Hard spheres information

Hard spheres are widely used as model particles in the statistical mechanical theory of fluids and solids. They are defined simply as impenetrable spheres...

sized hard spheres. Hard spheres are characterized as non-interacting and impenetrable spheres. These two fundamental properties of hard spheres are described...

2 R {\displaystyle b>2R} , where the colliding nuclei are viewed as hard spheres with radius R {\displaystyle R} .[citation needed] Because the color...

In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical...

atoms nor ions have sharp boundaries, they are treated as if they were hard spheres with radii such that the sum of ionic radii of the cation and anion gives...

used in engineering practice. If one models gas molecules as elastic hard spheres (with mass m {\displaystyle m} and diameter σ {\displaystyle \sigma }...

of a container is occupied by the spheres. The problem of predicting theoretically the random close pack of spheres is difficult mainly because of the...

of hard spheres. This is a model of perfectly hard spheres in thermal motion, and is a simple model of some colloids. For the crystallization of hard spheres...

the seven planetary spheres contained other secondary spheres within them. The planetary spheres were followed by the stellar sphere containing the fixed...

{\partial \rho }{\partial p}}\right)} . In the hard sphere model, the particles are described as impenetrable spheres with radius R {\displaystyle R} ; thus,...

terms of the mean free path. Typically, gas molecules do not behave like hard spheres, but rather attract each other at larger distances and repel each other...

packing of hard spheres with various sizes makes that smaller spheres have larger probability to move downwards by gravitation than larger spheres. The phenomenon...

Sphere packing in a cylinder is a three-dimensional packing problem with the objective of packing a given number of identical spheres inside a cylinder...

per unit time. In an ideal gas, assuming that the species behave like hard spheres, the collision frequency between entities of species A and species B...

if all other knowledge was lost. By modeling matter as collections of hard spheres, it is possible to describe the kinetic theory of gases, upon which classical...

proposed stellar engine designs are based on the Dyson sphere. A precursor to the concept of Dyson spheres was featured in the 1937 novel Star Maker by Olaf...

pellet to hard spheres. The raw material is rolled into a ball, then fired in a kiln or in travelling grate to sinter the particles into a hard sphere. The...

the crystal phase in a system of hard spheres, which is a simple model of colloids consisting of perfectly hard spheres in thermal motion. The agreement...

molecular interaction model; here we take the hard spheres model, which is the simplest. In the hard spheres model, the collision probability for the pair...

will collide, and experience a very high repulsive force (modelled by Hard spheres) which is a much stronger force than the attractions, so that any attraction...

\end{cases}}} r is the distance between the centers of the spheres and d is the distance where the hard spheres touch each other (twice the Van der Waals radius)...

The van der Waals radius, rw, of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom. It is...

nuclei can be understood as hard spheres that repel each other through the Coulomb force but fuse once the two spheres come close enough for contact...