Naofumi Ogita

A new algorithm for three-dimensional Voronoi tessellation

Abstract A new efficient algorithm for computing the Voronoi tessellation in three dimensions is presented. The Voronoi tessellation is obtained by constructing Delaunay tetrahedra. The complete set of these tetrahedra corresponds to that of a single Voronoi polyhedron.

Geometrical Analysis of Crystallization of the Soft-Core Model

vVith the use of the molecular dynamics method the crystallization process from supercooled fluid states is studied for the soft-core system o£ the pair potential ¢(r) =c(o/r) 12 , which has a simple property to characterize the relaxation towards crystalline states. The Voronoi polyhedron is introduced to examine local atomic configurations from topological point of view. Certain classes of polyhedra well characterize various phases, i.e., fluid, and bee and Icc solids. The final relaxed state becomes a bee crystalline state, when the system relaxes incompletely, while it becomes an fcc when the system relaxes perfectly. A unified way of defining a nucleus during the both crystallization processes is proposed. Growth of the nucleus suffers the effect of the periodic boundary condition imposed on the system.

Computer Simulation for the Melting Curve Maximum Phenomenon: Two-Species Soft-Core Model

Computer simulations by a Monte Carlo method are carried out for the two-species soft-core model to demonstrate an example of the melting curve maximum phenomena observed in many substances. In this model, atoms are assumed to have one excited internal level in which they have an effective radius smaller than that in the ground level. The atoms interact with each other through a soft-core potential with the inverse power 12. The effective radius of the soft core depends on the radii of relevant atoms. The density dependences of pressure and of free energy are obtained for the fluid and the single occupancy branches, respectively. The phase diagram in the temperature vs pressure plane is derived, showing a melting curve maximum, at which the melting transition occurs accompanying an entropy discontinuity without any volume change. The entropy discontinuity at melting is found to increase with increasing pressure around the melting curve maximum point. The obtained radial distribution functions have neither an extra shoulder nor a subsidiary peak even in the mixing region of the two species.

Geometrical Analysis of Crystallization of the Soft-Core Model in an FCC Crystal Formation

vVith the use of the molecular dynamics method the crystallization process from supercooled fluid states is studied for the soft-core system o£ the pair potential ¢(r) =c(o/r) 12 , which has a simple property to characterize the relaxation towards crystalline states. The Voronoi polyhedron is introduced to examine local atomic configurations from topological point of view. Certain classes of polyhedra well characterize various phases, i.e., fluid, and bee and Icc solids. The final relaxed state becomes a bee crystalline state, when the system relaxes incompletely, while it becomes an fcc when the system relaxes perfectly. A unified way of defining a nucleus during the both crystallization processes is proposed. Growth of the nucleus suffers the effect of the periodic boundary condition imposed on the system.

A Study on the Extensive Air Showers

Using totally-inelastic and half-elastic collision models, quantities in extensive air showers (EAS) are given as functions of the depth from the starting point of EAS. The effect of the fluctuation in the level of shower initiation is illustrated. The calculated results are compared with the experimental ones, taking into account the above fluctuation; the value of the average inelasticity is estimated. The consistency between the attenuation length obtained by using the correlation diagrams in some quantities and that of the shower intensity is examined in connection with the form of the energy spectrum of the primary panticles. (auth)

Percolation Approach to the Metal-Insulator Transition in Super-Critical Fluid Metals

The percolation theory is extended to a thermal equilibrium state of an interacting particle system. By a computer simulation method, percolation process in a square lattice gas model is studied in super-critical regions. Critical percolation density is found to be an increasing function of temperature. The critical index of percolation probability is almost independent of temperature and 0.145±0.027. The result obtained in the lattice gas model is applied to the metal-insulator transition in super-critical fluid metals and an effect of the atomic configuration to the transition is studied. A phase diagram of the transition is obtained. The percolation aspect of the conductivity near the critical point is discussed.

Fluctuating Free-Volume Analysis of the Soft-Core Model of High-Density Fluid States

The high-density fluid states of the soft core system are analysed in terms of fluctuating free volumes which are defined with use of atomic configurations simulated by a molecular dynamics method. Statistical properties of fluctuating free volumes are examined. They can be classified into extensive and intensive types. The fraction of intensive free volumes increases rather rapidly above ρ * ≃0.7, where ρ * is defined by ρ( e / k T ) 1/4 and ρ= N σ 3 / V . This fact is well correlated with the dynamic as well as the static features of the system found previously. The Helmholtz free energy is derived in terms of mean free volumes under Singers assumption. It is in a good agreement with the result obtained by computer experiments, but the difference between them is systematic. It is overestimated for stable fluid states, and underestimated for metastable supercooled fluid states.

Monte Carlo Simulation on Propagation of Cosmic-Rays in the Atmosphere

A simulation study is made on propagation and multiplication of the high energy cosmic-ray components in their passage through the atmosphere. The study is planned to simulate observation of high energy cosmic-ray phenomena by the emulsion chambers exposed at high altitude laboratories and to make clear how the observation of such kind will disclose unknown mechanism of the extremely high energy interactions-multiple production of mesons. In particular, the following two models of the multiple meson production are examined in the present simulation: 1) Two-fire-ball model,l> abbreviated as 2F; 2) H-quantum model,2> abbreviated as HQ. The outline of our simulation is as follows. A high energy primary cosmic-ray particle collides with an air nucleus of the upper atmosphere and causes the multiple meson production according to mechanism of the assumed models. The secondary nuclear-active particles, charged n-mesons and an outgoing nucleon, among the generated particles collide in their turn with air nuclei and they develop the so-called nuclear cascade processes while passing through the atmosphere. Gamma-rays, being the decay products of n°-mesons produced by the successive nuclear collisions, are the source of the atmospheric electromagnetic cascade showers. We make a record of particles with energies above a certain threshold energy both of the nuclear-active component and of the electro-magnetic component, which arrived at the observation level. The record consists of data of the arriving particles together with those on the primary particle. The present simulation calculation corresponds to observation of high energy cosmic-ray particles by the emulsion chamber exposed at the mountain altitudes. In particular, it provides us data of the artificial families: identity, energy and spatial distribution of member particles of the families. It is instructive to learn what kind of pattern the artificial families show at the observation plane under a certain assumption. This is indispensable for

Off-Diagonal Induction of Short-Range Order Spin Pair Correlation of the Quantum XXZ-Model

It is widely accepted among statistical physicists that quantum effects usually prevent a growth of long-range order of diagonal variables, which is originally present in classical systems. For example, iIi the two-dimensional (2D) Ising model the long-range spin-pair correlation below the transition temperature is broken when some amounts of exchange interactions of off-diagonal spin components are added to the original Hamiltonian of the Ising model. This breakdown of correlation results in the absence of phase transitions in 2D quantum isotropic Heisenb6:rg model. l }

On the Lateral Distribution of the Electron Component in Extensive Air Showers

Apparatus of wide span made it possible to measure the lateral distribution of the electron component in air showers. The result shows that the shape of the lateral distribution is practically independent of the shower sizes and altitudes at which observations were made, in agreement with the Nishimura- Kamatu (N-K) function of age 1.3. The results of the investigation are graphically shown. (A.C.)