Pinned fronts in heterogeneous media of jump type

In this paper, we analyse the impact of a (small) heterogeneity of jump type on the most simple localized solutions of a 3-component FitzHugh–Nagumo-type system. We show that the heterogeneity can pin a 1-front solution, which travels with constant (non-zero) speed in the homogeneous setting, to a fixed, explicitly determined, distance from the heterogeneity. Moreover, we establish the stability of this heterogeneous pinned 1-front solution. In addition, we analyse the pinning of 1-pulse, or 2-front, solutions. The paper is concluded with simulations in which we consider the dynamics and interactions of N-front patterns in domains with M heterogeneities of jump type (N = 3, 4, M ≥ 1).

Happily ever after: Romance, gender and the building blocks of domestic violence

My sister describes the state of something being a psychological or personal 'issue' - such as a trauma, compulsion, phobia, or obsession - as having 'brain spaghetti'. For example, apparently she has spaghetti about me pinning her down as a child and tickling her until she screamed for mercy. She knows this because when her spouse tried to do the same, the experience she had as a child came flooding back as a complex tangle of fears, feelings, and mental images. Notwithstanding the trauma inflicted on a sibling in my youth, the spaghetti metaphor is a simple but useful tool for explaining how complex our experiences are, and I bring it up here because I believe a lot of people have spaghetti about love. So much so, that often love becomes distorted, sometimes to the point of making one completely blind to manipulation and abuse. Part of the blame for 'love spaghetti' can be allotted to media depictions of romance and gender, which helps entrench and maintain our deeply held beliefs about what relationships should look like.