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We investigate the rigidity transition associated with shear jamming in frictionless, as well as frictional, disk packings in the quasi-static regime and at low shear rates. For frictionless disks, the transition under quasi-static shear is discontinuous, with an instantaneous emergence of a system spanning rigid clusters at the jamming transition. For frictional systems, the transition appears continuous for finite shear rates, but becomes sharper for lower shear rates. In the quasi-static limit, it is discontinuous as in the frictionless case. Thus, our results show that the rigidity transition associated with shear jamming is discontinuous, as demonstrated in the past for isotropic jamming of frictionless particles, and therefore a unifying feature of the jamming transition in general.

We investigate the dynamics of soft sphere liquids through computer simulations for spatial dimensions from d=3 to 8, over a wide range of temperatures and densities. Employing a scaling of density-temperature-dependent relaxation times, we precisely identify the density ϕ_{0}, which marks the ideal glass transition in the hard sphere limit, and a crossover from sub- to super-Arrhenius temperature dependence. The difference between ϕ_{0} and the athermal jamming density ϕ_{J}, small in 3 and 4 dimensions, increases with dimension, with ϕ_{0}>ϕ_{J} for d>4. We compare our results with recent theoretical calculations.

We consider the changes in the structure of supercooled Stillinger-Weber silicon at pressures at which the studied range of temperatures traverses the liquid-liquid transition or the "Widom line" (at which the isothermal compressibility or the specific heat exhibits a maximum). In addition to the conventional characterizations in terms of the pair-correlation function and bond orientational order, we analyze the statistics of rings in the bond network as well as the statistics of clusters of low density liquid (LDL)- and high density liquid (HDL)-like atoms. We investigate the nature of the change in these structural characterizations when the liquid-liquid transition line or the Widom line is crossed. We find that the isobaric temperature variation of these structural features reveals clear indications of maximal structural heterogeneity or frustration upon crossing the liquid-liquid transition or the Widom line, as in the case of water, but with some differences in detail, which we discuss.

A vast array of phenomena, ranging from chemical reactions to phase transformations, are analyzed in terms of a free energy surface defined with respect to a single or multiple order parameters. Enhanced sampling methods are typically used, especially in the presence of large free energy barriers, to estimate free energies using biasing protocols and sampling of transition paths. Kinetic reconstructions of free energy barriers of intermediate height have been performed, with respect to a single order parameter, employing the steady state properties of unconstrained simulation trajectories when barrier crossing is achievable with reasonable computational effort. Considering such cases, we describe a method to estimate free energy surfaces with respect to multiple order parameters from a steady state ensemble of trajectories. The approach applies to cases where the transition rates between pairs of order parameter values considered is not affected by the presence of an absorbing boundary, whereas the macroscopic fluxes and sampling probabilities are. We demonstrate the applicability of our prescription on different test cases of random walkers executing Brownian motion in order parameter space with an underlying (free) energy landscape and discuss strategies to improve numerical estimates of the fluxes and sampling. We next use this approach to reconstruct the free energy surface for supercooled liquid silicon with respect to the degree of crystallinity and density, from unconstrained molecular dynamics simulations, and obtain results quantitatively consistent with earlier results from umbrella sampling.

The existence of a phase transition between two distinct liquid phases in single-component network-forming liquids (e.g. water, silica, silicon) has elicited considerable scientific interest. The challenge, both for experiments and simulations, is that the liquid-liquid phase transition (LLPT) occurs under deeply supercooled conditions, where crystallization occurs very rapidly. Thus, early evidence from numerical equation of state studies was challenged with the argument that slow spontaneous crystallization had been misinterpreted as evidence of a second liquid state. Rigorous free-energy calculations have subsequently confirmed the existence of a LLPT in some models of water, and exciting new experimental evidence has since supported these computational results. Similar results have so far not been found for silicon. Here, we present results from free-energy calculations performed for silicon modeled with the classical, empirical Stillinger-Weber-potential. Through a careful study employing state-of-the-art constrained simulation protocols and numerous checks for thermodynamic consistency, we find that there are two distinct metastable liquid states and a phase transition. Our results resolve a long-standing debate concerning the existence of a liquid-liquid transition in supercooled liquid silicon and address key questions regarding the nature of the phase transition and the associated critical point., (© The Author(s) 2022. Published by Oxford University Press on behalf of National Academy of Sciences.)

A major challenge in simulating glassy systems is the ability to generate configurations that may be found in equilibrium at sufficiently low temperatures, in order to probe static and dynamic behavior close to the glass transition. A variety of approaches have recently explored ways of surmounting this obstacle. Here, we explore the possibility of employing mechanical agitation, in the form of cyclic shear deformation, to generate low energy configurations in a model glass former. We perform shear deformation simulations over a range of temperatures, shear rates, and strain amplitudes. We find that shear deformation induces faster relaxation toward low energy configurations, or overaging, in simulations at sufficiently low temperatures, consistently with previous results for athermal shear. However, for temperatures at which simulations can be run until a steady state is reached with or without shear deformation, we find that the inclusion of shear deformation does not result in any speed up of the relaxation toward low energy configurations. Although we find the configurations from shear simulations to have properties indistinguishable from an equilibrium ensemble, the cyclic shear procedure does not guarantee that we generate an equilibrium ensemble at a desired temperature. In order to ensure equilibrium sampling, we develop a hybrid Monte Carlo algorithm that employs cyclic shear as a trial generation step and has acceptance probabilities that depend not only on the change in internal energy but also on the heat dissipated (equivalently, work done). We show that such an algorithm, indeed, generates an equilibrium ensemble.

We study a mean field elastoplastic model, embedded within a disordered landscape of local yield barriers, to shed light on the behavior of athermal amorphous solids subject to oscillatory shear. We show that the model presents a genuine dynamical transition between an elastic and a yielded state, and qualitatively reproduces the dependence on the initial degree of annealing found in particle simulations. For initial conditions prepared below the analytically derived threshold energy, we observe a nontrivial, nonmonotonic approach to the yielded state. The timescale diverges as one approaches the yielding point from above, which we identify with the fatigue limit. We finally discuss the connections to brittle yielding under uniform shear.

We study numerically the critical behavior and marginal stability of the shear jamming transition for frictionless soft spheres, observed to occur over a finite range of densities, associated with isotropic jamming for densities above the minimum jamming (J-point) density. Several quantities are shown to scale near the shear jamming point in the same way as the isotropic jamming point. We compute the exponents associated with the small force distribution and the interparticle gap distribution and show that the corresponding exponents are consistent with the marginal stability condition observed for isotropic jamming and with predictions of the mean-field theory of jamming in hard spheres.

We investigate avalanches and clusters associated with plastic rearrangements and the nature of structural change in the prototypical strong glass, silica, computationally. We perform a detailed analysis of avalanches, and of spatially disconnected clusters that constitute them, for a wide range of system sizes. Although qualitative aspects of yielding in silica are similar to other glasses, the statistics of clusters exhibits significant differences, which we associate with differences in local structure. Across the yielding transition, anomalous structural change and densification, associated with a suppression of tetrahedral order, is observed to accompany strain localization.

Multicomponent self-assembly mixtures offer the possibility of encoding multiple target structures with the same set of interacting components. Selective retrieval of one of the stored structures has been attempted by preparing an initial state that favors the assembly of the required target, through seeding, concentration patterning, or specific choices of interaction strengths. This may not be possible in an experiment where on-the-fly reconfiguration of the building blocks to switch functionality may be required. In this paper, we explore principles of inverse design of a multicomponent, self-assembly mixture capable of encoding two competing structures that can be selected through simple temperature protocols. We design the target structures to realize the generic situation in which one of the targets has the lower nucleation barrier, while the other is globally more stable. We observe that, to avoid the formation of spurious or chimeric aggregates, the number of neighboring component pairs that occur in both structures should be minimal. Our design also requires the inclusion of components that are part of only one of the target structures. We observe, however, that to maximize the selectivity of retrieval, the component library itself should be maximally shared by the two targets, within such a constraint. We demonstrate that temperature protocols can be designed that lead to the formation of either one of the target structures with high selectivity. We discuss the important role played by secondary aggregation products in improving selectivity, which we term "vestigial aggregates.", Competing Interests: The authors declare no competing interest., (Copyright © 2022 the Author(s). Published by PNAS.)

The correlation between the local structure and the propensity for structural rearrangements has been widely investigated in glass forming liquids and glasses. In this paper, we use the excess two-body entropy S 2 and tetrahedrality n tet as the per-particle local structural order parameters to explore such correlations in a three-dimensional model glass subjected to cyclic shear deformation. We first show that for both liquid configurations and the corresponding inherent structures, local ordering increases upon lowering temperature, signaled by a decrease in the two-body entropy and an increase in tetrahedrality. When the inherent structures, or glasses, are periodically sheared athermally, they eventually reach absorbing states for small shear amplitudes, which do not change from one cycle to the next. Large strain amplitudes result in the formation of shear bands, within which particle motion is diffusive. We show that in the steady state, there is a clear difference in the local structural environment of particles that will be part of plastic rearrangements during the next shear cycle and that of particles that are immobile. In particular, particles with higher S 2 and lower n tet are more likely to go through rearrangements irrespective of the average energies of the configurations and strain amplitude. For high shear, we find very distinctive local order outside the mobile shear band region, where almost 30% of the particles are involved in icosahedral clusters, contrasting strongly with the fraction of <5% found inside the shear band.

We study numerically the yielding transition of a two dimensional model glass subjected to athermal quasi-static cyclic shear deformation, with the aim of investigating the effect on the yielding behavior of the degree of annealing, which in turn depends on the preparation protocol. We find two distinct regimes of annealing separated by a threshold energy. Poorly annealed glasses progressively evolve toward the threshold energy as the strain amplitude is increased toward the yielding value. Well annealed glasses with initial energies below the threshold energy exhibit stable behavior, with a negligible change in energy with increasing strain amplitude, until they yield. Discontinuities in energy and stress at yielding increase with the degree of annealing, consistent with recent results found in three dimensions. We observe a significant structural change with strain amplitude that closely mirrors the changes in energy and stresses. We investigate groups of particles that are involved in plastic rearrangements. We analyze the distributions of avalanche sizes, of clusters of connected rearranging particles, and related quantities, employing finite size scaling analysis. We verify previously investigated relations between exponents characterizing these distributions.

We explore current ideas around the representation of a protein as an amorphous material, in turn represented by an abstract graph G with edges weighted by elastic stiffnesses. By embedding this graph in physical space, we can map every graph to a spectrum of conformational fluctuations and responses (as a result of, say, ligandbinding). This sets up a 'genotype-phenotype' map, which we use to evolve the amorphous material to select for fitness. Using this, we study the emergence of allosteric interaction, hinge joint, crack formation and a slide bolt in functional proteins such as adenylate kinase, HSP90, calmodulin and GPCR proteins. We find that these emergent features are associated with specific geometries and mode spectra of floppy or liquid-like regions. Our analysis provides insight into understanding the architectural demands on a protein that enable a prescribed function and its stability to mutations.

We consider the yielding behavior of amorphous solids under cyclic shear deformation and show that it can be mapped into a random walk in a confining potential with an absorbing boundary. The resulting dynamics is governed by the first passage time into the absorbing state and suffices to capture the essential qualitative features recently observed in atomistic simulations of amorphous solids. Our results provide insight into the mechanism underlying yielding and its robustness. When the possibility of activated escape from absorbing states is added, it leads to a unique determination of a threshold energy and yield strain, suggesting thereby an appealing approach to understanding fatigue failure.

We study the kinetics of crystallization in deeply supercooled liquid silicon employing computer simulations and the Stillinger-Weber three-body potential. The free energy barriers to crystallization are computed using umbrella sampling Monte Carlo simulations and from unconstrained molecular dynamics simulations using a mean first passage time formulation. We focus on state points that have been described in earlier work [S. Sastry and C. A. Angell, Nat. Mater. 2, 739 (2003)] as straddling a liquid-liquid phase transition (LLPT) between two metastable liquid states. It was argued subsequently [Ricci et al., Mol. Phys. 117, 3254 (2019)] that the apparent transition is due to the loss of metastability of the liquid state with respect to the crystalline state. The presence of a barrier to crystallization for these state points is therefore of importance to ascertain, which we investigate, with due attention to ambiguities that may arise from the choice of order parameters. We find a well-defined free energy barrier to crystallization and demonstrate that both umbrella sampling and mean first passage time methods yield results that agree quantitatively. Our results thus provide strong evidence against the possibility that the liquids at state points close to the reported LLPT exhibit slow, spontaneous crystallization, but they do not address the existence of a LLPT (or lack thereof). We also compute the free energy barriers to crystallization at other state points over a broad range of temperatures and pressures and discuss the effect of changes in the microscopic structure of the metastable liquid on the free energy barrier heights.

We investigate the heterogeneity of dynamics, the breakdown of the Stokes-Einstein relation and fragility in a model glass forming liquid, a binary mixture of soft spheres with a harmonic interaction potential for spatial dimensions from 3 to 8. The dynamical heterogeneity is quantified through the dynamical susceptibility χ 4 and the non-Gaussian parameter α 2 . We find that the fragility, the degree of breakdown of the Stokes-Einstein relation, and the heterogeneity of the dynamics decrease with increasing spatial dimensionality. We briefly describe the dependence of fragility on the density and use it to resolve an apparent inconsistency with previous results.

Investigations of plastic deformation and yielding of amorphous solids reveal a strong dependence of their yielding behavior on the degree of annealing. Above a threshold degree of annealing, the nature of yielding changes qualitatively, becoming progressively more discontinuous. Theoretical investigations of yielding in amorphous solids have almost exclusively focused on uniform deformation, but cyclic deformation reveals intriguing features that remain uninvestigated. Focusing on athermal cyclic deformation, I investigate a family of models, which reproduce key features observed in simulations, and provide an interpretation for the intriguing presence of a threshold energy.

Recent experiments and simulations of amorphous solids plastically deformed by an oscillatory drive have found a surprising behavior-for small strain amplitudes the dynamics can be reversible, which is contrary to the usual notion of plasticity as an irreversible form of deformation. This reversibility allows the system to reach limit cycles in which plastic events repeat indefinitely under the oscillatory drive. It was also found that reaching reversible limit cycles can take a large number of driving cycles and it was surmised that the plastic events encountered during the transient period are not encountered again and are thus irreversible. Using a graph representation of the stable configurations of the system and the plastic events connecting them, we show that the notion of reversibility in these systems is more subtle. We find that reversible plastic events are abundant and that a large portion of the plastic events encountered during the transient period are actually reversible in the sense that they can be part of a reversible deformation path. More specifically, we observe that the transition graph can be decomposed into clusters of configurations that are connected by reversible transitions. These clusters are the strongly connected components of the transition graph and their sizes turn out to be power-law distributed. The largest of these are grouped in regions of reversibility, which in turn are confined by regions of irreversibility whose number proliferates at larger strains. Our results provide an explanation for the irreversibility transition-the divergence of the transient period at a critical forcing amplitude. The long transients result from transition between clusters of reversibility in a search for a cluster large enough to contain a limit cycle of a specific amplitude. For large enough amplitudes, the search time becomes very large, since the sizes of the limit cycles become incompatible with the sizes of the regions of reversibility.

The Kauzmann temperature (T K ) of a supercooled liquid is defined as the temperature at which the liquid entropy becomes equal to that of the crystal. The excess entropy, the difference between liquid and crystal entropies, is routinely used as a measure of the configurational entropy, whose vanishing signals the thermodynamic glass transition. The existence of the thermodynamic glass transition is a widely studied subject, and of particular recent interest is the role of dimensionality in determining the presence of a glass transition at a finite temperature. The glass transition in water has been investigated intensely and is challenging as the experimental glass transition appears to occur at a temperature where the metastable liquid is strongly prone to crystallization and is not stable. To understand the dimensionality dependence of the Kauzmann temperature in water, we study computationally bulk water (three-dimensions), water confined in the slit pore of the graphene sheet (two-dimensions), and water confined in the pore of the carbon nanotube of chirality (11,11) having a diameter of 14.9 Å (one-dimension), which is the lowest diameter where amorphous water does not always crystallize into nanotube ice in the supercooled region. Using molecular dynamics simulations, we compute the entropy of water in bulk and under reduced dimensional nanoscale confinement to investigate the variation of the Kauzmann temperature with dimension. We obtain a value of T K (133 K) for bulk water in good agreement with experiments [136 K (C. A. Angell, Science 319, 582-587 (2008) and K. Amann-Winkel et al., Proc. Natl. Acad. Sci. U. S. A. 110, 17720-17725 (2013)]. However, for confined water, in two-dimensions and one-dimension, we find that there is no finite temperature Kauzmann point (in other words, the Kauzmann temperature is 0 K). Analysis of the fluidicity factor, a measure of anharmonicity in the oscillation of normal modes, reveals that the Kauzmann temperature can also be computed from the difference in the fluidicity factor between amorphous and ice phases.

Yielding behavior in amorphous solids has been investigated in computer simulations using uniform and cyclic shear deformation. Recent results characterize yielding as a discontinuous transition, with the degree of annealing of glasses being a significant parameter. Under uniform shear, discontinuous changes in stresses at yielding occur in the high annealing regime, separated from the poor annealing regime in which yielding is gradual. In cyclic shear simulations, relatively poorly annealed glasses become progressively better annealed as the yielding point is approached, with a relatively modest but clear discontinuous change at yielding. To understand better the role of annealing on yielding characteristics, we perform athermal quasistatic cyclic shear simulations of glasses prepared with a wide range of annealing in two qualitatively different systems-a model of silica (a network glass) and an atomic binary mixture glass. Two strikingly different regimes of behavior emerge. Energies of poorly annealed samples evolve toward a unique threshold energy as the strain amplitude increases, before yielding takes place. Well-annealed samples, in contrast, show no significant energy change with strain amplitude until they yield, accompanied by discontinuous energy changes that increase with the degree of annealing. Significantly, the threshold energy for both systems corresponds to dynamical cross-over temperatures associated with changes in the character of the energy landscape sampled by glass-forming liquids., Competing Interests: Competing interest statement: P.G.D. and S.S. coauthored a research article in 2019.

Granular packings display the remarkable phenomenon of dilatancy, wherein their volume increases upon shear deformation. Conventional wisdom and previous results suggest that dilatancy, also being the related phenomenon of shear-induced jamming, requires frictional interactions. Here, we show that the occurrence of isotropic jamming densities φ j above the minimal density (or the J-point density) φ J leads both to the emergence of shear-induced jamming and dilatancy in frictionless packings. Under constant pressure shear, the system evolves into a steady-state at sufficiently large strains, whose density only depends on the pressure and is insensitive to the initial jamming density φ j . In the limit of vanishing pressure, the steady-state exhibits critical behavior at φ J . While packings with different φ j values display equivalent scaling properties under compression, they exhibit striking differences in rheological behaviour under shear. The yield stress under constant volume shear increases discontinuously with density when φ j > φ J , contrary to the continuous behaviour in generic packings that jam at φ J . Our results thus lead to a more coherent, generalised picture of jamming in frictionless packings, which also have important implications on how dilatancy is understood in the context of frictional granular matter.

Self-organization, and transitions from reversible to irreversible behavior, of interacting particle assemblies driven by externally imposed stresses or deformation is of interest in comprehending diverse phenomena in soft matter. They have been investigated in a wide range of systems, such as colloidal suspensions, glasses, and granular matter. In different density and driving regimes, such behavior is related to yielding of amorphous solids, jamming, memory formation, etc. How these phenomena are related to each other has not, however, been much studied. In order to obtain a unified view of the different regimes of behavior, and transitions between them, we investigate computationally the response of soft-sphere assemblies to athermal cyclic-shear deformation over a wide range of densities and amplitudes of shear deformation. Cyclic-shear deformation induces transitions from reversible to irreversible behavior in both unjammed and jammed soft-sphere packings. Well above the minimum isotropic jamming density ([Formula: see text]), this transition corresponds to yielding. In the vicinity of the jamming point, up to a higher-density limit, we designate [Formula: see text], an unjammed phase emerges between a localized, absorbing phase and a diffusive, irreversible, phase. The emergence of the unjammed phase signals the shifting of the jamming point to higher densities as a result of annealing and opens a window where shear jamming becomes possible for frictionless packings. Below [Formula: see text], two distinct localized states, termed point- and loop-reversible, are observed. We characterize in detail the different regimes and transitions between them and obtain a unified density-shear amplitude phase diagram., Competing Interests: The authors declare no competing interest.

We consider the slow and athermal deformations of amorphous solids and show how the ensuing sequence of discrete plastic rearrangements can be mapped onto a directed network. The network topology reveals a set of highly connected regions joined by occasional one-way transitions. The highly connected regions include hierarchically organized hysteresis cycles and subcycles. At small to moderate strains this organization leads to near-perfect return point memory. The transitions in the network can be traced back to localized particle rearrangements (soft spots) that interact via Eshelby-type deformation fields. By linking topology to dynamics, the network representations provide new insight into the mechanisms that lead to reversible and irreversible behavior in amorphous solids.

We study the inverse problem of tuning interaction parameters between charged colloidal particles interacting with a hard-core repulsive Yukawa potential, so that they assemble into specified crystal structures. Here, we target the body-centered-cubic (bcc) structure which is only stable in a small region in the phase diagram of charged colloids and is, therefore, challenging to find. In order to achieve this goal, we use the statistical fluctuations in the bond orientational order parameters to tune the interaction parameters for the bcc structure, while initializing the system in the fluid phase, using the Statistical Physics-inspired Inverse Design algorithm. We also find that this optimization algorithm correctly senses the fluid-solid phase boundaries for charged colloids. Finally, we repeat the procedure employing the covariance matrix adaptation-evolution strategy, a cutting edge optimization technique, and compare the relative efficacy of the two methods.

We explain the structural origin of the jamming transition in jammed matter as the sudden appearance of k-cores at precise coordination numbers which are related not to the isostatic point, but to the emergence of the giant 3- and 4-cores as given by k-core percolation theory. At the transition, the k-core variables freeze and the k-core dominates the appearance of rigidity. Surprisingly, the 3-D simulation results can be explained with the result of mean-field k-core percolation in the Erdös-Rényi network. That is, the finite-dimensional transition seems to be explained by the infinite-dimensional k-core, implying that the structure of the jammed pack is compatible with a fully random network.

The emergence of rigidity upon changes of temperature, density, or applied stresses in disordered assemblies of particles is of interest in a wide range of soft matter, from glass formers, gels, foams, and granular matter. Shear jamming of frictional grains presents an interesting special case wherein the application of shear stress leads to rigidity rather than its loss. The formation of self-organized structures that resist shear deformation offers an appealing geometric picture of shear jamming, which nevertheless is incompletely developed, and not well integrated with ideas concerning rigidity in frictionless systems. Exploiting the observation that athermally sheared sphere assemblies develop structural features necessary for shear jamming even in the absence of friction [H. A. Vinutha and S. Sastry, Nature Physics 12, 578 (2016)1745-247310.1038/nphys3658], we analyze conditions for jamming in such assemblies computationally. Solving force and torque balance conditions for their contact geometry, we show, and validate with frictional simulations, that the mean contact number Z equals D+1 (for spatial dimension D=2,3) at jamming for both finite and infinite friction, above the "random loose packing" limit density, at variance with previous analyses of frictional jamming. We show that the shear jamming threshold satisfies the marginal stability condition recently proposed for jamming in frictionless systems. Along lines explored in studying covalent glasses, we perform rigidity percolation analysis for D=2 and find that rigidity percolation precedes shear jamming, which, however, coincides with the percolation of over-constrained regions, leading to the identification of a regime analogous to the intermediate phase observed in covalent glasses. Together, these results provide a geometric description of shear jamming that relate closely with analyses of jamming, rigidity, and the glass transition in frictionless systems, and thus help develop a unified description of jamming phenomenology in diverse disordered matter.

We study a model amorphous solid that is subjected to repeated athermal cyclic shear deformation. It has previously been demonstrated that the memory of the amplitudes of shear deformation the system is subjected to (or trained at) is encoded, and can be retrieved by subsequent deformation cycles that serve as read operations. Here we consider different read protocols and measurements and show that single and multiple memories can be robustly retrieved through these different protocols. We also show that shear deformation by a larger amplitude always erases the stored memories. These observations are similar to those in experiments with non-Brownian colloidal suspensions and corresponding models, but differ in the possibility of storing multiple memories non-transiently. Such a possibility has been associated with the presence of cycles of transitions that take place in the model amorphous solids, between local energy minima. Here, we also study low-density sphere assemblies which serve as models for non-Brownian colloidal suspensions, under athermal deformation, and identify a regime where the signatures of memory encoding are similar to the model glass, even when transition between local energy minima are absent. We show that such a regime corresponds to the presence of loop reversibility, rather than point reversibility of configurations under cyclic deformation.

The origin of the rapid dynamical slowdown in glass forming liquids in the growth of static length scales, possibly associated with identifiable structural ordering, is a much debated issue. Growth of medium range crystalline order (MRCO) has been observed in various model systems to be associated with glassy behavior. Such observations raise the question of whether molecular mechanisms for the glass transition in liquids with and without MRCO are the same. In this study we perform extensive molecular dynamics simulations of a number of glass forming liquids and show that the static and dynamic properties of glasses with MRCO are different from those of other glass forming liquids with no predominant local order. We also resolve an important issue regarding the so-called point-to-set method for determining static length scales, and demonstrate it to be a robust method for determining static correlation lengths in glass formers.

The slow down of dynamics in glass forming liquids as the glass transition is approached has been characterised through the Adam-Gibbs relation, which relates relaxation time scales to the configurational entropy. The Adam-Gibbs relation cannot apply simultaneously to all relaxation times scales unless they are coupled, and exhibit closely related temperature dependences. The breakdown of the Stokes-Einstein relation presents an interesting situation to the contrary, and in analysing it, it has recently been shown that the Adam-Gibbs relation applies to diffusion coefficients rather than to viscosity or structural relaxation times related to the decay of density fluctuations. However, for multi-component liquids --the typical cases considered in computer simulations, metallic glass formers, etc.-- such a statement raises the question of which diffusion coefficient is described by the Adam-Gibbs relation. All diffusion coefficients can be consistently described by the Adam-Gibbs relation if they bear a power law relationship with each other. Remarkably, we find that for a wide range of glass formers, and for a wide range of temperatures spanning the normal and the slow relaxation regimes, such a relationship holds. We briefly discuss possible rationalisations of the observed behaviour.

The Adam-Gibbs (AG) relation connects the dynamics of a glass-forming liquid to its thermodynamics via the configurational entropy and is of fundamental importance in descriptions of glassy behavior. The breakdown of the Stokes-Einstein relation (SEB) between the diffusion coefficient and the viscosity (or structural relaxation times) in glass formers raises the question as to which dynamical quantity the AG relation describes. By performing molecular dynamics simulations, we show that the AG relation is valid over the widest temperature range for the diffusion coefficient and not for the viscosity or relaxation times. Studying relaxation times defined at a given wavelength, we find that SEB and the deviation from the AG relation occur below a temperature at which the correlation length of dynamical heterogeneity equals the wavelength probed.

In this paper, we establish a connection between the onset temperature of glassy dynamics with the change in the entropy for a wide range of model systems. We identify the crossing temperature of pair and excess entropies as the onset temperature. Below the onset temperature, the residual multiparticle entropy, the difference between excess and pair entropies, becomes positive. The positive entropy can be viewed as equivalent to the larger phase space exploration of the system. The new method of onset temperature prediction from entropy is less ambiguous, as it does not depend on any fitting parameter like the existing methods.

Amorphous solids are ubiquitous among natural and man-made materials. Often used as structural materials for their attractive mechanical properties, their utility depends critically on their response to applied stresses. Processes underlying such mechanical response, and in particular the yielding behaviour of amorphous solids, are not satisfactorily understood. Although studied extensively, observed yielding behaviour can be gradual and depend significantly on conditions of study, making it difficult to convincingly validate existing theoretical descriptions of a sharp yielding transition. Here we employ oscillatory deformation as a reliable probe of the yielding transition. Through extensive computer simulations for a wide range of system sizes, we demonstrate that cyclically deformed model glasses exhibit a sharply defined yielding transition with characteristics that are independent of preparation history. In contrast to prevailing expectations, the statistics of avalanches reveals no signature of the impending transition, but exhibit dramatic, qualitative, changes in character across the transition.

Competing Interests: The author declares no conflict of interest.

In this paper, we present a study of supercooled liquids interacting with the Lennard Jones potential and the corresponding purely repulsive (Weeks-Chandler-Andersen) potential, over a range of densities and temperatures, in order to understand the origin of their different dynamics in spite of their structures being similar. Using the configurational entropy as the thermodynamic marker via the Adam Gibbs relation, we show that the difference in the dynamics of these two systems at low temperatures can be explained from thermodynamics. At higher densities both the thermodynamical and dynamical difference between these model systems decrease, which is quantitatively demonstrated in this paper by calculating different parameters. The study also reveals the origin of the difference in pair entropy despite the similarity in the structure. Although the maximum difference in structure is obtained in the partial radial distribution function of the B type of particles, the rdf of AA pairs and AB pairs gives rise to the differences in the entropy and dynamics. This work supports the observation made in an earlier study [A. Banerjee et al., Phys. Rev. Lett. 113, 225701 (2014)] and shows that they are generic in nature, independent of density.

Temporal relaxation of density fluctuations in supercooled liquids near the glass transition occurs in multiple steps. Using molecular dynamics simulations for three model glass-forming liquids, we show that the short-time β relaxation is cooperative in nature. Using finite-size scaling analysis, we extract a growing length scale associated with beta relaxation from the observed dependence of the beta relaxation time on the system size. We find, in qualitative agreement with the prediction of the inhomogeneous mode coupling theory, that the temperature dependence of this length scale is the same as that of the length scale that describes the spatial heterogeneity of local dynamics in the long-time α-relaxation regime.

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.

We focus on the probability distribution function (PDF) P(Δγ;γ) where Δγ are the measured strain intervals between plastic events in a athermal strained amorphous solids, and γ measures the accumulated strain. The tail of this distribution as Δγ→0 (in the thermodynamic limit) scales like Δγ(η). The exponent η is related via scaling relations to the tail of the PDF of the eigenvalues of the plastic modes of the Hessian matrix P(λ) which scales like λ(θ), η=(θ-1)/2. The numerical values of η or θ can be determined easily in the unstrained material and in the yielded state of plastic flow. Special care is called for in the determination of these exponents between these states as γ increases. Determining the γ dependence of the PDF P(Δγ;γ) can shed important light on plasticity and yield. We conclude that the PDF's of both Δγ and λ are not continuous functions of γ. In slowly quenched amorphous solids they undergo two discontinuous transitions, first at γ=0(+) and then at the yield point γ=γ(Y) to plastic flow. In quickly quenched amorphous solids the second transition is smeared out due to the nonexisting stress peak before yield. The nature of these transitions and scaling relations with the system size dependence of 〈Δγ〉 are discussed.

We analyze the dynamics of model supercooled liquids in a temperature regime where predictions of mode coupling theory (MCT) are known to be valid qualitatively. In this regime, the Adam-Gibbs (AG) relation, based on an activation picture of dynamics, also describes the dynamics satisfactorily, and we explore the mutual consistency and interrelation of these descriptions. Although entropy and dynamics are related via phenomenological theories, the connection between MCT and entropy has not been argued for. In this work, we explore this connection and provide a microscopic derivation of the phenomenological Rosenfeld theory. At low temperatures, the overlap between the MCT power law regime and AG relation implies that the AG relation predicts an avoided divergence at Tc, the origin of which can be related to the vanishing of pair configurational entropy, which we find occurring at the same temperature. We also show that the residual multiparticle entropy plays an important role in describing the relaxation time.

Using an athermal quasistatic simulation protocol, we study the distribution of free volumes in sheared hard-particle packings close to, but below, the random-close packing threshold. We show that under shear, and independent of volume fraction, the free volumes develop features similar to close-packed systems - particles self-organize in a manner as to mimick the isotropically jammed state. We compare athermally sheared packings with thermalized packings and show that thermalization leads to an erasure of these structural features. The temporal evolution in particular the opening-up and the closing of free-volume patches is associated with the single-particle dynamics, showing a crossover from ballistic to diffusive behavior.

An understanding of the origin of fragility, which the rapidity of change of viscosity and related dynamical quantities, has been sought by a variety of approaches over the years. Within the framework of the Adam-Gibbs relation, fragility is in principle related to both the temperature variation of configurational entropy and the high temperature activation energy. Many theoretical analyses have been focused on the variation of configuration entropy, although the importance of the high temperature activation energy in determining the fragility of a glass former has also been emphasized. We explore the latter aspect by considering a model liquid whose high temperature activation energy is modified by hand, through the introduction of a tunable barrier to bond breaking. We show that changes in such a barrier are able to modify the fragility measured from the temperature dependence of dynamical quantities, while a thermodynamic measure of fragility obtained from the configurational entropy remains unchanged. We discuss the implications of our results to our understanding of fragility, and outline open questions that merit further investigation.

We consider two schematic models of glasses subjected to oscillatory shear deformation, motivated by the observations, in computer simulations of a model glass, of a nonequilibrium transition from a localized to a diffusive regime as the shear amplitude is increased, and of persistent memory effects in the localized regime. The first of these schematic models is the NK model, a spin model with disordered multi-spin interactions previously studied as a model for sheared amorphous solids. The second model, a transition matrix model, is an abstract formulation of the manner in which occupancy of local energy minima evolves under oscillatory deformation cycles. In both of these models, we find a behavior similar to that of an atomic model glass studied earlier. We discuss possible further extensions of the approaches outlined.

We present a study of two model liquids with different interaction potentials, exhibiting similar structure but significantly different dynamics at low temperatures. By evaluating the configurational entropy, we show that the differences in the dynamics of these systems can be understood in terms of their thermodynamic differences. Analyzing their structure, we demonstrate that differences in pair correlation functions between the two systems, through their contribution to the entropy, dominate the differences in their dynamics, and indeed overestimate the differences. Including the contribution of higher order structural correlations to the entropy leads to smaller estimates for the relaxation times, as well as smaller differences between the two studied systems.

Anomalous behaviour in density, diffusivity, and structural order is investigated for silicon modeled by the Stillinger-Weber potential by performing molecular dynamics simulations. As previously reported in the case of water [J. R. Errington and P. G. Debenedetti, Nature (London) 409, 318 (2001)] and silica [M. S. Shell, P. G. Debenedetti, and A. Z. Panagiotopoulos, Phys. Rev. E 66, 011202 (2002)], a cascading of thermodynamic, dynamic, and structural anomalous regions is also observed in liquid silicon. The region of structural anomaly includes the region of diffusivity anomaly, which in turn encompasses the region of density anomaly (which is unlike water but similar to silica). In the region of structural anomaly, a tight correlation between the translational and tetrahedrality order parameter is found, but the correlation is weaker when a local orientational order parameter (q3) is used as a measure of tetrahedrality. The total excess entropy and the pair correlation entropy are computed across the phase diagram and the correlation between the excess entropy and the regions of anomalies in the phase diagram of liquid silicon is examined. Scaling relations associating the excess entropy with the diffusion coefficient show considerable deviation from the quasi-universal behaviour observed in hard-sphere and Lennard-Jones liquids and some liquid metals. Excess entropy based criteria for diffusivity and structural anomalies fail to capture the observed regions of anomaly.

We calculate the free volume distributions of nearly jammed packings of monodisperse and bidisperse hard sphere configurations. These distributions differ qualitatively from those of the fluid, displaying a power law tail at large free volumes, which constitutes a distinct signature of nearly jammed configurations, persisting for moderate degrees of decompression. We reproduce and explain the observed distribution by considering the pair correlation function within the first coordination shell for jammed hard sphere configurations. We analyze features of the equation of state near jamming, and discuss the significance of observed asphericities of the free volumes to the equation of state.

By modifying the tetrahedrality (the strength of the three body interactions) in the well-known Stillinger-Weber model for silicon, we study the diffusivity of a series of model liquids as a function of tetrahedrality and temperature at fixed pressure. Previous work has shown that at constant temperature, the diffusivity exhibits a maximum as a function of tetrahedrality, which we refer to as the diffusivity anomaly, in analogy with the well-known anomaly in water upon variation of pressure at constant temperature. We explore to what extent the structural and thermodynamic changes accompanying changes in the interaction potential can help rationalize the diffusivity anomaly, by employing the Rosenfeld relation between diffusivity and the excess entropy (over the ideal gas reference value), and the pair correlation entropy, which provides an approximation to the excess entropy in terms of the pair correlation function. We find that in the modified Stillinger-Weber liquids, the Rosenfeld relation works well above the melting temperatures but exhibits deviations below, with the deviations becoming smaller for smaller tetrahedrality. Further we find that both the excess entropy and the pair correlation entropy at constant temperature go through maxima as a function of the tetrahedrality, thus demonstrating the close relationship between structural, thermodynamic, and dynamical anomalies in the modified Stillinger-Weber liquids.

We show that memory can be encoded in a model amorphous solid subjected to athermal oscillatory shear deformations, and in an analogous spin model with disordered interactions, sharing the feature of a deformable energy landscape. When these systems are subjected to oscillatory shear deformation, they retain memory of the deformation amplitude imposed in the training phase, when the amplitude is below a "localization" threshold. Remarkably, multiple persistent memories can be stored using such an athermal, noise-free, protocol. The possibility of such memory is shown to be linked to the presence of plastic deformations and associated limit cycles traversed by the system, which exhibit avalanche statistics also seen in related contexts.

Dynamical quantities e.g. diffusivity and relaxation time for some glass-formers may depend on density and temperature through a specific combination, rather than independently, allowing the representation of data over ranges of density and temperature as a function of a single scaling variable. Such a scaling, referred to as density-temperature (DT) scaling, is exact for liquids with inverse power law (IPL) interactions but has also been found to be approximately valid in many non-IPL liquids. We have analyzed the consequences of DT scaling on the density dependence of the fragility in a model glass-former. We find the density dependence of kinetic fragility to be weak, and show that it can be understood in terms of DT scaling and deviations of DT scaling at low densities. We also show that the Adam-Gibbs relation exhibits DT scaling and the scaling exponent computed from the density dependence of the activation free energy in the Adam-Gibbs relation, is consistent with the exponent values obtained by other means.

We report computer simulations of oscillatory athermal quasistatic shear deformation of dense amorphous samples of a three-dimensional model glass former. A dynamical transition is observed as the amplitude of the deformation is varied: For large values of the amplitude the system exhibits diffusive behavior and loss of memory of the initial conditions, whereas localization is observed for small amplitudes. Our results suggest that the same kind of transition found in driven colloidal systems is present in the case of amorphous solids (e.g., metallic glasses). The onset of the transition is shown to be related to the onset of energy dissipation. Shear banding is observed for large system sizes, without, however, affecting qualitative aspects of the transition.

We carefully examine common measures of dynamical heterogeneity for a model polymer melt and test how these scales compare with those hypothesized by the Adam and Gibbs (AG) and random first-order transition (RFOT) theories of relaxation in glass-forming liquids. To this end, we first analyze clusters of highly mobile particles, the string-like collective motion of these mobile particles, and clusters of relative low mobility. We show that the time scale of the high-mobility clusters and strings is associated with a diffusive time scale, while the low-mobility particles' time scale relates to a structural relaxation time. The difference of the characteristic times for the high- and low-mobility particles naturally explains the well-known decoupling of diffusion and structural relaxation time scales. Despite the inherent difference of dynamics between high- and low-mobility particles, we find a high degree of similarity in the geometrical structure of these particle clusters. In particular, we show that the fractal dimensions of these clusters are consistent with those of swollen branched polymers or branched polymers with screened excluded-volume interactions, corresponding to lattice animals and percolation clusters, respectively. In contrast, the fractal dimension of the strings crosses over from that of self-avoiding walks for small strings, to simple random walks for longer, more strongly interacting, strings, corresponding to flexible polymers with screened excluded-volume interactions. We examine the appropriateness of identifying the size scales of either mobile particle clusters or strings with the size of cooperatively rearranging regions (CRR) in the AG and RFOT theories. We find that the string size appears to be the most consistent measure of CRR for both the AG and RFOT models. Identifying strings or clusters with the "mosaic" length of the RFOT model relaxes the conventional assumption that the "entropic droplets" are compact. We also confirm the validity of the entropy formulation of the AG theory, constraining the exponent values of the RFOT theory. This constraint, together with the analysis of size scales, enables us to estimate the characteristic exponents of RFOT.