Solidification in soft-core fluids: disordered solids from fast solidification fronts

Using dynamical density functional theory we calculate the speed of solidification fronts advancing into a quenched two-dimensional model fluid of soft-core particles. We find that solidification fronts can advance via two different mechanisms, depending on the depth of the quench. For shallow quenches, the front propagation is via a nonlinear mechanism. For deep quenches, front propagation is governed by a linear mechanism and in this regime we are able to determine the front speed via a marginal stability analysis. We find that the density modulations generated behind the advancing front have a characteristic scale that differs from the wavelength of the density modulation in thermodynamic equilibrium, i.e., the spacing between the crystal planes in an equilibrium crystal. This leads to the subsequent development of disorder in the solids that are formed. For the one-component fluid, the particles are able to rearrange to form a well-ordered crystal, with few defects. However, solidification fronts in a binary mixture exhibiting crystalline phases with square and hexagonal ordering generate solids that are unable to rearrange after the passage of the solidification front and a significant amount of disorder remains in the system.Comment: 18 pages, 14 fig

Grid models versus TIN : geometric accuracy of multibeam data processing

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Domain/Mesh Decomposition of Unstructured Grids with Pre-Ordering and Smoothing. G.U. Aero Report 9506

Increasingly large scale computations are using unstructured discrete computational grids. A typical example is unstructured grid calculations based on finite volume methods (FVM) in computational fluid dynamics (CFD). One of the efficient ways to deal with such large scale problems is parallelization. The present paper will focus on domain/mesh decomposition. This is the first step for distributing unstructured computational domains on a MIMD-type parallel computer system. A graph theory framework for this problem will be constructed. Based on the framework three domain decomposition algorithms: recursive coordinate bisection (RCB), recursive angular bisection (RAB) and recursive graph bisection (RGB), will be introduced, tested and discussed. A pre-ordering and smoothing technique is proposed. It is necessary in the procedure for obtaining a 'good' domain partitioning result. Another interesting method, called the domain decomposition technique (DDT), is also investigated, which is driven in an inverse way, i.e. domain decomposition followed by mesh construction. Finally a simple and direct strategy called the mesh tailor technique (MTT) is discussed. Numerical comparisons using 2D CFD problems will be given. The further research work required to carry out a parallel implementation of a flow problem will be mentioned

Domain/Mesh Decomposition of Unstructured Grids with Pre-Ordering and Smoothing. G.U. Aero Report 9506

Increasingly large scale computations are using unstructured discrete computational grids. A typical example is unstructured grid calculations based on finite volume methods (FVM) in computational fluid dynamics (CFD). One of the efficient ways to deal with such large scale problems is parallelization. The present paper will focus on domain/mesh decomposition. This is the first step for distributing unstructured computational domains on a MIMD-type parallel computer system. A graph theory framework for this problem will be constructed. Based on the framework three domain decomposition algorithms: recursive coordinate bisection (RCB), recursive angular bisection (RAB) and recursive graph bisection (RGB), will be introduced, tested and discussed. A pre-ordering and smoothing technique is proposed. It is necessary in the procedure for obtaining a 'good' domain partitioning result. Another interesting method, called the domain decomposition technique (DDT), is also investigated, which is driven in an inverse way, i.e. domain decomposition followed by mesh construction. Finally a simple and direct strategy called the mesh tailor technique (MTT) is discussed. Numerical comparisons using 2D CFD problems will be given. The further research work required to carry out a parallel implementation of a flow problem will be mentioned

An intelligent real time 3D vision system for robotic welding tasks

MARWIN is a top-level robot control system that has been designed for automatic robot welding tasks. It extracts welding parameters and calculates robot trajectories directly from CAD models which are then verified by real-time 3D scanning and registration. MARWIN's 3D computer vision provides a user-centred robot environment in which a task is specified by the user by simply confirming and/or adjusting suggested parameters and welding sequences. The focus of this paper is on describing a mathematical formulation for fast 3D reconstruction using structured light together with the mechanical design and testing of the 3D vision system and show how such technologies can be exploited in robot welding tasks

Aerodynamic design optimisation for complex geometries using unstructured grids

These lecture notes, prepared for the 1997 VKI Lecture Course on Inverse Design, discuss the use of unstructured grid CFD methods in the design of complex aeronautical geometries. The emphasis is on gradient-based optimisation approaches. The evaluation of approximate and exact linear sensitivities is described, as are different ways of formulating the adjoint equations to greatly reduce the computational cost when dealing with large numbers of design parameters. \ud \ud The current state-of-the-art is illustrated by two examples from turbomachinery and aircraft design

Solidification and structure formation in soft-core fluids

This thesis analyses the structure, phase behaviour and dynamics of two dimensional (2D) systems of interacting soft-core particles, focussing in particular on how these can solidify and the properties of the resulting crystalline structures. Classical density functional theory (DFT) and dynamical density functional theory (DDFT) is used in the analysis, and an introduction to these is given. The first systems studied are particles interacting via the generalised exponential model of index n (GEM-n) pair potential, including binary mixtures of different types of GEM-n particles. We confirm that a simple mean-field approximate DFT (the RPA-DFT) provides a good approximation for the structure and thermodynamics. We study how solidification fronts advance into the unstable liquid after a temperature quench. We find that the length scale of the density modulations chosen by the front is not necessarily the length scale corresponding the equilibrium crystal structure. This results in the presence of defects and disorder in the structures formed. We analyse how these evolve over time, after the front has passed. We also find that for the binary mixtures, the defects and disorder persists for much longer and in-fact can remain indefinitely. In the final part of this thesis we analyse the Barkan-Engel-Lifshitz (BEL) model, which consists of particles interacting via a soft core potential that is more complicated than the GEM-n potential and can include a minimum in the potential and soft repulsion over several competing length scales. The form of the BEL potential gives good control over the shape of the dispersion relation, which allows it to be tuned to the regime where the system forms quasicrystals. In this regime, we study in detail the nature of the liquid state pair correlations and in particular the form of the asymptotic decay as the distance between the particles r tends to infinity. The usual approach used for fluids in three dimensions has to be generalised, in order to be applicable in 2D. It is found that there is a line in the phase diagram at which the asymptotic decay crosses over from being oscillatory with one wavelength to oscillatory with a different wavelength. We expect this to be a general characteristic of systems that form quasicrystals