Piecewise linear critical levels and collapsing

Collapsing Sub-critical Bubbles *

In the standard scenario, the electroweak phase transition is a first order phase transition which completes by the nucleation of critical bubbles. Recently, there has been speculation that the standard picture of the electroweak phase transition is incorrect. Instead, it has been proposed that throughout the phase transition appreciable amounts of both broken and unbroken phases of SU(2) coexi...

Piecewise Constant Controlled Linear Fuzzy Systems

Critical behavior of collapsing surfaces

We consider the mean curvature evolution of rotationally symmetric surfaces. Using numerical methods, we detect critical behavior at the threshold of singularity formation resembling the one of gravitational collapse. In particular, the mean curvature simulation of a one-parameter family of initial data reveals the existence of a critical initial surface that develops a degenerate neckpinch. Th...

Linear colorings of simplicial complexes and collapsing

A vertex coloring of a simplicial complex ∆ is called a linear coloring if it satisfies the property that for every pair of facets (F1, F2) of ∆, there exists no pair of vertices (v1, v2) with the same color such that v1 ∈ F1\F2 and v2 ∈ F2\F1. We show that every simplicial complex ∆ which is linearly colored with k colors includes a subcomplex ∆ with k vertices such that ∆ is a strong deformat...

Piecewise-linear and birational toggling

We define piecewise-linear and birational analogues of toggle-involutions, rowmotion, and promotion on order ideals of a poset P as studied by Striker and Williams. Piecewise-linear rowmotion relates to Stanley’s transfer map for order polytopes; piecewise-linear promotion relates to Schützenberger promotion for semistandard Young tableaux. When P = [a] × [b], a reciprocal symmetry property rec...