Corrosion and interlacement percolation

Conversion of radioactive waste, spread of epidemics, computer network failure… Although very different, all of these events involve transition from one state to another, a process which is described today using percolation theory. “When applied to materials science, the drawback of this theory is that it considers each element of the material under study independently.
However, this does not reflect reality,” explained Dr. Augusto Teixeira. He is participating in the development of an alternative model, known as random interlacement, which incorporates the notion of dependence between the different elements of a crystalline material. His aim is to pinpoint the differences and similarities between these two types of models. This should help scientists choose the most appropriate model based on their applications.

Augusto Teixeira is Brazilian and studied Physics at the Federal University of Minas Gerais (UFMG). He later decided to complete a Master’s degree in Mathematics at the Institute for Pure and Applied Mathematics (IMPA) in Rio de Janeiro. This Master’s programme was decisive for him, leading him to pursue a PhD at the ETH Zurich – a very important step in his career. Under the supervision of Professor Alain-Sol Sznitman, he published various research papers in the fields of probability theory and percolation. He currently holds a fellowship from the AXA Research Fund and is working on a project at the ENS involving the analysis of corrosion and percolation.

What has your AXA fellowship brought you?
It is still too early to appreciate the full benefits of my fellowship, since I have only been in Paris for three months, but it is already clear that it will be an amazing time for me professionally. Paris is perhaps the best place in the world to work in probability theory, and the opportunity to be at the Ecole normale supérieure (ENS) has already brought me in contact with several researchers that have extensive experience in my area of research. I am very excited about the near future.

Could you describe your experiences with the AXA Research Fund community?
My closest experience with the AXA Research Fund was the Talent Day. It was definitely very inspiring. At first I was a bit apprehensive about being a mathematician at a conference about environmental risks. But quite to the contrary, it was very rewarding to interact with the AXA Research Fund staff, the speakers of the Talent Day and especially the other fellows. Although there was a big gap between our areas of research, it was very inspiring to hear about the work of several other talented researchers, especially in this decisive moment of my career.

Can you briefly describe what your research project is about?
I am mainly interested in studying new models for the corrosion of materials. Recently, a model called random interlacements was introduced by Alain-Sol Sznitman. We believe that random interlacements can give a better description of certain types of corrosion, such as gel degradation by proteins. In this project we seek to obtain a better theoretical description of the model in question and compare it with the usual percolation models.