Efficient integration of software components for scientific simulations

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A fast Monte Carlo algorithm for site or bond percolation

We describe in detail a new and highly efficient algorithm for studying site or bond percolation on any lattice. The algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time which scales linearly with the size of the system. We demonstrate our algorithm by using it to investigate a number of issues in percolation theory, including the position of the percolation transition for site percolation on the square lattice, the stretched exponential behavior of spanning probabilities away from the critical point, and the size of the giant component for site percolation on random graphs.Comment: 17 pages, 13 figures. Corrections and some additional material in this version. Accompanying material can be found on the web at http://www.santafe.edu/~mark/percolation

A practical guide to computer simulations

Here practical aspects of conducting research via computer simulations are discussed. The following issues are addressed: software engineering, object-oriented software development, programming style, macros, make files, scripts, libraries, random numbers, testing, debugging, data plotting, curve fitting, finite-size scaling, information retrieval, and preparing presentations. Because of the limited space, usually only short introductions to the specific areas are given and references to more extensive literature are cited. All examples of code are in C/C++.Comment: 69 pages, with permission of Wiley-VCH, see http://www.wiley-vch.de (some screenshots with poor quality due to arXiv size restrictions) A comprehensively extended version will appear in spring 2009 as book at Word-Scientific, see http://www.worldscibooks.com/physics/6988.htm

Planar graphs : a historical perspective.

The field of graph theory has been indubitably influenced by the study of planar graphs. This thesis, consisting of five chapters, is a historical account of the origins and development of concepts pertaining to planar graphs and their applications. The first chapter serves as an introduction to the history of graph theory, including early studies of graph theory tools such as paths, circuits, and trees. The second chapter pertains to the relationship between polyhedra and planar graphs, specifically the result of Euler concerning the number of vertices, edges, and faces of a polyhedron. Counterexamples and generalizations of Euler\u27s formula are also discussed. Chapter III describes the background in recreational mathematics of the graphs of K5 and K3,3 and their importance to the first characterization of planar graphs by Kuratowski. Further characterizations of planar graphs by Whitney, Wagner, and MacLane are also addressed. The focus of Chapter IV is the history and eventual proof of the four-color theorem, although it also includes a discussion of generalizations involving coloring maps on surfaces of higher genus. The final chapter gives a number of measurements of a graph\u27s closeness to planarity, including the concepts of crossing number, thickness, splitting number, and coarseness. The chapter conclused with a discussion of two other coloring problems - Heawood\u27s empire problem and Ringel\u27s earth-moon problem

An extensive English language bibliography on graph theory and its applications

Bibliography on graph theory and its application

Enumerating molecules.

This report is a comprehensive review of the field of molecular enumeration from early isomer counting theories to evolutionary algorithms that design molecules in silico. The core of the review is a detail account on how molecules are counted, enumerated, and sampled. The practical applications of molecular enumeration are also reviewed for chemical information, structure elucidation, molecular design, and combinatorial library design purposes. This review is to appear as a chapter in Reviews in Computational Chemistry volume 21 edited by Kenny B. Lipkowitz

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

Calculation of the Electronic and Optical Properties of Nanoscale Systems

At the nanometer length scale, the size of surface features in crystalline semiconductor systems is of the same order as the electron wavelength. This can result in unusual behaviour in the systems electronic, magnetic and optical properties due to electron confinement effects. Such effects can have practical and commercial applications and are currently the subject of considerable study in the disciplines of theoretical, computational and materials technology within nanoscience. This thesis uses molecular dynamics computational methods to examine such effects in the electronic structure of semiconductor-based crystalline systems. Three unique surfaces were studied in detail - the SiC(111) surface, the SiC(100) surface, and the prototypical In-Si(111) surface. Silicon carbide is of importance in the development of semiconductor technologies due to its physical robustness and relatively high power capabilities. An understanding of surface metallisation in semiconductors is of paramount importance since modern technology relies on the interaction of metals with semiconductors in integrated circuit and device construction. If Mooreʼs Law is to be adhered to, transistors must become smaller and the metal contacts between transistors must likewise shrink. This work explores the possibility that potassium deposited on the SiC(100) surface may provide a solution for nanoscale contacts between devices on this surface. Using modified and highly efficient molecular dynamics code, the energies and reconstructions of a number of possible surface configurations were studied in detail, resulting in proposed new candidates for surface reconstruction for a range of coverages of potassium on the SiC(100) surface. The SiC(111) surface has previously been shown to undergo an interesting metal-insulator transition where the surface band states split. This has been observed by experimentally probing the surface states with scanning tunneling spectroscopy and photoemission techniques. By applying ab-initio molecular dynamics techniques to simulate this surface, this research has found compelling evidence for the actual mechanism that results in this transition. A number of time-dependent simulations of the surface in question were carried out, over ranges of tens of thousands of picoseconds. The results show that the surface is dynamical in nature. Furthermore, the transition is shown to be due to a soft phonon interaction on the surface, and thus surface dangling bonds are seen to split because they are in constant motion. Finally, computational studies of the In-Si(111) surface are also presented. The results indicate a dynamical surface exhibiting surface phonon effects, similar to the SiC(111) surface studied and metallisation in a similar vein to results obtained for the K-SiC(100) surface. The study of the In-Si(111) surface therefore represents a natural progression in studies of this nature. The computational work presented here was carried out using the FIREBALL suite of tools. During the course of this study, the codebase was rewritten and modernised to improve performance and to allow for easier future modification. The extensive changes to the code are discussed, as are its potential future applications in the field of computational solid state physics. Practical methods are presented that allow for the work to progress to the calculation of optical transitions directly in FIREBALL, with a full description of how a reflectance anisotropy spectrum could be calculated as a logical extension of the present work. The calculation of a reflectance anisotropy spectrum would be of considerable interest to experiments in the field