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

ASP as a Cognitive Modeling Tool: Short-Term Memory and Long-Term Memory

In this paper we continue our investigation on the viability of Answer Set Programming (ASP) as a tool for formalizing, and reasoning about, psychologicalmodels. Inthefieldofpsychology,aconsiderableamountofknowledgeis still expressed using only natural language. This lack of a formalization complicates accurate studies, comparisons, and verification of theories. We believe that ASP, a knowledgerepresentationformalismallowingforconcise andsimplerepresentation of defaults, uncertainty, and evolving domains, can be used successfully for the formalization of psychological knowledge. In previous papers we haveshownhowASPcanbeusedtoformalizearather well-establishedmodelof Short-Term Memory, and how the resulting encoding can be applied to practical tasks, such as those from the area of human-computer interaction. In this paper we extend the model of Short-Term Memory and introduce the model of a substantialportionof Long-Term Memory, whose formalization is made particularly challenging by the ability to learn proper of this part of the brain. Furthermore, we compare our approach with various established techniques from the area of cognitive modeling