Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics

This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of magnetized fluids. In order to be self-contained we first motivate the physical properties of a magnetic fluid and how it should behave under the laws of thermodynamics. Next, we introduce a mathematical model built from hyperbolic partial differential equations (PDEs) that translate physical laws into mathematical equations. After an overview of the continuous analysis, we thoroughly describe the derivation of a numerical approximation of the ideal MHD system that remains consistent to the continuous thermodynamic principles. The derivation of the method and the theorems contained within serve as the bulk of the review article. We demonstrate that the derived numerical approximation retains the correct entropic properties of the continuous model and show its applicability to a variety of standard numerical test cases for MHD schemes. We close with our conclusions and a brief discussion on future work in the area of entropy consistent numerical methods and the modeling of plasmas

Progress and Promise in using Arabidopsis to Study Adaptation, Divergence, and Speciation

Fundamental questions remain to be answered on how lineages split and new species form. The Arabidopsis genus, with several increasingly well characterized species closely related to the model system A. thaliana, provides a rare opportunity to address key questions in speciation research. Arabidopsis species, and in some cases populations within a species, vary considerably in their habitat preferences, adaptations to local environments, mating system, life history strategy, genome structure and chromosome number. These differences provide numerous open doors for understanding the role these factors play in population divergence and how they may cause barriers to arise among nascent species. Molecular tools available in A. thaliana are widely applicable to its relatives, and together with modern comparative genomic approaches they will provide new and increasingly mechanistic insights into the processes underpinning lineage divergence and speciation. We will discuss recent progress in understanding the molecular basis of local adaptation, reproductive isolation and genetic incompatibility, focusing on work utilizing the Arabidopsis genus, and will highlight several areas in which additional research will provide meaningful insights into adaptation and speciation processes in this genus