A magneto-optically modulated CH3OH laser for Faraday rotation measurements in Tokamaks

Distortion-free intracavity polarization modulation of an optically pumped CH₃OH laser is shown to be viable. The possible use of this modulation technique to make a multichannel Faraday rotation measurement on a Tokamak device is discussed. In addition, the CdTe Faraday modulator employed in this study is shown to have an anomalously large Verdet constant.     

Infrared and Raman imaging of biological and biomimetic samples

Established methods for imaging of biological or biomimetic samples, such as fluorescence and optical microscopy, magnetic resonance imaging (MRI), X-ray tomography or positron emission tomography (PET) are currently complemented by infrared (both near-IR and mid-IR) as well as Raman spectroscopic imaging, whether it be on a microscopic or macroscopic scale. These vibrational spectroscopic techniques provide a wealth of information without a priori knowledge of either the spectral data or the composition of the sample. Infrared radiation does not harm the organism, no electric potential needs to be applied, and the measurements are not influenced by electromagnetic fields. In addition, no extrinsic labeling or staining, which may perturb the system under investigation, has to be added. The immense volume of information contained in spectroscopic images requires multivariate analysis methodologies in order to effectively mine the chemical and spatial information contained within the data as well as to analyze a time-series of images in order to reveal the origin of a chemical or biochemical process. The promise and limitations of this new analytical tool are surveyed in this review.     

Moving Frames and Conservation Laws for Euclidean Invariant Lagrangians

In recent work, the authors show the mathematical structure behind both the Euler–Lagrange system and the set of conservation laws, in terms of the differential invariants of the group action and a moving frame. In this paper, the authors demonstrate that the knowledge of this structure allows to find the first integrals of the Euler–Lagrange equations, and subsequently, to solve by quadratures, variational problems that are invariant under the special Euclidean groups SE(2) and SE(3) .     

On Moving Frames and Noether’s Conservation Laws

Noether’s Theorem yields conservation laws for a Lagrangian with a variational symmetry group. The explicit formulae for the laws are well known and the symmetry group is known to act on the linear space generated by the conservation laws. The aim of this paper is to explain the mathematical structure of both the Euler‐Lagrange system and the set of conservation laws, in terms of the differential invariants of the group action and a moving frame. For the examples, we demonstrate, knowledge of this structure allows the Euler‐Lagrange equations to be integrated with relative ease. Our methods take advantage of recent advances in the theory of moving frames by Fels and Olver, and in the symbolic invariant calculus by Hubert. The results here generalize those appearing in Kogan and Olver [ 1 ] and in Mansfield [ 2 ]. In particular, we show results for high‐dimensional problems and classify those for the three inequivalent SL(2) actions in the plane.     

Efficient knot group identification as a tool for studying entanglements of polymers

A technique is presented for the identification of the knot group of knots, links, and other embedded graphs as a tool in numerical studies of entanglements of polymers. With this technique, the knot group is simultaneously more discriminating and easier to calculate than the knot invariants that have been used in such studies in the past. It can be applied even in cases of very complex knot projections with hundreds of crossings. Starting from an arbitrary projection of an embedded graph, we generate a sequence of representations, any one of which is a full and complete representation of the knot group. Any two knot groups are isomorphic if they have identical representations. Therefore, we compare the sequence of representations of any given knot or link against a previously determined lookup table, and if the group of the knot or link is represented in this table we eventually find a match and identify the knot group.     

Enhanced energy confinement and performance in a low-recycling tokamak

Extensive lithium wall coatings and liquid lithium plasma-limiting surfaces reduce recycling, with dramatic improvements in Ohmic plasma discharges in the Current Drive Experiment-Upgrade. Global energy confinement times increase by up to 6 times. These results exceed confinement scalings such as ITER98P(y,1) by 2-3 times, and represent the largest increase in energy confinement ever observed for an Ohmic tokamak plasma. Measurements of Dalpha emission indicate that global recycling coefficients decrease to approximately 0.3, the lowest documented for a magnetically confined hydrogen plasma.     

Lithium and aluminium complexes supported by chelating phosphaguanidinates

Diisopropylcarbodiimide, (i)PrN[double bond, length as m-dash]C[double bond, length as m-dash]N(i)Pr, inserts into the lithium-phosphorus bond of in situ prepared "Ph(2)PLi(THF)(n)" to afford the lithium salt, [Li(Ph(2)PC{N(i)Pr}(2))(THF)(n)](x)(2a); alternatively, this compound can be made by deprotonation of the neutral phosphaguanidine, Ph(2)PC{N(i)Pr}{NH(i)Pr}(1a) with (n)BuLi. Displacement of the THF solvate in 2a is readily achieved with TMEDA to afford Li(Ph(2)PC{N(i)Pr}(2))(TMEDA)(3a). X-Ray crystallographic analyses show that 2a exists as a dimer in the solid state with a folded ladder structure and an N,N' chelating phosphaguanidinate, while 3a is monomeric with N,P-coordination of the ligand to lithium. Compound 2a reacts via a transmetallation pathway with AlMe(2)Cl to afford the dimethylaluminium complex, Al(Ph(2)PC{N(i)Pr}(2))Me(2)(4a), which can also be prepared by protonation of a methyl group of AlMe(3) using 1a. The formation of a series of dialkylaluminium compounds has been investigated employing this latter pathway using both 1a and the N,N'-dicyclohexyl analogue, Ph(2)PC{NCy}{NHCy}(1b), affording Al(Ph(2)PC{NR}(2))Et(2)(5a,b), Al(Ph(2)PC{NR}(2))(i)Bu(2)(6a,b) and the diphenylaluminium compound Al(Ph(2)PC{N(i)Pr}(2))Ph(2)(7a). The oily nature of most of the dialkyl compounds and high sensitivity to oxygen and moisture lead to difficulty in manipulation and characterization; however, NMR spectroscopy indicated highly pure products (>95%) upon removal of the solvent. The molecular structures of the crystalline examples 4a and 7a are reported, showing monomeric aluminium species with symmetrically chelating phosphaguanidinate ligands. The series of aluminium compounds AlLCl(2){L=[EC{NiPr}(2)](-): A, E=Me; B, E=Me(2)N; C, E=(Me(3)Si)(2)N and D, E=Ph(2)P} were investigated using density functional theory. In the more simple cases A and B, the delocalized electron density of the metallacycle was represented by a combination of the HOMO and an orbital of lower energy (A, HOMO-5; B, HOMO-6). The HOMO-1 in B was pi-bonded across the Me(2)N-C bond suggesting delocalization of electron density into the metallacycle. In the more complex systems C and D, delocalization within the metallacycle was less extensive due to the (Me(3)Si)(2)N- and Ph(2)P-moieties. A number of occupied orbitals in D, however, display phosphorus 'lone-pair' characteristics, indicating that these species have the potential to behave as Lewis bases in the formation of poly(metallic) systems.