STATE EQUATION FOR THE THREE-DIMENSIONAL SYSTEM OF "COLLAPSING" HARD SPHERES

2008 ◽  
Vol 22 (32) ◽  
pp. 3153-3157 ◽  
Author(s):  
I. KLEBANOV ◽  
N. GINCHITSKII ◽  
P. GRITSAY
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Hard Spheres ◽  
Van Der Waals ◽  
Three Dimensional ◽  
State Equation ◽  
Dimensional System ◽  
Step Potential ◽  
System Of Particles ◽  
Three Dimensional System

By the Wertheim method, the exact solution of the Percus–Yevick integral equation for a system of particles with the "repulsive step potential" interacting ("collapsing" hard spheres) is obtained. On the basis of this solution, the state equation for the "repulsive step potential" is built and determined, that the Percus–Yevick equation does not show the Van der Waals loop for "collapsing" hard spheres.

scholarly journals COMMENTS ON "STATE EQUATION FOR THE THREE-DIMENSIONAL SYSTEM OF 'COLLAPSING' HARD SPHERES"

2009 ◽  
Vol 23 (27) ◽  
pp. 3305-3308 ◽  
Author(s):  
ANDRÉS SANTOS
Keyword(s):  
Integral Equation ◽  
Hard Sphere ◽  
Hard Spheres ◽  
Three Dimensional ◽  
State Equation ◽  
Dimensional System ◽  
Low Density ◽  
Step Potential ◽  
Low Density Limit ◽  
Three Dimensional System

A recent paper [I. Klebanov et al., Mod. Phys. Lett. B22 (2008) 3153] claims that the exact solution of the Percus–Yevick (PY) integral equation for a system of hard spheres plus a step potential is obtained. The aim of this paper is to show that Klebanov et al.'s result is incompatible with the PY equation since it violates two known cases: the low density limit and the hard sphere limit.

scholarly journals The Formation of Disks by Inelastic Collisions of Gravitating Particles. Applications to the Dynamics of the Saturn's Ring and to the Formation of the Solar System

1974 ◽  
Vol 62 ◽  
pp. 83-93
Author(s):  
A. Brahic
Keyword(s):  
Solar System ◽  
Three Dimensional ◽  
Inelastic Collisions ◽  
Dimensional System ◽  
Central Mass ◽  
System Of Particles ◽  
Final Equilibrium State ◽  
First Results ◽  
Three Dimensional System ◽  
Collision Mechanism

We integrate numerically the evolution of a three-dimensional system of particles with finite dimensions, which bounce inelastically upon each other. The particles are subjected to the attraction of a central mass; their mutual attraction is neglected. This model is used to study the evolution of Saturn's ring. The first results are presented: such a collision mechanism can flatten very quickly the Saturn's ring and the system tends towards a final equilibrium state.

scholarly journals Quasibinary amorphous phase in a three-dimensional system of particles with repulsive-shoulder interactions

2008 ◽  
Vol 129 (6) ◽  
pp. 064512 ◽  
Author(s):  
Yu. D. Fomin ◽  
N. V. Gribova ◽  
V. N. Ryzhov ◽  
S. M. Stishov ◽  
Daan Frenkel
Keyword(s):  
Amorphous Phase ◽  
Three Dimensional ◽  
Dimensional System ◽  
System Of Particles ◽  
Three Dimensional System

scholarly journals Numerical Study of a Gravitating System of Colliding Particles; Formation and Dynamics of Discs

1975 ◽  
Vol 69 ◽  
pp. 287-295
Author(s):  
A. Brahic
Keyword(s):  
Numerical Study ◽  
Finite Thickness ◽  
Three Dimensional ◽  
Galactic Nuclei ◽  
Inelastic Collisions ◽  
Dimensional System ◽  
Central Mass ◽  
System Of Particles ◽  
Gravitating Systems ◽  
Three Dimensional System

The study of gravitating systems of colliding particles has many potential astrophysical applications, for instance the dynamics of Saturn's ring, the formation of the solar system, the flattening of protogalaxies and the evolution of galactic nuclei. We consider numerically a three-dimensional system of particles moving in the gravitational field of a central mass point and interacting through inelastic collisions. After a very fast flattening, the system forms a disc of finite thickness: this disc spreads slowly, and collisions still occur. A central condensation is formed and there is an outward flux of angular momentum. The energy which is continually lost in the inelastic collisions is obtained at the expense of the bodies which fall inwards.

Size distribution in collisional systems distribution de tailles dans les systemes collisionnels

1984 ◽  
Vol 75 ◽  
pp. 397-402 ◽  
Author(s):  
S. Clairemidi
Keyword(s):  
Gravitational Field ◽  
Size Distribution ◽  
Central Body ◽  
Three Dimensional ◽  
Dynamical Evolution ◽  
Inelastic Collisions ◽  
Dimensional System ◽  
Planetary Rings ◽  
System Of Particles ◽  
Three Dimensional System

ABSTRACTThe dynamical evolution of a three dimensional system of particles of different masses and sizes, orbiting in the gravitational field of a central body, and interacting through inelastic collisions is studied here. Recent fly-bys of planetary rings and observations of flat galaxies with modern receptors indicate that a number of structures discovered in collisional systems can be understood only of three ingredients are included in the models, namely interparticles collisions , distributions of particles sizes and self attraction of the particles.

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