Mitsugu Matsushita

Fractal Viewpoint of Fracture and Accretion

A model from a point of view of the fractal is presented to describe fracture and accretion, It is shown to give a power-law dependence of the cumulative number of similar objects in their collection whose sizes are larger than r , N ( r )∼ r - x , which has been observed in many phenomena associated with fracture and accretion. The case of drift ice is shown as an example. A relationship is also derived among exponents of cumulative number and mass, and a fractal dimension of similar objects.

Anomalous temperature dependence of the frequency and damping constant of phonons near Tλ in ammonium halides

The mechanism which gives rise to the anomalous temperature dependence of nonsoft phonons near the lambda transition point in ammonium halides is discussed. The orientation of an ammonium ion in its unit cell is treated as a pseudo‐Ising spin, and the Hamiltonian of a pseudospin–phonon coupled system is derived from simple assumptions. Perturbation theory is used to evaluate pseudospin–phonon scattering terms in the Hamiltonian. The resulting expressions for the frequency and the damping constant of phonons are seen to include a long‐range order parameter and a correlation function of the pseudo‐Ising spins, which are well known to show characteristic temperature variations near a lambda point. The results qualitatively explain the anomalous temperature variation in the frequency and the damping constant of nonsoft optical phonons near the lambda point, as measured by means of Raman scattering experiments in NH4Cl and NH4Br. The difference between the temperature dependences of the frequency in these two materials is also discussed.

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.

On the Possibility of a Biaxial Smectic A Phase

Abstract The existence of a uniaxial-biaxial phase transition in a smectic A phase is shown theoretically, based on the more realistic anisotropic pair potential and within the mean field approximation. The resulting phase diagram exhibits successive phase transitions of isotropic-uniaxial nematic-uniaxial smectic A-biaxial smectic A and a uniaxial nematic-uniaxial smectic A-biaxial smectic A triple point. The possible assignment of the predicted biaxial smectic A to some phase classified recently as a smectic C is discussed.

A note on the microscopic derivation of sound attenuation near the clear point in nematics

Abstract The complex sound attenuation coefficient α(ω) near the clear point in nematic liquid crystals is investigated theoretically. Starting from the microscopic hamiltonian, α(ω) is formulated statistical-mechanically and calculated by applying the mode-coupling theory to the order-parameter correlation function.

On the anomalous sound propagation of nematics just above the clearing point

Abstract The sound attenuation coefficient due to the critical fluctuations of the order parameter is formulated in the isotropic phase of nematics by taking account of the mode-coupling effects between the order parameter and the hydrodynamic shear mode. The result is compared with the available experimental data.

A note on the sound attenuation near the lambda point in ammonium halides

Abstract The sound attenuation coefficient α ( ω ) is investigated theoretically for ammonium halides (typically NH 4 Cl and NH 4 Br ) near their lambda temperature from the viewpoint of the pseudospin-phonon coupled system.

Ultrasonic attenuation near the smectic A to C transition temperature of TBBA and TBPA

Abstract The temperature dependence of the acoustic attenuation near the transition point from smectic A to C phases of TBBA and TBPA was found to follow a power law with a critical exponent of 0.5 ± 0.1. The attenuation is highly anisotropic and the peak temperature shifts with frequency of the acoustic waves. No noticeable difference was observed between TBBA and TBPA.

Critical dynamics of the order parameter fluctuations and the anomalous sound propagation of nematics just above the clearing point

Kinetic equations are derived for two kinds of gross variables of nematics in the isotropic phase, i.e., the independent components of orientational tensor order parameter and the transverse local momentum density, using Kawasaki’s mode‐coupling theory. Based on them, the time correlation function and the relaxation rate for the critical fluctuations of the order parameter is obtained. The latter result explains why the conventional Landau–de Gennes theory is valid for the usual experiments like flow birefringence and light scattering. The sound attenuation coefficient due to the critical fluctuations of the order parameter is formulated by taking account of the mode‐coupling effects between the two kinds of gross variables. The result is compared with the available experimental data with good improvement upon previous conventional theory.