Narrow Results

When a system's activity alternates between a resting state (e.g. a stable equilibrium) and an active state (e.g. a stable periodic orbit), the system is said to exhibit bursting behavior. We use bifurcation theory to identify three distinct topological types of bursting in one-dimensional mappings and 20 topological types in two-dimensional mappings having one fast and one slow variable. We show that different bursters can interact, synchronize, and process information differently. Our study suggests that bursting mappings do not occur only in a few isolated examples, rather they are robust nonlinear phenomena.

Given a triangulation T of n points in the plane, we are interested in the minimal set of edges in T such that T can be reconstructed from this set (and the vertices of T) using constrained Delaunay triangulation. We show that this minimal set is precisely the set of non locally Delaunay edges, and that its cardinality is less than or equal to n+i/2 (if i is the number of interior points in T), which is a tight bound.

The model of weak localization in 2D semiconductor structures in the whole range of classically weak magnetic fields in the presence of the Elliot–Yafet spin relaxation has been developed. It was shown that the spin–orbit interaction influences the value of magnetoresistance in small magnetic fields (within diffusion approximation) and when diffusion approximation is no longer valid.

Dual phase (DP) steels were modeled using 2D and 3D representative volume elements (RVE). Both the 2D and 3D models were generated using the Monte-Carlo-Potts method to represent the realistic microstructural details. In the 2D model, a balance between computational efficiency and required accuracy in truly representing heterogeneous microstructure was achieved. In the 3D model, a stochastic template was used to generate a model with high spatial fidelity. The 2D model proved to be efficient for characterization of the mechanical properties of a DP steel where the effect of phase distribution, morphology and strain partitioning was studied. In contrast, the current 3D modeling technique was inefficient and impractical due to significant time cost. It is shown that the newly proposed 2D model generation technique is versatile and sufficiently accurate to capture mechanical properties of steels with heterogeneous microstructure.