Quest for frustration driven distortion in Y2(Mo2)O(7)

We investigated the nature of the freezing in the geometrically frustrated Heisenberg spin glass Y2(Mo2)O(7) by measuring the temperature dependence of the static internal magnetic field distribution above the spin-glass temperature, Tg, using the muon spin relaxation technique. The evolution of the field distribution cannot be explained by changes in the spin susceptibility alone and suggests a lattice deformation. This possibility is addressed by numerical simulations of the Heisenberg Hamiltonian with magnetoelastic coupling at T > 0.     

A high-speed optical multi-drop bus for computer interconnections

Buses have historically provided a flexible communications structure in computer systems. However, signal integrity constraints of high-speed electronics have made multi-drop electrical buses infeasible. Instead, we propose an optical data bus for computer interconnections. It has two sets of optical waveguides, one as a fan-out and the other as a fan-in, that are used to interconnect different modules attached to the bus. A master module transmits optical signals which are received by all the slave modules attached to the bus. Each slave module in turn sends data back on the bus to the master module. Arrays of lasers, photodetectors, waveguides, microlenses, beamsplitters, and Tx/Rx integrated circuits are used to realize the optical data bus. With 1 mW of laser power, we are able to interconnect eight different modules at 10 Gb/s per channel. An aggregate bandwidth of over 25 GB/s is achievable with 10-bit wide signaling paths.     

Compensation of beam walk-off in hollow metal waveguides

Hollow metal waveguides feature well collimated beams and small losses across air gaps. This enables introduction of multiple optical beam splitters, or taps, along the waveguide to multicast signals from a source to multiple receivers. The splitters need to be of sufficient thickness to provide mechanical integrity and ease of handling. As a result, passing through the thickness leads to a beam walk-off. Walk-off dependence on the splitter thickness and its effect on the system optical efficiency are investigated. Two methods to compensate the walk-off are described: by offsetting the outgoing waveguide, and by introducing an additional symmetric optical element to shift the beam back to the original optical path. Both methods have been shown to effectively mitigate the walk-off effects.     

Free-space optical links for board-to-board interconnects

We describe two free-space optical links for multichannel optical interconnects. The targeted aggregate data rate is 240 Gb/s. In one implementation we use a unique implementation of telecentric optics and achieved an optical link that is simple, robust, and modular. We describe a simple, inexpensive telecentric lens that can accommodate all optical channels within a 1-mm-diameter sweet zone. We also describe the performance of an optical link with a 4×4 array of VCSELs and matching detectors. The integrity of the optical link is not significantly degraded with a>±2 mm translational misalignment between the VCSEL and detector arrays. With the telecentric optical link, we need only two low-bandwidth, single-axis active servomechanisms to compensate for static tilt and possibly low-frequency thermally-driven shift between the transmitter and receiver arrays. In the other implementaion we use two matching arrays of 1×12 optical fibers. Data are coupled optically through an air gap of 2 mm by means of a pair of collimating microlens arrays that are aligned to one another via precision mechanical subassemblies. We describe a simple, inexpensive, and robust mechanical coupling for the optical link achieved by using miniature high-flux magnets.     

Nonassociative Strict Deformation Quantization of C*-Algebras and Nonassociative Torus Bundles

In this paper, we initiate the study of nonassociative strict deformation quantization of C*-algebras with a torus action. We shall also present a definition of nonassociative principal torus bundles, and give a classification of these as nonassociative strict deformation quantization of ordinary principal torus bundles. We then relate this to T-duality of principal torus bundles with H-flux. In particular, the Octonions fit nicely into our theory.     

Arithmetic Properties of Eigenvalues of Generalized Harper Operators on Graphs

Let denote the field of algebraic numbers in A discrete group G is said to have the σ-multiplier algebraic eigenvalue property, if for every matrix A ∈ M_d((G, σ)), regarded as an operator on l²(G)^d, the eigenvalues of A are algebraic numbers, where σ ∈ Z²(G, ) is an algebraic multiplier, and denotes the unitary elements of . Such operators include the Harper operator and the discrete magnetic Laplacian that occur in solid state physics. We prove that any finitely generated amenable, free or surface group has this property for any algebraic multiplier σ. In the special case when σ is rational (σⁿ=1 for some positive integer n) this property holds for a larger class of groups containing free groups and amenable groups, and closed under taking directed unions and extensions with amenable quotients. Included in the paper are proofs of other spectral properties of such operators. The second and third authors acknowledge support from the Australian Research Council.     

Organocatalyzed cycloaddition reactions of azomethine imines—A lookback

The versatile and convergent nature of 1,3-dipolar cycloaddition reactions has made them an indispensable tool in organic chemistry for synthesizing five-membered heterocycles. Among the various dipoles, azomethine imines (AMI) constitute a versatile class, increasingly used to synthesize biologically relevant heterocycles. The organocatalytic cycloaddition reactions of azomethine imines are relatively unexplored compared to the corresponding transition metal-catalyzed reactions. This review highlights the unique organocatalytic cycloaddition reactions of AMI with different dipolarophiles. The cycloaddition of azomethine imines catalyzed by organic bases such as prolinol, proline, alkaloids, 1,4-diazabicyclo[2.2.2]octane, 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU), primary amines, tertiary amines, N-heterocyclic carbene, and phosphine are discussed here. The mechanistic and electronic aspects, including broad functional group tolerance, catalyst loading, and reaction conditions, are evaluated. This review also demonstrates the scope and potential reactivity of azomethine imines in organocatalytic cycloadditions. We are positive that the reactions of azomethine imines discussed here will aid in discovering new and efficient reaction pathways in synthesizing biologically active and industrially relevant molecules.