The geometry of Lagrangian fibres

If the generic fibre f−1(c) of a Lagrangian fibration f : X → B on a complex Poisson– variety X is smooth, compact, and connected, it is isomorphic to the compactification of a complex abelian Lie–group. For affine Lagrangian fibres it is not clear what the structure of the fibre is. Adler and van Moerbeke developed a strategy to prove that the generic fibre of a Lagrangian fibration is isomorphic to the affine part of an abelian variety.rnWe extend their strategy to verify that the generic fibre of a given Lagrangian fibration is the affine part of a (C∗)r–extension of an abelian variety. This strategy turned out to be successful for all examples we studied. Additionally we studied examples of Lagrangian fibrations that have the affine part of a ramified cyclic cover of an abelian variety as generic fibre. We obtained an embedding in a Lagrangian fibration that has the affine part of a C∗–extension of an abelian variety as generic fibre. This embedding is not an embedding in the category of Lagrangian fibrations. The C∗–quotient of the new Lagrangian fibration defines in a natural way a deformation of the cyclic quotient of the original Lagrangian fibration.

Dynamic wetting of complex liquids

A simple dependency between contact angle θ and velocity or surface tension has been predicted for the wetting and dewetting behavior of simple liquids. According to the hydrodynamic theory, this dependency was described by Cox and Voinov as θ ∼ Ca^(1/3) (Ca: Capillary number). For more complex liquids like surfactant solutions, this prediction is not directly given.rnHere I present a rotating drum setup for studying wetting/dewetting processes of surfactant solutions on the basis of velocity-dependent contact angle measurements. With this new setup I showed that surfactant solutions do not follow the predicted Cox-Voinov relation, but showed a stronger contact angle dependency on surface tension. All surfactants independent of their charge showed this difference from the prediction so that electrostatic interactions as a reason could be excluded. Instead, I propose the formation of a surface tension gradient close to the three-phase contact line as the main reason for the strong contact angle decrease with increasing surfactant concentration. Surface tension gradients are not only formed locally close to the three-phase contact line, but also globally along the air-liquid interface due to the continuous creation/destruction of the interface by the drum moving out of/into the liquid. By systematically hindering the equilibration routes of the global gradient along the interface and/or through the bulk, I was able to show that the setup geometry is also important for the wetting/dewetting of surfactant solutions. Further, surface properties like roughness or chemical homogeneity of the wetted/dewetted substrate influence the wetting/dewetting behavior of the liquid, i. e. the three-phase contact line is differently pinned on rough/smooth or homogeneous/inhomogeneous surfaces. Altogether I showed that the wetting/dewetting of surfactant solutions did not depend on the surfactant type (anionic, cationic, or non-ionic) but on the surfactant concentration and strength, the setup geometry, and the surface properties.rnSurfactants do not only influence the wetting/dewetting behavior of liquids, but also the impact behavior of drops on free-standing films or solutions. In a further part of this work, I dealt with the stability of the air cushion between drop and film/solution. To allow coalescence between drop and substrate, the air cushion has to vanish. In the presence of surfactants, the vanishing of the air is slowed down due to a change in the boundary condition from slip to no-slip, i. e. coalescence is suppressed or slowed down in the presence of surfactant.

Complex tracer mobilities in polymer networks revealed by fluorescence correlation spectroscopy

Gels are elastic porous polymer networks that are accompanied by pronounced mechanical properties. Due to their biocompatibility, ‘responsive hydrogels’ (HG) have many biomedical applications ranging from biosensors and drug delivery to tissue engineering. They respond to external stimuli such as temperature and salt by changing their dimensions. Of paramount importance is the ability to engineer penetrability and diffusion of interacting molecules in the crowded HG environment, as this would enable one to optimize a specific functionality. Even though the conditions under which biomedical devices operate are rather complex, a bottom-up approach could reduce the complexity of mutually coupled parameters influencing tracer mobility. The present thesis focuses on the interaction-induced tracer diffusion in polymer solutions and their homologous gels, probed by means of Fluorescence Correlation Spectroscopy (FCS). This is a single-molecule-sensitive technique having the advantage of optimal performance under ultralow tracer concentrations, typically employed in biosensors. Two different types of hydrogels have been investigated, a conventional one with broad polydispersity in the distance between crosslink points and a so-called ‘ideal’, with uniform mesh size distribution. The former is based on a thermoresponsive polymer, exhibiting phase separation in water at temperatures close to the human body temperature. The latter represents an optimal platform to study tracer diffusion. Mobilities of different tracers have been investigated in each network, varying in size, geometry and in terms of tracer-polymer attractive strength, as perturbed by different stimuli. The thesis constitutes a systematic effort towards elucidating the role of the strength and nature of different tracer-polymer interactions, on tracer mobilities; it outlines that interactions can still be very important even in the simplified case of dilute polymer solutions; it also demonstrates that the presence of permanent crosslinks exerts distinct tracer slowdown, depending on the tracer type and the nature of the tracer-polymer interactions, expressed differently by each tracer with regard to the selected stimulus. In aqueous polymer solutions, the tracer slowdown is found to be system-dependent and no universal trend seems to hold, in contrast to predictions from scaling theory for non-interacting nanoparticle mobility and empirical relations concerning the mesh size in polymer solutions. Complex tracer dynamics in polymer networks may be distinctly expressed by FCS, depending on the specific synergy among-at least some of - the following parameters: nature of interactions, external stimuli employed, tracer size and type, crosslink density and swelling ratio.

Flame Synthesis of Complex Fluoride-Based Nanoparticles as Upconversion Phosphors

Recent improvements in precursor chemistry, reactor geometry and run conditions extend the manufacturing capability of traditional flame aerosol synthesis of oxide nanoparticles to metals, alloys and inorganic complex salts. As an example of a demanding composition, we demonstrate here the one-step flame synthesis of nanoparticles of a 4-element non-oxide phosphor for upconversion applications. The phosphors are characterized in terms of emission capability, phase purity and thermal phase evolution. The preparation of flame-made beta-NaYF4 with dopants of Yb, Tm or Yb, Er furthermore illustrates the now available nanoparticle synthesis tool boxes based on modified flamespray synthesis from our laboratories at ETH Zurich. Since scaling concepts for flame synthesis, including large-scale filtration and powder handling, have become available commercially, the development of industrial applications of complex nanoparticles of metals, alloys or most other thermally stable, inorganic compounds can now be considered a feasible alternative to traditional top-down manufacturing or liquid-intense wet chemistry.

Characterization of granite matrix porosity and pore-space geometry by in situ and laboratory methods

Most available studies of interconnected matrix porosity of crystalline rocks are based on laboratory investigations; that is, work on samples that have undergone stress relaxation and were affected by drilling and sample preparation. The extrapolation of the results to in situ conditions is therefore associated with considerable uncertainty, and this was the motivation to conduct the ‘in situ Connected Porosity’ experiment at the Grimsel Test Site (Central Swiss Alps). An acrylic resin doped with fluorescent agents was used to impregnate the microporous granitic matrix in situ around an injection borehole, and samples were obtained by overcoring. The 3-D structure of the porespace, represented by microcracks, was studied by U-stage fluorescence microscopy. Petrophysical methods, including the determination of porosity, permeability and P -wave velocity, were also applied. Investigations were conducted both on samples that were impregnated in situ and on non-impregnated samples, so that natural features could be distinguished from artefacts. The investigated deformed granites display complex microcrack populations representing a polyphase deformation at varying conditions. The crack population is dominated by open cleavage cracks in mica and grain boundary cracks. The porosity of non-impregnated samples lies slightly above 1 per cent, which is 2–2.5 times higher than the in situ porosity obtained for impregnated samples. Measurements of seismic velocities (Vp ) on spherical rock samples as a function of confining pressure, spatial direction and water saturation for both non-impregnated and impregnated samples provide further constraints on the distinction between natural and induced crack types. The main conclusions are that (1) an interconnected network of microcracks exists in the whole granitic matrix, irrespective of the distance to ductile and brittle shear zones, and (2) conventional laboratory methods overestimate the matrix porosity. Calculations of contaminant transport through fractured media often rely on matrix diffusion as a retardation mechanism.

Upper crustal deformation in continent-continent collision: A case study from the Bernard nappe complex (Valais, Switzerland)

The Penninic nappes in the Swiss Alps formed during continental collision between the Adriatic and European plates in Cenozoic times. Although intensely studied, the finite geometry of the basement-bearing Penninic nappes in western Switzerland has remained a matter of debate for decades (e.g., “Siviez-Mischabel dilemma”) and the paleogeographic origin of various nappes has been disputed. Here, we present new structural data for the central part of the Penninic Bernard nappe complex, which contains pre-Permian basement and Permo-Mesozoic metasedimentary units. Our lithological and structural observations indicate that the discrepancy between the different structural models proposed for the Bernard nappe complex can be explained by a lateral discontinuity. In the west, the presence of a Permian graben caused complex isoclinal folding, whereas in the east, the absence of such a graben resulted mainly in imbricate thrusting. The overall geometry of the Bernard nappe complex is the result of three main deformation phases: (1) detachment of Mesozoic cover sediments along Triassic evaporites (Evolène phase) during the early stages of collision, (2) Eocene top-to-the-N(NW) nappe stacking (Anniviers phase), and (3) subsequent backfolding and backshearing (Mischabel phase). The southward localized backshearing is key to understand the structural position and paleogeographic origin of units, such as the Frilihorn and Cimes Blanches “nappes” and the Antrona ophiolites. Based on these observations, we present a new tectonic model for the entire Penninic region of western Switzerland and discuss this model in terms of continental collision zone processes.

Syntheses, characterization and crystal structures of a new functionalised TTF derivative and its Ni(II) complex

The new ligand 4,5-bis (2-pyridylmethylsulfanyl)-4',5'-bis(cyanoethylthio)tetrathiafulvalene (BPM-BCET-TTF) and its nickel(II) complex have been prepared and crystallographically characterized. The Ni(II) complex shows octahedral geometry around the metal ion with the coordination site occupied by the pyridyl nitrogen atoms, the thioether sulfur atoms of the ligand and cis coordination of the halide ions.

Mathematical Analysis of the Effect of Rotor Geometry on Cup Anemometer Response

The calibration coefficients of two commercial anemometers equipped with different rotors were studied. The rotor cups had the same conical shape, while the size and distance to the rotation axis varied.The analysis was based on the 2-cup positions analytical model, derived using perturbation methods to include second-order effects such as pressure distribution along the rotating cups and friction.Thecomparison with the experimental data indicates a nonuniformdistribution of aerodynamic forces on the rotating cups, with higher forces closer to the rotating axis. The 2-cup analytical model is proven to be accurate enough to study the effect of complex forces on cup anemometer performance.

The making of the architecture of the plant cell wall: How cells exploit geometry

Cell wall deposition is a key process in the formation, growth, and differentiation of plant cells. The most important structural components of the wall are long cellulose microfibrils, which are synthesized by synthases embedded in the plasma membrane. A fundamental question is how the microfibrils become oriented during deposition at the plasma membrane. The current textbook explanation for the orientation mechanism is a guidance system mediated by cortical microtubules. However, too many contraindications are known in secondary cell walls for this to be a universal mechanism, particularly in the case of helicoidal arrangements, which occur in many situations. An additional construction mechanism involves liquid crystalline self-assembly [A. C. Neville (1993) Biology of Fibrous Composites: Development Beyond the Cell Membrane (Cambridge Univ. Press, Cambridge, U.K.)], but the required amount of bulk material that is able to equilibrate thermally is not normally present at any stage of the wall deposition process. Therefore, we have asked whether the complex ordered texture of helicoidal cell walls can be formed in the absence of direct cellular guidance mechanisms. We propose that they can be formed by a mechanism that is based on geometrical considerations. It explains the genesis of the complicated helicoidal texture and shows that the cell has intrinsic, versatile tools for creating a variety of textures. A compelling feature of the model is that local rules generate global order, a typical phenomenon of life.

Ultrafast diffraction and structural dynamics: The nature of complex molecules far from equilibrium

Studies of molecular structures at or near their equilibrium configurations have long provided information on their geometry in terms of bond distances and angles. Far-from-equilibrium structures are relatively unknown—especially for complex systems—and generally, neither their dynamics nor their average geometries can be extrapolated from equilibrium values. For such nonequilibrium structures, vibrational amplitudes and bond distances play a central role in phenomena such as energy redistribution and chemical reactivity. Ultrafast electron diffraction, which was developed to study transient molecular structures, provides a direct method for probing the nature of complex molecules far from equilibrium. Here we present our ultrafast electron diffraction observations of transient structures for two cyclic hydrocarbons. At high internal energies of ≈4 eV, these molecules display markedly different behavior. For 1,3,5-cycloheptatriene, excitation results in the formation of hot ground-state structures with bond distances similar to those of the initial structure, but with nearly three times the average vibrational amplitude. Energy is redistributed within 5 ps, but with a negative temperature characterizing the nonequilibrium population. In contrast, the ring-opening reaction of 1,3-cyclohexadiene is shown to result in hot structures with a C—C bond distance of over 1.7 Å, which is 0.2 Å away from any expected equilibrium value. Even up to 400 ps, energy remains trapped in large-amplitude motions comprised of torsion and asymmetric stretching. These studies promise a new direction for studying structural dynamics in nonequilibrium complex systems.

BeF\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{3}^{-}}}\end{equation*}\end{document} acts as a phosphate analog in proteins phosphorylated on aspartate: Structure of a BeF\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{3}^{-}}}\end{equation*}\end{document} complex with phosphoserine phosphatase

Protein phosphoaspartate bonds play a variety of roles. In response regulator proteins of two-component signal transduction systems, phosphorylation of an aspartate residue is coupled to a change from an inactive to an active conformation. In phosphatases and mutases of the haloacid dehalogenase (HAD) superfamily, phosphoaspartate serves as an intermediate in phosphotransfer reactions, and in P-type ATPases, also members of the HAD family, it serves in the conversion of chemical energy to ion gradients. In each case, lability of the phosphoaspartate linkage has hampered a detailed study of the phosphorylated form. For response regulators, this difficulty was recently overcome with a phosphate analog, BeF\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{3}^{-}}}\end{equation*}\end{document}, which yields persistent complexes with the active site aspartate of their receiver domains. We now extend the application of this analog to a HAD superfamily member by solving at 1.5-Å resolution the x-ray crystal structure of the complex of BeF\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{3}^{-}}}\end{equation*}\end{document} with phosphoserine phosphatase (PSP) from Methanococcus jannaschii. The structure is comparable to that of a phosphoenzyme intermediate: BeF\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{3}^{-}}}\end{equation*}\end{document} is bound to Asp-11 with the tetrahedral geometry of a phosphoryl group, is coordinated to Mg2+, and is bound to residues surrounding the active site that are conserved in the HAD superfamily. Comparison of the active sites of BeF\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{3}^{-}}}\end{equation*}\end{document}⋅PSP and BeF\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{3}^{-}}}\end{equation*}\end{document}⋅CeY, a receiver domain/response regulator, reveals striking similarities that provide insights into the function not only of PSP but also of P-type ATPases. Our results indicate that use of BeF\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{3}^{-}}}\end{equation*}\end{document} for structural studies of proteins that form phosphoaspartate linkages will extend well beyond response regulators.

Fos and Jun bend the AP-1 site: effects of probe geometry on the detection of protein-induced DNA bending.

The effect of Fos and Jun binding on the structure of the AP-1 recognition site is controversial. Results from phasing analysis and phase-sensitive detection studies of DNA bending by Fos and Jun have led to opposite conclusions. The differences between these assays, the length of the spacer between two bends and the length of the sequences flanking the bends, are investigated here using intrinsic DNA bend standards. Both an increase in the spacer length as well as a decrease in the length of flanking sequences resulted in a reduction in the phase-dependent variation in electrophoretic mobilities. Probes with a wide separation between the bends and short flanking sequences, such as those used in the phase-sensitive detection studies, displayed no phase-dependent mobility variation. This shape-dependent variation in electrophoretic mobilities was reproduced by complexes formed by truncated Fos and Jun. Results from ligase-catalyzed cyclization experiments have been interpreted to indicate the absence of DNA bending in the Fos-Jun-AP-1 complex. However, truncated Fos and Jun can alter the relative rates of inter- and intramolecular ligation through mechanisms unrelated to DNA bending, confounding the interpretation of cyclization data. The analogous phase- and shape-dependence of the electrophoretic mobilities of the Fos-Jun-AP-1 complex and an intrinsic DNA bend confirm that Fos and Jun bend DNA, which may contribute to their functions in transcription regulation.

The influence of magnetic field geometry on magnetars X-ray spectra

Nowadays, the analysis of the X-ray spectra of magnetically powered neutron stars or magnetars is one of the most valuable tools to gain insight into the physical processes occurring in their interiors and magnetospheres. In particular, the magnetospheric plasma leaves a strong imprint on the observed X-ray spectrum by means of Compton up-scattering of the thermal radiation coming from the star surface. Motivated by the increased quality of the observational data, much theoretical work has been devoted to develop Monte Carlo (MC) codes that incorporate the effects of resonant Compton scattering (RCS) in the modeling of radiative transfer of photons through the magnetosphere. The two key ingredients in this simulations are the kinetic plasma properties and the magnetic field (MF) configuration. The MF geometry is expected to be complex, but up to now only mathematically simple solutions (self-similar solutions) have been employed. In this work, we discuss the effects of new, more realistic, MF geometries on synthetic spectra. We use new force-free solutions [14] in a previously developed MC code [9] to assess the influence of MF geometry on the emerging spectra. Our main result is that the shape of the final spectrum is mostly sensitive to uncertain parameters of the magnetospheric plasma, but the MF geometry plays an important role on the angle-dependence of the spectra.

Greenland and Antarctic ice sheet topography, cavity geometry, and global bathymetry (RTopo-2), links to NetCDF files

The ocean plays an important role in modulating the mass balance of the polar ice sheets by interacting with the ice shelves in Antarctica and with the marine-terminating outlet glaciers in Greenland. Given that the flux of warm water onto the continental shelf and into the sub-ice cavities is steered by complex bathymetry, a detailed topography data set is an essential ingredient for models that address ice-ocean interaction. We followed the spirit of the global RTopo-1 data set and compiled consistent maps of global ocean bathymetry, upper and lower ice surface topographies and global surface height on a spherical grid with now 30-arc seconds resolution. We used the General Bathymetric Chart of the Oceans (GEBCO, 2014) as the backbone and added the International Bathymetric Chart of the Arctic Ocean version 3 (IBCAOv3) and the Interna- tional Bathymetric Chart of the Southern Ocean (IBCSO) version 1. While RTopo-1 primarily aimed at a good and consistent representation of the Antarctic ice sheet, ice shelves and sub-ice cavities, RTopo-2 now also contains ice topographies of the Greenland ice sheet and outlet glaciers. In particular, we aimed at a good representation of the fjord and shelf bathymetry sur- rounding the Greenland continent. We corrected data from earlier gridded products in the areas of Petermann Glacier, Hagen Bræ and Sermilik Fjord assuming that sub-ice and fjord bathymetries roughly follow plausible Last Glacial Maximum ice flow patterns. For the continental shelf off northeast Greenland and the floating ice tongue of Nioghalvfjerdsfjorden Glacier at about 79°N, we incorporated a high-resolution digital bathymetry model considering original multibeam survey data for the region. Radar data for surface topographies of the floating ice tongues of Nioghalvfjerdsfjorden Glacier and Zachariæ Isstrøm have been obtained from the data centers of Technical University of Denmark (DTU), Operation Icebridge (NASA/NSF) and Alfred Wegener Institute (AWI). For the Antarctic ice sheet/ice shelves, RTopo-2 largely relies on the Bedmap-2 product but applies corrections for the geometry of Getz, Abbot and Fimbul ice shelf cavities.

The preparation and characterization of seven-coordinate tin(IV) complexes of the 2,6-diacetylpyridine Schiff bases of S-alkyl/aryl-dithiocarbazates and the X-ray crystal structure of the [Sn(dapsme)I-2] complex (dapsme=doubly deprotonated form of the 2,6

New tin(IV) complexes of empirical formula, Sn(SNNNS)I-2 (SNNNS = anionic form of the 2,6-diacetylpyridine Schiff bases of S-methyl- or S-benzyldithiocarbazate) have been prepared and characterized by a variety of physico-chemical techniques. The structure of Sn(dapsme)I-2 has been determined by single crystal X-ray crystallographic structural analysis. The complex has a seven-coordinate distorted pentagonal-bipyramidal geometry with the Schiff base coordinated to the tin(IV) ion as a dinegatively charged pentadentate chelating agent via the pyridine nitrogen atom, the two azomethine nitrogen atoms and the two thiolate sulfur atoms. The ligand occupies the equatorial plane and the iodo ligands are coordinated to the tin(IV) ion at axial positions. The distortion from an ideal pentagonal bipyramidal geometry is attributed to the restricted bite size of the pentadentate ligands. (C) 2004 Elsevier Ltd. All rights reserved.