Automatic constraint-based synthesis of non-uniform rational B-spline surfaces

In this dissertation a technique for the synthesis of sculptured surface models subject to several constraints based on design and manufacturability requirements is presented. A design environment is specified as a collection of polyhedral models which represent components in the vicinity of the surface to be designed, or regions which the surface should avoid. Non-uniform rational B-splines (NURBS) are used for surface representation, and the control point locations are the design variables. For some problems the NURBS surface knots and/or weights are included as additional design variables. The primary functional constraint is a proximity metric which induces the surface to avoid a tolerance envelope around each component. Other functional constraints include: an area/arc-length constraint to counteract the expansion effect of the proximity constraint, orthogonality and parametric flow constraints (to maintain consistent surface topology and improve machinability of the surface), and local constraints on surface derivatives to exploit part symmetry. In addition, constraints based on surface curvatures may be incorporated to enhance machinability and induce the synthesis of developable surfaces;The surface synthesis problem is formulated as an optimization problem. Traditional optimization techniques such as quasi-Newton, Nelder-Mead simplex and conjugate gradient, yield only locally good surface models. Consequently, simulated annealing (SA), a global optimization technique is implemented. SA successfully synthesizes several highly multimodal surface models where the traditional optimization methods failed. Results indicate that this technique has potential applications as a conceptual design tool supporting concurrent product and process development methods

anamorphic projection analogical digital algorithms

The study presents the first results of a wider research project dealing with the theme of "anamorphosis", a specific technique of geometric projection of a shape on a surface. Here we investigate how new digital techniques make it possible to simplify the anamorphic applications even in cases of projections on complex surfaces. After a short excursus of the most famous historical and contemporary applications, we propose several possible approaches for managing the geometry of anamorphic curves both in the field of descriptive geometry (by using interactive tools such as Cabri and GeoGebra) and during the complex surfaces realization process, from concept design to manufacture, through CNC systems (by adopting generative procedural algorithms elaborated in Grasshopper)

Application of general semi-infinite Programming to Lapidary Cutting Problems

We consider a volume maximization problem arising in gemstone cutting industry. The problem is formulated as a general semi-infinite program (GSIP) and solved using an interiorpoint method developed by Stein. It is shown, that the convexity assumption needed for the convergence of the algorithm can be satisfied by appropriate modelling. Clustering techniques are used to reduce the number of container constraints, which is necessary to make the subproblems practically tractable. An iterative process consisting of GSIP optimization and adaptive refinement steps is then employed to obtain an optimal solution which is also feasible for the original problem. Some numerical results based on realworld data are also presented

Origamic Architectural Form Design System

In this research we will try to define a more accurate knowledge about origami. We will be able to see the origami from the mathematical point of view. Also establish the connection between the origami, architecture and design. The methods for the exploring the use of three-dimensional symmetries in the design of spatial structures will be reviewed. Examples in architecture and decorative arts were collected and analyzed. We will define the use of origami as a method to explore shapes in the design process, which can even lead to the discovery of new forms and construction methods. The use of origami techniques as a method for exploring the use of three-dimensional symmetries in the design of spatial structures

On the Pricing of Forward Starting Options under Stochastic Volatility

We consider the problem of pricing European forward starting options in the presence of stochastic ­volatility. By performing a change of measure using the asset price at the time of strike determination as a numeraire, we derive a closed-form solution based on Heston’s model of stochastic volatility

Characterisation of flow structures inside an engine cylinder under steady state condition

The in-cylinder flow of internal combustion (IC) engines, formed during the intake stroke, is one of the most important factors that affect the quality of air-fuel mixture and combustion. The inducted airflow through the inlet valve is primarily influenced by the intake port design, intake valve design, valve lift and valve timing. Such parameters have a significant influence on the generation and development of in-cylinder flow motion. In most combustion systems the swirl and tumble motions are used to aid the air-fuel mixing with the subsequent decay of these bulk flow motions generating increased turbulence levels which then enhance the combustion processes in terms of rate of chemical reactions and combustion stability. Air motion formed inside the engine cylinder is three-dimensional, transient, highly turbulent and includes a wide spectrum of length and time scales. The significance of in-cylinder flow structures is mainly reflected in large eddy formation and its subsequent break down into turbulence kinetic energy. Analysis of the large scale and flow motions within an internal combustion engine are of significance for the improvement of engine performance. A first approximation of these flow structures can be obtained by steady state analysis of the in-cylinder flow with fixed valve lifts and pressure drops. Substantial advances in both experimental methods and numerical simulations provide useful research tools for better understanding of the effects of rotational air motion on engine performance. This study presents results from experimental and numerical simulations of in-cylinder flow structures under steady state conditions. Although steady state flow problem still includes complex three-dimensional geometries with high turbulence intensities and rotation separation, it is significantly less complex than the transient problem. Therefore, preliminary verifications are usually performed on steady state flow rig. For example, numerical investigation under steady state condition can be considered as a precondition for the feasibility of calculations of real engine cylinder flow. Particle Image Velocimetry (PIV) technique is used in the experimental investigations of the in-cylinder flow structures. The experiments have been conducted on an engine head of a pent-roof type (Lotus) for a number of fixed valve lifts and different inlet valve configurations at two pressure drops, 250mm and 635mm of H2O that correlate with engine speeds of 2500 and 4000 RPM respectively. From the 2-D in-cylinder flow measurements, a tumbling vortex analysis is carried out for six planes parallel to the cylinder axis. In addition, a swirl flow analysis is carried out for one horizontal plane perpendicular to the cylinder axis at half bore downstream from the cylinder head (44mm). Numerically, modelling of the in-cylinder flow is proving to be a key part of successful combustion simulation. The numerical simulations require an accurate representation of turbulence and initial conditions. This Thesis deals with numerical investigation of the in-cylinder flow structures under steady state conditions utilizing the finite-volume CFD package, STAR CCM+. Two turbulence models were examined to simulate the turbulent flow structure namely, Realizable k-ε and Reynolds Stress Turbulence Model, RSM. Three densities of generated mesh, which is polyhedral type, are examined. The three-dimensional numerical investigation has been conducted on the same engine head of a pent-roof type (Lotus) for a number of fixed valve lifts and both valves are opened configuration at two pressure drops 250mm and 635mm of H2O that is equivalent to engine speeds of 2500 and 4000 RPM respectively. The nature and modelling of the flow structure together with discussions on the influence of the pressure drop and valve lift parameters on the flow structures are presented and discussed. The experimental results show the advantage of using the planar technique (PIV) for investigating the complete flow structures developed inside the cylinder. It also highlighted areas where improvements need to be made to enhance the quality of the collected data in the vertical plane measurements. Based on the comparison between the two turbulence models, the RSM model results show larger velocity values of about 15% to 47% than those of the Realizable k-ε model for the whole regions. The computational results were validated through qualitative and quantitative comparisons with the PIV data obtained from the current investigation and published LDA data on both horizontal and vertical cross sections. The calculated correlation coefficient, which is above 0.6, indicated that a reasonable prediction accuracy for the RSM model. This verifies that the numerical simulation with the RSM model is a useful tool to analyse turbulent flows in complex engine geometries where anisotropic turbulence is created

Surface Patterns On Single Cells: A Consequence Of A Phase Transition To Modulated Phases

Patterns are ubiquitous in the world around us, and we have only begun to scratch the surface of understanding their complexity and formation. In this thesis, we draw inspiration from rigid, extracellular surface patterns found on single living cells in many taxa and try to understand if there is a common thread in their pattern formation mechanisms that can be described by a single physical formalism. Pollen grains, butterfly wing scales, and deep-sea protists called phaeodarians all have beautifully ornate and varied hard surface structures that are likely patterned by the deposition of some soft organic matrix originating inside of the cell. We focus on pollen grain surfaces because of their remarkable geometric variety that is well documented. We find, through our own electron microscopy and careful histological techniques, that the patterns arise due to a phase separation of a transient polysaccharide material mechanically coupled to the underlying elastic cell membrane. We then show that the entire evolved diversity of patterns can be recapitulated by exploring both the equilibrium states and the dynamics of a modified Landau-Ginzburg model of phase transitions to modulated phases. We observe the surprising fact that only ~10% of extant species exhibit patterns that reach equilibrium. Furthermore, we find that although these patterns have evolved many times in seed plants, they are not, on average, selected for. The remaining 90% of pollen grain surfaces resemble arrested intermediate states of the phase transition process. We then document the pattern formation process in butterfly wing scales and show that a transient, spatially periodic surface material sits between the global surface features of the scales (the ridges). We postulate that the phase transition of this material may also contribute to the regular patterns on wing scale cells. We finally image the full three-dimensional features of geodesic phaeodarians tests using x-ray-computed tomography