Irreversible Dynamos in Butterflies

On time versus size for monotone dynamic monopolies in regular topologies

We consider a well known distributed coloring game played on a simple connected graph: initially, each vertex is colored black or white; at each round, each vertex simultaneously recolors itself by the color of the simple (strong) majority of its neighbours. A set of vertices is said to be a dynamo, if starting the game with only the vertices of colored black, the computation eventually reaches...

Optimal Irreversible Dynamos in Chordal Rings

Irreversible Dynamos in Tori

We study the dynamics of majority-based distributed systems in presence of permanent faults. In particular, we are interested in the patterns of initial faults which may lead the entire system to a faulty behaviour. Such patterns are called dynamos and their properties have been studied in many diierent contexts. In this paper we investigate dynamos for meshes with diierent types of toroidal cl...

Bounding the Number of Tolerable Faults in Majority-Based Systems

Consider the following coloring process in a simple directed graph G(V,E) with positive indegrees. Initially, a set S of vertices are white. Thereafter, a black vertex is colored white whenever the majority of its in-neighbors are white. The coloring process ends when no additional vertices can be colored white. If all vertices end up white, we call S an irreversible dynamic monopoly (or dynamo...

Magnetic Helicity Evolution

The term “dynamo” means different things to the laboratory fusion plasma and astrophysical plasma communities. To alleviate the resulting confusion and to facilitate interdisciplinary progress, we pinpoint conceptual differences and similarities between laboratory plasma dynamos and astrophysical dynamos. We can divide dynamos into three types: 1. magnetically dominated helical dynamos which su...