芝 隼人

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.

Abstract Recently, a two-dimensional liquid cooled toward the glass transition was found to exhibit a t⁻¹ long-time tail in the velocity autocorrelation function (VACF) owing to the presence of long-wavelength fluctuations. To directly observe this power-law behaviour, it is necessary to simulate a large system with millions of particles, which is a challenging task from the computational viewpoint. In this study, to address this difficulty, I first show that this power-law tail can be reproduced by differentiating the finite-time diffusivity with respect to time. In addition, the feasibility of another direction, a direct on-the-fly computation of the VACFs utilizing GPGPUs, wherein VACFs are evaluated as the simulation runs, is also demonstrated. A performance benchmark was executed on Wisteria/BDEC-01 (Aquarius subsystem) supercomputer using a simulation code developed by the author, which enabled the direct computation of the VACF of 4 million particlesx for as long as the 10⁸ simulation steps within 10 days.

<p>The out-of-equilibrium phase diagrams obtained by the oscillatory shear in a 1-dodecyl-3-methylimidazolium hexafluorophosphate ([C₁₂mim][PF₆]) ionic liquid crystal on molecular-dynamics simulations.</p>

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.

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.

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 phenomeno-logical 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.

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.

The smoothed profile method is extended to study the rheological behaviour of colloidal dispersions under shear flow by using the Lees-Edwards boundary conditions. We start with a reformulation of the smoothed profile method, a direct numerical simulation method for colloidal dispersions, so that it can be used with the Lees-Edwards boundary condition, under steady or oscillatory-shear flow. By this reformulation, all the resultant physical quantities, including local and total shear stresses, become available through direct calculation. Three simple rheological simulations are then performed for (1) a spherical particle, (2) a rigid bead chain and (3) a collision of two spherical particles under shear flow. Quantitative validity of these simulations is examined by comparing the viscosity with that obtained from theory and Stokesian dynamics calculations. Finally, we consider the shear-thinning behaviour of concentrated colloidal dispersions.

Three types of surface tensions can be defined for lipid membranes: the internal tension, sigma, conjugated to the real membrane area in the Hamiltonian, the mechanical frame tension, tau, 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 s and t 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 t in the standard Gaussian models where the tension is controlled by s. However, contrary to the conjecture in the above paper, we find that r exhibits no significant difference from t 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.

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. (C) 2013 AIP Publishing LLC.

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. (C) 2013 AIP Publishing LLC.

The entropic effects of anchored polymers on biomembranes are studied using simulations of a meshless membrane model combined with anchored linear polymer chains. The bending rigidity and spontaneous curvature are investigated for anchored ideal and excluded-volume polymer chains. Our results are in good agreement with the previous theoretical predictions. It is found that the polymer reduces the line tension of membrane edges, as well as the interfacial line tension between membrane domains, leading to microdomain formation. Instead of the mixing of two phases as observed in typical binary fluids, densely anchored polymers stabilize small domains. A mean field theory is proposed for the edge line tension reduced by anchored ideal chains, which reproduces our simulation results well.

To understand the quantitative properties of dynamic heterogeneities on glassy particle systems, we use the theoretical scheme of bond-breakage which can detect configuration rearrangements corresponding to the structural relaxations. It is compared with the four-point correlation scheme for the results of binary mixtures with molecular dynamics simulations of two dimensional NVE ensembles. From the comparisons in the systems, we find superpositions of heterogeneity of configuration rearrangements and that induced by low-frequency vibration modes. The bond breakage scheme detects the long-time relaxations without short-time vibrations. The four-point scheme detects the mixed dynamics of the both. We find that the results on four-point scheme are sensitive to the influence of such vibration modes which gives rise to detectable system-size effects in physical properties. © 2013 American Institute of Physics.

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) -&gt; 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.

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 alpha(j)(t) and a disorder variable D(j)(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.

We examine the changeover in the particle configurations and the dynamics in dense Lennard-Jones binary mixtures composed of small and large particles. By varying the composition at a low temperature, we realize crystal with defects, polycrystal with small grains, and glass with various degrees of disorder. In particular, we show configurations where small crystalline regions composed of the majority species are enclosed by percolated amorphous layers composed of the two species. We visualize the dynamics of configuration changes using the method of bond breakage and following the particle displacements. In quiescent jammed states, the dynamics is severely slowed down and is highly heterogeneous at any compositions. We apply shear flow by relative motions of boundary layers. Then plastic deformations multiply occur in relatively fragile regions, growing into large-scale shear bands where the strain is highly localized. Such bands appear on short time scales and evolve on long time scales with finite lifetimes.

Using molecular-dynamics simulation, we study structural and dynamical heterogeneities at melting in two-dimensional one-component systems with 36000 particles. Between crystal and liquid we find intermediate hexatic states, where the density fluctuations are enhanced at small wave number k as well as those of the sixfold orientational order parameter. Their structure factors both grow up to the smallest wave number equal to the inverse system length. The intermediate scattering function of the density S( k, t) is found to relax exponentially with decay rate Gamma(k) alpha k(z) with z similar to 2.6 at small k in the hexatic phase. Copyright (C) EPLA, 2009

Equilibrium autocorrelation functions of heat flux in a model of three-dimensional insulating solids are investigated through nonequilibrium particle dynamics simulations. We employ the Fermi-Pasta-Ulam(FPU)-beta nonlinear lattice in which there exist only nearest-neighbor interactions with harmonic and bi-quadratic nonlinear terms. In an fcc lattice of the size of 192(3), power-law decay of the equilibrium autocorrelation function. which is often referred to as a long-time tail, is confirmed, but its decay exponent has turned out to be 0.74(1) which is different from 1.5 expected from hydrodynamic phenomenology for three-dimension systems. This value, 0.74(1), of a decay exponent implies that thermal conductivity of this system diverges with size. Finite size effects are studied using one-dimensional FPU-beta lattices.

Heat conduction in three-dimenisional nonlinear lattice models is studied using nonequilibrium molecular dynamics simulations. We employ the Fermi-Pasta-Ulam-beta model, in which nonlinearity exists in the interaction of the biquadratic form. It is confirmed that the thermal conductivity, the ratio of the energy flux to the temperature gradient, diverges with increasing system size up to 128 x 128 x 256 lattice sites. This size corresponds to nanoscopic to mesoscopic scales of approximately 100 run. From these results, we conjecture that the energy transport in insulators with perfect crystalline order exhibits anomalous behavior. The effects of the lattice structure, random impurities, and the natural length in interactions are also examined. We find that fcc lattices display stronger divergence than simple cubic lattices. When impurity sites of infinitely large mass, which are thus fixed, are randomly distributed, such divergence vanishes.

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) over dot. 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.

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.

Heat conduction in three-dimensional nonlinear lattices is investigated using particle dynamics simulations. The system is a simple three-dimensional extension of the Fermi-Pasta-Ulam beta nonlinear lattices, in which the interparticle potential has a biquadratic term together with a harmonic term. The system size is L x L x 2L, and the heat is made to flow in the 2L direction using the Nose-Hoover method. Although a linear temperature profile is realized, the ratio of energy flux to temperature gradient shows logarithmic divergence with L. The autocorrelation function of energy flux C(t) is observed to show power-law decay as t(-0.98 +/- 0.25), which is slower than the decay in conventional momentum-conserving three-dimensional systems (t(-3/2)). Similar behavior is also observed in the four-dimensional system.