ME 574: Nano/Microstructural Evolution

Advantages

Compared with other migration simulation methods, our method has the following advantages.

1. It is theoretically possible to simulate the growth of any shape. Based on our algorithm, it can be seen that the particle grows due to the forces acting on each of the nodes. At the very beginning, the particle can be any random shape, but is transformed over time to a sphere (for 2-dimensional case, it's a circle) because that takes the least energy. The initial shape only determines the length of time until the spherical form is achieved. Restrictions on the initial shape are discussed in Limitations.

2. Any number of nodes is possible on the particles. Some simulation methods work on the assumption that the particles must have the same number of nodes. However, our code can work with any number of nodes even though the size of the particles may differ. The only inputs that are required are the node coordinates and in what order these nodes are connected.

3. Creates new nodes on combining. Once two particles intersect, the coordinates of the two points of contact are calculated. These two points are assigned as new nodes to replace the nodes which are lost through combination of the particles. Hence, it is more accurate than simply deleting the corresponding elements.

Limitations

Nothing is perfect; our code still has the potential to be improved in order to be more successful in the future by fixing the following limitations.

1. Length of the element cannot be too small or too large. Since our MATLAB code is based on an algorithm which involves the calculation of the shortest distance between nodes, an element that has unreasonably short lengths compared to the others would create errors in our simulation. Also, it is interesting to note that an anomaly would occur if some of the elements are too long compared to the others. These elements could take a long time to shrink, thus making the phase coarsening disproportionate. A solution to this problem would be to input nodes that are not too far or too close from each other, or we can create an additional code to eliminate or add a node when the element gets too long or too short. However, this method will make the code more complicated, and the running time will become much longer.

2. Limitation in the number of particles. Our code is designed for the simulation of only two particles. If the simulation is more than 2 particles, a more extensive code needs to be produced due to complications in the H matrix.

3. The polygons must be convex. Our intersection detection method is based on the assumption that if two polygons are intersecting, there are two points of contact. Hence, the polygon must be convex. If the polygon is concave, the number of points of contact may exceed two. Hence, the code may not detect all the intersected points, and the generated combined particle may be formed incorrectly.