulations, the plastic response of a two-dimensional amorphous solid to artificially triggered local shear transformations. We show that while the plastic response is virtually absent in as-quenched configurations, it becomes apparent if a shear strain was previously imposed on the system. Plastic response has a fourfold symmetry, which is characteristic of the shear stress redistribution following the local transformation. At high shear rate we report evidence for a fluctuation-dissipation relation, connecting plastic response and correlation, which seems to break down if lower shear rates are considered.

Anatomy of plastic events in magnetic amorphous solids

Plastic events in amorphous solids can be much more than just "shear transformation zones" when the positional degrees of freedom are coupled nontrivially to other degrees of freedom. Here we consider magnetic amorphous solids where mechanical and magnetic degrees of freedom interact, leading to rather complex plastic events whose nature must be disentangled. In this paper we uncover the anatomy of the various contributions to some typical plastic events. These plastic events are seen as Barkhausen noise or other "serrated noises." Using theoretical considerations we explain the observed statistics of the various contributions to the considered plastic events. The richness of contributions and their different characteristics imply that in general the statistics of these serrated noises cannot be universal, but rather highly dependent on the state of the system and on its microscopic interactions.

Length scales in glass-forming liquids and related systems: a review

The central problem in the study of glass-forming liquids and other glassy systems is the understanding of the complex structural relaxation and rapid growth of relaxation times seen on approaching the glass transition. A central conceptual question is whether one can identify one or more growing length scale(s) associated with this behavior. Given the diversity of molecular glass-formers and a vast body of experimental, computational and theoretical work addressing glassy behavior, a number of ideas and observations pertaining to growing length scales have been presented over the past few decades, but there is as yet no consensus view on this question. In this review, we will summarize the salient results and the state of our understanding of length scales associated with dynamical slow down. After a review of slow dynamics and the glass transition, pertinent theories of the glass transition will be summarized and a survey of ideas relating to length scales in glassy systems will be presented. A number of studies have focused on the emergence of preferred packing arrangements and discussed their role in glassy dynamics. More recently, a central object of attention has been the study of spatially correlated, heterogeneous dynamics and the associated length scale, studied in computer simulations and theoretical analysis such as inhomogeneous mode coupling theory. A number of static length scales have been proposed and studied recently, such as the mosaic length scale discussed in the random first-order transition theory and the related point-to-set correlation length. We will discuss these, elaborating on key results, along with a critical appraisal of the state of the art. Finally we will discuss length scales in driven soft matter, granular fluids and amorphous solids, and give a brief description of length scales in aging systems. Possible relations of these length scales with those in glass-forming liquids will be discussed.

Fundamental differences between glassy dynamics in two and three dimensions

The two-dimensional freezing transition is very different from its three-dimensional counterpart. In contrast, the glass transition is usually assumed to have similar characteristics in two and three dimensions. Using computer simulations, here we show that glassy dynamics in supercooled two- and three-dimensional fluids are fundamentally different. Specifically, transient localization of particles on approaching the glass transition is absent in two dimensions, whereas it is very pronounced in three dimensions. Moreover, the temperature dependence of the relaxation time of orientational correlations is decoupled from that of the translational relaxation time in two dimensions but not in three dimensions. Last, the relationships between the characteristic size of dynamically heterogeneous regions and the relaxation time are very different in two and three dimensions. These results strongly suggest that the glass transition in two dimensions is different than in three dimensions.

The existing glass transition theories show little dimensional dependence. Here Flenner et al. disprove this general consensus by finding that, for instance, the bond-orientational relaxation is decoupled from the translational relaxation in two dimensions, but not in three dimensions.

Identifying structural flow defects in disordered solids using machine-learning methods

We use machine-learning methods on local structure to identify flow defects-or particles susceptible to rearrangement-in jammed and glassy systems. We apply this method successfully to two very different 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.

Mechanical properties and plasticity of a model glass loaded under stress control

Much of the progress achieved in understanding plasticity and failure in amorphous solids had been achieved using experiments and simulations in which the materials were loaded using strain control. There is paucity of results under stress control. Here we present a method that was carefully geared to allow loading under stress control either at T=0 or at any other temperature, using Monte Carlo techniques. The method is applied to a model-perfect crystalline solid, to a crystalline solid contaminated with topological defects, and to a generic glass. The highest yield stress belongs to the crystal, the lowest to the crystal with a few defects, with the glass in between. Although the glass is more disordered than the crystal with a few defects, it yields stress much higher than that of the latter. We explain this fact by considering the actual microscopic interactions that are typical of glass-forming materials, pointing out the reasons for the higher cohesive nature of the glass. The main conclusion of this paper is that the instabilities encountered in stress-control condition are the identical saddle-node bifurcation seen in strain control. Accordingly one can use the latter condition to infer the former. Finally we discuss temperature effects and comment on the time needed to see a stress-controlled material failure.

Time-dependent elastic response to a local shear transformation in amorphous solids

The elastic response of a two-dimensional amorphous solid to induced local shear transformations, which mimic the elementary plastic events occurring in deformed glasses, is investigated via molecular-dynamics simulations. We show that for different spatial realizations of the transformation, despite relative fluctuations of order one, the long-time equilibrium response averages out to the prediction of the Eshelby inclusion problem for a continuum elastic medium. We characterize the effects of the underlying dynamics on the propagation of the elastic signal. A crossover from a propagative transmission in the case of weakly damped dynamics to a diffusive transmission for strong damping is evidenced. In the latter case, the full time-dependent elastic response is in agreement with the theoretical prediction, obtained by solving the diffusion equation for the displacement field in an elastic medium.

Predicting plasticity with soft vibrational modes: from dislocations to glasses

We show that quasilocalized 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 two and three dimensions 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.

Theory of activated dynamics and glass transition of hard colloids in two dimensions

The microscopic nonlinear Langevin equation theory is applied to study the localization and activated hopping of two-dimensional hard disks in the deeply supercooled and glass states. Quantitative comparisons of dynamic characteristic length scales, barrier, and their dependence on the reduced packing fraction are presented between hard-disk and hard-sphere suspensions. The dynamic barrier of hard disks emerges at higher absolute and reduced packing fractions and correspondingly, the crossover size of the dynamic cage which correlates to the Lindemann length for melting is smaller. The localization lengths of both hard disks and spheres decrease exponentially with packing fraction. Larger localization length of hard disks than that of hard spheres is found at the same reduced packing fraction. The relaxation time of hard disks rises dramatically above the reduced packing fraction of 0.88, which leads to lower reduced packing fraction at the kinetic glass transition than that of hard spheres. The present work provides a foundation for the subsequent study of the glass transition of binary or polydisperse mixtures of hard disks, normally adopted in experiments and simulations to avoid crystallization, and further, the rheology and mechanical response of the two-dimensional glassy colloidal systems.

Finite-size scaling for the glass transition: the role of a static length scale

Over the past decade, computer simulations have had an increasing role in shedding light on difficult statistical physical phenomena, and in particular on the ubiquitous problem of the glass transition. Here in a wide variety of materials the viscosity of a supercooled liquid increases by many orders of magnitude upon decreasing the temperature over a modest range. A natural concern in these computer simulations is the very small size of the simulated systems compared to experimental ones, raising the issue of how to assess the thermodynamic limit. Here we turn this limitation to our advantage by performing finite size scaling on the system size dependence of the relaxation time for supercooled liquids to emphasize the importance of a growing static length scale in the theory of glass transition. We demonstrate that the static length scale that was discovered by us in Physica A 391, 1001 (2012) fits the bill extremely well, allowing us to provide a finite-size scaling theory for the α-relaxation time of the glass transition, including predictions for the thermodynamic limit based on simulations in small systems.

Adam-Gibbs relation for glass-forming liquids in two, three, and four dimensions

The Adam-Gibbs relation between relaxation times and the configurational entropy has been tested extensively for glass formers using experimental data and computer simulation results. Although the form of the relation contains no dependence on the spatial dimensionality in the original formulation, subsequent derivations of the Adam-Gibbs relation allow for such a possibility. We test the Adam-Gibbs relation in two, three, and four spatial dimensions using computer simulations of model glass formers. We find that the relation is valid in three and four dimensions. But in two dimensions, the relation does not hold, and interestingly, no single alternate relation describes the results for the different model systems we study.

The role of attractive forces in viscous liquids

We present evidence from computer simulation that the slowdown of relaxation of a standard Lennard-Jones glass-forming liquid and that of its reduction to a model with truncated pair potentials without attractive tails are quantitatively and qualitatively different in the viscous regime. The pair structure of the two models is however very similar. This finding, which appears to contradict the common view that the physics of dense liquids is dominated by the steep repulsive forces between atoms, is characterized in detail, and its consequences are explored. Beyond the role of attractive forces themselves, a key aspect in explaining the differences in the dynamical behavior of the two models is the truncation of the interaction potentials beyond a cutoff at typical interatomic distance. This leads us to question the ability of the jamming scenario to describe the physics of glass-forming liquids and polymers.

Mode-coupling glass transition in a fluid confined by a periodic potential

We show that a fluid under strong spatially periodic confinement displays a glass transition within mode-coupling theory at a much lower density than the corresponding bulk system. We use fluctuating hydrodynamics, with confinement imposed through a periodic potential whose wavelength plays an important role in our treatment. To make the calculation tractable we implement a detailed calculation in one dimension. Although we do not expect simple 1d fluids to show a glass transition, our results are indicative of the behavior expected in higher dimensions. In a certain region of parameter space we observe a three-step relaxation reported recently in computer simulations [S. H. Krishnan, Ph.D. thesis, Indian Institute of Science (2005); Kim et al., Eur. Phys. J. Special Topics 189, 135 (2010)] and a glass-glass transition. We compare our results to those of Krakoviack [Phys. Rev. E 75, 031503 (2007)] and Lang et al. [Phys. Rev. Lett. 105, 125701 (2010)].

Glass transition of hard spheres in high dimensions

We have investigated analytically and numerically the liquid-glass transition of hard spheres for dimensions d-->infinity in the framework of mode-coupling theory. The numerical results for the critical collective and self-nonergodicity parameters fc(k;d) and fc(s)(k;d) exhibit non-Gaussian k dependence even up to d=800.fc(s)(k;d) and fc(k;d) differ for k approximately d1/2, but become identical on a scale k approximately d, which is proven analytically. The critical packing fraction phic(d) approximately d(2)2(-d) is above the corresponding Kauzmann packing fraction phiK(d) derived by a small cage expansion. Its quadratic pre-exponential factor is different from the linear one found earlier. The numerical values for the exponent parameter and therefore the critical exponents a and b depend on d, even for the largest values of d.

Spatial dimension and the dynamics of supercooled liquids

Inspired by recent theories that apply ideas from critical phenomena to the glass transition, we have simulated an atomistic model of a supercooled liquid in three and four spatial dimensions. At the appropriate temperatures and density, dynamic density correlation functions in three and four spatial dimensions correspond nearly exactly. Dynamic heterogeneity, quantified through the breakdown of the Stokes-Einstein relationship, is weaker in four dimensions than in three. We discuss this in the context of recent theories for dynamical heterogeneity. Because dimensionality is a crucially important variable, our work adds a stringent test for emerging theories of glassy dynamics.

Slow dynamics in a driven two-lane particle system

We study a two-lane model of two species of particles that perform biased diffusion. Extensive numerical simulations show that when bias q is strong enough, oppositely drifting particles form some clusters that block each other. Coarsening of such clusters is very slow and their size increases logarithmically in time. For smaller q, particles collapse essentially on a single cluster whose size seems to diverge at a certain value of q=qc. Simulations show that despite slow coarsening, the model has rather large power-law cooling-rate effects. It makes its dynamics different from glassy systems but similar to some three-dimensional Ising-type models (gonihedric models).