Professor Filip Rindler of the Warwick Mathematics Institute has been awarded £1.75 million from the European Research Council to investigate concentration phenomena in Mathematical Analysis with applications to Material Science.

One aspect of this research programme is a new approach to understand how crystalline materials, such as metals, move and deform.

The importance of a full theory to describe the plastic deformation of metals is of such practical, as well as theoretical, importance that it is sometimes referred to as the “Holy Grail” of Solid Mechanics.

The microscopic mechanism by which metals deform, namely by the movement of defects in the crystal lattice, was discovered in the first decades of the 20th century.

However, despite a century of research, many aspects of the puzzle remain mysterious to this day.

For example, these defects always occur along curves, which can get "entangled" with each other like spaghetti in a bowl. Understanding precisely how these entangled defect lines determine the material properties is still a wide-open problem.

This 5-year research project aims to tackle these deep questions, which lead to many difficult problems at the intersection of several areas of Mathematics.

Professor Rindler commented: “In my research, theoretical investigations in Mathematical Analysis go hand-in-hand with applications to Material Science: Abstract mathematical techniques yield new insights into concrete physical problems, which in turn serve as inspiration for the development of new theories. This generous funding will allow me to build a strong group to tackle these pressing open problems.”

To view more about Professor Rindler’s work please click here.