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We investigate the effects of random pinning, where we freeze the relaxation degrees of freedom for a fraction of randomly selected particles, on the yielding transition under oscillatory shear through extensive computer simulations. Using Kob-Anderson model as our model glass former, we pin a fraction of the particles. These pinned particles can move affinely under the imposed oscillatory shear deformation but are not allowed to relax through subsequent rearrangements due to plastic events. As the fraction of pinned particles increases, the system transitions from being a fragile glass former to a strong glass former. This gives us opportunity to examine how changes in fragility impact the yielding transition. Our results demonstrate notable differences in the yielding transition between strong and fragile glass formers under random pinning. This aligns with previous observations where fragility was altered by changing the packing fraction in soft sphere model albeit with a main difference that random pinning significantly suppresses the formation of shear bands, even in well-annealed glass samples.

We consider a class of non-standard, two-dimensional (2D) Hamiltonian models that may show features of active particle dynamics, and therefore, we refer to these models as active Hamiltonian (AH) systems. The idea is to consider a spin fluid where -- on top of spin-spin and particle-particle interactions -- spins are coupled to the particle's velocities via a vector potential. Continuous spin variables interact with each other as in a standard $XY$ model. Typically, the AH models exhibit non-standard thermodynamic properties (e.g., for temperature and pressure) and equations of motion with non-standard forces. This implies that the derivation of symplectic algorithms to solve Hamilton's equations of motion numerically, as well as the thermostatting for these systems, is not straightforward. Here, we derive a symplectic integration scheme and propose a Nos\'e-Poincar\'e thermostat, providing a correct sampling in the canonical ensemble. The expressions for AH systems that we find for temperature and pressure might have parallels with the ongoing debate about the definition of pressure and the equation of state in active matter systems. For a specific AH model, recently proposed by Casiulis et al. [Phys. Rev. Lett. {\bf 124}, 198001 (2020)], we rationalize the symplectic algorithm and the proposed thermostatting, and investigate the transition from a fluid at high temperature to a cluster phase at low temperature where, due to the coupling of velocities and spins, the cluster phase shows a collective motion that is reminiscent to that observed in a variety of active systems.

We study the effect of the fragility of glass formers on the yielding transition under oscillatory shear via extensive computer simulations. Employing sphere assemblies interacting with a harmonic potential as our model glass former, we tune fragility by changing the system's density - higher density corresponds to large fragility. Our study reveals significant differences in the yielding transition between strong and fragile glass formers. While both glass formers exhibit similar behaviour under poorly annealed initial conditions, the yielding transition shifts to larger values with increased annealing for fragile glasses while remaining relatively constant for strong glasses. We rationalize our results by introducing a new elastoplastic model, which qualitatively reproduces the simulation results and offers valuable insight into the physics of yielding transition under oscillatory shear deformation.

Dynamics is central to living systems. In the last two decades, experiments have revealed that the dynamics in diverse biological systems - from intracellular cytoplasm to cellular and organismal aggregates - are remarkably similar to that in dense systems of inanimate particles in equilibrium. They show a glass transition from a solid-like jammed state to a fluid-like flowing state, where a moderate change in control parameter leads to an enormous variation in relaxation time. However, biological systems have crucial differences from the equilibrium systems: the former have activity that drives them out of equilibrium, novel control parameters, and enormous levels of complexity. These active systems showing glassy dynamics are known as active glasses. The field is at the interface of physics and biology, freely borrowing tools from both disciplines and promising novel, fascinating discoveries. We review the experiments that started this field, simulations that have been instrumental for insights, and theories that have helped unify diverse phenomena, reveal correlations, and make novel quantitative predictions. We discuss the primary characteristics that define a glassy system. For most concepts, we first discuss the known equilibrium scenario and then present the key aspects when activity is introduced. We end the article with a discussion of the challenges in the field and possible future directions., Comment: 25 pages, 13 figures

In the realm of two-dimensional (2D) systems, the renowned Mermin-Wagner effect plays a significant role, giving rise to striking dimensionality effects marked by far-reaching density fluctuations and the divergence of various dynamic properties. This effect also unequivocally negates the possibility of stable crystalline phases in 2D particulate systems characterized by continuous degrees of freedom. This effect has been recently discerned in glass-forming liquids, displaying characteristic signatures like the logarithmic divergence of mean squared displacement in the plateau regime. We explored these long-wavelength fluctuations in crystalline solids and in glass-forming liquids in the presence of non-equilibrium active forces. These systems are known in the literature as active crystals and glasses, and they can be thought of as a minimalistic model for understanding various non-equilibrium systems where the constituent particles dynamics are controlled by both temperature and other active forces, which can be external or internal. Such models often offer valuable insights into the dynamical behavior of biological systems, such as collections of cells, bacteria, ant colonies, or even synthetic self-propelled particles like Janus colloids. Our study reveals that fluctuations stemming from active forces get strongly coupled with long wavelength fluctuations arising from thermal effects, resulting in dramatic dynamical effects, particularly in 2D systems. We also shed light on how these fluctuations impact dynamical heterogeneity, a defining characteristic of glassy dynamics.

The dynamics of dense particle packings near the jamming transition is characterized by correlated particle motion. The growth of dynamical heterogeneities, or strong spatial variations in the motion of the particles constituting the system, is a hallmark feature of slow glassy dynamics. We report here a systematic confocal microscopy study that characterizes the cooperative dynamics of fluorescently-labelled colloidal particles in dense aqueous suspensions. We demonstrate that jammed particulate suspensions can be fluidized by increasing the width of the particle size distribution. Our molecular dynamics simulations, performed to numerically investigate the effects of continuous-size polydispersity on dense particle packing dynamics, show an excellent match with our experimental results. Besides shedding light on the fundamental aspects of particle-scale dynamics at the jamming-unjamming transition, our findings are significant in the processing of commonly-encountered dense suspensions such as paints, cosmetics, and food.

We investigate the memory effects under oscillatory shear deformation of amorphous solids through computer simulations. Applications of shear deformations in all orthogonal directions show that encoded memories via this protocol are more robust while performing reading. Our extensive system size analysis of memory effects shows that memory encoding in small systems is faster than in larger systems and is probably impossible in thermodynamically large system sizes. In addition to demonstrating how to encode robust memories in 3D bulk amorphous materials, we devise protocols for encoding and reading memories in pseudo-1D materials in the form of amorphous nano-rods. With this, we show that memory encoding and retrieving can also be done in systems with open surfaces, which all materials would necessarily have in practice, and is thus essential to capitalise on the effectiveness of smaller system sizes to encode memories faster. All in all, we provide protocols for encoding robust and faster memories in amorphous solids both at bulk and nanoscale.

Understanding the mechanical properties of amorphous solids is a crucial area of research due to the fascinating phenomena they exhibit under external deformations and their importance in industrial applications. Although these solids have higher yield strength compared to crystalline solids of similar composition, they often fail catastrophically through shear band formation. Tuning their mechanical behavior is vital for material design. Engineers have long been seeking ways to improve the ability of amorphous solids to withstand external deformations, with micro-alloying being a popular method. By adding small amounts of different materials to pure samples, microalloying can enhance yield strain, although the microscopic mechanisms behind this process remain poorly understood. We conducted a study with extensive molecular dynamics simulations on model amorphous solids to investigate the effect of asphericity of the impurity particles on their yielding behaviour. Our results indicate that aspherical impurities free to rotate can significantly increase the yield threshold. Conversely, when impurities are unable to rotate, they can lead to the formationof extremely brittle, ultrastable-like systems. The rotational degrees of freedom are controlled bychanging the aspect ratio of the impurity,and they play a crucial role in influencing shear bandformation. Additionally, we found that including larger impurities enhances the structural stabilityof the parent glass matrix., Comment: 10 pages, 6 figures

One of the central challenges in condensed matter physics is to comprehend systems that have strong disorder and strong interactions. In the strongly localized regime, their subtle competition leads to glassy electron dynamics which ceases to exist well before the insulator-to-metal transition is approached as a function of doping. Here, we report on the discovery of glassy electron dynamics deep inside the good metal regime of an electron-doped quantum paraelectric system: KTaO$_3$. We reveal that upon excitation of electrons from defect states to the conduction band, the excess injected carriers in the conduction band relax in a stretched exponential manner with a large relaxation time, and the system evinces simple aging phenomena - a telltale sign of glassy dynamics. Most significantly, we observe a critical slowing down of carrier dynamics below 35 K, concomitant with the onset of quantum paraelectricity in the undoped KTaO$_3$. Our combined investigation using second harmonic generation technique, density functional theory and phenomenological modeling demonstrates quantum fluctuation-stabilized soft polar modes as the impetus for the glassy behavior. This study addresses one of the most fundamental questions regarding the potential promotion of glassiness by quantum fluctuations and opens a route for exploring glassy dynamics of electrons in a well-delocalized regime., Comment: 51 pages and 18 figures including supplemental

Stokes-Einstein (SE) relation, which relates diffusion constant with the viscosity of a liquid at high temperatures in equilibrium, is violated in the supercooled temperature regime. Whether this relation is obeyed in nonequilibrium active liquids is a question of significant current interest to the statistical physics community trying to develop the theoretical framework of nonequilibrium statistical mechanics. Via extensive computer simulations of model active glass-forming liquids in three dimensions, we show that SE is obeyed at a high temperature similar to the equilibrium behaviour, and it gets violated in the supercooled temperature regimes. The degree of violation increases systematically with the increasing activity which quantifies the amount the system is driven out of equilibrium. First passage-time (FPT) distributions helped us to gain insights into this enhanced breakdown from the increased short-time peak, depicting hoppers. Subsequently, we study the wave vector dependence of SE relation and show that it gets restored at a wave vector that decreases with increasing activity, and the cross-over wave vector is found to be proportional to the inverse of the dynamical heterogeneity length scale in the system. Our work showed how SE violation in active supercooled liquids could be rationalized using the growth of dynamic length scale, which is found to grow enormously with increasing activity in these systems.

Amorphous solids are known to fail catastrophically via fracture, wherein cavitation at nano-metric scales is known to play a significant role. 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 move only affinely and do not participate in plastic relaxation, 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. Further, 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.

Amorphous solids yield upon crossing a strain threshold, after an initial elastic response, when subjected to mechanical deformation. The yielding process is characterized by local plastic events leading to non-affine displacements, and their interactions. Despite the lack of long-range structural order, these disordered materials exhibit long-range spatial correlations in the non-affine displacement fields, which stems from the underlying elasticity. Measuring a correlation length scale in deformed amorphous solids, during the plastic process, is a non-trivial challenge, often requiring an ad-hoc definition of localized regions. In this paper, we introduce a novel computational approach called the "soft matrix" that enables systematic analysis of mechanical response of local regions within a disordered solid. In this method, we subject the amorphous solid to a quasistatic shear and allow a local region of interest to relax freely while allowing for elastic relaxation of the background. The dependence of the yield strain upon the size of the probe region naturally reveals the existence of an intrinsic length scale ($\zeta$) that governs the elasto-plastic properties, as observed in four distinct model amorphous solids. This finding demonstrates the universality of this characteristic length scale across a wide range of materials. We investigate the dependence of this length scale on the material's preparation history and find that $\zeta$ increases with better annealing. Furthermore, the local mechanical properties measured within this framework provide more accurate estimates compared to existing techniques. Our study paves the way for a comprehensive understanding of amorphous solids and facilitates improved characterization and design of these materials.

Investigating the behavior of amorphous solids under various external loading conditions continues to be an intriguing area of research with significant practical implications. In this study, we demonstrate the utilization of self-motility as a means to anneal glasses and use that as a means to fine-tune the failure mode of the system under uniaxial tensile deformation. We begin by highlighting the annealing effects of activity and draw parallels with other well-known mechanical annealing processes, such as oscillatory shearing (both uni- and multi-directional). Furthermore, we explore the annealing effects in the presence of open boundaries, observing enhanced surface relaxations due to activity. By implementing various activity-induced annealing protocols, we successfully induce a transition in the failure mode from ductile to brittle. This is demonstrated via performing tensile tests on the glass samples resulting from the active-annealing process. The intricate effects of geometry on the formation of shear bands are also examined. We find that samples having an aspect ratio greater than one fail via shear band formation, owing to their formation angle of $45\degree$ from the strain axis. In conclusion, we introduce a novel method for producing well-annealed glasses in silico and establish a correspondence between sheared and actively driven glasses.

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 $D(\omega) \sim \omega^4$ law changes to $D(\omega) \sim \omega^\delta$ with $\delta \approx 5$ in two dimensions and $\delta \approx 4.5$ 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 $D(\omega) \sim \omega^4$ behavior is recovered., Comment: 12 pages, 11 figures

Amorphous solids are known to fail catastrophically and in some situations, nano-scaled cavities are believed to play a significant role in the failure. In a recent work, using numerical simulations, we have shown the correspondence between cavitation under uniform expansion of amorphous solids and the yielding under shear. In this study, we probe the stability of spatially-homogeneous states sampled from expansion trajectories to alternate modes of driving, viz. macroscopic cyclic shear or local random deformation via activity. We find that, under cyclic shear and activity, the cavitation instabilities can occur in expanded states at much higher densities than under pure uniform-expansion, and the shift in density is determined by the magnitude of the secondary deformation. We also show that barriers to cavitation on the energy landscape are much smaller for cyclic-shear and activity than seen under expansion. Further, we also analyse the spatial manifestation of cavitation and investigate whether large scale irreversible plasticity can set in due to the combination of expansion and the secondary deformation. Overall, our study reveals the interplay between expansion and other deformation modes leading to cavitation instabilities and the existence of abundant relaxation pathways for such processes.

All-atom molecular dynamics simulations of 1,2-dimyristoyl-sn-glycerol-3-phosphocholine lipid membranes reveal a membrane phase transition dictated drastic growth in the interface water (IW) heterogeneity length scales. It acts as an alternate probe to capture the ripple size of the membrane and follows an activated dynamical scaling with the relaxation time scale solely within the gel phase. The results quantify the mostly unknown correlations between the spatio-temporal scales of the IW and membranes at various phases under physiological and supercooled condition

The growth of correlation lengths in equilibrium glass-forming liquids near the glass transition is considered a critical finding in the quest to understand the physics of glass formation. These understandings helped us understand various dynamical phenomena observed in supercooled liquids. It is known that at least two different length scales exist - one is of thermodynamic origin, while the other is dynamical in nature. Recent observations of glassy dynamics in biological and synthetic systems where the external or internal driving source controls the dynamics, apart from the usual thermal noise, led to the emergence of the field of active matter. A question of whether the physics of glass formation in these active systems is also accompanied by growing dynamic and static lengths is indeed timely. In this article, we probe the growth of dynamic and static lengths in a model active glass system using rod-like elongated probe particles, an experimentally viable method. We show that the dynamic and static lengths in these non-equilibrium systems grow much more rapidly than their passive counterparts. We then offer an understanding of the violation of the Stokes-Einstein relation and Stokes-Einstein-Debye relation using these lengths via a scaling theory.

The electroviscous effect deals with the change in the viscosity of fluids due to an external electric field. Here, we report experimental studies on the electroviscous effects in a ferroelectric nematic liquid crystal. It was synthesised accomplishing a new synthetic route which provides higher yield than conventional one. We measure electric field-dependent viscosity under a steady shear at different temperatures. In the low field range, the increase in viscosity ($\Delta\eta=\eta(E)-\eta_0$) is proportional to $E^2$ and the corresponding viscoelectric coefficient ($f\approx10^{-9}$m\textsuperscript{2}/V\textsuperscript{2}) of the ferroelectric nematic is 2 orders of magnitude larger than the apolar nematic liquid crystals and largest ever measured for a fluid. The apparent viscosity measured under a high electric field shows a power-law divergence $\eta\sim(T-T_c)^{-0.7\pm0.05}$, followed by nearly an order of magnitude drop below the N-N\textsubscript{F} phase transition. Experimental results within the dynamical scaling approximation demonstrate rapid growth of polar domains under a strong electric field as the N-N\textsubscript{F} phase transition is approached. The gigantic electroviscous effects demonstrated here are important for emerging applications and understanding striking electrohydromechanical effects in ferroelectric nematic liquid crystals., Comment: 5 figures

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 $\phi_0$ which marks the ideal glass transition in the hard sphere limit, and a crossover from sub- to super-Arrhenius temperature dependence. The difference between $\phi_0$ and the athermal jamming density $\phi_J$, small in 3 and 4 dimensions, increases with dimension, with $\phi_0 > \phi_J$ for $d > 4$. We compare our results with recent theoretical calculations., Comment: Supplemental Material included as ancillary file

Active glassy systems can be thought of as simple model systems that imitate complex biological systems. Sometimes, it becomes crucial to estimate the amount of the activity present in such biological systems, such as predicting the progression rate of the cancer cells or the healing time of the wound. In this work, we study a model active glassy system to understand a possible quantification of the degree of activity from the collective, long-range phonon response in the system. We find that the four-point dynamic susceptibility, $\chi_4(t)$ at the phonon timescale, grows with increased activity. We then show how one can estimate the degree of the activity at such a small timescale by measuring the growth of $\chi_4(t)$ with changing activity. A detailed finite size analysis of this measurement, shows that the peak height of $\chi_4(t)$ at this phonon timescale increases strongly with increasing system size suggesting a possible existence of an intrinsic dynamic length scale that grows with increasing activity. Finally, we show that this peak height is a unique function of effective activity across all system sizes, serving as a possible parameter for characterizing the degree of activity in a system.

We study the effects of cyclic, athermal quasi-static shear on a model glass-forming system in three dimensions. We utilize the three available orthogonal shear planes, namely $XY, YZ \text{ and } XZ$ to better explore the energy landscape. Using measurements of the stroboscopic $(\gamma = 0)$ energy, we study the effects of using an orthogonal shear direction to perturb unidirectional steady-states. We find that that each sequence of the unidirectional protocol leads to compaction with the universal, $\Delta E \sim N^{-1}$ behavior as a function of the number of cycles, $N$. Additionally we find that cyclic shear utilizing multiple shear planes presents hierarchical compaction, producing progressively lower steady state energies compared to a protocol involving unidirectional cyclic shear alone. Furthermore, with the periodicity of the stroboscopic energy as reference, we show that it is possible to achieve steady state limit-cycles of tunable periodicities using different combinations of the three orthogonal strain directions. We find that such protocols exhibit better annealing as compared to protocols with steady states created using unidirectional shear. Importantly, we find a non-trivial trend in the annealing energy and the period of the steady-state limit-cycle, with an aperiodic protocol appearing to produce the most well annealed states. Finally, we compare the phase diagram of the average steady state energy $\langle E_{\text{S.S.}} \rangle$, as a function of the shearing amplitude $\gamma_{\max}$, using unidirectional and multidirectional protocols, and find that the universal features are preserved., Comment: 8 pages, 6 figures

Effects of activity on glassy dynamics are fundamental in several biological processes. Active glasses extend the scope of the equilibrium problem and provide new control parameters to probe different theoretical aspects. In the theory of glassy dynamics, different length scales play pivotal roles. Here, for the first time, we present results for the static length scale, $\xi_S$, in an active glass via large-scale molecular dynamics simulations for model active glasses in three spatial dimensions. We show that although the relaxation dynamics are equilibrium-like, activity has non-trivial effects on $\xi_S$. $\xi_S$ plays the central role in the random first-order transition (RFOT) theory. Thus, our work provides critical tests for the active RFOT theory, a phenomenological extension of its equilibrium counterpart. We find that the two exponents, $\theta$ and $\psi$, within the theory, become activity-dependent, exposing the non-trivial effects of activity on $\xi_S$. However, the combination of $\theta$ and $\psi$, which controls the relaxation dynamics, remains nearly independent of activity leading to the effectively equilibrium-like behavior. Interestingly, $\xi_S$ shows higher growth in an active glass; this should help better comparison of theories with simulations and experiments., Comment: 6+5 pages, 3+4 figures

Using numerical simulations, we study the failure of an amorphous solid under quasi-static expansion starting from a homogeneous high-density state. During the volume expansion, we demonstrate the existence of instabilities manifesting via saddle-node bifurcation in which a minimum meets a saddle. During all such events, the smallest eigenvalue of the Hessian matrix vanishes as a square-root singularity. The plastic instabilities are manifested via sudden jumps in pressure and energy, with the largest event happening when a cavity appears, leading to the yielding of the material. We show that during cavitation and prior to complete fracture, the statistics of pressure or energy jumps corresponding to the plastic events show sub-extensive finite-size scaling, similar to the case of simple shear but with different exponents. Thus, overall, our study reveals universality in the fundamental characteristics during mechanical failure in amorphous solids under any quasi-static deformation protocol., Comment: 4 figures, ancillary pdf

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. Dynamical heterogeneity is quantified through the dynamical susceptibility $\chi_4$, and the non-Gaussian parameter $\alpha_2$. We find that the fragility, the degree of breakdown of the Stokes-Einstein relation, as well as heterogeneity of dynamics, decrease with increasing spatial dimensionality. We briefly describe the dependence of fragility on density, and use it to resolve an apparent inconsistency with previous results.

The term "fragility" describes the rate at which viscosity grows when a supercooled liquid approaches its putative glass transition temperature. The field of glassy materials is actively searching for a structural origin that governs this dynamical slowing down in the supercooled liquid, which occurs without any discernible change in structure. Our work shows clear evidence that growing many-body static amorphous order is intimately correlated with the kinetic fragility of glass-forming liquids. It confirms that the system's dynamical response to temperature is concealed in its micro-structures. This finding may pave the way for a deeper understanding of the different temperature dependence of the relaxation time or viscosity in a wide variety of glass-forming liquids.

Recently, some of us developed a novel model glass-forming liquid with k extra interactions with pseudo neighbours to each liquid particle over and above the regular interactions with its neighbours. Analysis of the structure and dynamics of these systems showed that with an increase in k the systems have more mean-field like properties. This work presents an extensive study of the thermodynamics of the above-mentioned model for several values of k and its correlation with the dynamics. We surprisingly find that the usual thermodynamic integration (TI) method of calculating the entropy provides unphysical results for this model. It predicts the vanishing of configurational entropy at state points at which both the collective and the single-particle dynamics of the system show complete relaxation. We then employ a new method known as the two-phase thermodynamics (2PT) method to calculate the entropy. We find that with an increase in k the difference in the entropy computed using the two methods (2PT and TI) increases. We also find that in the temperature range studied, the entropy calculated via the 2PT method satisfies the Adam-Gibbs (AG) relationship between the relaxation time and the configurational entropy, whereas the entropy calculated via the TI method shows a strong violation of the same. We then apply the 2PT method to calculate the entropy in another system where some fractions of particles are pinned randomly in their equilibrium positions. This system also shows a similar breakdown of the AG relationship as reported earlier. We show that the difference in entropy calculated via the 2PT and TI methods increases with an increase in pinning density. We also find that when the entropy is calculated using the 2PT method, the AG relationship between the dynamics and the entropy holds., Comment: 16 pages, 27 figures, 3 tables

Enormous enhancement in the viscosity of a liquid near its glass transition is generally connected to the growing many-body static correlations near the transition, often coined as `amorphous ordering'. Estimating the length scales of such correlations in different glass-forming liquids is highly important to unravel the physics of glass formation. Experiments on molecular glass-forming liquids become pivotal in this scenario as the viscosity grows several folds ($\sim 10^{14}$), simulations or colloidal glass experiments fail to access the long-time scales required. Here we design an experiment to extract the static length scales in molecular liquids using dilute amounts of another large molecule as a pinning site. Results from dielectric relaxation experiments on supercooled glycerol with different pinning concentrations of sorbitol and the simulations on a few model glass-forming liquids with pinning sites indicate the robustness of the proposed method, opening a plethora of opportunity to study the physics of other glass-forming liquids.

Activity-driven glassy dynamics, while ubiquitous in collective cell migration, intracellular transport, dynamics in bacterial and ant colonies, etc., also extend the scope and extent of the as-yet mysterious physics of glass transition. Active glasses are hitherto assumed to be qualitatively similar to their equilibrium counterparts at an effective temperature, $T_{eff}$. Here we combine large-scale simulations and an analytical mode-coupling theory (MCT) for such systems and show that, in fact, an active glass is inherently different from an equilibrium glass. Although the relaxation dynamics can be equilibrium-like at a $T_{eff}$, the effects of activity on the dynamical heterogeneity (DH), which has emerged as a cornerstone of glassy dynamics, are quite nontrivial and complex. With no preexisting data, we employ four distinct methods for reliable estimates of the DH length scales. Our work shows active glasses exhibit dramatic growth of DH and systems with similar relaxation times, and $T_{eff}$ can have widely varying DH. To theoretically study DH, we extend active MCT and find excellent agreement between the theory and simulation results. Our results question the supposedly central role of DH in glassy dynamics and can have fundamental significance even in equilibrium.

We study energy minimized configurations of amorphous solids with a simple shear degree of freedom. We show that the low-frequency regime of the vibrational density of states of structural glass formers is crucially sensitive to the stress-ensemble from which the configurations are sampled. In both two and three dimensions, a shear-stabilized ensemble displays a $D(\omega_{\min}) \sim \omega^{5}_{\min}$ regime, as opposed to the $\omega^{4}_{\min}$ regime observed under unstrained conditions. We also study an ensemble of two dimensional, strained amorphous solids near a plastic event. We show that the minimum eigenvalue distribution at a strain $\gamma$ near the plastic event occurring at $\gamma_{P}$, displays a collapse when scaled by $\sqrt{\gamma_P - \gamma}$, and with the number of particles as $N^{-0.22}$. Notably, at low-frequencies, this scaled distribution displays a robust $D(\omega_{\min}) \sim \omega^{6}_{\min}$ power-law regime, which survives in the large $N$ limit. Finally, we probe the universal properties of this ensemble through a characterization of the second and third eigenvalues of the Hessian matrix near a plastic event., Comment: 6 pages, 4 figures, +Supplemental Material, changes: clarifications, 3D data, schematics

The use of probe molecules to extract the local dynamical and structural properties of complex dynamical systems is an age-old technique both in simulations and experiments. A lot of important information which is not immediately accessible from the bulk measurements can be accessed via these local measurements. Still, a detailed understanding of how a probe particle's dynamics are affected by the surrounding liquid medium is not very well understood, especially in the supercooled temperature regime. This work shows how translational dynamics of a rod-like particle immersed in a supercooled liquid can give us information on the growth of the correlation length scale associated with dynamical heterogeneity and the multi-body static correlations in the medium. A unified scaling theory rationalizes all the observed results leading to the development of a novel yet simple method that is accessible in experiments to measure the growth of these important length-scales in molecular glass-forming liquids.

Probing dynamic and static correlation in glass-forming supercooled liquids has been a challenge for decades in spite of extensive research. Dynamic correlation which manifests itself as Dynamic Heterogeneity is ubiquitous in a vast variety of systems starting from molecular glass-forming liquids, dense colloidal systems to collections of cells. On the other hand, the mere concept of static correlation in these dense disordered systems remain somewhat elusive and its existence is still actively debated. We propose a novel method to extract both dynamic and static correlations using rod-like particles as probe. This method can be implemented in molecular glass-forming liquids in experiments as well as in other soft matter systems including biologically relevant systems. We also rationalize the observed log-normal like distribution of rotational decorrelation time of elongated probe molecules in reported experimental studies along with a proposal of a novel methodology to extract dynamic and static correlation lengths in experiments.

We show that the distribution of elements $H$ in the Hessian matrices associated with amorphous materials exhibit singularities $P(H) \sim {\lvert H \rvert}^{\gamma}$ with an exponent $\gamma < 0$, as $\lvert H \rvert \to 0$. We exploit the rotational invariance of the underlying disorder in amorphous structures to derive these exponents exactly for systems interacting via radially symmetric potentials. We show that $\gamma$ depends only on the degree of smoothness $n$ of the potential of interaction between the constituent particles at the cut-off distance, independent of the details of interaction in both two and three dimensions. We verify our predictions with numerical simulations of models of structural glass formers. Finally, we show that such singularities affect the stability of amorphous solids, through the distributions of the minimum eigenvalue of the Hessian matrix., Comment: 6 pages, 4 figures, 1 table, +Supplemental Material

Dynamic heterogeneity, believed to be one of the hallmarks of the dynamics of supercooled liquids, is expected to affect the diffusion of the particles comprising the liquid. We have carried out extensive molecular dynamics simulations of two model glass-forming liquids in three dimensions to study the time scales at which Fick's law of diffusion starts to set in. We have identified two different Fickian timescales: one at which the mean squared displacement begins to show a linear dependence on time, and another one at which the distribution of particle displacements becomes Gaussian. These two times scales are found to be very different from each other and from the $\alpha$ relaxation time in both systems. An interesting connection is found between one of these Fickian time scales and the time scale obtained from the bond-breakage correlation function. We discuss the relationships between these different timescales and their connection to dynamic heterogeneity in the system.

Amorphous solids, confined on the nano-scale, exhibit a wealth of novel phenomena yet to be explored. In particular, the response of such solids to a mechanical load is not well understood and, as has been demonstrated experimentally, it differs strongly from bulk samples made of the same materials. Failure patterns and mechanisms are strongly affected by the geometry of the confinement and the interplay between interfacial effects in the sample and the time scale, imposed by an external mechanical field. Here, we present the mechanism of cavity formation in a confined model glass, subjected to expansion with a constant strain rate. This system is studied for varying geometric aspect ratio and sample size. Our results show that for a given temperature and straining condition, the sample shows cavitation when the aspect ratio reaches a critical value and below this aspect ratio the sample breaks by forming a neck. The critical aspect ratio is associated with a critical curvature of the neck that depends on strain rate and temperature. If this critical curvature is exceeded, the free energy of the system is minimized by the formation of a cavity. Our study reveals a novel mechanism of cavity formation on the nanoscale. This is probably a generic mechanism for material's failure in small confined systems under mechanical load.

The existence of heterogeneity in the dynamics of supercooled liquids is believed to be one of the hallmarks of the glass transition. Intense research has been carried out in the past to understand the origin of this heterogeneity in dynamics and a possible length scale associated with it. We have done extensive molecular dynamics simulations of few model glass-forming liquids in three dimensions to understand the temporal evolution of the dynamic heterogeneity and the heterogeneity length scale. We find that although the strength of the dynamic heterogeneity is maximum at a timescale close to characteristic $\alpha$-relaxation time of the system, dynamic heterogeneity itself is well-developed at timescale as short as $\beta$-relaxation time and survives up to a timescale as long as few tens of $\alpha$-relaxation time. Moreover, we discovered that temperature dependence of heterogeneity length remains the same in the whole time window although its absolute value changes over time in a non-monotonic manner.

Strained amorphous solids often fail mechanically by creating a shear-band. It had been understood that the shear banding instability is usefully described as crossing a spinodal point (with disorder) in an appropriate thermodynamic description. It remained contested however whether the spinodal is critical (with divergent correlation length) or not. Here we offer evidence for critical spinodal by using particle pinning. For a finite concentration of pinned particles the correlation length is bounded by the average distance between pinned particles, but without pinning it is bounded by the system size., Comment: 5 pages, 5 figures - error bars have been added to figure 2, all figures have been reformatted

Using numerical simulations, we have studied the yielding response, in the athermal quasi static 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 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.

A hydrated 1,2-dimyristoyl-sn-glycero-3-phosphorylcholine (DMPC) lipid membrane is investigated using an all atom molecular dynamics simulation at 308K to find out the physical sources of universal slow relaxation of hydration layers. Continuously residing interface water (IW) hydrogen bonded to each other and concertedly to different moieties of lipid heads are identified. The non-gaussian parameter of all IW show a crossover from cage vibration to translational diffusion. A significant non-gaussianity is observed for the IW prevailing large length correlations in translational van Hove functions. Two time-scales for the ballisitic motions and hopping transitions are obtained from the self intermediate scattering functions of the IW with an additional long relaxation which disappears for the BW. This is attributed to the coupled dynamics of IW cages hydrogen bonded to lipid heads. Our calculations reveal that the water near membranes are slowed down due to dynamical heterogeneities above room temperature and have implications to bioprotection mechanism at freezing conditions., Comment: 6 pages, 5 figures

Non-Gaussian nature of the probability distribution of particles' displacements in the supercooled temperature regime in glass-forming liquids are believed to be one of the major hallmarks of glass transition. It is already been established that this probability distribution which is also known as the van Hove function show universal exponential tail. The origin of such an exponential tail in the distribution function is attributed to the hopping motion of particles observed in the supercooled regime. The non-Gaussian nature can also be explained if one assumes that the system has heterogeneous dynamics in space and time. Thus exponential tail is the manifestation of dynamic heterogeneity. In this work we directly show that non-Gaussanity of the distribution of particles' displacements occur over the dynamic heterogeneity length scale and dynamical behaviour course grained over this length scale becomes homogeneous. We study the non-Gaussianity of van Hove function by systematically coarse graining at different length scale and extract the length scale of dynamic heterogeneity at which the shape of the van Hove function crosses over from non-Gaussian to Gaussian. The obtained dynamic heterogeneity scale is found to be in very good agreement with the scale obtained from other conventional methods.

We show that a flat two dimensional network of connected vertices, when stretched, may deform plastically by producing `pleats'; system spanning linear structures with width comparable to the lattice spacing, where the network overlaps on itself. To understand the pleating process, we introduce an external field that couples to local {\em non-affine} displacements, i.e. those displacements of neighbouring vertices that cannot be represented as a local affine strain. We obtain both zero and finite temperature phase diagrams in the strain -- field plane. Pleats occur here as a result of an equilibrium first-order transition from the homogeneous network to a heterogeneous phase where stress is localised within pleats and eliminated elsewhere. We show that in the thermodynamic limit the un-pleated state is always metastable at vanishing field for infinitesimal strain. Plastic deformation of the initially homogeneous network is akin to the decay of a metastable phase via a dynamical transition. We make predictions concerning local stress distributions and thermal effects associated with pleats which may be observable in suitable experimental systems., Comment: 9 pages, 10 figures

Customarily, crystalline solids are defined to be {\em rigid} since they resist changes of shape determined by their boundaries. However, rigid solids cannot exist in the thermodynamic limit where boundaries become irrelevant. Particles in the solid may rearrange to adjust to shape changes eliminating stress without destroying crystalline order. Rigidity is therefore valid only in the {\em metastable} state that emerges because these particle rearrangements in response to a deformation, or strain, are associated with slow collective processes. Here, we show that a thermodynamic collective variable may be used to quantify particle rearrangements that occur as a solid is deformed at zero strain rate. Advanced Monte Carlo simulation techniques are then employed to obtain the equilibrium free energy as a function of this variable. Our results lead to a new view on rigidity: While at zero strain a rigid crystal coexists with one that responds to infinitesimal strain by rearranging particles and expelling stress, at finite strain the rigid crystal is metastable, associated with a free energy barrier that decreases with increasing strain. The rigid phase becomes thermodynamically stable by switching on an external field, which penalises particle rearrangements. This produces a line of first-order phase transitions in the field - strain plane that intersects the origin. Failure of a solid once strained beyond its elastic limit is associated with kinetic decay processes of the metastable rigid crystal deformed with a finite strain rate. These processes can be understood in quantitative detail using our computed phase diagram as reference., Comment: 11 pages, 7 figures

Relaxation processes in supercooled liquids are known to exhibit interesting as well as complex behavior. One of the hallmarks of this relaxation process observed in the measured auto correlation function is occurrence of multiple steps of relaxation. The shorter time relaxation is known as the $\beta$-relaxation which is believed to be due to the motion of particles in the cage formed by their neighbors. One the other hand longer time relaxation, the $\alpha$-relaxation is believed to be the main relaxation process in the liquids. The timescales of these two relaxations processes dramatically separate out with supercooling. In spite of decades of researches, it is still not clearly known how these relaxation processes are related to each other. In this work we show that, there is a possible universal relation between short time $\beta$-relaxation and the long time $\alpha$-relaxation. This relation is found to be quite robust across many different model systems. Finally we show that length scale obtained from the finite size scaling analysis of $\beta$ timescale is same as that of length scale associated with the dynamic heterogeneity in both two and three dimensions., Comment: 8 pages and 8 figures with supplementary information

Understanding the effect of glassy dynamics on the stability of bio-macromolecules and investigating the underlying relaxation processes governing degradation processes of these macromolecules are of immense importance in the context of bio-preservation. In this work we have studied the stability of a model polymer chain in a supercooled glass-forming liquid at different amount of supercooling in order to understand how dynamics of supercooled liquids influence the collapse behavior of the polymer. Our systematic computer simulation studies find that apart from long time relaxation processes ($\alpha$ relaxation), short time dynamics of the supercooled liquid, known as $\beta$ relaxation plays an important role in controlling the stability of the model polymer. This is in agreement with some recent experimental findings. These observations are in stark contrast with the common belief that only long time relaxation processes are the sole player. We find convincing evidence that suggest that one might need to review the the vitrification hypothesis which postulates that $\alpha$ relaxations control the dynamics of biomolecules and thus $\alpha$-relaxation time should be considered for choosing appropriate bio-preservatives. We hope that our results will lead to understand the primary factors in protein stabilization in the context of bio-preservation.

We present {\it block analysis}, an efficient method to perform finite-size scaling for obtaining the length scale of dynamic heterogeneity and the point-to-set length scale for generic glass-forming liquids. This method involves considering blocks of varying sizes embedded in a system of a fixed (large) size. The length scale associated with dynamic heterogeneity is obtained from a finite-size scaling analysis of the dependence of the four-point dynamic susceptibility on the block size. The block size dependence of the variance of the $\alpha$-relaxation time yields the static point-to-set length scale. The values of the obtained length scales agree quantitatively with those obtained from other conventional methods. This method provides an efficient experimental tool for studying the growth of length scales in systems such as colloidal glasses for which performing finite-size scaling by carrying out experiments for varying system sizes may not be feasible., Comment: 5 pages, 3 figures

The origins of rapid dynamical slow down 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 behaviour. Such observations raise the question about the eventual state reached by a glass former, if allowed to relax for sufficiently long times. Is a slowly growing crystalline order responsible for slow dynamics? Are the molecular mechanisms for glass transition in liquids with and without MRCO the same? If yes, glass formers with MRCO provide a paradigm for understanding glassy behaviour generically. If not, systems with MRCO form a new class of glass forming materials whose molecular mechanism for slow dynamics may be easier to understand in terms of growing crystalline order, and should be approached in that manner, even while they will not provide generic insights. In this study we perform extensive molecular dynamics simulations of a number of glass forming liquids in two dimensions and show that the static and dynamic properties of glasses with MRCO are different from 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, order agnostic, method for determining static correlation lengths in glass formers.

We describe a phase transition that gives rise to structurally non-trivial states in a two-dimensional ordered network of particles connected by harmonic bonds. Monte Carlo simulations reveal that the network supports, apart from the homogeneous phase, a number of heterogeneous "pleated" phases, which can be stabilised by an external field. This field is conjugate to a global collective variable quantifying "non-affineness", i.e.~the deviation of local particle displacements from local affine deformation. In the pleated phase, stress is localised in ordered rows of pleats and eliminated from the rest of the lattice. The {\em kinetics} of the phase transition is unobservably slow in molecular dynamics simulation near coexistence, due to very large free energy barriers. When the external field is increased further to lower these barriers, the network exhibits rich dynamic behaviour: it transforms into a {\em metastable} phase with the stress now localised in a {\em disordered} arrangement of pleats. The pattern of pleats shows ageing dynamics and slow relaxation to equilibrium. Our predictions may be checked by experiments on tethered colloidal solids in dynamic laser traps., Comment: 10 pages, 8 figures