Raymond J. Matela

Styles of volcano-induced deformation: numerical models of substratum flexure, spreading and extrusion

The gravitational deformation of volcanoes is largely controlled by ductile layers of substrata. Using numerical finite-element modelling we investigate the role of ductile layer thickness and viscosity on such deformation. To characterise the deformation we introduce two dimensionless ratios; Πa (volcano radius/ductile layer thickness) and Πb (viscosity of ductile substratum/failure strength of volcano). We find that the volcanic edifice spreads laterally when underlain by thin ductile layers (Πa>1), while thicker ductile layers lead to inward flexure (Πa<1). The deformation style is related to the switch from predominantly horizontal to vertical flow in the ductile layer with increasing thickness (increasing Πa). Structures produced by lateral spreading include concentric thrust belts around the volcano base and radial normal faulting in the cone itself. In contrast, flexure on thick ductile substrata leads to concentric normal faults around the base and compression in the cone. In addition, we show that lower viscosities in the ductile layer (low Πb) lead to faster rates of movement, and also affect the deformation style. Considering a thin ductile layer, if viscosity is high compared to the failure strength of the volcano (high Πb) then deformation is coupled and spreading is produced. However, if the viscosity is low (low Πb) substratum is effectively decoupled from the volcano and extrudes from underneath it. In this latter case evidence is likely to be found for basement compression, but corresponding spreading features in the volcano will be absent, as the cone is subject to a compressive stress regime similar to that produced by flexure. At volcanoes where basement extrusion is operating, high volcano stresses and outward substratum movement may combine to produce catastrophic sector collapse. An analysis of deformation features at a volcano can provide information about the type of basement below it, a useful tool for remote sensing and planetary geology. Also, knowledge of substratum geology can be used to predict styles of deformation operating at volcanoes, where features have not yet become well developed, or are obscured.

A topological exchange model for cell self-sorting

A new model of cell sorting based on a geometric representation (trivalent map) and its associated structure (triangulated graph) is presented. This model varies substantially from existing mathematical models in that individual cells are represented by variable n-gons, n ⩾ 3, whereas in current models cells are considered to be fixed (non-deformable) geometric, i.e. hexagonal or square objects. An exchange mechanism which operates on this graph is investigated and possible drivers are discussed.

Computer simulation of cellular self-sorting: A topological exchange model

Computer simulation results of the topological exchange model proposed by Martela & Fletterick (1979) are presented. These results, which utilize primitive binary tables and their associated drivers in the formation of internal clusters, indicate that this type of model (topological) is capable of simulating the cellular self-sorting phenomenon.

A topological model of cell division: structure of the computer program.

The general structure of a computer program (CD3D) simulating division in a sheet of cells is presented. The program is based on a topological representation of cell division previously developed by the authors, and the biological background to the model is discussed. The computer modelling of the various elements of the model (i.e. vertices, edges and meshes) is described, and an annotated description of the subroutines making up the program is given in an Appendix. Although the program and model are specifically designed to represent cell division processes, the graph framework may have applicability in other biological subject areas where dynamic relationships between elements are involved.

Modelling heat transfer through a novel design of rotary kiln

A novel form of rotary kiln has been developed which confers advantages over conventional designs. Details are given of the main features of the kiln, along with an approach used to study its heat transfer characteristics when hot processing waste products into a lightweight synthetic aggregate for recycling in building materials. Computer aided finite element modelling was used to predict temperature profiles and heat fluxes involving non-linear properties of the exterior insulation materials and internal radiation effects. Observations are given comparing predicted temperatures for two different cross sectional shapes and with those measured in practice on a prototype novel kiln. Observations are also given on the methods of approach to the modelling.

Computer simulation of compartment maintenance in the Drosophila wing imaginal disc

A new method for modelling cell division is reported which uses a cellular representation based on graph theory. This allows us to model the adjacencies of non-regular dividing cells accurately, avoiding the rigid geometrical constraints present in earlier simulations. We use this system to simulate compartment boundary maintenance in the Drosophila wing imaginal disc. We show that a boundary of minimum length between two growing polyclones of cells could depend on sorting between cells in the different polyclones. We also investigate the response of the model to differential cell division rates within polyclones. This is the first demonstration that cell sorting can generate a smooth boundary in a dividing cell mass. We suggest that biological analogs of our computer sorting rules are responsible for the similar straight polyclone borders seen in the real wing disc. A possible strategy for showing the existence of these analogs is also given.

Simulation and Animation

If you have read through the earlier chapters of this book you will have already learnt many of the fundamental techniques of graphics programming. Some of these techniques involve the most straightforward kinds of movement of graphic data: transformations like rotation, scaling, and translation. You have seen for example in Chapter 10 that application of rotations in real-time can give a dynamic picture of the structure of molecules. The present chapter will consider the general question of how movement of graphic images can be carried out in real-time. Examples of both research simulations and animations suitable for teaching purposes will be discussed with reference to a number of different graphics systems.

Computer Graphics in Biology

1. An Introduction to Computer Graphics.- 1.1 The beginnings of computer graphics.- 1.2 What is computer graphics?.- 1.3 Computer graphics and biology.- 1.4 The elements of a computer graphics system.- 1.5 Computer graphics in perspective.- 1.6 References.- 2. Graphics Hardware.- 2.1 An overview.- 2.2 Input devices.- 2.3 Display devices.- 2.4 Display processors.- 2.5 The computer.- 2.6 References and bibliography.- 3. Graphics Software.- 3.1 Connecting computers and graphic devices.- 3.2 Graphics software packages.- 3.3 Graphics packages on mini computers and mainframe computers.- 3.4 Microcomputer graphics software.- 3.5 Graphics workstations.- 3.6 The applications program.- 3.7 References and bibliography.- 4. Two-dimensional Graphics.- 4.1 The elements of two-dimensional transformations.- 4.2 Representation of points.- 4.3 Straight line transformations.- 4.4 Rotation.- 4.5 Reflection.- 4.6 Multi-operation transformations (composition).- 4.7 Two-dimensional homogeneous coordinates.- 4.8 Two-dimensional rotation about an arbitrary axis.- 4.9 References.- 5. Three-dimensional Graphics.- 5.1 Basic concepts.- 5.2 Three-dimensional homogeneous coordinates.- 5.3 Three-dimensional scaling.- 5.4 Three-dimensional shearing.- 5.5 Three-dimensional rotations.- 5.6 Reflection in three dimensions.- 5.7 Three-dimensional translation.- 5.8 Three-dimensional rotation about an arbitrary axis.- 5.9 Projections.- 5.10 Conclusions.- 5.11 References.- 6. Hidden Lines and Hidden Surfaces.- 6.1 An introduction to hidden lines and surfaces.- 6.2 A simple hidden lines algorithm.- 6.3 The Galimberti and Montanari algorithm.- 6.4 The hidden surface problem.- 6.5 A preliminary classification.- 6.6 Surface representation and hidden surface methods.- 6.7 Conclusions.- 6.8 References and bibliography.- 7. Graphical Representation of Biological Data.- 7.1 Introduction.- 7.2 Graphs and histograms.- 7.3 Point plots and transforms.- 7.4 Graphics data structures.- 7.5 A data structure for hidden lines treatment.- 7.6 References.- 8. Reconstruction Methods for Cell Systems.- 8.1 Tissue reconstruction.- 8.2 The role of computer graphics.- 8.3 Input of data.- 8.4 Two-dimensional analyses.- 8.5 Three-dimensional reconstruction.- 8.6 Three-dimensional reconstruction of neurones (CELL).- 8.7 Three-dimensional reconstruction of non-neural tissue (RECON).- 8.8 Other three-dimensional reconstruction programs.- 8.9 References and bibliography.- 9. Image Capture and Image Analysis.- 9.1 Biological images.- 9.2 Image capture devices.- 9.3 Analysis of periodic images.- 9.4 The Joyce-Loebl Magiscan.- 9.5 Reconstruction from X-ray data.- 9.6 References and bibliography.- 10. Molecular Graphics.- 10.1 An introduction to molecular graphics.- 10.2 Components of a molecular graphics system.- 10.3 Molecular data.- 10.4 Examples of molecular graphics packages.- 10.5 Some existing systems.- 10.6 References and bibliography.- 11. Simulation and Animation.- 11.1 Moving pictures.- 11.2 Hardware for real-time animations.- 11.3 Concepts of graphic animation.- 11.4 Dynamic graph construction.- 11.5 Simulation of cell division and cell interaction processes.- 11.6 Animation of genetic events.- 11.7 References and bibliography.- Appendix 1: Matrix Manipulations.- A1.1 Basic definitions.- A1.2 Vectors.- A1.3 Matrix addition.- A1.4 The trace of a matrix.- A1.5 The determinants of a matrix.- A1.6 Multiplication by a scalar.- A1.7 Matrix multiplication.- A1.8 References.- Appendix 2: A Graphics Glossary.

Image Capture and Image Analysis

We saw in the last chapter that computer graphics has been widely used in the reconstruction of sectioned biological material. A prerequisite of this type of analysis is that individual elements should be identifiable on the sections for digitization. Often, however, this kind of analysis is not feasible: the complexity of the data may preclude digitization altogether, for example, and in many cases the computer analysis is itself needed to work out the two-dimensional structure of the section.

Graphical Representation of Biological Data

We have looked at the manipulation of two and three-dimensional data in the last three chapters, concentrating mainly on general methodologies. We will now turn to consider specific biological applications of computer graphics. The present chapter deals with aspects of simple data manipulation, while Chapters 8 to 11 are concerned with areas of specific applications.