Abstract This paper provides a pedagogical introduction to recent developments in geometrical and topological band theory following the discovery of graphene insulators. Amusingly, many these have connection contributions high-energy physics by Dirac. The review starts presentation Dirac magnetic monopole, goes on with Berry phase two-level system geometrical/topological for Bloch electrons cry...

Any fracture process ultimately involves the rupture of atomic bonds. Processes at the atomic scale therefore critically influence the toughness and overall fracture behavior of materials. Atomistic simulationmethods including large-scalemolecular dynamics simulations with classical potentials, density functional theory calculations and advanced concurrent multiscale methods have led to new ins...

Cracking of laser hybrid welding of eccentric fillet joints has been studied for stainless steel. Laser hybrid welding enables narrow deep welds with freedom for shaping the upper weld geometry. The significance of geometrical aspects like weld toe radius, weld surface topography and lack of fusion on fatigue cracking is discussed. Constant amplitude four point bending tests, S/N-curve, topogra...

Geometry plays an important role in modern statistical learning theory, and many different aspects of geometry can be found in this fast developing field. This thesis addresses some of these aspects. A large part of this work will be concerned with so called manifold methods, which have recently attracted a lot of interest. The key point is that for a lot of real-world data sets it is natural t...