Hayato Shiba

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.

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).

Anomalous Heat Conduction in Three-Dimensional Nonlinear Lattices

Heat conduction in three-dimenisional nonlinear lattice models is studied using nonequilibrium molecular dynamics simulations. We employ the Fermi–Pasta–Ulam-β 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 128×128×256 lattice sites. This size corresponds to nanoscopic to mesoscopic scales of approximately 100 nm. 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.

Continuum limit of the vibrational properties of amorphous solids

Significance The thermal properties of crystalline solids follow universal laws that are explained by theories based on phonons. Amorphous solids are also characterized by universal laws that are, however, anomalous with respect to their crystalline counterparts. These anomalies begin to emerge at very low temperatures, suggesting that the vibrational properties of amorphous solids differ from phonons, even in the continuum limit. In this work, we reveal that phonons coexist with soft localized modes in the continuum limit of amorphous solids. Importantly, we discover that the phonons follow the Debye law, whereas the soft localized modes follow another universal non-Debye law. Our findings provide a firm theoretical basis for explaining the thermal anomalies 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.

Structural and dynamical heterogeneities in two-dimensional melting

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 Γkkz with z~2.6 at small k in the hexatic phase.

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.

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.

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.

Jammed Particle Configurations and Dynamics in High-Density Lennard-Jones Binary Mixtures in Two Dimensions

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.

Divergent Thermal Conductivity in Three-Dimensional Nonlinear Lattices

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 β nonlinear lattices, in which the interparticle potential has a biquadratic term together with a harmonic term. The system size is L × L ×2 L , and the heat is made to flow in the 2 L 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.