No description available.

Developments are reported of unstructured-mesh methods for simulating stratified, turbulent and shear flows. The numerical model employs nonoscillatory forward in-time integrators for anelastic and incompressible flow PDEs, built on Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) and a preconditioned conjugate residual elliptic solver. Finite-volume spatial discretisation adopts an edge-based data structure. Tetrahedral-based and hybrid-based median-dual options for unstructured meshes are developed, enabling flexible spatial resolution. Viscous laminar and detached eddy simulation (DES) flow solvers are developed based on the edge-based NFT MPDATA scheme. The built-in implicit large eddy simulation (ILES) capability of the NFT scheme is also employed and extended to fully unstructured tetrahedral and hybrid meshes. Challenging atmospheric and engineering problems are solved numerically to validate the model and to demonstrate its applications. The numerical problems include simulations of stratified, turbulent and shear flows past obstacles involving complex gravity-wave phenomena in the lee, critical-level laminar-turbulence transitioning and various vortex structures in the wake. Qualitative flow patterns and quantitative data analysis are both presented in the current study.

Dada uma ação isométrica livre do grupo binário tetraedral G sobre esferas de dimensão ímpar, obtemos uma decomposição celular finita explícita para as formas espaciais esféricas tetraedrais, fazendo uso do conceito de região (ou domínio) fundamental. A estrutura celular deixa explícita uma descrição do complexo de cadeias sobre o grupo G. Como aplicações, utilizamos o complexo de cadeias e a interpretação geométrica do produto cup para calcular o anel de cohomologia da forma espacial esférica tetraedral em dimensão três, e também calculamos a torção de Reidemeister destes espaços para uma determinada representação de G / Given a free isometric action of a binary tetrahedral group G on odd dimensional spheres, we obtain an explicit finite cellular decomposition of the tetrahedral spherical space forms, using the concept of fundamental domain. The cellular structure gives an explicit description of the associated cellular chain complex over the group G. As applications we use the chain complex and the geometric interpretation of the cup product to calculate the cohomology ring of the tetrahedral spherical space form in three dimension, and also compute the Reidemeister torsion of these spaces for a determined representation of G

The understanding of complex condensed matter systems is an area of intense study. In this thesis, some properties of simple liquids with strong preference for tetrahedral local ordering are explored. These liquids are amenable to supercooling, and give complex crystalline structures on eventual crystallisation. All liquids studied are simple, monatomic and are similar to real metallic liquids. The vibrational density of states of a glass created in simulation is calculated. We show a correspondence between the vibrational properties of the crystal and the glass, indicating that the vibrational spectra of crystals can be used to understand the more complex vibrational spectra of the glass of the same substance. The dynamics of supercooled liquids is investigated using a previously not implemented comprehensive measure of structural relaxation. This new measure decays more slowly in the deeply supercooled domain than the commonly used measure. A new atomic model for octagonal quasicrystals is presented. The model is based on findings from a molecular dynamics simulation that resulted in 45˚ twinned β-Mn. A decoration is derived from the β-Mn unit cell and the unit cell of the intermediate structure found at the twinning interface. Extensive simulations are used to explore the phase diagram of a liquid at low densities. The resulting phase diagram shows a spinodal line and a phase coexistence region between a liquid and a crystalline phase ending in a critical point. This contradicts the old conclusion of the Landau theory -- that continuous transitions between liquids and crystals cannot exist The same liquid is explored at higher densities. Upon cooling the liquid performs a first order liquid-liquid phase transition. The low temperature liquid is shown to be strong and to have very good glass forming abilities. This result offers new insights into fragile to strong transitions and suggests the possibility of a good metallic glass former. / At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Submitted. Paper 3: In progress.

The crystal structures of two thermostable carboxylesterase Est30 and Est55 from Geobacillus stearothermophilus were determined to help understand their functions and applications in industry or medicine. The crystal structure of Est30 was determined at 1.63 Å resolution by the multiple anomalous dispersion method. The two-domain Est30 structure showed a large domain with a modified alpha/beta hydrolase core including a seven, rather than an eight-stranded beta sheet, and a smaller cap domain comprising three alpha helices. A 100 Da tetrahedral ligand, propyl acetate, was observed to be covalently bound to the side chain of Ser94 in the catalytic triad. This ligand complex represents the first tetrahedral intermediate in the reaction mechanism. Therefore, this Est30 crystal structure will help understand the mode of action of all enzymes in the serine hydrolase superfamily. Est55 is a bacterial homologue of the mammalian carboxylesterases involved in hydrolysis and detoxification of numerous peptides and drugs and in prodrug activation. Est55 crystals were grown at pH 6.2 and pH 6.8 and the structures were determined at resolutions of 2.0 and 1.58 Å respectively. Est55 folds into three domains, a catalytic domain, an α/β domain and a regulatory domain. This structure is in an inactive form; the side chain of His409, one of the catalytic triad residues, is pointing away from the active site. Moreover, the adjacent Cys408 is triply oxidized and lies in the oxyanion hole, which would block the entry of substrate to its binding site. This structure suggested a self-inactivation mechanism, however, Cys408 is not essential for enzyme activity. Mutation of Cys408 showed that hydrophobic side chains at this position were favorable, while polar serine was unfavorable for enzyme activity. Both Est30 and Est55 were shown to hydrolyze the prodrug CPT-11 into the active form SN-38. Therefore, Est30 and Est55 are potential candidates for use with irinotecan in cancer therapy. The catalytic efficiency (kcat/Km) of Est30 is about 10-fold lower than that of Est55. The effects of the Cys408 substitutions on Est55 activity differed for the two substrates, p-NP butyrate and CPT-11. Mutant C408V may provide a more stable form of Est55.

Many physical problems lead to boundary value problems for partial differential equations, which can be solved with the finite element method. In order to construct adaptive solution algorithms or to measure the error one aims at reliable a posteriori error estimators. Many such estimators are known, as well as their theoretical foundation. Some boundary value problems yield so-called anisotropic solutions (e.g. with boundary layers). Then anisotropic finite element meshes can be advantageous. However, the common error estimators for isotropic meshes fail when applied to anisotropic meshes, or they were not investigated yet. For rectangular or cuboidal anisotropic meshes a modified error estimator had already been derived. In this paper error estimators for anisotropic tetrahedral or triangular meshes are considered. Such meshes offer a greater geometrical flexibility. For the Poisson equation we introduce a residual error estimator, an estimator based on a local problem, several Zienkiewicz-Zhu estimators, and an L_2 error estimator, respectively. A corresponding mathematical theory is given.For a singularly perturbed reaction-diffusion equation a residual error estimator is derived as well. The numerical examples demonstrate that reliable and efficient error estimation is possible on anisotropic meshes. The analysis basically relies on two important tools, namely anisotropic interpolation error estimates and the so-called bubble functions. Moreover, the correspondence of an anisotropic mesh with an anisotropic solution plays a vital role. AMS(MOS): 65N30, 65N15, 35B25

No description available.

The objective of this PhD research programme is to investigate the effectiveness of a finite volume method incorporating radial basis functions for simulating nonlinear transport processes. The finite volume method is the favoured numerical technique for solving the advection-diffusion equations that arise in transport simulation. The method transforms the original problem into a system of nonlinear, algebraic equations through the process of discretisation. The accuracy of this discretisation determines to a large extent the accuracy of the final solution. A new method of discretisation is presented that employs radial basis functions (rbfs) as a means of local interpolation. When combined with Gaussian quadrature integration methods, the resulting finite volume discretisation leads to accurate numerical solutions without the need for very fine meshes, and the additional overheads they entail. The resulting nonlinear, algebraic system is solved efficiently using a Jacobian-free Newton-Krylov method. By employing the new method as an extension of existing shape function-based approaches, the number of nonlinear iterations required to obtain convergence can be reduced. Furthermore, information obtained from these iterations can be used to increase the efficiency of subsequent rbf-based iterations, as well as to construct an effective parallel reconditioner to further reduce the number of nonlinear iterations required. Results are presented that demonstrate the improved accuracy offered by the new method when applied to several test problems. By successively refining the meshes, it is also possible to demonstrate the increased order of the new method, when compared to a traditional shape function basedmethod. Comparing the resources required for both methods reveals that the new approach can be many times more efficient at producing a solution of a given accuracy.

Dada uma ação isométrica livre do grupo binário tetraedral G sobre esferas de dimensão ímpar, obtemos uma decomposição celular finita explícita para as formas espaciais esféricas tetraedrais, fazendo uso do conceito de região (ou domínio) fundamental. A estrutura celular deixa explícita uma descrição do complexo de cadeias sobre o grupo G. Como aplicações, utilizamos o complexo de cadeias e a interpretação geométrica do produto cup para calcular o anel de cohomologia da forma espacial esférica tetraedral em dimensão três, e também calculamos a torção de Reidemeister destes espaços para uma determinada representação de G / Given a free isometric action of a binary tetrahedral group G on odd dimensional spheres, we obtain an explicit finite cellular decomposition of the tetrahedral spherical space forms, using the concept of fundamental domain. The cellular structure gives an explicit description of the associated cellular chain complex over the group G. As applications we use the chain complex and the geometric interpretation of the cup product to calculate the cohomology ring of the tetrahedral spherical space form in three dimension, and also compute the Reidemeister torsion of these spaces for a determined representation of G

Some boundary value problems yield anisotropic solutions, e.g. solutions with boundary layers. If such problems are to be solved with the finite element method (FEM), anisotropically refined meshes can be advantageous. In order to construct these meshes or to control the error one aims at reliable error estimators. For isotropic meshes such estimators are known but they fail when applied to anisotropic meshes. Rectangular (or cuboidal) anisotropic meshes were already investigated. In this paper an error estimator is presented for tetrahedral or triangular meshes which offer a much greater geometrical flexibility.