TABLE OF CONTENTS / Trajectory Isomorphisms / Lucy Fluid / Equilibrium Thermodynamic Properties for the Lucy Fluid / Transport Properties for the Lucy Fluid / Properties of the Embedded-Atom Fluid / Structural Relaxation
/ 9 Figures /
Example Problems :
[ Embedded-Atom Column Relaxation, Embedded-Atom Column Collapse, Lucy Fluid Free Expansion, Lucy Fluid Stationary Shockwave ]
There is often a striking resemblance between smooth-particle trajectories and the trajectories of particles obeying ordinary Newtonian mechanics. This is not a coincidence. In fact there are two significant special cases in which the apparent resemblance is actually a precise identity. One, the Lucy fluid, corresponds to the flow of an ideal ?-law gas, with P ? ? 2. Sections 5.9 and 6.13 describe the shear flow of this fluid.
The other, an embedded-atom fluid, corresponds to the flow of a dense fluid with stress-free density ? 0 > where the pressure, P ? ? 3 - ? 0 ? 2 , vanishes. The need for an additional surface tension potential for fluids or solids, as well as a potential able to stabilize "solid" phases (the "invariant curvature" potential), was discussed in Section 5.6 . Here we consider the constitutive relations for both these special cases from the standpoints of equilibrium statistical mechanics and nonequilibrium kinetic theory. We then illustrate the use of the two models by solving four example problems.
Provided that the pressure varies as ? 2, the macroscopic
