Exploration of The Duality Between Generalized Geometry and Extraordinary Magnetoresistance

We outline the duality between the extraordinary magnetoresistance (EMR), observed in semiconductor-metal hybrids, and non-symmetric gravity coupled to a diffusive $U(1)$ gauge field. The corresponding gravity theory may be interpreted as the generalized complex geometry of the semi-direct product of the symmetric metric and the antisymmetric Kalb-Ramond field: ($g_{\mu\nu}+\beta_{\mu\nu}$). We construct the four dimensional covariant field theory and compute the resulting equations of motion. The equations encode the most general form of EMR within a well defined variational principle, for specific lower dimensional embedded geometric scenarios. Our formalism also reveals the emergence of additional diffusive pseudo currents for a completely dynamic field theory of EMR. The proposed equations of motion now include terms that induce geometrical deformations in the device geometry in order to optimize the EMR. This bottom-up dual description between EMR and generalized geometry/gravity lends itself to a deeper insight into the EMR effect with the promise of potentially new physical phenomena and properties.Comment: 13 pages and 6 figures. Revised/edited for clarity and purpose. Several references added. Updated title based on suggestions and comments received. Version accepted for publication in Phys.Rev.

Discovery Learning Experiments in a New Machine Design Laboratory

A new Machine Design Laboratory at Marquette University has been created to foster student exploration with hardware and real-world systems. The Laboratory incorporates areas for teaching and training, and has been designed to promote “hands-on” and “minds-on” learning. It reflects the spirit of transformational learning that is a theme in the College of Engineering. The goal was to create discovery learning oriented experiments for a required junior-level “Design of Machine Elements” course in mechanical engineering that would give students practical experiences and expose them to physical hardware, actual tools, and real-world design challenges. In the experiments students face a range of real-world tasks: identify and select components, measure parameters (dimensions, speed, force), distinguish between normal and used (worn) components and between proper and abnormal behavior, reverse engineer systems, and justify design choices. The experiments serve to motivate the theory and spark interest in the subject of machine design. This paper presents details of the experiments and summarizes student reactions and our experiences in the Machine Design Laboratory. In addition, the paper provides some insights for others who may wish to develop similar types of experiments