Cohomology of matching rules

Quasiperiodic patterns described by polyhedral "atomic surfaces" and admitting matching rules are considered. It is shown that the cohomology ring of the continuous hull of such patterns is isomorphic to that of the complement of a torus $T^N$ to an arrangement $A$ of thickened affine tori of codimension two. Explicit computation of Betti numbers for several two-dimensional tilings and for the icosahedral Ammann-Kramer tiling confirms in most cases the results obtained previously by different methods. The cohomology groups of $T^N \backslash A$ have a natural structure of a right module over the group ring of the space symmetry group of the pattern and can be decomposed in a direct sum of its irreducible representations. An example of such decomposition is shown for the Ammann-Kramer tiling

Soft rectangular sub-5 nm tiling patterns by liquid crystalline self-assembly of T-shaped bolapolyphiles

Square and other rectangular nanoscale tiling patterns are of contemporary interest for soft lithography. Though soft square patterns on a ≈40 nm length scale can be achieved with block copolymers, even smaller tiling patterns below 5 nm can be expected for liquid crystalline phases of small molecules. However, these usually form lamellar and hexagonal morphologies and thus the challenge is to specifically design liquid crystal (LC) phases forming square and rectangular structures, being compatible with industrial standards. Here, two distinct types of liquid crystalline rectangular tiling patterns are reported occurring in a series of T‐shaped p‐terphenyl‐based bolapolyphiles. By directed side chain engineering sub‐5 nm sized quadrangular honeycombs with rhombic (c2mm), square (p4mm), and rectangular (p2mm) shapes of the cells are formed by spontaneous self‐assembly. The rectangular honeycomb with p2mm lattice represents a new mode of LC self‐assembly in polygonal honeycombs. In addition, pentagonal and hexagonal tiling motifs can be obtained by molecular fine tuning

Courbure discrète : théorie et applications

International audienceThe present volume contains the proceedings of the 2013 Meeting on discrete curvature, held at CIRM, Luminy, France. The aim of this meeting was to bring together researchers from various backgrounds, ranging from mathematics to computer science, with a focus on both theory and applications. With 27 invited talks and 8 posters, the conference attracted 70 researchers from all over the world. The challenge of finding a common ground on the topic of discrete curvature was met with success, and these proceedings are a testimony of this wor

Active cellular mechanics and its consequences for animal development

A central goal of developmental biology is to understand how an organism shapes itself, a process referred to as morphogenesis. While the molecular components critical to determining the initial body plan have been well characterized, the control of the subsequent dynamics of cellular rearrangements which ultimately shape the organism are far less understood. A major roadblock to a more complete picture of morphogenesis is the inability to measure tissue-scale mechanics throughout development and thus answer fundamental questions: How is the mechanical state of the cell regulated by local protein expression and global pattering? In what way does stress feedback onto the larger developmental program?In this dissertation, we begin to approach these questions through the introduction and analysis of a multi-scale model of epithelial mechanics which explicitly connects cytoskeletal protein activity to tissue-level stress. In Chapter 2, we introduce the discrete Active Tension Network (ATN) model of cellular mechanics. ATNs are tissues that satisfy two primary assumptions: that the mechanical balance of cells is dominated by cortical tension and that myosin actively remodels the actin cytoskeleton in a stress-dependent manner. Remarkably, the interplay of these features allows for angle-preserving, i.e. `isogonal', dilations or contractions of local cell geometry that do not generate stress. Asymptotically this model is stabilized provided there is mechanical feedback on expression of myosin within the cell; we take this to be a strong prediction to be tested. The ATN model exposes a fundamental connection between equilibrium cell geometry and its underlying force network. In Chapter 3, we relax the tension-net approximation and demonstrate that at equilibrium, epithelial tissues with non-uniform pressure have non-trivial geometric constraints that imply the network is described by a weighted `dual' triangulation. We show that the dual triangulation encodes all information about the mechanical state of an epithelial tissue. Utilizing the stress-geometry ‘duality’, we formulate a local "Mechanical Inference" of cellular-level stress using solely cell geometry that dramatically improves over past image-based inference techniques.In Chapter 4, we generalize the ATN model to explore the controlled re-arrangement of cells within epithelial tissues. This requires us to explicitly consider the effects of cadherin mediated adhesion, and its regulation, on tissue morphogenesis. We find that positive feedback between myosin and cortical tension, along with traction-dependent depletion of cytoskeletal cadherin is sufficient to recapitulate the morphogenetic movement of cells observed during convergent extension of the lateral ectoderm during Drosophila embryogenesis. Statistical analyses of live-imaging data supports the fundamentals of the model.Chapter 5 focuses on morphogenesis at a mesoscopic scale by coarse-graining the cellular ATN model. Under this limit, we expect an epithelial tissue should behave as an effective viscous, compressible fluid driven by myosin gradients on intermediate time-scales. Theoretical predictions are empirically tested against in-toto microscopy data obtained during early Drosophila embryogenesis

Regular Hierarchical Surface Models: A conceptual model of scale variation in a GIS and its application to hydrological geomorphometry

Environmental and geographical process models inevitably involve parameters that vary spatially. One example is hydrological modelling, where parameters derived from the shape of the ground such as flow direction and flow accumulation are used to describe the spatial complexity of drainage networks. One way of handling such parameters is by using a Digital Elevation Model (DEM), such modelling is the basis of the science of geomorphometry. A frequently ignored but inescapable challenge when modellers work with DEMs is the effect of scale and geometry on the model outputs. Many parameters vary with scale as much as they vary with position. Modelling variability with scale is necessary to simplify and generalise surfaces, and desirable to accurately reconcile model components that are measured at different scales. This thesis develops a surface model that is optimised to represent scale in environmental models. A Regular Hierarchical Surface Model (RHSM) is developed that employs a regular tessellation of space and scale that forms a self-similar regular hierarchy, and incorporates Level Of Detail (LOD) ideas from computer graphics. Following convention from systems science, the proposed model is described in its conceptual, mathematical, and computational forms. The RHSM development was informed by a categorisation of Geographical Information Science (GISc) surfaces within a cohesive framework of geometry, structure, interpolation, and data model. The positioning of the RHSM within this broader framework made it easier to adapt algorithms designed for other surface models to conform to the new model. The RHSM has an implicit data model that utilises a variation of Middleton and Sivaswamy (2001)’s intrinsically hierarchical Hexagonal Image Processing referencing system, which is here generalised for rectangular and triangular geometries. The RHSM provides a simple framework to form a pyramid of coarser values in a process characterised as a scaling function. In addition, variable density realisations of the hierarchical representation can be generated by defining an error value and decision rule to select the coarsest appropriate scale for a given region to satisfy the modeller’s intentions. The RHSM is assessed using adaptions of the geomorphometric algorithms flow direction and flow accumulation. The effects of scale and geometry on the anistropy and accuracy of model results are analysed on dispersive and concentrative cones, and Light Detection And Ranging (LiDAR) derived surfaces of the urban area of Dunedin, New Zealand. The RHSM modelling process revealed aspects of the algorithms not obvious within a single geometry, such as, the influence of node geometry on flow direction results, and a conceptual weakness of flow accumulation algorithms on dispersive surfaces that causes asymmetrical results. In addition, comparison of algorithm behaviour between geometries undermined the hypothesis that variance of cell cross section with direction is important for conversion of cell accumulations to point values. The ability to analyse algorithms for scale and geometry and adapt algorithms within a cohesive conceptual framework offers deeper insight into algorithm behaviour than previously achieved. The deconstruction of algorithms into geometry neutral forms and the application of scaling functions are important contributions to the understanding of spatial parameters within GISc

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

The Transmission Electron Microscope

The book "The Transmission Electron Microscope" contains a collection of research articles submitted by engineers and scientists to present an overview of different aspects of TEM from the basic mechanisms and diagnosis to the latest advancements in the field. The book presents descriptions of electron microscopy, models for improved sample sizing and handling, new methods of image projection, and experimental methodologies for nanomaterials studies. The selection of chapters focuses on transmission electron microscopy used in material characterization, with special emphasis on both the theoretical and experimental aspect of modern electron microscopy techniques. I believe that a broad range of readers, such as students, scientists and engineers will benefit from this book