Particles In Three-dimensional Space Research Articles

A cost optimal parallel algorithm for computing force field in [formula omitted]-body simulations on a CREW PRAM

We consider the following force field computation problem: given a cluster of n particles in three-dimensional space, compute the force exerted on each particle by the other particles. Depending on different applications, the pairwise interaction could be either gravitational or Lennard–Jones. In both cases, the force between two particles vanishes as the distance between them approaches to infinity. Since there are n(n−1)/2 pairs, direct method requires Θ(n 2) time for force evaluation, which is very expensive for astronomical simulations. In 1985 and 1986, two famous Θ(n logn) time hierarchical tree algorithms were published by Appel (SIAM J. Sci. Statist. Comput. 6 (1985) 85–103) and by Barnes and Hut (Nature, 324 (1980) 446 – 449), respectively. In a recent paper, we presented a linear time algorithm which builds the oct tree bottom-up and showed that Appel's algorithm can be implemented in Θ(n) sequential time. In this paper, we present an algorithm which computes the force field in Θ( logn) time on a Θ(n/ log n) processor CREW PRAM. A key to this optimal parallel algorithm is replacing a recursive top-down force calculation procedure of Appel by an equivalent non-recursive bottom-up procedure. Our parallel algorithm also yields a new Θ(n) time-sequential algorithm for force field computation.

Fluidization in dry landslides

This paper aims at determining the physical properties affecting the distance travelled by landslides with dry particles, and elucidating the mechanism of the properties affecting landslide fluidization. The procedure is as follows: laboratory landslide experiments were conducted to verify the simulation model which was proposed to represent the movement of landslides. Further, sensitivity analysis for some physical properties affecting the travel distance were conducted using this model. The simulation model could identify the coordinates, velocity and angular velocity for every particle in three-dimensional space, and the kinetic energy of particles consumed by inelastic and frictional collision with each other in the model. The travel distances of landslides simulated by the model were verified by laboratory experiments statistically where the physical properties for the particles and slope angle were changed. Then, sensitivity analysis for the physical properties were conducted using the model to clarify the effect of the properties on the travel distance. It was proven that there were no significant differences between the travel distances represented by the simulation model and those found experimentally using statistical analysis (i.e. the simulation model could represent virtual real landslides). From the sensitivity analysis using the simulation model, the travel distances were positively correlated to volume, or number of particles, and negative correlated to the slope angle, kinetic friction and rolling friction of particles when the initial potential energies were the same. The mass of particles of equal size did not affect the distance travelled. As the number of particles increased, the simulated travel distances tended to be longer compared with theoretical travel distances calculated using the friction between particles and the slope. Consequently, we could determine the distance of the lumped mass model as being critical between fluidized and non-fluidized landslides.

An O( n) time hierarchical tree algorithm for computing force field in n-body simulations

We consider the following force field computation problem: given a cluster of n particles in three-dimensional space, compute the force exerted on each particle by the other particles. Depending on different applications, the pairwise interaction could be either gravitational or Lennard-Jones. In both cases, the force between two particles vanishes as the distance between them approaches to infinity. Since there are n( n − 1)/2 pairs, direct method requires Θ( n 2) time for force-evaluation, which is very expensive for astronomical simulations. In 1985 and 1986, two famous O( n log n) time hierarchical tree algorithms were published by Appel (1985) and by Barnes and Hut (1986), respectively. In this paper, we show that Appel's algorithm can be implemented in O( n) time.

Three-Dimensional Labeling Program for Elucidation of the Geometric Properties of Biological Particles in Three-Dimensional Space

For all biological particles such as cells or cellular organelles, there are three-dimensional coordinates representing the centroid or center of gravity. These coordinates and other numerical parameters such as volume, fluorescence intensity, surface area, and shape are referred to in this paper as geometric properties, which may provide critical information for the clarification ofin situmechanisms of molecular and cellular functions in living organisms. We have established a method for the elucidation of these properties, designated the three-dimensional labeling program (3DLP). Algorithms of 3DLP are so simple that this method can be carried out through the use of software combinations in image analysis on a personal computer. To evaluate 3DLP, it was applied to a 32-cell-stage sea urchin embryo, double stained with FITC for cellular protein of blastomeres and propidium iodide for nuclear DNA. A stack of optical serial section images was obtained by confocal laser scanning microscopy. The method was found effective for determining geometric properties and should prove applicable to the study of many different kinds of biological particles in three-dimensional space.

Anyonlike particles in three dimensions

We consider particles in three-dimensional space, which have a certain probability to find themselves in a thin layer (``plane''), where they are assumed to be well described by a planar Hamiltonian and are subjected to Aharonov-Bohm-type interaction. We demonstrate that their planar motion is then anyonlike, with the ``effective statistical parameter'' proportional essentially to the square of the probability. We also show that charge-flux composites with solenoids of finite length, provided they are themselves fermions, can form a bound state in which they behave like anyons, without any external potential confining them to a plane.

Exact solution of the four-body Faddeev-Yakubovsky equations for the harmonic oscillator.

The Faddeev-Yakubovsky equations for four identical spinless particles in three-dimensional space interacting via harmonic-oscillator two-body potentials are solved analytically for any excitation and for an arbitrary value of the total angular momentum.

Analytic solution of the harmonic-oscillator Faddeev equations for three nonidentical particles.

The coupled Faddeev equations for three nonidentical particles in three-dimensional space interacting via different harmonic-oscillator two-body potentials are solved analytically for any excitation and for an arbitrary value of the total angular momentum.

Exact solution of the Faddeev equations for the harmonic oscillator.

The Faddeev equations for three identical spinless particles in three-dimensional space interacting via harmonic-oscillator two-body potentials are solved analytically for any excitation and for an arbitrary value of the total angular momentum.

Collectivity and geometry. III. The three-dimensional case in the Sp(6)⊇Sp(2)×𝒪(3) chain for closed shells

As was indicated in previous papers, general Hamiltonians for systems of n particles in three-dimensional space can be formulated in the enveloping algebra of the symplectic group Sp(6n). This group admits, among others, the subgroup Sp(6)×O(n) and, as has been noticed by many authors, collective Hamiltonians can be formulated in the enveloping algebra of Sp(6), so that their eigenstates can be characterized by a definite irreducible representation (irrep) of this group. The mathematical problem is then to determine the matrix elements of the generators of Sp(6) in a basis characterized by irreps of this group as well as of appropriate subgroups. In the present series of papers the subgroups chosen where Sp(2)×𝒪(3) as the Casimir operator of Sp(2) when n → ∞ is formally related to the Bohr–Mottelson vibrational Hamiltonian (BMVH), while 𝒪(3) gives the angular momentum of the state. We give an algorithm for determining these states that closely parallels the procedure followed for the BMVH. Programs are being developed to convert our algorithm into a computational tool for determining collective excitations in nuclei.