Rydberg atoms are atoms with one electron excited to an orbital with very high principal quantum number, giving rise to exaggerated properties such as high sensitivity to external fields and extremely strong and tunable interactions. After reviewing the relevant single particle properties of rubidium Rydberg atoms, we calculate the interaction strengths between atoms occupying either of two Rydberg S-states. Interactions in the van der Waals regime are considered, and in the presence of electric fields. When the principal quantum numbers of the two atoms differ by one, an interaction process can occur in which the two atoms swap states. It is shown how quantum simulations of several paradigmatic spin systems known from condensed matter physics can be realised, by arranging many interacting Rydberg atoms on a lattice. Besides a previously known quantum Ising model, novel Rydberg implementations are found of a spin-1 system and the famous Heisenberg XXZ model. External electric fields allow tuning through a large parameter regime. The inclusion of a second Rydberg level is essential; it provides a key ingredient in the form of the swapping interaction. The work presented in this Chapter has been performed in collaboration with R. Nath and T. Pohl. Parts of Sec. 2.4 of this Chapter will be submitted for publication.

Quantum engineering with ultracold atoms

This anatomical study sought to investigate the morphological characteristics and biomechanical properties of the oblique popliteal ligament (OPL). Embalmed cadaveric knees were used for the study. The OPL and its surrounding structures were dissected; its morphology was carefully observed, analyzed and measured; its biomechanical properties were investigated. The origins and insertions of the OPL were relatively similar, but its overall shape was variable. The OPL had two origins: one originated from the posterior surface of the posteromedial tibia condyle, merged with fibers from the semimembranosus tendon, the other originated from the posteromedial part of the capsule. The two origins converged and coursed superolaterally, then attached to the fabella or to the tendon of the lateral head of the gastrocnemius and blended with the posterolateral joint capsule. The OPL was classified into Band-shaped, Y-shaped, Z-shaped, Trident-shaped, and Complex-shaped configurations. The mean length, width, and thickness of the OPL were 39.54, 22.59, and 1.44 mm, respectively. When an external rotation torque (18 N·m) was applied both before and after the OPL was sectioned, external rotation increased by 8.4° (P = 0.0043) on average. The OPL was found to have a significant role in preventing excessive external rotation and hyperextension of the knee.

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Anatomical Characteristics and Biomechanical Properties of the Oblique Popliteal Ligament

Pseudorigid bodies are regarded here as globally constrained threedimensional homogeneous continua. The constraint reaction stresses play a fundamental role in maintaining the homogeneity of the de...

Pseudo-rigid continua: basic theory and a geometrical derivation of Lagrange's equations

Davies Gilbert's work on the catenary is notable on two counts. First, it influenced Thomas Telford in formulating his final design for the Menai Strait suspension bridge (1826); and second, it est...

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2014.0346

An amateur's contribution to the design of Telford's Menai Suspension Bridge: a commentary on Gilbert (1826) On the mathematical theory of suspension bridges

Scientific Reports 7: Article number: 42698; published online: 16 February 2017; updated: 10 April 2017 This Article contains an error in the Discussion section. “Even so, there remains an area without external support between the OPL, the expansion over the popliteus muscle, and the lateral side ofthe posterior cruciate ligament, which are strongly related to the formation of popliteal cysts”.

Corrigendum: Anatomical Characteristics and Biomechanical Properties of the Oblique Popliteal Ligament.

THIS volume finishes Dr. Routh's work on the subject of analytical statics, the first volume of which was reviewed in NATURE, June 16, 1892. It contains, in three long Sections or Books, the subjects of Attraction, Bending of Rods, and Astatics, left over from Vol. I. A Treatise on Analytical Statics. With numerous Examples. Vol. II. By Edward John Routh. (Cambridge: at the University Press, 1892.)

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A. G. Greenhill

Papers

A Treatise on Analytical Statics