Computing Distance Functions from Generalized Sources on Weighted Polyhedral Surfaces

We present algorithms for computing approximate distance functions and shortest paths from a generalized source (point, segment, polygonal chain or polygonal region) on a weighted non-convex polyhedral surface in which obstacles (represented by polygonal chains or polygons) are allowed. We also describe an algorithm for discretizing, by using graphics hardware capabilities, distance functions. Finally, we present algorithms for computing discrete k-order Voronoi diagrams

Generalized Higher-Order Voronoi Diagrams on Polyhedral Surfaces

We present an algorithm for computing exact shortest paths, and consequently distances, from a generalized source (point, segment, polygonal chain or polygonal region) on a possibly non-convex polyhedral surface in which polygonal chain or polygon obstacles are allowed. We also present algorithms for computing discrete Voronoi diagrams of a set of generalized sites (points, segments, polygonal chains or polygons) on a polyhedral surface with obstacles. To obtain the discrete Voronoi diagrams our algorithms, exploiting hardware graphics capabilities, compute shortest path distances defined by the sites

Basis set superposition error-counterpoise corrected potential energy surfaces : application to hydrogen peroxide ... X (X=F-, Cl-, Br-, Li+, Na+) complexes

Møller-Plesset (MP2) and Becke-3-Lee-Yang-Parr (B3LYP) calculations have been used to compare the geometrical parameters, hydrogen-bonding properties, vibrational frequencies and relative energies for several X- and X+ hydrogen peroxide complexes. The geometries and interaction energies were corrected for the basis set superposition error (BSSE) in all the complexes (1-5), using the full counterpoise method, yielding small BSSE values for the 6-311 + G(3df,2p) basis set used. The interaction energies calculated ranged from medium to strong hydrogen-bonding systems (1-3) and strong electrostatic interactions (4 and 5). The molecular interactions have been characterized using the atoms in molecules theory (AIM), and by the analysis of the vibrational frequencies. The minima on the BSSE-counterpoise corrected potential-energy surface (PES) have been determined as described by S. Simón, M. Duran, and J. J. Dannenberg, and the results were compared with the uncorrected PES

C-H···O H-bonded complexes: how does basis set superposition error change their potential-energy surfaces?

Geometries, vibrational frequencies, and interaction energies of the CNH⋯O3 and HCCH⋯O3 complexes are calculated in a counterpoise-corrected (CP-corrected) potential-energy surface (PES) that corrects for the basis set superposition error (BSSE). Ab initio calculations are performed at the Hartree-Fock (HF) and second-order Møller-Plesset (MP2) levels, using the 6-31G(d,p) and D95++(d,p) basis sets. Interaction energies are presented including corrections for zero-point vibrational energy (ZPVE) and thermal correction to enthalpy at 298 K. The CP-corrected and conventional PES are compared; the unconnected PES obtained using the larger basis set including diffuse functions exhibits a double well shape, whereas use of the 6-31G(d,p) basis set leads to a flat single-well profile. The CP-corrected PES has always a multiple-well shape. In particular, it is shown that the CP-corrected PES using the smaller basis set is qualitatively analogous to that obtained with the larger basis sets, so the CP method becomes useful to correctly describe large systems, where the use of small basis sets may be necessary

How does basis set superposition error change the potential surfaces for hydrogen-bonded dimers?

We describe a simple method to automate the geometric optimization of molecular orbital calculations of supermolecules on potential surfaces that are corrected for basis set superposition error using the counterpoise (CP) method. This method is applied to the H-bonding complexes HF/HCN, HF/H2O, and HCCH/H2O using the 6-31G(d,p) and D95 + + (d,p) basis sets at both the Hartree-Fock and second-order Møller-Plesset levels. We report the interaction energies, geometries, and vibrational frequencies of these complexes on the CP-optimized surfaces; and compare them with similar values calculated using traditional methods, including the (more traditional) single point CP correction. Upon optimization on the CP-corrected surface, the interaction energies become more negative (before vibrational corrections) and the H-bonding stretching vibrations decrease in all cases. The extent of the effects vary from extremely small to quite large depending on the complex and the calculational method. The relative magnitudes of the vibrational corrections cannot be predicted from the H-bond stretching frequencies alone

Visibility and proximity on triangulated surfaces

En aquesta tesi es solucionen problemes de visibilitat i proximitat sobre superfícies triangulades considerant elements generalitzats. Com a elements generalitzats considerem: punts, segments, poligonals i polígons. Les estrategies que proposem utilitzen algoritmes de geometria computacional i hardware gràfic. Comencem tractant els problemes de visibilitat sobre models de terrenys triangulats considerant un conjunt d'elements de visió generalitzats. Es presenten dos mètodes per obtenir, de forma aproximada, mapes de multi-visibilitat. Un mapa de multi-visibilitat és la subdivisió del domini del terreny que codifica la visibilitat d'acord amb diferents criteris. El primer mètode, de difícil implementació, utilitza informació de visibilitat exacte per reconstruir de forma aproximada el mapa de multi-visibilitat. El segon, que va acompanyat de resultats d'implementació, obté informació de visibilitat aproximada per calcular i visualitzar mapes de multi-visibilitat discrets mitjançant hardware gràfic. Com a aplicacions es resolen problemes de multi-visibilitat entre regions i es responen preguntes sobre la multi-visibilitat d'un punt o d'una regió. A continuació tractem els problemes de proximitat sobre superfícies polièdriques triangulades considerant seus generalitzades. Es presenten dos mètodes, amb resultats d'implementació, per calcular distàncies des de seus generalitzades sobre superfícies polièdriques on hi poden haver obstacles generalitzats. El primer mètode calcula, de forma exacte, les distàncies definides pels camins més curts des de les seus als punts del poliedre. El segon mètode calcula, de forma aproximada, distàncies considerant els camins més curts sobre superfícies polièdriques amb pesos. Com a aplicacions, es calculen diagrames de Voronoi d'ordre k, i es resolen, de forma aproximada, alguns problemes de localització de serveis. També es proporciona un estudi teòric sobre la complexitat dels diagrames de Voronoi d'ordre k d'un conjunt de seus generalitzades en un poliedre sense pesos.

Improvements in the ray tracing of implicit surfaces based on interval arithmetic

Las superfícies implícitas son útiles en muchas áreasde los gráficos por ordenador. Una de sus principales ventajas es que pueden ser fácilmente usadas como primitivas para modelado. Aun asi, no son muy usadas porque su visualización toma bastante tiempo. Cuando se necesita una visualización precisa, la mejor opción es usar trazado de rayos. Sin embargo, pequeñas partes de las superficies desaparecen durante la visualización. Esto ocurre por la truncación que se presenta en la representación en punto flotante de los ordenadores; algunos bits se puerden durante las operaciones matemáticas en los algoritmos de intersección. En este tesis se presentan algoritmos para solucionar esos problemas. La investigación se basa en el uso del Análisis Intervalar Modal el cual incluye herramientas para resolver problemas con incertidumbe cuantificada. En esta tesis se proporcionan los fundamentos matemáticos necesarios para el desarrollo de estos algoritmos.

New insights on growth mechanisms of protein clusters at surfaces: an AFM and simulation study

Despite its relevance to a wide range of technological and fundamental areas, a quantitative understanding of protein surface clustering dynamics is often lacking. In inorganic crystal growth, surface clustering of adatoms is well described by diffusion-aggregation models. In such models, the statistical properties of the aggregate arrays often reveal the molecular scale aggregation processes. We investigate the potential of these theories to reveal hitherto hidden facets of protein clustering by carrying out concomitant observations of lysozyme adsorption onto mica surfaces, using atomic force microscopy. and Monte Carlo simulations of cluster nucleation and growth. We find that lysozyme clusters diffuse across the substrate at a rate that varies inversely with size. This result suggests which molecular scale mechanisms are responsible for the mobility of the proteins on the substrate. In addition the surface diffusion coefficient of the monomer can also be extracted from the comparison between experiments and simulations. While concentrating on a model system of lysozyme-on-mica, this 'proof of concept' study successfully demonstrates the potential of our approach to understand and influence more biomedically applicable protein-substrate couples.

Boundary integral equations on unbounded rough surfaces: Fredholmness and the finite section method

We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form $D = \{(x, z)\in \mathbb{R}^{n+1} : x\in \mathbb{R}^n, z > f(x)\}$ where $f : \mathbb{R}^n \to\mathbb{R}$ is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example acoustic scattering problems, problems involving elastic waves, and problems in potential theory, have been reformulated as second kind integral equations $u+Ku = v$ in the space $BC$ of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator $A = I + K$ under consideration, with an emphasis on the function space setting $BC$. Firstly, under which conditions is $A$ a Fredholm operator, and, secondly, when is the finite section method applicable to $A$?

Multilayered hydrogel coatings covalently-linked to glass surfaces showing a potential to mimic mucosal tissues

Multilayered hydrogel coatings can be developed on the surface of glass slides via layer-by-layer deposition of hydrogen-bonded interpolymer complexes formed by poly(acrylic acid) and methylcellulose. Chemical modification of the glass surface with (3-aminopropyl)triethoxysilane with subsequent layer-by-layer deposition and cross-linking of interpolymer complexes by thermal treatment allows fabrication of ultrathin hydrogel coatings, not detachable from the substrate. The thickness of these coatings is directly related to the number of deposition cycles and cross-linking conditions. An unusual dependence of the hydrogel swelling properties on the sample thickness is observed and can be interpreted by gradual transitions between two- and three-dimensional networks. The hydrogels exhibit pH-responsive swelling behaviour, achieving higher swelling degrees at pH > 6.0. These coatings can be used as model substrates to study the adhesive properties of pharmaceutical tablets and can potentially mimic the total work of adhesion observed for the detachment of mucoadhesives from porcine buccal mucosa but fail to exhibit identical detachment profiles.

Hiatal surfaces from the Miocene Globigerina Limestone Formation of Malta: Biostratigraphy, sedimentology, trace fossils and early diagenesis

The Miocene Globigerina Limestone of the Maltese islands contains widespread omission surfaces with very different characteristics and origins. The terminal Lower Globigerina Limestone hardground (TLGLHg) formed during a period of falling sea level. Coccolith assemblages suggest shallowness. Sedimentary structures and trace fossil assemblages, indicate increasing frequency of storm events and erosional episodes, towards the surface. Calcite cementation which took place around Thalassinoides burrows and formed irregular nodules was followed by dissolution of aragonite. It is suggested that lithification was linked to microbial reactions involving organic matter. In contrast two later surfaces, the terminal Middle Globigerina Limestone omissionground (TMGLOg), which marks the Lower to Middle Miocene boundary, and the Fomm-ir-Rih local hardground (FiRLHg) both contain early diagenetic dolomite. Lithification took place in two phases. The dolomite is interpreted to have formed beneath the sea floor: it was subsequently exhumed and partially corroded as the precipitation of calcitic and phosphatic cements took place around burrows open to the circulation of sea water. (C) 2008 Elsevier B.V. All rights reserved.

Weathering microenvironments on feldspar surfaces: implications for understanding fluid-mineral reactions in soils

The mechanisms by which coatings develop on weathered grain surfaces, and their potential impact on rates of fluid-mineral interaction, have been investigated by examining feldspars from a 1.1 ky old soil in the Glen Feshie chronosequence, Scottish highlands. Using the focused ion beam technique, electron-transparent, foils for characterization by transmission electron microscopy were cut from selected parts of grain surfaces. Some parts were bare whereas others had accumulations, a few micrometres thick, of Weathering products, often mixed with mineral and microbial debris. Feldspar exposed at bare grain surfaces is crystalline throughout and so there is no evidence for the presence of the amorphous 'leached layers' that typically form in acid-dissolution experiments and have been described from some natural Weathering contexts. The weathering products comprise sub-mu m thick crystallites of an Fe-K aluminosilicate, probably smectite, that have grown within an amorphous and probably organic-rich matrix. There is also evidence for crystallization of clays having been mediated by fungal hyphae. Coatings formed within Glen Feshie soils after similar to 1.1 ky are insufficiently continuous or impermeable to slow rates Of fluid-feldspar reactions, but provide valuable insights into the complex Weathering microenvironments oil debris and microbe-covered mineral surfaces.