Tomoaki Nogawa

Local anisotropy of fluids using Minkowski tensors

Statistics of the free volume available to individual particles have previously been studied for simple and complex fluids, granular matter, amorphous solids, and structural glasses. Minkowski tensors provide a set of shape measures that are based on strong mathematical theorems and easily computed for polygonal and polyhedral bodies such as free volume cells (Voronoi cells). They characterize the local structure beyond the two-point correlation function and are suitable to define indices 0 ≤ βνa, b ≤ 1 of local anisotropy. Here, we analyze the statistics of Minkowski tensors for configurations of simple liquid models, including the ideal gas (Poisson point process), the hard disks and hard spheres ensemble, and the Lennard-Jones fluid. We show that Minkowski tensors provide a robust characterization of local anisotropy, which ranges from βνa, b≈0.3 for vapor phases to \beta_\nu^{a,b}\rightarrow 1 for ordered solids. We find that for fluids, local anisotropy decreases monotonically with increasing free volume and randomness of particle positions. Furthermore, the local anisotropy indices βνa, b are sensitive to structural transitions in these simple fluids, as has been previously shown in granular systems for the transition from loose to jammed bead packs.

Monte Carlo simulation study of the two-stage percolation transition in enhanced binary trees

We perform Monte Carlo simulations to study the Bernoulli (p) bond percolation on the enhanced binary tree which belongs to the class of nonamenable graphs with one end. Our numerical results show that the system has two distinct percolation thresholds pc1 and pc2. The mean cluster size diverges as p approaches pc1 from below. The system is critical at all the points in the intermediate phase (pc1 < p < pc2) and there exist infinitely many infinite clusters. In this phase, the corresponding fractal exponent continuously increases with p from zero to unity. Above pc2 the system has a unique infinite cluster.

Dynamical study of a polydisperse hard-sphere system.

We study the interplay between the fluid-crystal transition and the glass transition of elastic sphere system with polydispersity using nonequilibrium molecular dynamics simulations. It is found that the end point of the crystal-fluid transition line, which corresponds to the critical polydispersity above which the crystal state is unstable, is on the glass transition line. This means that crystal and fluid states at the melting point becomes less distinguishable as polydispersity increases and finally they become identical state, i.e., marginal glass state, at critical polydispersity.

Profile and scaling of the fractal exponent of percolations in complex networks

We propose a novel finite-size scaling analysis for percolation transition observed in complex networks. While it is known that cooperative systems in growing networks often undergo an infinite-order transition with inverted Berezinskii-Kosterlitz-Thouless singularity, it is very hard for numerical simulations to determine the transition point precisely. Since the neighbor of the ordered phase is not a simple disordered phase but a critical phase, conventional finite-size scaling technique does not work. In our finite-size scaling, the forms of the scaling functions for the order parameter and the fractal exponent determine the transition point and critical exponents numerically for an infinite-order transition as well as a standard second-order transition. We confirm the validity of our scaling hypothesis through Monte Carlo simulations for bond percolations in some network models: the decorated (2,2)-flower and the random attachment growing network, where an infinite-order transition occurs, and the configuration model, where a second-order transition occurs.

Generalized scaling theory for critical phenomena including essential singularities and infinite dimensionality.

We propose a generic scaling theory for critical phenomena that includes power-law and essential singularities in finite and infinite dimensional systems. In addition, we clarify its validity by analyzing the Potts model in a simple hierarchical network, where a saddle-node bifurcation of the renormalization-group fixed point governs the essential singularity.

Evaporation-condensation transition of the two-dimensional Potts model in the microcanonical ensemble.

The evaporation-condensation transition of the Potts model on a square lattice is numerically investigated by the Wang-Landau sampling method. An intrinsically system-size-dependent discrete transition between supersaturation state and phase-separation state is observed in the microcanonical ensemble by changing constrained internal energy. We calculate the microcanonical temperature, as a derivative of microcanonical entropy, and condensation ratio, and perform a finite-size scaling of them to indicate the clear tendency of numerical data to converge to the infinite-size limit predicted by phenomenological theory for the isotherm lattice gas model.

Vortex jamming in superconductors and granular rheology

We demonstrate that a highly frustrated anisotropic Josephson junction array (JJA) on a square lattice exhibits a zero-temperature jamming transition, which shares much in common with those in granular systems. Anisotropy of the Josephson couplings along the horizontal and vertical directions plays roles similar to normal load or density in granular systems. We studied numerically static and dynamic response of the system against shear, i.e. injection of external electric current at zero temperature. Current–voltage curves at various strength of the anisotropy exhibit universal scaling features around the jamming point much as do the flow curves in granular rheology, shear-stress versus shear-rate. It turns out that at zero temperature the jamming transition occurs right at the isotropic coupling and anisotropic JJA behaves as exotic fragile vortex matter: it behaves as a superconductor (vortex glass) in one direction, whereas it is a normal conductor (vortex liquid) in the other direction even at zero temperature. Furthermore, we find a variant of the theoretical model for the anisotropic JJA quantitatively reproduces universal master flow-curves of the granular systems. Our results suggest an unexpected common paradigm stretching over seemingly unrelated fields—the rheology of soft materials and superconductivity.

Nonequilibrium relaxation analysis of a quasi-one-dimensional frustrated xy model for charge-density waves in ring-shaped crystals

We propose a model for charge-density waves in ring-shaped crystals, which depicts frustration between intra- and interchain couplings coming from cylindrical bending. It is then mapped to a three-dimensional uniformly frustrated

Criticality governed by the stable renormalization fixed point of the Ising model in the hierarchical small-world network

XY

Vortex Solid Phase with Frozen Undulations in Superconducting Josephson-Junction Arrays in External Magnetic Fields

model with one-dimensional anisotropy in connectivity. The nonequilibrium relaxation dynamics is investigated by Monte Carlo simulations to find a phase transition which is quite different from that of usual whisker crystal. We also find that the low-temperature state is a three-dimensional phase vortex lattice with a two-dimensional phase coherence in a cylindrical shell and the system shows power-law relaxation in the ordered phase.