Matlab Code:

Two Nucleation Sites: FilmEvolution_2NucleationSites.m

For details on the code itself, download the code via the links above. Descriptions of the functions used, their purpose, and the values used are described on the code.

The differential equation (see Computational Design) that is to be solved in order to descirbe the think film growth was solved via Euler's Method. When initially running the code, we ran into some problems that we had to write additional code in order to address them.

One of the issues that we ran into was that the nodes in the simulation are prone to congregate at areas of high curvature which in turn can get too close for the timescale of the simulation. When this happens nodes get placed out of order and the surface explodes. Likewise, areas of low curvature end up being defined by a very small number of nodes, which drastically reduces the spacial resolution in those areas. To address this issue and allow our simulation to progress smoothly and maintain a reasonably fine surface mesh, we wrote a “Cleannodes”  loop to check the sizes of each element and to delete and create nodes as defined by a minimum and maximum element size parameters that a user can define in the code, if desired. 

Another issue is that during some simulations, nodes were created and destroyed very rapidly. This led to the surface picking up shape characteristics defined more by the surface interpolating function than by the dynamics of the simulation. For example,  if a linear interpolating function was used, a gaussian peak would eventually morph into a triangle with flat sides and a sharp peak. If the interpolating function was changed to a quadratic function, the result was a perfect parabola, regardless of the simulation dynamics.  In order to fix this problem, the minimum and maximum node sizes were carefully tweaked and a cubic spline interpolating function was used to provide the best possible surface shape as nodes were replaced.