Combinatorial Lie bialgebras of curves on surfaces

Goldman (Invent. Math. 85(2) (1986) 263) and Turaev (Ann. Sci. Ecole Norm. Sup. (4) 24 (6) (1991) 635) found a Lie bialgebra structure on the vector space generated by non-trivial free homotopy classes of curves on a surface. When the surface has non-empty boundary, this vector space has a basis of cyclic reduced words in the generators of the fundamental group and their inverses. We give a combinatorial algorithm to compute this Lie bialgebra on this vector space of cyclic words. Using this presentation, we prove a variant of Goldman's result relating the bracket to disjointness of curve representatives when one of the classes is simple. We exhibit some examples we found by programming the algorithm which answer negatively Turaev's question about the characterization of simple curves in terms of the cobracket. Further computations suggest an alternative characterization of simple curves in terms of the bracket of a curve and its inverse. Turaev's question is still open in genus zero.     

Self-intersections in combinatorial topology: statistical structure

Oriented closed curves on an orientable surface with boundary are described up to continuous deformation by reduced cyclic words in the generators of the fundamental group and their inverses. By self-intersection number one means the minimum number of transversal self-intersection points of representatives of the class. We prove that if a class is chosen at random from among all classes of m letters, then for large m the distribution of the self-intersection number approaches the Gaussian distribution. The theorem was strongly suggested by a computer experiment with four million curves producing a very nearly Gaussian distribution.     

Spontaneous Assembly of Magnetic LEGO Bricks

This paper describes simple methods of demonstrating macroscale spontaneous assembly. These demonstrations can illustrate topics in college or high school chemistry courses, such as the thermodynamics of crystallization and the chelate effect. The assembling units are built from a combination of magnetic and conventional LEGO building blocks. Unlike many other spontaneous-assembly experiments, these assemblies do not require surface flotation to form.     

Zum Nachweis des Titans und Cyans

Ohne Zusammenfassung     

Structure elucidation and stereoselective total synthesis of pavettamine, the causal agent of gousiekte

The structure elucidation of a novel natural product pavettamine (1), the causal agent of the plant toxicosis gousiekte, is reported. The structure was defined by analysis of NMR and MS data and the relative configuration followed from the ¹³C NMR data of the acetonide derivative. The absolute stereochemistry was established by total synthesis from (2S)-malic acid using chiral sulfoxide methodology as (2S,4R,8R,10S)-1,11-diamino-6-aza-undecane-2,4,8,10-tetraol.     

Direct observation of spin-forbidden formation of O(D) in the near-UV photolysis of ozone

Time-of-flight measurements have been made of the O(¹D) fragment following the photolysis of ozone in the near-UV. At 321.9 nm fragments are seen with kinetic energies the values of which are those expected from spin-forbidden dissociation with ground state O₂(X³Σ_g⁻) molecules as the co-product. Spin-allowed dissociation of internally excited ozone molecules is also seen to produce translationally cold O(¹D) and O₂(a¹Δ_g) products. The implications for the dissociation of tropospheric ozone are briefly discussed.     

Theoretical and experimental correlations of gas dissolution, diffusion, and thermodynamic properties in determination of gas permeability and selectivity in supported ionic liquid membranes

Supported ionic liquid membranes (SILMs) has the potential to be a new technological platform for gas/organic vapour separation because of the unique non-volatile nature and discriminating gas dissolution properties of room temperature ionic liquids (ILs). This work starts with an examination of gas dissolution and transport properties in bulk imidazulium cation based ionic liquids [C(n)mim][NTf2] (n=2.4, 6, 8.10) from simple gas H(2), N(2), to polar CO(2), and C(2)H(6), leading to a further analysis of how gas dissolution and diffusion are influenced by molecular specific gas-SILMs interactions, reflected by differences in gas dissolution enthalpy and entropy. These effects were elucidated again during gas permeation studies by examining how changes in these properties and molecular specific interactions work together to cause deviations from conventional solution-diffusion theory and their impact on some remarkably contrasting gas perm-selectivity performance. The experimental perm-selectivity for all tested gases showed varied and contrasting deviation from the solution-diffusion, depending on specific gas-IL combinations. It transpires permeation for simpler non-polar gases (H(2), N(2)) is diffusion controlled, but strong molecular specific gas-ILs interactions led to a different permeation and selectivity performance for C(2)H(6) and CO(2). With exothermic dissolution enthalpy and large order disruptive entropy, C(2)H(6) displayed the fastest permeation rate at increased gas phase pressure in spite of its smallest diffusivity among the tested gases. The C(2)H(6) gas molecules "peg" on the side alkyl chain on the imidazulium cation at low concentration, and are well dispersed in the ionic liquids phase at high concentration. On the other hand strong CO(2)-ILs affinity resulted in a more prolonged "residence time" for the gas molecule, typified by reversed CO(2)/N(2) selectivity and slowest CO(2) transport despite CO(2) possess the highest solubility and comparable diffusivity in the ionic liquids. The unique transport and dissolution behaviour of CO(2) are further exploited by examining the residing state of CO(2) molecules in the ionic liquid phase, which leads to a hypothesis of a condensing and holding capacity of ILs towards CO(2), which provide an explanation to slower CO(2) transport through the SILMs. The pressure related exponential increase in permeations rate is also analysed which suggests a typical concentration dependent diffusion rate at high gas concentration under increased gas feed pressure. Finally the strong influence of discriminating and molecular specific gas-ILs interactions on gas perm-selectivity performance points to future specific design of ionic liquids for targeted gas separations.     

Biocalorimetry as a process analytical technology process analyser; robust in-line monitoring and control of aerobic fed-batch cultures of crabtree-negative yeast cells

Control of bioprocesses requires reliable and robust on- or in-line monitoring tools providing real-time information on process dynamics. Heat generation related to metabolic activity of living systems is currently gaining importance in bioprocess industry due to its non-invasive and essentially instantaneous characteristics. This study deals with monitoring and control of pure aerobic fed-batch cultures of three Crabtree-negative yeast strains, Kluyveromyces marxianus, Candida utilis and Pichia pastoris, based on in-line measured, metabolic heat flow signals. A high resolution biocalorimeter (BioRC1) was developed from a standard bench-scale heat flow calorimeter (RC1). The BioRC1 was equipped with in-line (dielectric spectroscopy, pH probe and dissolved oxygen probe) and at-line (exit gas analyser) sensors to characterise the growth behaviour of the yeast cells. Both metabolic heat flow and biomass profiles exhibited similar behaviour proving the significance of employing heat flow signal as a key-parameter for the system under investigation. A simple estimator for biomass concentration and specific growth rate was formulated based on heat flow values. In order to evaluate the potential of calorimetry as a reliable and powerful process monitoring tool, the robustness, reliability as well as the broad applicability of the developed estimators was assessed through comparison with off-line measurement techniques and showed promising results for general applicability with a wide range of bioprocesses.