Level 2

Problem 1. Based upon the universal deformation curve, physical constants for argon, and the scaling analysis discussed in the Background section, what would you expect for the final deformation in the Atomistic simulation from Example 1? Run this simulation for at least 200 picoseconds and compare your results.

Problem 2. Run Atomistic simulations for various values of the squeezing force (1.0 to 8.0 in increments of 1.0 Angtsroms per square picosecond), and run each of these for at least 200 picoseconds to obtain the final deformation and an estimate of its uncertainty. Calculating the Bond number for each case, plot up your own "experimental" universal deformation curve. How does this compare with the universal curve in the Background section. If there is a difference, would adjusting the surface tension by a correction factor bring the two curves in correspondence? How well does a nano-droplet mimmick the behavior of a macroscopic drop?

Problem 3. Consider the Continuum simulation from Level 1 Problem 3. Taking a hint from equations 16 and 17 in the Background section, what functional form would you use to describe the deformation-versus-time curve? Compare a plot of your function wuth the actual deformation curve.

Problem 4. Carry out a Continuum simulation with the following parameters.

    Time step: 0.2

    Number of Atoms: 2000

    Initial deformation: 0.5 (prolate)

    Cohesion Strength (Bulk Cohesion): 1.0

    Squeezing Force: 0.0

Compare your deformation-versus-time curve with equation (17) from the Background section. How accurate is the theoretical formula? Repeat this problem for a smaller initial deformation (0.3). For which case do you expect the theoretical curve to be more accurate? Why?

Problem 5: Repeat Problem 4 with oblate initial deformations of -0.5 and -0.3.