Collision models response theory

Before the quantum theory of solids (see description in Chapter 21), microscopic descriptions of metals were based on the Drude model, named for the German physicist Paul Drude. The solid was viewed as a fixed array of positively charged metal ions, each localized to a site on the solid lattice. These fixed ions were surrounded by a sea of mobile electrons, one contributed by each of the atoms in the solid. The number density of the electrons, is then equal to the number density of atoms in the solid. As the electrons move through the ions in response to an applied electric field, they can be scattered away from their straight-line motions by collisions with the fixed ions this influences the mobility of the electrons. As temperature increases, the electrons move more rapidly and the number of their collisions with the ions increases therefore, the mobility of the electrons decreases as temperature increases. Equation 22.7 applied to the electrons in the Drude model gives... 

It was noticeable that university students were more likely to use reasoning based on sub-microscopic or mathematical levels. However, around half (45.8%) of the first-year undergraduates did not refer to any ideas concerning the dynamic nature of particles. Undergraduates (particularly university third-year students) responses were richer in the terminology and the range of justifications provided, in that they used the principles of collision or transition-state theory/model more... 

Two of the most common classes of particle-dynamic simulations are termed hard-particle and soft-particle methods. Hard-particle methods calculate particle trajectories in response to instantaneous, binary collisions between particles, and allow particles to follow ballistic trajectories between collisions. This class of simulation permits only instantaneous contacts and is consequently often used in rapid flow situations such as are found in chutes, fluidized beds, and energetically agitated systems. Soft-particle methods, on the other hand, allow each particle to deform elastoplastically and compute responses using standard models from elasticity and tribology theory. This approach permits enduring particle contacts and is therefore the method of choice for mmbler apphcations. The simulations described in this chapter use soft-particle methods and have been validated and found to agree in detail with experiments. 

---