Understanding Microscopic Variations in Materials

Martin Strömqvist received his Ph.D. in Mathematics at the KTH Royal Institute of Technology in Stockholm in 2014. Thanks to a grant from the Knut and Alice Wallenberg Foundation, he will hold a postdoctoral position in Professor Peter Lindqvist’s research group at the Norwegian University of Science and Technology in Trondheim, Norway.

Many materials are composites and their properties can vary significantly across the material’s different segments. Variations exist on a microscopic scale as well, which makes exact calculations almost impossible. A description of material’s properties, for example its strength or heat conductivity, requires analysis which takes macro scale into account.

Standard mathematical methods to solve the problem and analyze porous or impure materials are to make a more homogeneous model of the material. How this may be done is developed by the homogenization theory. The properties of the material are then described quantitatively using partial differential equations.

The goal of Martin Strömqvist’s project is an extension of such methods to materials with variable inhomogeneities by assuming certain degree of randomness. More specifically, the study will focus on analyzing randomly perforated material. It will include, for example, an analysis of the way sand grains are distributed when modeling fluid flow through sand. Heat transfer in porous materials will be another application of the study. Allowing arbitrary distances between microscopic holes, will be of particular importance here because this case has not been explored yet even though it describes realistic applications, as for example modeling of underground flows of water or oil.