BOTAN: BOnd TArgeting Network for prediction of slow glassy dynamics by machine learning relative motion.

Recent developments in machine learning have enabled accurate predictions of the dynamics of slow structural relaxation in glass-forming systems. However, existing machine learning models for these tasks are mostly designed such that they learn a single dynamic quantity and relate it to the structural features of glassy liquids. In this study, we propose a graph neural network model, "BOnd TArgeting Network," that learns relative motion between neighboring pairs of particles, in addition to the self-motion of particles. By relating the structural features to these two different dynamical variables, the model autonomously acquires the ability to discern how the self motion of particles undergoing slow relaxation is affected by different dynamical processes, strain fluctuations and particle rearrangements, and thus can predict with high precision how slow structural relaxation develops in space and time.

Molecular-dynamics simulations on the mesophase transition induced by oscillatory shear in imidazolium-based ionic liquid crystals.

Molecular dynamics simulations were performed on a 1-dodecyl-3-methylimidazolium hexafluorophosphate ([C12mim][PF6]) ionic liquid crystal (ILC) with the application of an oscillatory shear. We found that the oscillatory shear can both accelerate and suppress mesophase formation depending on shear amplitude. A small amplitude shear can speed up the mesophase transition dynamics and result in a more ordered mesomorphic structure than that without shear, i.e., an effect of accelerated aging. The mesophase is destabilized when the shear amplitude is large enough, resulting in a smectic A (SmA) to liquid or a smectic B (SmB) to SmA transition, with the mesophase behaviour summarized in an out-of-equilibrium phase diagram. Inside the layer plane a medium-range hexatic order was observed, with the correlation length extending to several nanometres in the shear-induced SmA phase. We rationalize the nonequilibrium mesophase behaviour from the rheology of isotropic liquids, finding a temperature-independent critical relaxation time for the mesophase transition in the translational or rotational dynamics. This finding can be used to predict the mesophase behaviour in the sheared ILCs from the rheology of isotropic liquids.

Continuum limit of the vibrational properties of amorphous solids.

The low-frequency vibrational and low-temperature thermal properties of amorphous solids are markedly different from those of crystalline solids. This situation is counterintuitive because all solid materials are expected to behave as a homogeneous elastic body in the continuum limit, in which vibrational modes are phonons that follow the Debye law. A number of phenomenological explanations for this situation have been proposed, which assume elastic heterogeneities, soft localized vibrations, and so on. Microscopic mean-field theories have recently been developed to predict the universal non-Debye scaling law. Considering these theoretical arguments, it is absolutely necessary to directly observe the nature of the low-frequency vibrations of amorphous solids and determine the laws that such vibrations obey. Herein, we perform an extremely large-scale vibrational mode analysis of a model amorphous solid. We find that the scaling law predicted by the mean-field theory is violated at low frequency, and in the continuum limit, the vibrational modes converge to a mixture of phonon modes that follow the Debye law and soft localized modes that follow another universal non-Debye scaling law.

Local Density Fluctuation Governs the Divergence of Viscosity Underlying Elastic and Hydrodynamic Anomalies in a 2D Glass-Forming Liquid.

If a liquid is cooled rapidly to form a glass, its structural relaxation becomes retarded, producing a drastic increase in viscosity. In two dimensions, strong long-wavelength fluctuations persist, even at low temperature, making it difficult to evaluate the microscopic structural relaxation time. This Letter shows that, in a 2D glass-forming liquid, relative displacement between neighbor particles yields a relaxation time that grows in proportion to the viscosity. In addition to thermal elastic vibrations, hydrodynamic fluctuations are found to affect the long-wavelength dynamics, yielding a logarithmically diverging diffusivity in the long-time limit.

Molecular dynamics study of mesophase transitions upon annealing of imidazolium-based ionic liquids with long-alkyl chains.

Molecular dynamics simulations are performed on a 1-dodecyl-3-methylimidazolium hexafluorophosphate ([C12mim][PF6]) ionic liquid using a united-atom model. The ionic liquid exhibits second step relaxation at temperatures below a crossover point, where the diffusion coefficient shows an Arrhenius to non-Arrhenius transition. Annealing below this crossover temperature makes an isotropic to mesophase transition, where the smectic A (SmA) phase or crystal-like smectic B (SmB) phase forms. Hundreds of nanoseconds are required for completing these transitions. A normal diffusion process is found for anions along the layer-normal and -lateral directions in the SmA phase, but only in the lateral directions in the SmB phase. We find a preserved orientational order for the imidazolium-ring rotational and the alkyl-chain reorientational dynamics in both of the smectic phases.

Unveiling Dimensionality Dependence of Glassy Dynamics: 2D Infinite Fluctuation Eclipses Inherent Structural Relaxation.

By using large-scale molecular dynamics simulations, the dynamics of two-dimensional (2D) supercooled liquids turns out to be dependent on the system size, while the size dependence is not pronounced in three-dimensional (3D) systems. It is demonstrated that the strong system-size effect in 2D amorphous systems originates from the enhanced fluctuations at long wavelengths which are similar to those of 2D crystal phonons. This observation is further supported by the frequency dependence of the vibrational density of states, consisting of the Debye approximation in the low-wave-number limit. However, the system-size effect in the intermediate scattering function becomes negligible when the length scale is larger than the vibrational amplitude. This suggests that the finite-size effect in a 2D system is transient and also that the structural relaxation itself is not fundamentally different from that in a 3D system. In fact, the dynamic correlation lengths estimated from the bond-breakage function, which do not suffer from those enhanced fluctuations, are not size dependent in either 2D or 3D systems.

Monte Carlo study of the frame, fluctuation and internal tensions of fluctuating membranes with fixed area.

Three types of surface tensions can be defined for lipid membranes: the internal tension, σ, conjugated to the real membrane area in the Hamiltonian, the mechanical frame tension, τ, conjugated to the projected area, and the "fluctuation tension", r, obtained from the fluctuation spectrum of the membrane height. We investigate these surface tensions by means of a Monge gauge lattice Monte Carlo simulation involving the exact, nonlinear, Helfrich Hamiltonian and a measure correction for the excess entropy of the Monge gauge. Our results for the relation between σ and τ agrees well with the theoretical prediction of [J.-B. Fournier and C. Barbetta, Phys. Rev. Lett., 2008, 100, 078103] based on a Gaussian approximation. This provides a valuable knowledge of τ in the standard Gaussian models where the tension is controlled by σ. However, contrary to the conjecture in the above paper, we find that r exhibits no significant difference from τ over more than five decades of tension. Our results appear to be valid in the thermodynamic limit and are robust to changing the ensemble in which the membrane area is controlled.

SIZ1 deficiency causes reduced stomatal aperture and enhanced drought tolerance via controlling salicylic acid-induced accumulation of reactive oxygen species in Arabidopsis.

Transpiration and gas exchange occur through stomata. Thus, the control of stomatal aperture is important for the efficiency and regulation of water use, and for the response to drought. Here, we demonstrate that SIZ1-mediated endogenous salicylic acid (SA) accumulation plays an important role in stomatal closure and drought tolerance. siz1 reduced stomatal apertures. The reduced stomatal apertures of siz1 were inhibited by the application of peroxidase inhibitors, salicylhydroxamic acid and azide, which inhibits SA-dependent reactive oxygen species (ROS) production, but not by an NADPH oxidase inhibitor, diphenyl iodonium chloride, which inhibits ABA-dependent ROS production. Furthermore, the introduction of nahG into siz1, which reduces SA accumulation, restored stomatal opening. Stomatal closure is generally induced by water deficit. The siz1 mutation caused drought tolerance, whereas nahG siz1 suppressed the tolerant phenotype. Drought stresses also induced expression of SA-responsive genes, such as PR1 and PR2. Furthermore, other SA-accumulating mutants, cpr5 and acd6, exhibited stomatal closure and drought tolerance, and nahG suppressed the phenotype of cpr5 and acd6, as did siz1 and nahG siz1. Together, these results suggest that SIZ1 negatively affects stomatal closure and drought tolerance through the accumulation of SA.

Spatiotemporal heterogeneity of local free volumes in highly supercooled liquid.

We discuss the spatiotemporal behavior of local density and its relation to dynamical heterogeneity in a highly supercooled liquid by using molecular dynamics simulations of a binary mixture with different particle sizes in two dimensions. To trace voids heterogeneously existing with lower local densities, which move along with the structural relaxation, we employ the minimum local density for each particle in a time window whose width is set along with the structural relaxation time. Particles subject to free volumes correspond well to the configuration rearranging region of dynamical heterogeneity. While the correlation length for dynamical heterogeneity grows with temperature decrease, no growth in the correlation length of heterogeneity in the minimum local density distribution takes place. A comparison of these results with those of normal mode analysis reveals that superpositions of lower-frequency soft modes extending over the free volumes exhibit spatial correlation with the broken bonds. This observation suggests a possibility that long-ranged vibration modes facilitate the interactions between fragile regions represented by free volumes, to induce dynamical correlations at a large scale.

Structure formation of surfactant membranes under shear flow.

Shear-flow-induced structure formation in surfactant-water mixtures is investigated numerically using a meshless-membrane model in combination with a particle-based hydrodynamics simulation approach for the solvent. At low shear rates, uni-lamellar vesicles and planar lamellae structures are formed at small and large membrane volume fractions, respectively. At high shear rates, lamellar states exhibit an undulation instability, leading to rolled or cylindrical membrane shapes oriented in the flow direction. The spatial symmetry and structure factor of this rolled state agree with those of intermediate states during lamellar-to-onion transition measured by time-resolved scatting experiments. Structural evolution in time exhibits a moderate dependence on the initial condition.

Plastic flow in polycrystal states in a binary mixture.

Using molecular dynamics simulation, we examine the dynamics of sheared polycrystal states in a binary mixture composed of small and large particles in two dimensions. We vary the composition c of the large particles and the shear rate ._gamma to realize changeovers among crystal, polycrystal, and glass. We find large stress fluctuations arising from sliding motions of the particles at the grain boundaries, which occur cooperatively to release the elastic energy stored. These stress fluctuations decrease as the system crosses over from polycrystal to glass. The dynamic processes are visualized with the aid of a sixfold angle alpha(j)(t) representing the local crystal orientation and a disorder variable D(j)(t) representing a deviation from the hexagonal order for particle j.

Isolating long-wavelength fluctuation from structural relaxation in two-dimensional glass: cage-relative displacement.

It has recently been revealed that long-wavelength fluctuation exists in two-dimensional (2D) glassy systems, having the same origin as that given by the Mermin-Wagner theorem for 2D crystalline solids. In this paper, we discuss how to characterise quantitatively the long-wavelength fluctuation in a molecular dynamics simulation of a lightly supercooled liquid. We employ the cage-relative mean-square displacement (MSD), defined on relative displacement to its cage, to quantitatively separate the long-wavelength fluctuation from the original MSD. For increasing system size the amplitude of acoustic long wavelength fluctuations not only increases but shifts to later times causing a crossover with structural relaxation of caging particles. We further analyse the dynamic correlation length using the cage-relative quantities. It grows as the structural relaxation becomes slower with decreasing temperature, uncovering an overestimation by the four-point correlation function due to the long-wavelength fluctuation. These findings motivate the usage of cage-relative MSD as a starting point for analysis of 2D glassy dynamics.

Ca2+-permeable mechanosensitive channels MCA1 and MCA2 mediate cold-induced cytosolic Ca2+ increase and cold tolerance in Arabidopsis.

Cold shock triggers an immediate rise in the cytosolic free calcium concentration ([Ca2+]cyt) in Arabidopsis thaliana and this cold-induced elevation of [Ca2+]cyt is inhibited by lanthanum or EGTA. It is suggested that intracellular calcium mainly contributes to the cold-induced [Ca2+]cyt response by entering into the cytosol. Two calcium-permeable mechanosensitive channels, MCA1 and MCA2 (mid1-complementing activity), have been identified in Arabidopsis. Here, we demonstrate that MCA1 and MCA2 are involved in a cold-induced increase in [Ca2+]cyt. The cold-induced [Ca2+]cyt increase in mca1 and mca2 mutants was markedly lower than that in wild types. The mca1 mca2 double mutant exhibited chilling and freezing sensitivity, compared to wild-type plants. Expression of At5g61820, At3g51660, and At4g15490, which are not regulated by the CBF/DREB1s transcription factor, was down-regulated in mca1 mca2. These results suggest that MCA1 and MCA2 are involved in the cold-induced elevation of [Ca2+]cyt, cold tolerance, and CBF/DREB1-independent cold signaling.

Erratum: Relationship between bond-breakage correlations and four-point correlations in heterogeneous glassy dynamics: Configuration changes and vibration modes [Phys. Rev. E 86, 041504 (2012)].

This corrects the article DOI: 10.1103/PhysRevE.86.041504.

Relationship between bond-breakage correlations and four-point correlations in heterogeneous glassy dynamics: configuration changes and vibration modes.

We investigate the dynamic heterogeneities of glassy particle systems in the theoretical schemes of bond breakage and four-point correlation functions. In the bond-breakage scheme, we introduce the structure factor S(b)(q,t) and the susceptibility χ(b)(t) to detect the spatial correlations of configuration changes. Here χ(b)(t) attains a maximum at t=t(b)(max) as a function of time t, where the fraction of the particles with broken bonds φ(b)(t) is about 1/2. In the four-point scheme, treating the structure factor S(4)(q,t) and the susceptibility χ(4)(t), we detect superpositions of the heterogeneity of bond breakage and that of thermal low-frequency vibration modes. While the former grows slowly, the latter emerges quickly to exhibit complex space-time behavior. In two dimensions, the vibration modes extending over the system yield significant contributions to the four-point correlations, which depend on the system size logarithmically. A maximum of χ(4)(t) is attained at t=t(4)(max), where these two contributions become of the same order. As a result, t(4)(max) is considerably shorter than t(b)(max).

Estimation of the bending rigidity and spontaneous curvature of fluid membranes in simulations.

Several numerical methods for measuring the bending rigidity and the spontaneous curvature of fluid membranes are studied using two types of meshless membrane models. The bending rigidity is estimated from the thermal undulations of planar and tubular membranes and the axial force of tubular membranes. We found a large dependence of its estimate value from the thermal undulation analysis on the upper-cutoff frequency q(cut) of the least-squares fit. The inverse power-spectrum fit with an extrapolation to q(cut)→0 yields the smallest estimation error among the investigated methods. The spontaneous curvature is estimated from the axial force of tubular membranes and the average curvature of bent membrane strips. The results of these methods show good agreement with each other.

Plastic deformations in crystal, polycrystal, and glass in binary mixtures under shear: collective yielding.

Using molecular dynamics simulation, we examine the dynamics of crystal, polycrystal, and glass in a Lennard-Jones binary mixture composed of small and large particles in two dimensions. The crossovers occur among these states as the composition c is varied at fixed size ratio. Shear is applied to a system of 9000 particles in contact with moving boundary layers composed of 1800 particles. The particle configurations are visualized with a sixfold orientation angle αj(t) and a disorder variable Dj(t) defined for particle j, where the latter represents the deviation from hexagonal order. Fundamental plastic elements are classified into dislocation gliding and grain boundary sliding. At any c, large-scale yielding events occur on the acoustic time scale. Moreover, they multiply occur in narrow fragile areas, forming shear bands. The dynamics of plastic flow is highly hierarchical with a wide range of time scales for slow shearing. We also clarify the relationship between the shear stress averaged in the bulk region and the wall stress applied at the boundaries.

Elastic convection in vibrated viscoplastic fluids.

We observe a new type of behavior in a shear-thinning yield stress fluid: freestanding convection rolls driven by vertical oscillation. The convection occurs without the constraint of container boundaries, yet the diameter of the rolls is spontaneously selected for a wide range of parameters. The transition to the convecting state occurs without hysteresis when the amplitude of the plate acceleration exceeds a critical value. We find that a nondimensional stress, the stress due to the inertia of the fluid normalized by the yield stress, governs the onset of the convective motion.