Flaws in the current method for calculating methane emissions during dairy manure management in New Zealand

New Zealand's Greenhouse Gas Inventory (the NZ Inventory) currently estimates methane (CH4) emissions from anaerobic dairy effluent ponds by: (1) determining the total pond volume across New Zealand; (2) dividing this volume by depth to obtain the total pond surface area; and (3) multiplying this area by an observational average CH4 flux. Unfortunately, a mathematically erroneous determination of pond volume has led to an imbalanced equation and a geometry error was made when scaling-up the observational CH4 flux. Furthermore, even if these errors are corrected, the nationwide estimate still hinges on field data from a study that used a debatable method to measure pond CH4 emissions at a single site, as well as a potentially inaccurate estimation of the amount of organic waste anaerobically treated. The development of a new methodology is therefore critically needed.

Formal description, compression and transformation of digital pictures II. Picture algebra and geometry

In an earlier paper (Part I) we described the construction of Hermite code for multiple grey-level pictures using the concepts of vector spaces over Galois Fields. In this paper a new algebra is worked out for Hermite codes to devise algorithms for various transformations such as translation, reflection, rotation, expansion and replication of the original picture. Also other operations such as concatenation, complementation, superposition, Jordan-sum and selective segmentation are considered. It is shown that the Hermite code of a picture is very powerful and serves as a mathematical signature of the picture. The Hermite code will have extensive applications in picture processing, pattern recognition and artificial intelligence.

Mathematical modelling of human corneal oxygenation and cell kinetics in corneal epithelial wound healing

Healthy transparent cornea depends upon the regulation of fluid, nutrient and oxygen transport through the tissue to sustain cell metabolism and other critical processes for normal functioning. This research considers the corneal geometry and investigates oxygen distribution using a two-dimensional Monod kinetic model, showing that previous studies make assumptions that lead to predictions of near-anoxic levels of oxygen tension in the limbal regions of the cornea. It also considers the comparison of experimental spatial and temporal data with the predictions of novel mathematical models with respect to distributed mitotic rates during corneal epithelial wound healing.

On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

Experimental and numerical investigation of jet injection in a wall bounded supersonic flow

Numerical and experimental studies of a supersonic jet (Helium) inclined at 45 degrees to a oncoming Mach 2 flow have been carried out. The numerical study has been used to arrive at a geometry that could reduce an oncoming Mach 5.75 flow to Mach 2 flow and in determining the jet parameters. Experiments are carried out in the IISc. hypersonic shock tunnel HST2 at similar conditions obtained from numerical studies. Flow visualization studies carried out using Schlieren technique clearly show the presence of the bow shock in front of the jet exposed to supersonic cross flow. The jet Mach number is experimentally found to be approximate to 3. Visual observations show that the jet has penetrated up to 60% of the total height of the chamber.

Laminar and turbulent natural convection in rectangular cavities

A computer program has been developed for the prediction of buoyancy-driven laminar and turbulent flow in rectangular air-filled two-dimensional cavities with differentially heated side walls. Laminar flow predictions for a square cavity and Rayleigh numbers from Ra = 10^3 up to the onset of unsteady flow have been obtained. Accurate solutions for Ra = 5 x 10^6, 10^7, 5 x 10^7 and 10^8 are presented and an estimate for the critical Rayleigh number at which the steady laminar flow becomes unsteady is given for this geometry. Numerical predictions of turbulent flow have been obtained for RaH~0(10^9 -10^11 ) and compared with existing experimental data. A previously developed second moment closure model (Behnia et al. 1987) has been used to model the turbulence. Results indicate that a second moment closure model is capable of predicting the observed flow features.

Coordination properties of vic-isonitrosoimines in their copper (II) and palladium (II) complexes

Preparation and structural characterization of palladium (II) complexes of ligands III-V and copper (II) complexes of III are reported. The elemental analyses of the complexes show that the metal: ligand ratio is 1 : 2. The electrical conductance in acetone shows the non-electrolytic nature of the complexes. The diamagnetic character suggests a gross square-planar geometry for the palladium (II) complexes. Copper (II) complexes are paramagnetic with/~eff.~l'90 B.M. Spectral data suggest that in all the complexes the ligand coordinates to the metal (II) symmetrically through isonitroso-nitrogen and imine-nitrogen, forming a ¡ membered chelate ring. Amine-exchange reactions of the complexes are discussed and compared on the basis of their structures.

Steroechemistry of the Pyrrolidine rings in the collagen structure

In the collagen triple-helical structure, large side groups occuring at location 3 in the repeating triplet sequences (Gly-Rz-Rz)n are appreciably constrained if a proline residue occurs as Rz in a neighbouring chain. The severity of the steric hindrance depends on the geometry of the prolyl ring. In this paper we propose two different puckerir.gs for the proline ring, the first one being energetically favorable for most types of residue sequences commonly found in collegen while the second is preferable when an amino acid residue with a large side group occurs at location 3 in a neighbouring chain. The puckering of the pyrrolidine ring of hydroxyproline, as proposed earlier, is quite favorable from energy as well as stereochemical considerations.

Computation of turbulent flow in an IFRF quarl burner

A computational model for isothermal axisymmetric turbulent flow in a quarl burner is set up using the CFD package FLUENT, and numerical solutions obtained from the model are compared with available experimental data. A standard k-e model and and two versions of the RNG k-e model are used to model the turbulence. One of the aims of the computational study is to investigate whether the RNG based k-e turbulence models are capable of yielding improved flow predictions compared with the standard k-e turbulence model. A difficulty is that the flow considered here features a confined vortex breakdown which can be highly sensitive to flow behaviour both upstream and downstream of the breakdown zone. Nevertheless, the relatively simple confining geometry allows us to undertake a systematic study so that both grid-independent and domain-independent results can be reported. The systematic study includes a detailed investigation of the effects of upstream and downstream conditions on the predictions, in addition to grid refinement and other tests to ensure that numerical error is not significant. Another important aim is to determine to what extent the turbulence model predictions can provide us with new insights into the physics of confined vortex breakdown flows. To this end, the computations are discussed in detail with reference to known vortex breakdown phenomena and existing theories. A major conclusion is that one of the RNG k-e models investigated here is able to correctly capture the complex forward flow region inside the recirculating breakdown zone. This apparently pathological result is in stark contrast to the findings of previous studies, most of which have concluded that either algebraic or differential Reynolds stress modelling is needed to correctly predict the observed flow features. Arguments are given as to why an isotropic eddy-viscosity turbulence model may well be able to capture the complex flow structure within the recirculating zone for this flow setup. With regard to the flow physics, a major finding is that the results obtained here are more consistent with the view that confined vortex breakdown is a type of axisymmetric boundary layer separation, rather than a manifestation of a subcritical flow state.

Geometry of the de-Sitter universe

By making use of the fact that the de-Sitter metric corresponds to a hyperquadric in a five-dimensional flat space, it is shown that the three Robertson-Walker metrics for empty spacetime and positive cosmological constant, corresponding to 3-space of positive, negative and zero curvative, are geometrically equivalent. The 3-spaces correspond to intersections of the hyperquadric by hyperplanes, and the time-like geodesics perpendicular to them correspond to intersections by planes, in all three cases.

Modes of deformation in aluminium rings subjected to static axial compression

Aluminium rings of varying Image Image diameter ratios machined from extruded solid bars, were subjected to static axial compression. Etched diametral planes of deformed cylinders revealed the existence of shear bands, the configuration of which were found to change with initial specimen geometry and deformation.

Bending the Rules of Cell Protrusions : Molecular Mechanisms and Biological Roles of Inverse-BAR Proteins in Cell Morphogenesis

Plasma membrane adopts myriad of different shapes to carry out essential cellular processes such as nutrient uptake, immunological defence mechanisms and cell migration. Therefore, the details how different plasma membrane structures are made and remodelled are of the upmost importance. Bending of plasma membrane into different shapes requires substantial amount of force, which can be provided by the actin cytoskeleton, however, the molecules that regulate the interplay between the actin cytoskeleton and plasma membrane have remained elusive. Recent findings have placed new types of effectors at sites of plasma membrane remodelling, including BAR proteins, which can directly bind and deform plasma membrane into different shapes. In addition to their membrane-bending abilities, BAR proteins also harbor protein domains that intimately link them to the actin cytoskeleton. The ancient BAR domain fold has evolved into at least three structurally and functionally different sub-groups: the BAR, F-BAR and I-BAR domains. This thesis work describes the discovery and functional characterization of the Inverse-BAR domains (I-BARs). Using synthetic model membranes, we have shown that I-BAR domains bind and deform membranes into tubular structures through a binding-surface composed of positively charged amino acids. Importantly, the membrane-binding surface of I-BAR domains displays an inverse geometry to that of the BAR and F-BAR domains, and these structural differences explain why I-BAR domains induce cell protrusions whereas BAR and most F-BAR domains induce cell invaginations. In addition, our results indicate that the binding of I-BAR domains to membranes can alter the spatial organization of phosphoinositides within membranes. Intriguingly, we also found that some I-BAR domains can insert helical motifs into the membrane bilayer, which has important consequences for their membrane binding/bending functions. In mammals there are five I-BAR domain containing proteins. Cell biological studies on ABBA revealed that it is highly expressed in radial glial cells during the development of the central nervous system and plays an important role in the extension process of radial glia-like C6R cells by regulating lamellipodial dynamics through its I-BAR domain. To reveal the role of these proteins in the context of animals, we analyzed MIM knockout mice and found that MIM is required for proper renal functions in adult mice. MIM deficient mice displayed a severe urine concentration defect due to defective intercellular junctions of the kidney epithelia. Consistently, MIM localized to adherens junctions in cultured kidney epithelial cells, where it promoted actin assembly through its I-BAR andWH2 domains. In summary, this thesis describes the mechanism how I-BAR proteins deform membranes and provides information about the biological role of these proteins, which to our knowledge are the first proteins that have been shown to directly deform plasma membrane to make cell protrusions.

Optic phonon-magnetoplasmon surface oscillations in polar semiconductors

An interface between two polar semiconductors in parallel magnetic field geometry can support at most four types of surface oscillations; the actual number (less-than-or-equals, slant4), however, depends on the strength of the magnetic field. The interface effects on these relevant ranges of magnetic field are analysed in detail.

Conformations of Heterochiral and Homochiral Proline-Pseudoproline Segments in Peptides: Context Dependent Cis-Trans Peptide Bond Isomerization

The pseudoproline residue (Psi Pro, L-2,2-dimethyl-1,3-thiazolidine-4-carboxylic acid) has been introduced into heterochiral diproline segments that have been previously shown to facilitate the formation of beta-hairpins, containing central two and three residue turns. NMR studies of the octapeptide Boc-Leu-Phe-Val-(D)Pro-Psi Pro-Leu-Phe-Val-OMe (1), Boc-Leu-Val-Val-(D)Pro-Psi Pro-Leu-Val-Val-OMe (2), and the nonapeptide sequence Boc-Leu-Phe-Val-(D)Pro-Psi Pro-(D)Ala-Leu-Phe-Val-OMe (3) established well-registered beta-hairpin structures in chloroform solution, with the almost exclusive population of the trans conformation for the peptide bond preceding the Psi Pro residue. The beta-hairpin conformation of 1 is confirmed by single crystal X-ray diffraction. Truncation of the strand length in Boc-Val-(D)Pro-Psi Pro-Leu-OMe (4) results in air increase in the population of the cis conformer, with a cis/trans ratio of 3.65. Replacement of Psi Pro in 4 by (L)Pro in 5, results in almost exclusive population of the trans form, resulting in an incipient beta-hairpin conformation, stabilized by two intramolecular hydrogen bonds. Further truncation of the sequence gives an appreciable rise in the population of cis conformers in the tripeptide piv-(D)Pro-Psi Pro-Leu-OMe (6). In the homochiral segment Piv-Pro Psi Pro-Leu-OMe (7) only the cis form is observed with the NMR evidence strongly supporting a type VIa beta-turn conformation, stabilized by a 4 -> 1 hydrogen bond between the Piv (CO) and Leu (3) NH groups. The crystal structure of the analog peptide 7a (Piv-Pro-Psi(H,CH3)Pro-Leu-NHMe) confirms the cis peptide bond geometry for the Pro-Psi(H,CH3)pro peptide bond, resulting in a type VIa beta-turn conformation.

A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area

Motivated by a problem from fluid mechanics, we consider a generalization of the standard curve shortening flow problem for a closed embedded plane curve such that the area enclosed by the curve is forced to decrease at a prescribed rate. Using formal asymptotic and numerical techniques, we derive possible extinction shapes as the curve contracts to a point, dependent on the rate of decreasing area; we find there is a wider class of extinction shapes than for standard curve shortening, for which initially simple closed curves are always asymptotically circular. We also provide numerical evidence that self-intersection is possible for non-convex initial conditions, distinguishing between pinch-off and coalescence of the curve interior.