Curved Finite Elements and Curve Approximation

The approximation of parameterized curves by segments of parabolas that pass through the endpoints of each curve segment arises naturally in all quadratic isoparametric transformations. While not as popular as cubics in curve design problems, the use of parabolas allows the introduction of a geometric measure of the discrepancy between given and approximating curves. The free parameters of the parabola may be used to optimize the fit, and constraints that prevent overspill and curve degeneracy are introduced. This leads to a constrained optimization problem in two varibles that can be solved quickly and reliably by a simple method that takes advantage of the special structure of the problem. For applications in the field of computer-aided design, the given curves are often cubic polynomials, and the coefficient may be calculated in closed form in terms of polynomial coefficients by using a symbolic machine language so that families of curves can be approximated with no further integration. For general curves, numerical quadrature may be used, as in the implementation where the Romberg quadrature is applied. The coefficient functions C sub 1 (gamma) and C sub 2 (gamma) are expanded as polynomials in gamma, so that for given A(s) and B(s) the integrations need only be done once. The method was used to find optimal constrained parabolic approximation to a wide variety of given curves

Cloth Seals at Iroquois Sites

Textiles represent a very significant component of the Dutch goods that were exported to New Netherland for trade with the Iroquois Indians. These textiles varied greatly in quality. These differences were indicated on lead cloth seals that were affixed to the cloths. The lead cloth seals that are excavated at Iroquois sites provide useful information about the origins and quality of the traded cloth; They also .are a source of information about Dutch textile manufacture in the 17th century, a period during which the cloth industry was the most important urban industry in the Netherlands. Amsterdam was the staple market from , which a,n kinds of textiles from various towns a,:d cities were exported. Amsterdam itselJ was specialized in the dyeing of cloth. A catalogue of the lead cloth seals found at Iroquois and Dutch sites, in New Netherland reveals that. between 1630 and 1670, four Dutch cities were represent~\u27d: Kampen, Leiden, Haarlem, and Amsterdam. There are both round and tubular seals from Kampen. Leiden seals are prima7;ily round. The Amsterdam seals found in Iroquois sites are all seals that verify the quality of the dyeing of the doth. \u27 Haarlem is represented by just one seal, found in Albany, suggesting that cloth from Haarlem was used by the Dutch .colonists themselves, rather than for the trade with the Iroquois. The numbers scratcl:zed on cloth seals indicate cloth lengths. Actual textile fragments excavated at some Iroquois sites represent coarse duffels probably from Kampen as well as finer cloth types probably from Amsterdam. Based on the excavated cloth seals, it can be concluded that most of the cloth fC!r trade with the Iroquois came from Kilmpen

Nanosecond-timescale spin transfer using individual electrons in a quadruple-quantum-dot device

The ability to coherently transport electron-spin states between different sites of gate-defined semiconductor quantum dots is an essential ingredient for a quantum-dot-based quantum computer. Previous shuttles using electrostatic gating were too slow to move an electron within the spin dephasing time across an array. Here we report a nanosecond-timescale spin transfer of individual electrons across a quadruple-quantum-dot device. Utilizing enhanced relaxation rates at a so-called `hot spot', we can upper bound the shuttle time to at most 150 ns. While actual shuttle times are likely shorter, 150 ns is already fast enough to preserve spin coherence in e.g. silicon based quantum dots. This work therefore realizes an important prerequisite for coherent spin transfer in quantum dot arrays.Comment: 7 pages including 2 pages of supplementary materia

Coherent shuttle of electron-spin states

We demonstrate a coherent spin shuttle through a GaAs/AlGaAs quadruple-quantum-dot array. Starting with two electrons in a spin-singlet state in the first dot, we shuttle one electron over to either the second, third or fourth dot. We observe that the separated spin-singlet evolves periodically into the $m=0$ spin-triplet and back before it dephases due to nuclear spin noise. We attribute the time evolution to differences in the local Zeeman splitting between the respective dots. With the help of numerical simulations, we analyse and discuss the visibility of the singlet-triplet oscillations and connect it to the requirements for coherent spin shuttling in terms of the inter-dot tunnel coupling strength and rise time of the pulses. The distribution of entangled spin pairs through tunnel coupled structures may be of great utility for connecting distant qubit registers on a chip.Comment: 21 pages, 10 figure