Model billiard ball

Fig. 8.2 An example of a Partitioning CA reversible rule, /, mapping (2x 2)-blocks of two-valued states to (2 X 2-blocks / (2 X 2) —> (2 X 2). Note that this rule conserves the total number of I s (indicated by a solid circle) and O s (indicated by an empty square). The system that evolves under this rule is in fact a universal CA (see Billiard Ball Model, later in this section).

Billiard-ball model, see also Elastic-collision model... 

Ridley and Amato (1981) Cr, an Yes Bloch functions, including Coulomb correction Hard-core envelope modulated by periodic part ( Billiard ball model) Nonparabolicity included... 

This illustration shows an atom as John Dalton (1766-1844) imagined it. Many reference materials refer to Dalton s concept of the atom as the "billiard ball model. Dalton, however, was an avid lawn bowler. His concept of the atom was almost certainly influenced by the smooth, solid bowling balls used in the game. 

It is therefore remarkable that 100 years or so before the laws of thermodynamics were formulated, Daniel Bernoulli developed a billiard ball model of a gas that gave a molecular interpretation to pressure and was later extended to give an understanding of temperature. This is truly a wonderful thing, because all it starts with is the assumption that the atoms or molecules of a gas can be treated as if they behave like perfectly elastic hard spheres—minute and perfect billiard balls. Then Newton s laws of motion are applied and all the gas laws follow, together with a molecular interpretation of temperature and absolute zero. You have no doubt... 

We have been using the word, particle, to indicate that we are still referring to a billiard ball model of atoms or molecules. Molecules also have internal motion, the vibrations of their bonds, etc., so in that case, the velocity refers to the motion of the center of mass of the molecule treated as a whole. 

Since such a molecule has rotational energy, various authors have used the com-pletely smooth billiard ball model which is incapable of changing its rotational energy on collisions (i.e., it slips), while others have used a rough billiard ball with a coefficient aR (0 < aR < 1) to describe the extent to which its rotational energy is involved in a collision. 

Physical chemists are well aware of the usefulness of models. An understanding of the fundamental properties of matter can hardly be gained from watching reality, requiring instead the posing of if-then questions that can be answered only by models. The nature of pressure or temperature of a gas as a collective property of its individual atomic or molecular constituents became obvious only through the billiard ball models of Clausius, Maxwell, and Boltzmann, despite our later insights that true atoms or molecules have quantized motion. 

The billiard ball model is unique in that 9 depends only on b, and not on g. 

Adopting the molecular billiard ball model considering molecules that are smooth and symmetric rigid elastic spheres not surrounded by fields of force, the molecules affect each other motion only at contact. 

Onsager Dupuis (i960) and Jaccard (1959, 1964, 1965). The essence of the theory can be seen from a simple billiard-ball model of the molecular processes involved, while a detailed consideration of some of the mechanisms requires, as we shall... 

Such a billiard-ball model of a simple liquid, initiated by J.D. Bernal, has dominated theoretical studies/approaches towards the liquid state of matter for half a century. Such a billiard-ball model, and its generalization to include non-spherical shapes, works not only for liquid argon and krypton, but also for many liquids such as methane, ethane, and carbon tetrachloride, to name a few. However,... 

The billiard ball model is unique in that 9 depends only on b, and not on g. From the previous result, the quantity b db can be determined ... 

---