Shonosuke Ohta

Irregular Fractal-Like Crystal Growth of Ammonium Chloride

Irregular dendritic crystals of ammonium chloride (NH 4 Cl) are grown two-dimensionally between two parallel glasses, one of which has rough surface. The pattern clearly reminds us of those of Witten-Sander diffusion-limited aggregation (DLA) model. The radius of gyration is measured to give the fractal dimension d f =1.67±0.002, which is in good agreement with two-dimensional DLA. Our result implies that any random perturbations strong enough to overcome crystalline anisotropy always give rise to random DLA-like crystals, instead of otherwise regular dendritic crystals.

Onset of chaos in Yang-Mills-Higgs systems

Abstract The onset of dynamical chaos is studied in the SU(2) Yang-Mills-Higgs theories with topological solutions in order to address the question whether the order-to-chaos transition is an inherent phenomenon observed only in the magnetic monopole solution. Among these solutions we study numerically the time evolution of the sphaleron solution from the viewpoint of chaos. The step-wise behaviour of the maximal Lyapunov exponents of fields shows that the sphaleron solution also exhibits the order-to-chaos transition. It is pointed out that this transition is characteristic of the YMH systems.

ANNIHILATIVE FRACTALS FORMED IN RAYLEIGH-TAYLOR INSTABILITY

We report on a fractal pattern formed in Rayleight-Taylor instability. The fractal dimension is 1.88 ± 0.06, which is constant in time t > t1 = 70 s. The pattern area decreases according to exp(-t/τ), where t and τ are time and time constant 69.8 s, respectively. τ agrees with t1. This result leads that it is important for the fractal formation that sufficient annihilation of the heavier solution at the surface.

Crossover on Fractal and Branching Structures of Radial Diffusion-Limited Growth in Laplace Field of Finite Size

Two-dimensional off-lattice diffusion-limited clusters simulated in circular boundary of finite size are studied by comparison with analytical solution in annular Laplace field and trajectory density of Brownian particles. Radial growth rate in annular field classifies into two different areas. The one is cluster size dominated area, and the other is the area dominated by distance from the boundary. Results clarify that the ordinary diffusion-limited aggregation (DLA) grows under the condition of size dominated area. Radial density, fractal dimension, and branching structure of cluster growing in the circular boundary of finite size support a crossover at ∼ 0.37 that agrees with the analytical suggestion of 1/ e =0.368 for the ratio of cluster size to boundary radius. Fractal to non-fractal change on self-similarity and change from tip splitting to side branching on micro branching structure characterize the morphological crossover of diffusion-limited cluster.

Regular tip-splitting growth of an NH4Cl dendrite

Abstract We have experimentally investigated the regular tip-splitting (RTS) behavior of an NH 4 Cl dendrite. In the RTS phenomenon, 〈110〉 growth occurs very close to the 〈100〉 growing tip and stops at once because of a concentrational interaction with the tip and a nearby side-branch. The formation of the tip changes under the influence of the 〈110〉 growth. The tip velocity oscillates in time like a square wave.

Control Parameter of Branching Dynamics in Diffusion-Limited Aggregation

Branching dynamics is studied on two-dimensional diffusion-limited aggregation (DLA). Both tip-growth probability of \(\alpha\cong 0.785\) and probability distribution p m for branch length m are steady in the DLA cluster of N ≥5000. A new model branching dynamics controlled only by the tip-growth probability α is proposed. The selection probability of m branch is proportional not to perimeter length but to branch number. We find that the simulation results and the theoretical analysis of the present model for α=0.785 agree with the branched structures of DLA.

Mode Selection of Diffusion-limited Aggregation

The diffusion-limited aggregation (DLA) is a pattern formation governed only by the nature of diffusion field. Irreversible sticking process of particles gives rise to isotropic random fractal structure of DLA. Since Witten and Sander proposed such a simulation model, many researchers have been devoted to various structures of offlattice DLA, such as self-similarity, active zone, multifractality, branching distribution, fractal dimension, and so on. However, many authors have indicated complex structures of DLA cluster. Mysterious one among them is near pentagonal symmetry with the outline shape of DLA cluster. A wedge model was proposed from the viewpoint of harmonic measure, which gives the fractal dimension D 1:714 for a symmetric cone of pentagon. The details of mysterious symmetry in DLA cluster are studied by numerical simulations. In order to study the exterior shape of DLA, we measure the coordinates of 10 sticking particles without cluster growth that is the same manner as the study of active zone. The sticking simulations are performed on the 2500 offlattice clusters composed of 3 10 particles. Here, simulation methods with high accuracy are used as reported in ref. 14. Averaged power spectrum of sticking distribution in angle direction is shown in Fig. 1 as a function of spectrum mode. The peak position of mean spectrum can be estimated as the mode of 5:4 by the fitting of parabolic curve near the peak. Thus, the mysterious symmetry of DLA is characterized by the near pentagon as indicated before reports. However, this peak mode is slightly increasing with increasing of cluster size in the present simulation up to 3 10 particles. Above ordinary DLA simulation is started from the initial condition of a seed particle with the radius RS 1⁄4 0. In order to clarify the stability of near pentagonal symmetry, following DLA simulations are performed on the initial conditions of circular seed up to RS 1⁄4 500. As shown in Fig. 2 for RS 1⁄4 500, it is obvious that the near pentagonal mode in angle direction is extremely stable for large size of cluster independent of initial condition. Cluster density as a function of angle is analyzed by power spectrum, and then spectrum peak is obtained from the mean data for 1000 clusters (30000 clusters for RS 1⁄4 0). An example of power spectrum along the cluster growth from the seed of RS 1⁄4 500 is drawn in Fig. 3(a), which shows decreasing of peak mode with increasing of cluster size. As shown in Fig. 3(b), the Fig. 1. Power spectrum of angle distribution for sticking particles onto the surface of 2500 ordinary DLA clusters composed of N 1⁄4 3000000 particles. The peak position is estimated as the mode of 5:4.

Mode selection hypothesis in diffusion-limited aggregation

A hypothesis for the angular mode selection of diffusion-limited aggregation (DLA) is presented as the width of distribution function for sticking Brownian particles. The expected mode \(\sqrt{3}\pi\) agrees with a near pentagonal symmetry of 5.44 in an actual DLA. The mode-controlled DLA formed by anisotropic random walk is consistent with the mode derived on the basis of the hypothesis. The relationship between the preferred mode and fractal dimension is indicated.

Abnormal Stability in Growth of Diffusion-Limited Aggregation

An abnormal and unsteady growth of an isotropic cluster in diffusion-limited aggregation (DLA) is observed in stability analyses. Macroscopic fluctuation due to the delay of transition from a dendritic tip to a tip-splitting growth induces the anisotropy of DLA. An asymptotic deformation factor e ∞ = 0.0888 is obtained from large DLA clusters. A symmetric oval model proposed from the dual-stability growth of DLA gives an asymptotic fractal dimension of 1.7112 using e ∞ . The correspondence of this model to the box dimension is excellent.

Dynamic Tip Front Dimension in Diffusion-limited Aggregation

A new fractal dimension of diffusion-limited aggregation (DLA) is studied by tip front angle near hottest branch projecting bare field, which is obtained from envelope line considering near pentago...