Symmetry of Traveling Wave Solutions to the Allen-Cahn Equation in \Er^2

In this paper, we prove even symmetry of monotone traveling wave solutions to the balanced Allen-Cahn equation in the entire plane. Related results for the unbalanced Allen-Cahn equation are also discussed

Transport cost and endogenous quality choice

This paper examines how the quality of exports depends on relative country size and its remoteness. Specific transportation cost is the key variable in our analysis as it gives rise to the Alchian-Allen effect. In the model, we allow for endogenous quality choice by a producer serving many international locations. Higher quality comes at higher marginal cost of production, but can be delivered at the same absolute, and thus proportionally lower, transportation cost to a given destination. Our model complements the well documented demandside response to the distribution of transportation costs (known as the Alchian-Allen effect) by the supply side response. We show that, ceteris paribus, equilibrium quality decreases in the domestic country size and increases in remoteness from foreign markets. This happens because a larger portion of the demand is affected by the Alchian-Allen effect for smaller countries’ producers, and the Alchian-Allen effect is stronger for remote countries. We confirm our predictions empirically on a detailed product level dataset of all exporters worldwide into a sample of Latin American importers

An alternative to the Allen-Cahn phase field model for interfaces in solids - numerical efficiency

The derivation of the Allen-Cahn and Cahn-Hilliard equations is based on the Clausius-Duhem inequality. This is not a derivation in the strict sense of the word, since other phase field equations can be fomulated satisfying this inequality. Motivated by the form of sharp interface problems, we formulate such an alternative equation and compare the properties of the models for the evolution of phase interfaces in solids, which consist of the elasticity equations and the Allen-Cahn equation or the alternative equation. We find that numerical simulations of phase interfaces with small interface energy based on the alternative model are more effective then simulations based on the Allen-Cahn model.Comment: arXiv admin note: text overlap with arXiv:1505.0544

[Review of] Paula Gunn Allen. Grandmothers of the Light: A Medicine Woman\u27s Source Book

As Allen points out in her preface, the stories in this collection were gleaned from the vast oral tradition of North American tribes. Allen adds that they (the stories) have served as her spiritual guides. She feels that in these tales the great Goddess has many guises, such as Xmucane, Sky Woman, Thinking Woman, Scomalt, et al