Geometry Study of an Isotropic 3D Silicon Hall Sensor

Isotropic cosmologies in Weyl geometry

We study homogeneous and isotropic cosmologies in a Weyl spacetime. We show that for homogeneous and isotropic spacetimes, the field equations can be reduced to the Einstein equations with a twofluid source. We write the equations as a two-dimensional dynamical system and analyze the qualitative, asymptotic behavior of the models. We examine the possibility that in certain theories the Weyl 1-f...

Discrete Surfaces in Isotropic Geometry

Meshes with planar quadrilateral faces are desirable discrete surface representations for architecture. The present paper introduces new classes of planar quad meshes, which discretize principal curvature lines of surfaces in so-called isotropic 3-space. Like their Euclidean counterparts, these isotropic principal meshes meshes are visually expressing fundamental shape characteristics and they ...

A 3D Event-Based Silicon Retina Stereo Sensor

On the geometry of isotropic arrays

We consider array geometries whose direction-of-arrival (DOA) estimation performance is isotropic. An isotropic array is one whose Cramér–Rao bound (CRB) on the DOA of a single source is uniform for all angles. For both planar arrays and volume arrays we derive necessary and sufficient conditions on array element locations so that the array is isotropic. We also present several designs of isotr...

Is Hall Conductance in Hall Bar Geometry a Topological Invariant ?

A deep connection between the Hall conductance in realistic situation and a topological invariant is pointed out based on von-Neumann lattice representation in which Landau level electrons have minimum spatial extensions. We show that the Hall conductance has no finite size correction in quantum Hall regime, but a coefficient of induced Chern-Simons term in QED 3 has a small finite size correct...