Takayuki Narumi

Spatial and temporal dynamical heterogeneities approaching the binary colloidal glass transition

We study concentrated binary colloidal suspensions, a model system which has a glass transition as the volume fraction ϕ of particles is increased. We use confocal microscopy to directly observe particle motion within dense samples with ϕ ranging from 0.4 to 0.7. Our binary mixtures have a particle diameter ratio dS/dL = 1/1.3 and particle number ratio NS/NL = 1.56, which are chosen to inhibit crystallization and enable long-time observations. Near the glass transition we find that particle dynamics are heterogeneous in both space and time. The most mobile particles occur in spatially localized groups. The length scales characterizing these mobile regions grow slightly as the glass transition is approached, with the largest length scales seen being ∼ 4 small particle diameters. We also study temporal fluctuations using the dynamic susceptibility χ4, and find that the fluctuations grow as the glass transition is approached. Analysis of both spatial and temporal dynamical heterogeneity show that the smaller species play an important role in facilitating particle rearrangements. The glass transition in our sample occurs at ϕg ≈ 0.58, with characteristic signs of aging observed for all samples with ϕ > ϕg.

Size Dependence of Current-Voltage Properties in Coulomb Blockade Networks

We theoretically investigate the current–voltage ( I – V ) property of two-dimensional Coulomb blockade (CB) arrays by conducting Monte Carlo simulations. The I – V property can be divided into three regions and we report the dependence of the aspect ratio δ (namely, the lateral size N y over the longitudinal one N x ). We show that the average CB threshold obeys a power-law decay as a function of δ. Its exponent γ corresponds to a sensitivity of the threshold depending on δ, and is inversely proportional to N x (i.e., δ at fixed N y ). Further, the power-law exponent ζ, characterizing the nonlinearity of the I – V property in the intermediate region, logarithmically increases as δ increases. Our simulations describe the experimental result ζ=2.25 obtained by Parthasarathy et al. [Phys. Rev. Lett. 87 (2001) 186807]. In addition, the asymptotic I – V property of one-dimensional arrays obtained by Bascones et al. [Phys. Rev. B 77 (2008) 245422] is applied to two-dimensional arrays. The asymptotic equation c...

Active Brownian motion in threshold distribution of a Coulomb blockade model

Randomly distributed offset charges affect the nonlinear current-voltage property via the fluctuation of the threshold voltage above which the current flows in an array of a Coulomb blockade (CB). We analytically derive the distribution of the threshold voltage for a model of one-dimensional locally coupled CB arrays and propose a general relationship between conductance and distribution. In addition, we show that the distribution for a long array is equivalent to the distribution of the number of upward steps for aligned objects of different heights. The distribution satisfies a novel Fokker-Planck equation corresponding to active Brownian motion. The feature of the distribution is clarified by comparing it with the Wigner and Ornstein-Uhlenbeck processes. It is not restricted to the CB model but is instructive in statistical physics generally.

Simulation study of spatial–temporal correlation functions in supercooled liquids

We perform molecular dynamics simulations on Lennard-Jones binary mixtures of the Kob-Andersen type to investigate the properties of the dynamical heterogeneity near the glass transition. To characterize it, we focus on two types of spatial correlation functions of the direction and mobility fluctuations. Then, we predict the correlation lengths from those correlation functions. Although the correlation length obtained from the direction converges away from the glass transition point, that from the mobility fluctuation increases as the system approaches the glass transition point and has a peak near the glass transition. It suggests that the correlation of the mobility fluctuation plays an important role, more than that of the direction near the glass transition.

Relationship between the Diffusive Coefficient and the Specific Heat for Lennard‐Jones Binary Mixture

We perform the extensive molecular dynamics simulations on the Kob‐Andersen type Lennard‐Jones binary mixtures. We study not only dynamical behavior near the glass transition but also the static one, including the specific heat. We then analyze the simulation results from a unified point of view suggested by Tokuyama. The view suggests the definition of the glass transition by using the long‐time self‐diffusion coefficient. Thus, we show that the temperature at the peak of the specific heat coincides with the glass transition temperature calculated from the long‐time self‐diffusion coefficient. We also discuss the relationship between the specific heat and the long‐time self‐diffusion coefficient from a new standpoint.

Relaxation with long-period oscillation in defect turbulence of planar nematic liquid crystals

Through experiments, we studied defect turbulence, a type of spatiotemporal chaos in planar systems of nematic liquid crystals, to clarify the chaotic advection of weak turbulence. In planar systems of large aspect ratio, structural relaxation, which is characterized by the dynamic structure factor, exhibits a long-period oscillation that is described well by a combination of a simple exponential relaxation and underdamped oscillation. The simple relaxation arises as a result of the roll modulation while the damped oscillation is manifest in the repetitive gliding of defect pairs in a local area. Each relaxation is derived analytically by the projection operator method that separates turbulent transport into a macroscopic contribution and fluctuations. The analysis proposes that the two relaxations are not correlated. The nonthermal fluctuations of defect turbulence are consequently separated into two independent Markov processes. Our approach sheds light on diversity and universality from a unified viewpoint for weak turbulence.

Compressed exponential relaxation as superposition of dual structure in pattern dynamics of nematic liquid crystals

Soft-mode turbulence (SMT) is the spatiotemporal chaos observed in homeotropically aligned nematic liquid crystals, where non-thermal fluctuations are induced by nonlinear coupling between the Nambu-Goldstone and convective modes. The net and modal relaxations of the disorder pattern dynamics in SMT have been studied to construct the statistical physics of nonlinear nonequilibrium systems. The net relaxation dynamics is well-described by a compressed exponential function and the modal one satisfies a dual structure, dynamic crossover accompanied by a breaking of time-reversal invariance. Because the net relaxation is described by a weighted mean of the modal ones with respect to the wave number, the compressed-exponential behavior emerges as a superposition of the dual structure. Here, we present experimental results of the power spectra to discuss the compressed-exponential behavior and the dual structure from a viewpoint of the harmonic analysis. We also derive a relationship of the power spectra from t...

Memory function of turbulent fluctuations in soft-mode turbulence.

Modal relaxation dynamics has been observed experimentally to clarify statistical-physical properties of soft-mode turbulence, the spatiotemporal chaos observed in homeotropically aligned nematic liquid crystals. We found a dual structure, dynamical crossover associated with violation of time-reversal invariance, the corresponding time scales satisfying a dynamical scaling law. To specify the origin of the dual structure, the memory function due to nonthermal fluctuations has been defined by a projection-operator method and obtained numerically using experimental results. The results of the memory function suggest that the nonthermal fluctuations can be divided into Markov and non-Markov contributions; the latter is called the turbulent fluctuation (TF). Consequently, the relaxation dynamics is separated into three characteristic stages: bare-friction, early, and late stages. If the dissipation due to TFs dominates over that of the Markov contribution, the bare-friction stage contracts; the early and late stages then configure the dual structure. The memory effect due to TFs results in a time-reversible relaxation at the early stage, and the disappearance of the memory by turbulent mixing leads to a simple exponential relaxation at the late stage. Furthermore, the memory effect due to TFs is shown to originate from characteristic spatial coherency called the patch structure.

Glassy dynamics in relaxation of soft-mode turbulence

The autocorrelation function of pattern fluctuation is used to study soft-mode turbulence (SMT), a spatiotemporal chaos observed in homeotropic nematics. We show that relaxation near the electroconvection threshold deviates from the exponential. To describe this relaxation, we propose a compressed exponential appearing in dynamics of glass-forming liquids. Our findings suggest that coherent motion contributes to SMT dynamics. We also confirmed that characteristic time is inversely proportional to electroconvections control parameter.