Cellular automaton supercolliders

Gliders in one-dimensional cellular automata are compact groups of non-quiescent and non-ether patterns (ether represents a periodic background) translating along automaton lattice. They are cellular-automaton analogous of localizations or quasi-local collective excitations travelling in a spatially extended non-linear medium. They can be considered as binary strings or symbols travelling along a one-dimensional ring, interacting with each other and changing their states, or symbolic values, as a result of interactions. We analyse what types of interaction occur between gliders travelling on a cellular automaton `cyclotron' and build a catalog of the most common reactions. We demonstrate that collisions between gliders emulate the basic types of interaction that occur between localizations in non-linear media: fusion, elastic collision, and soliton-like collision. Computational outcomes of a swarm of gliders circling on a one-dimensional torus are analysed via implementation of cyclic tag systems

Automatic Filters for the Detection of Coherent Structure in Spatiotemporal Systems

Most current methods for identifying coherent structures in spatially-extended systems rely on prior information about the form which those structures take. Here we present two new approaches to automatically filter the changing configurations of spatial dynamical systems and extract coherent structures. One, local sensitivity filtering, is a modification of the local Lyapunov exponent approach suitable to cellular automata and other discrete spatial systems. The other, local statistical complexity filtering, calculates the amount of information needed for optimal prediction of the system's behavior in the vicinity of a given point. By examining the changing spatiotemporal distributions of these quantities, we can find the coherent structures in a variety of pattern-forming cellular automata, without needing to guess or postulate the form of that structure. We apply both filters to elementary and cyclical cellular automata (ECA and CCA) and find that they readily identify particles, domains and other more complicated structures. We compare the results from ECA with earlier ones based upon the theory of formal languages, and the results from CCA with a more traditional approach based on an order parameter and free energy. While sensitivity and statistical complexity are equally adept at uncovering structure, they are based on different system properties (dynamical and probabilistic, respectively), and provide complementary information.Comment: 16 pages, 21 figures. Figures considerably compressed to fit arxiv requirements; write first author for higher-resolution version

Stochastic modeling of discontinuous dynamic recrystallization at finite strains in hcp metals

We present a model that aims to describe the effective, macroscale material response as well as the underlying mesoscale processes during discontinuous dynamic recrystallization under severe plastic deformation. Broadly, the model brings together two well-established but distinct approaches – first, a continuum crystal plasticity and twinning approach to describe complex deformation in the various grains, and second, a discrete Monte-Carlo-Potts approach to describe grain boundary migration and nucleation. The model is implemented within a finite-strain Fast Fourier Transform-based framework that allows for efficient simulations of recrystallization at high spatial resolution, while the grid-based Fourier treatment lends itself naturally to the Monte-Carlo approach. The model is applied to pure magnesium as a representative hexagonal closed packed metal, but is sufficiently general to admit extension to other material systems. Results demonstrate the evolution of the grain architecture in representative volume elements and the associated stress–strain history during the severe simple shear deformation typical of equal channel angular extrusion. We confirm that the recrystallization kinetics converge with increasing grid resolution and that the resulting model captures the experimentally observed transition from single- to multi-peak stress–strain behavior as a function of temperature and rate

From Models to Simulations

This book analyses the impact computerization has had on contemporary science and explains the origins, technical nature and epistemological consequences of the current decisive interplay between technology and science: an intertwining of formalism, computation, data acquisition, data and visualization and how these factors have led to the spread of simulation models since the 1950s. Using historical, comparative and interpretative case studies from a range of disciplines, with a particular emphasis on the case of plant studies, the author shows how and why computers, data treatment devices and programming languages have occasioned a gradual but irresistible and massive shift from mathematical models to computer simulations

Mesoscale fluid simulation with the Lattice Boltzmann method

PhDThis thesis describes investigations of several complex fluid effects., including hydrodynamic spinodal decomposition, viscous instability. and self-assembly of a cubic surfactant phase, by simulating them with a lattice Boltzmann computational model. The introduction describes what is meant by the term "complex fluid", and why such fluids are both important and difficult to understand. A key feature of complex fluids is that their behaviour spans length and time scales. The lattice Boltzmann method is presented as a modelling technique which sits at a "mesoscale" level intermediate between coarse-grained and fine-grained detail, and which is therefore ideal for modelling certain classes of complex fluids. The following chapters describe simulations which have been performed using this technique, in two and three dimensions. Chapter 2 presents an investigation into the separation of a mixture of two fluids. This process is found to involve several physical mechanisms at different stages. The simulated behaviour is found to be in good agreement with existing theory, and a curious effect, due to multiple competing mechanisms, is observed, in agreement with experiments and other simulations. Chapter 3 describes an improvement to lattice Boltzmann models of Hele-Shaw flow, along with simulations which quantitatively demonstrate improvements in both accuracy and numerical stability. The Saffman-Taylor hydrodynamic instability is demonstrated using this model. Chapter 4 contains the details and results of the TeraGyroid experiment, which involved extremely large-scale simulations to investigate the dynamical behaviour of a self-assembling structure. The first finite- size-effect- free dynamical simulations of such a system are presented. It is found that several different mechanisms are responsible for the assembly; the existence of chiral domains is demonstrated, along with an examination of domain growth during self-assembly. Appendix A describes some aspects of the implementation of the lattice Boltzmann codes used in this thesis; appendix B describes some of the Grid computing techniques which were necessary for the simulations of chapter 4. Chapter 5 summarises the work, and makes suggestions for further research and improvement.Huntsman Corporation Queen Mary University Schlumberger Cambridge Researc

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008