Discreteness causes waves

discreteness in

Bloch-like oscillations induced by charge discreteness in quantum mesoscopic rings. We study the effect of charge discreteness in a quantum mesoscopic ring wih inductance L. The ring is pierced by a time depending external magnetic field. When the external magnetic flux varies uniformly, the current induced in the ring oscillates with a frequency proportional to the charge discreteness and the ...

Discreteness Causes Bias in Percentage-Based Comparisons: A Case Study From Educational Testing

Complexity and Discreteness Criteria

Let G be a subgroup of PSL(2, C). The discreteness problem for G is the problem of determining whether or not G is discrete. In this paper we assume that all groups considered are non-elementary. If G is generated by two elements, A and B of PSL(2, C), we have what is called the two-generator discreteness problem. Two-generator groups are important because, by a result of Jorgensen, an arbitrar...

Continuum approach to discreteness.

We study analytically and numerically continuum models derived on the basis of Padé approximations and their effectiveness in modeling spatially discrete systems. We not only analyze features of the temporal dynamics that can be captured through these continuum approaches (e.g., shape oscillations, radiation effects, and trapping) but also point out ones that cannot be captured (such as Peierls...

Arithmeticity, Discreteness and Volume

We give an arithmetic criterion which is sufficient to imply the discreteness of various two-generator subgroups of PSL(2,C). We then examine certain two-generator groups which arise as extremals in various geometric problems in the theory of Kleinian groups, in particular those encountered in efforts to determine the smallest co-volume, the Margulis constant and the minimal distance between el...