[en] Abstract The magnetorotational instability (MRI) has long been considered a plausibly ubiquitous mechanism to destabilize otherwise stable Keplerian flows to support radially outward transport of angular momentum. Such an efficient transport process would allow fast accretion in astrophysical objects such as stars and black holes to release copious kinetic energy that powers many of the most luminous sources in the universe. But the standard MRI under a purely vertical magnetic field has heretofore never been directly measured despite numerous efforts over more than a decade. Here we report an unambiguous laboratory demonstration of the spring-mass analogue to the standard MRI by comparing motion of a spring-tethered ball within different rotating flows. The experiment corroborates the theory: efficient outward angular momentum transport manifests only for cases with a weak spring in quasi-Keperian flow. Our experimental method accomplishes this in a new way, thereby connecting solid and fluid mechanics to plasma astrophysics.

[en] The current flow pattern, together with the contact resistance, is calculated analytically in a Cartesian 3-terminal thin film contact with dissimilar materials. The resistivities and the geometric dimensions in the individual contact members, as well as the terminal voltages, may assume arbitrary values. We show that the current flow patterns and the contact resistance may be conveniently decomposed into the even and odd solution. The even solution gives exclusively and totally the current flowing from the source to the gate. The odd solution gives exclusively and totally the current flowing from the source to the drain. Current crowding at the edges, and current partition in different regions are displayed. The analytic solutions are validated using a simulation code. The bounds on the variation of the contact resistance are given. This paper may be considered as the generalization of the transmission line model and the Kennedy-Murley model that were used extensively in the characterization of thin-film devices. For completeness, we include the general results for the cylindrical geometry, which are qualitatively similar to the even solution of the Cartesian geometry.