Kontsevich integral for knots and Vassiliev invariants

We review quantum field theory approach to the knot theory. Using holomorphic gauge we obtain the Kontsevich integral. It is explained how to calculate Vassiliev invariants and coefficients in Kontsevich integral in a combinatorial way which can be programmed on a computer. We discuss experimental results and temporal gauge considerations which lead to representation of Vassiliev invariants in terms of arrow diagrams. Explicit examples and computational results are presented.Comment: 25 pages, 17 figure

Explicit computation of Drinfeld associator in the case of the fundamental representation of gl(N)

We solve the regularized Knizhnik-Zamolodchikov equation and find an explicit expression for the Drinfeld associator. We restrict to the case of the fundamental representation of $gl(N)$. Several tests of the results are presented. It can be explicitly seen that components of this solution for the associator coincide with certain components of WZW conformal block for primary fields. We introduce the symmetrized version of the Drinfeld associator by dropping the odd terms. The symmetrized associator gives the same knot invariants, but has a simpler structure and is fully characterized by one symmetric function which we call the Drinfeld prepotential.Comment: 14 pages, 2 figures; several flaws indicated by referees correcte

Magnetic induction mapping of magnetite chains in magnetotactic bacteria at room temperature and close to the Verwey transition using electron holography

Off-axis electron holography in the transmission electron microscope is used to record magnetic induction maps of closely spaced magnetite crystals in magnetotactic bacteria at room temperature and after cooling the sample using liquid nitrogen. The magnetic microstructure is related to the morphology and crystallography of the particles, and to interparticle interactions. At room temperature, the magnetic signal is dominated by interactions and shape anisotropy, with highly parallel and straight field lines following the axis of each chain of crystals closely. In contrast, at low temperature the magnetic induction undulates along the length of the chain. This behaviour may result from a competition between interparticle interactions and an easy axis of magnetisation that is no longer parallel to the chain axis. The quantitative nature of electron holography also allows the change in magnetisation in the crystals with temperature to be measured

Non-adiabatic spin torque investigated using thermally activated magnetic domain wall dynamics

Using transmission electron microscopy, we investigate the thermally activated motion of domain walls (DWs) between two positions in permalloy (Ni80Fe20) nanowires at room temperature. We show that this purely thermal motion is well described by an Arrhenius law, allowing for a description of the DW as a quasi-particle in a 1D potential landscape. By injecting small currents, the potential is modified, allowing for the determination of the non-adiabatic spin torque: the non-adiabatic coefficient is 0.010 +/- 0.004 for a transverse DW and 0.073 +/- 0.026 for a vortex DW. The larger value is attributed to the higher magnetization gradients present

Characterization of Fe-N nanocrystals and nitrogen–containing inclusions in (Ga,Fe)N thin films using transmission electron microscopy

Nanometric inclusions filled with nitrogen, located adjacent to FenN (n¼3 or 4) nanocrystals within (Ga,Fe)N layers, are identified and characterized using scanning transmission electron microscopy (STEM) and electron energy-loss spectroscopy (EELS). High-resolution STEM images reveal a truncation of the Fe-N nanocrystals at their boundaries with the nitrogen-containing inclusions. A controlled electron beam hole drilling experiment is used to release nitrogen gas from an inclusion in situ in the electron microscope. The density of nitrogen in an individual inclusion is measured to be 1.460.3 g/cm3. These observations provide an explanation for the location of surplus nitrogen in the (Ga,Fe)N layers, which is liberated by the nucleation of FenN (n>1) nanocrystals during growth

Hydrothermal synthesis, off-axis electron holography and magnetic properties of Fe3_{3}O4_{4} nanoparticles

The hydrothermal synthesis of Fe3O4 nanoparticles (NPs) (< 50 nm) from mixed FeCl3 / FeCl2 precursor solution at pH ~ 12 has been confirmed using complementary characterisation techniques of transmission electron microscopy and X-ray diffractometry. Off-axis electron holography allowed for visualisation of their single domain (SD) nature, as well as inter-particle interactions, with the latter attributed to explain the pseudo-SD/multi-domain behaviour demonstrated by bulk magnetic measurements

Hydrological change: reaping prosperity and pain in Australia

International audienceThe adage: "There is no such thing as a free lunch?, is relevant to land-use hydrology in Australia. Changes in land use to achieve greater productivity of food and fibre may have an adverse effect on the water balance and hence on the natural resource capital of a catchment. An altered regime of catchment outflow accompanies those land-use changes which, together with land degradation, impairs available water resources in quantity and quality and threatens enterprise sustainability, notwithstanding the initial improvement in productivity. Central to any hydrological change is an altered pattern of seasonal and annual water use by vegetation that has become modified in function with an amended transpiration fraction of daily evapotranspiration. In Australia, since measurement of evapotranspiration became feasible, the hydrological consequences of changes in land use have been determined, allowing the benefits in terms of plant productivity achieved through enhanced water use efficiency to be weighed against changed catchment outflows, diminished in either quantity or quality. Four case studies are presented as examples of ecological and hydrological changes: two deal with the upland forest environment and two with arable lowlands. In an upland eucalypt forest, following wildfire with subsequent regeneration from natural seedling establishment, substantial reduction in water yield occurred throughout a 50-year period of succession in the even-aged stand. In comparison, the effect of converting eucalypt forest to pine plantations was less detrimental to the yield of water from the catchments, with substantial growth increases over 30 years. In the lowlands, agricultural productivity, both as annual pasture and as crop, far exceeds that of natural perennial grassland and woodland. This increase in productivity comes not so much from any change to the yield of total water outflow but at the expense of water quality, compromised with increased material transport in suspension and solution resulting from accelerated erosion in association with outbreaks of soil salinity and acidity. The present study is aimed at optimising management to give plant production outcomes that ensure environmental protection through resource conservation. In the uplands, harvesting of water is the dominant consideration so that conservative management with limited plant productivity is sought. In the lowlands, the objective is to devise novel ecosystems with profitable plant production that exercises due control on outflow in maintaining the chemical and physical integrity of the edaphic environment

Direct measurement of the charge distribution along a biased carbon nanotube bundle using electron holography

Nanowires and nanotubes can be examined in the transmission electron microscope under an applied bias. Here we introduce a model-independent method, which allows the charge distribution along a nanowire or nanotube to be measured directly from the Laplacian of an electron holographic phase image. We present results from a biased bundle of carbon nanotubes, in which we show that the charge density increases linearly with distance from its base, reaching a value of similar to 0.8 electrons/nm near its tip. (C) 2011 American Institute of Physics. [doi:10.1063/1.3598468

Voids and Mn-rich inclusions in a (Ga,Mn)As ferromagnetic semiconductor investigated by transmission electron microscopy

Voids adjacent to both cubic (ZnS-type) and hexagonal (NiAs-type) Mn-rich nanocrystals are characterized using aberration-corrected transmission electron microscopy in annealed Ga0.995Mn0.005As magnetic semiconductor specimen grown by molecular beam epitaxy. Nano-beam electron diffraction measurements suggest that the nanocrystals exhibit deviations in lattice parameter from that of bulk MnAs. In situ annealing inside the electron microscope is used to study the nucleation, coalescence, and grain growth of individual nanocrystals. After annealing at 903 K, the magnetic transition temperature of the specimen likely to be dominated by the presence of cubic ferromagnetic nanocrystals