Mathematicians model snowflakes using physical laws

Scientific American : A group of researchers in Germany has succeeded in using computer modeling to simulate the faceted pattern of snowflake formation. Using basic conservation laws and thermodynamics, Harald Garcke of the University of Regensburg and colleagues were able to model the way the crystal surface changes over time. They also managed to model, simultaneously, the two main types of snowflake growth: dendritic growth, in which the flakes form treelike branches, and faceted growth, dominated by flat plates, such as hexagons and triangles. Among the unexpected aspects of snowflake formation, the group found that the speed at which the snowflakes’ tips grow is directly proportional to the amount of water vapor in the air and that molecular bonds on the crystal surface have a larger effect on crystal growth than previously expected. The researchers’ approach can be applied to a variety of other systems, such as red blood cells, soap bubbles, and polycrystalline materials.