The Landau-Lifshitz equation,elliptic curves and the ward transform

The Landau-Lifshitz (LL) equation is studied from a point of view that is close to that of Segal and Wilson's work on KdV. The LL hierarchy is defined and shown to exist using a dressing transformation that involves parameters ₁, ₂, ₃ that live on an elliptic curve . The crucial role of the groupK ₂ × ₂ of translations by the half-periods of and its non-trivial central extension is brought out and an analogue of Birkhoff factorisation for -equivariant loops in is given. This factorisation theorem is given two treatments, one in terms of the geometry of an infinite-dimensional Grassmannian, and the other in terms of the algebraic geometry of bundles over . Further, a Ward-like transform between a class of holomorphic vector bundles on the total spaceZ of a line-bundle over and solutions of LL is constructed. An appendix is devoted to a careful definition of the Grassmannian of the Frechet spaceC (S ¹).     

Time variations in environmental pollution

Two programmes of work are described involving the measurement of environmental pollution over periods from two hours to many years. The long period measurements are deduced from neutron activation analysis of whole wood samples taken from individual tree rings for trees grown in various locations, and some results for cadmium, antimony and germanium levels are reported. In a second series of experiments the concentration of airborne particulate matter is being measured using a moving filter (streak sampler) technique to give a continuous record with two hour resolution. The filter samples are being analysed by proton induced X-ray emission (PIXE) and preliminary data is presented.     

The temperature dependence of the d-electron dipole strengths of cobalt(II) tetrahalides

The dipole strengths of the ⁴A₂ → ⁴T₁(F), ⁴T₁(P), d-electron transitions of the cobalt(II) tetrahalides are found to decrease with an increase in temperature, in agreement with a dynamic ligand-polarisation model for the absorption mechanism. The reduction in dipole strength is accounted for by a decrease in the coulombic coupling between the quadrupole moment of the d-electron transition of the metal ion and the transient electric dipole moment induced in the ligands, due to the anharmonic increase in the mean bond length and the progressively larger mean-square amplitudes of the bending modes of the complex ion in its ground electronic state as the temperature is raised.     

Electronic absorption and MCD spectra for Pt(AuPPh3)8(2+) and Au(AuPPh3)8(3+) cluster complexes in poly(methyl methacrylate) thin films at 295 and 10 K

Electronic absorption and 8 T magnetic circular dichroism (MCD) spectra are reported for nitrate salts of Pt(AuPPh3)8(2+) and Au(AuPPh3)8(3+) in poly(methyl methacrylate) (PMM) thin films at 295 and 10 K in the vis-UV region from 1.6 to 3.6 microm(-1) (1 microm(-1) = 10(4) cm(-1). Enhanced resolution is observed at low temperature, especially for Pt(AuPPh3)8(2+), which emphasizes the differences in the nature of the low-energy excited configurations and states between Pt(AuPPh3)8(2+) and Au(AuPPh3)8(3+). The absorption and MCD spectra for Pt(AuPPh3)8(2+) are interpreted in terms of a combination of excitations from filled Pt 5d orbitals to empty Au framework 6s orbitals and intraframework Au8(2+) (IF) transitions, whereas the spectra for Au(AuPPh3)8(3+) are ascribed entirely to Au IF transitions.     

Cooperative hydrogen-bonding effects in a water square: a single-crystal neutron and partial atomic charges and hardness analysis study

Four isomorphous complexes of formula [M(L)(4)(H(2)O)(2)]SO(4).2H(2)O (M = Co, 1a; Ni, 1b; Cu, 1c; Zn, 1d) have been isolated and characterized by single-crystal X-ray diffraction and neutron diffraction using the quasi-Laue diffractometer VIVALDI at the Institut Laue-Langevin as well as by thermogravimetric analysis. The structures contain a discrete, strongly hydrogen-bonded water tetramer which causes a significant distortion of the metal coordination sphere in each case. Partial atomic charges and hardness analysis (PACHA) calculations reveal that the shortest hydrogen bonds are not the strongest in this constrained, cyclic solid-state structure and show that the distortion at the metal center is caused by the drive to maintain the integrity of the water tetramer. The system undergoes a disorder-order transition on slow cooling that provides insight into the nature of communication between water squares.     

Comparison of whole blood, plasma and nails as monitors for the dietary intake of selenium

Haem peroxidases are globular proteins with an iron-porphyrin complex as prosthetic group. They catalyze the oxidation of substrate by peroxides, frequently via free-radical intermediates. The catalytic cycle involves changes in the redox states of the prosthetic group, that can be monitored by changes in the intense absorption spectra. During the past decades, considerable scientific effort has been put into the elucidation of the mechanisms of reactions catalyzed by these enzymes. Radiation-chemical techniques have made an important contribution by providing information on the redox states of the enzymes and their interconversions, as well as on the properties of the free-radical intermediates involved.     

Bis(m-phenylene)-32-crown-10-based cryptands, powerful hosts for paraquat derivatives

Four new bis(m-phenylene)-32-crown-10-based cryptands with different third bridges were prepared. Their complexes with paraquat derivatives were studied by proton NMR spectroscopy, mass spectrometry, and X-ray analysis. It was found that these cryptands bind paraquat derivatives very strongly. Specifically, a diester cryptand with a pyridyl nitrogen atom located at a site occupied by either water or a PF(6) anion in analogous complexes exhibited the highest association constant K(a) = 5.0 x 10(6) M(-1) in acetone with paraquat, 9000 times greater than the crown ether system. X-ray structures of this and analogous complexes demonstrate that improved complexation with this host is a consequence of preorganization, adequate ring size for occupation by the guest, and the proper location of the pyridyl N-atom for binding to the beta-pyridinium hydrogens of the paraquat guests. This readily accessible cryptand is one of the most powerful hosts reported for paraquats.     

Neutron Diffraction Analysis of H3Co2[C5H2(t-Bu)3]2, a Molecule with a Triply Hydrogen-Bridged Metal–Metal Bond: Some Comments on Structural Patterns in M(μ-H)nM Systems (n=1, 2, 3, 4)

The structure of H₃Co₂[C₅H₂(t-Bu)₃]₂ has been analyzed by low-temperature single-crystal neutron diffraction techniques, and shown to consist of two CoCp moieties with three hydride ligands bridging the central Co–Co bond. Despite a fairly extensive twinning problem, the structure could be solved and successfully refined to a final R factor of 9.2% for 2024 reflections. Average molecular parameters in the H₃Co₂ core of the molecule are as follows: Co–Co=2.275(21) Å, Co–H=1.637(16) Å, HH=2.050(20) Å, Co–H–Co=88.0(9)°, H–Co–H=77.0(7)°. Also included in this paper is a discussion on the molecular dimensions of symmetric hydride-bridged dinuclear systems (M(-H)_nM, n=1, 2, 3, 4) that have been studied to date by neutron diffraction.     

Anisotropic contributions in the ligand polarization model for the f-f transition probabilities of Eu(III) complexes

The intensities of the ΔM = ± 1 component of the ⁷f_o→ ⁵D₂ transition in D₃ complexes containing the [ EuO₉] cluster, and of other d-d or f-f transitions in D₃ complexes with the yz- and xz-components of the electric quadrupole as the leading moment, are found to be dependent upon the polarizability anisotropy of the ligands. The expectation is supported by determinations of the single-crystal absorption intensities of Na₃ [Eu(diglycollate)₃]·2NaClO₄·6H₂O and [Eu(H₂O)₉] (C₂H₅SO₄)₃.