Relaxed equilibrium configurations to model fossil fields

Large-scale Magnetic Fields in Stellar Interiors I – Relaxed Equilibrium Configurations to Model Fossil Fields

The understanding of fossil fields origin, topology and stability is one of the corner stone of the stellar magnetism theory. On one hand, since they survive over secular time-scales, they may modify the structure and the evolution of their host stars. On the other hand, they must have a complex stable structure since it has been demonstrated by Tayler and collaborators that simplest purely pol...

Equilibrium Configurations for a Territorial Model

We consider a territorial model based on Voronoi tessellations, which form a partition of a planar region by enclosing each agent in a polygon such that every point within the polygon is closest to that agent instead of any other. Equilibria for this model correspond to centroidal Voronoi tessellations. For rectangular domains and for small population sizes, we show that there can be distinct c...

Equilibrium configurations of defective crystals

Equilibrium configurations of tripolar charges

It is shown that an ensemble of particles with tripolar (colour) charges will necessarily cohere in a hierarchy of structures, from simple clusters and strings to complex aggregates and cyclic moleculelike structures. The basic combinatoric rule remains essentially the same on different levels of the hierarchy, thus leading to a pattern of resemblance between different levels. The number of pri...

Generalized Equilibrium Problem with Mixed Relaxed Monotonicity

We extend the concept of relaxed α-monotonicity to mixed relaxed α-β-monotonicity. The concept of mixed relaxed α-β-monotonicity is more general than many existing concepts of monotonicities. Finally, we apply this concept and well known KKM-theory to obtain the solution of generalized equilibrium problem.