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

Simulation of pore-scale flow using finite element-methods

I present a new finite element (FE) simulation method to simulate pore-scale flow. Within the pore-space, I solve a simplified form of the incompressible Navier-Stoke’s equation, yielding the velocity field in a two-step solution approach. First, Poisson’s equation is solved with homogeneous boundary conditions, and then the pore pressure is computed and the velocity field obtained for no slip conditions at the grain boundaries. From the computed velocity field I estimate the effective permeability of porous media samples characterized by thin section micrographs, micro-CT scans and synthetically generated grain packings. This two-step process is much simpler than solving the full Navier Stokes equation and therefore provides the opportunity to study pore geometries with hundreds of thousands of pores in a computationally more cost effective manner than solving the full Navier-Stoke’s equation. My numerical model is verified with an analytical solution and validated on samples whose permeabilities and porosities had been measured in laboratory experiments (Akanji and Matthai, 2010). Comparisons were also made with Stokes solver, published experimental, approximate and exact permeability data. Starting with a numerically constructed synthetic grain packings, I also investigated the extent to which the details of pore micro-structure affect the hydraulic permeability (Garcia et al., 2009). I then estimate the hydraulic anisotropy of unconsolidated granular packings. With the future aim to simulate multiphase flow within the pore-space, I also compute the radii and derive capillary pressure from the Young-Laplace equation (Akanji and Matthai,2010

ABC of multi-fractal spacetimes and fractional sea turtles

We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with $q$-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes.Comment: 20 pages, 1 figure. v2: typos corrected, minor improvements of the tex

Sorption in disordered porous media

The lattice-gas model of sorption in disordered porous media is studied for a variety of settings, using existing, updated and newly developed numerical techniques. Firstly, we construct an efficient algorithm to calculate the exact partition function for small lattice-gas systems. The exact partition function is used for detailed analysis of the core features exhibited by such systems. We proceed to develop an interactive Monte Carlo (MC) simulation engine, that simulates sorption in a porous media sample and provides real-time visual data of the state space projection and the 3d view of the sample among other parameters of interest, as the external fields are manipulated. The use of such tool provides a more intuitive understanding of the system behaviour. The MC simulations are employed to study sorption in several porous solids: silica aerogel, Vycor glass and soil. We investigate how the phenomena depend on the microstructure of the original samples, how the behaviour varies with the external conditions, and how it is reflected in the paths that the system takes across its state space. Secondly, we develop two methods for estimation of the relative degeneracy (the number of microstates that have the same value of some macroscopic variables) in the systems that are too large to be handled exactly. The methods, based on a restricted infinite temperature sampling, obtain equidegenerate surfaces and the degeneracy gradient across the state space. Combined with the knowledge of an internal energy of a microstate, it enables us to construct the free energy map and thus the equilibrium probability distribution for the studied projection of the state space. Thirdly, the jump-walking Monte-Carlo algorithm is revisited and updated to study the equilibrium properties of systems exhibiting quasi-ergodicity. It is designed for a single processing thread as opposed to currently predominant algorithms for large parallel processing systems. The updated algorithm is tested on the Ising model and applied to the lattice-gas model for sorption in aerogel and Vycor glass at low temperatures, when dynamics of the system is significantly slowed down. It is demonstrated that the updated jump-walking simulations are able to produce equilibrium isotherms which are typically hidden by the hysteresis effect characteristic of the standard single-flip simulations. As a result, we answer the long standing question about the existence of the first-order phase transitions in Vycor. Finally, we investigate sorption in several distinct topology network representations of soil and aerogel samples and demonstrate that the recently developed analytical techniques for random networks can be used to achieve a qualitative understanding of the phenomena in real materials.EPSR

Specifying a hybrid, multiple material CAD system for next-generation prosthetic design

For many years, the biggest issue that causes discomfort and hygiene issues for patients with lower limb amputations have been the interface between body and prosthetic, the socket. Often made of an inflexible, solid polymer that does not allow the residual limb to breathe or perspire and with no consideration for the changes in size and shape of the human body caused by changes in temperature or environment, inflammation, irritation and discomfort often cause reduced usage or outright rejection of the prosthetic by the patient in their day to day lives. To address these issues and move towards a future of improved quality of life for patients who suffer amputations, Loughborough University formed the Next Generation Prosthetics research cluster. This work is one of four multidisciplinary research studies conducted by members of this research cluster, focusing on the area of Computer Aided Design (CAD) for improving the interface with Additive Manufacture (AM) to solve some of the challenges presented with improving prosthetic socket design, with an aim to improve and streamline the process to enable the involvement of clinicians and patients in the design process. The research presented in this thesis is based on three primary studies. The first study involved the conception of a CAD criteria, deciding what features are needed to represent the various properties the future socket outlined by the research cluster needs. These criteria were then used for testing three CAD systems, one each from the Parametric, Non Uniform Rational Basis Spline (NURBS) and Polygon archetypes respectively. The result of these tests led to the creation of a hybrid control workflow, used as the basis for finding improvements. The second study explored emerging CAD solutions, various new systems or plug-ins that had opportunities to improve the control model. These solutions were tested individually in areas where they could improve the workflow, and the successful solutions were added to the hybrid workflow to improve and reduce the workflow further. The final study involved taking the knowledge gained from the literature and the first two studies in order to theorise how an ideal CAD system for producing future prosthetic sockets would work, with considerations for user interface issues as well as background CAD applications. The third study was then used to inform the final deliverable of this research, a software design specification that defines how the system would work. This specification was written as a challenge to the CAD community, hoping to inform and aid future advancements in CAD software. As a final stage of research validation, a number of members of the CAD community were contacted and interviewed about their feelings of the work produced and their feedback was taken in order to inform future research in this area

Advances in shape measurement in the digital world

The importance of particle shape in terms of its effects on the behaviour of powders and other particulate systems has long been recognised, but particle shape information has been rather difficult to obtain and use until fairly recently, unlike its better-known counterpart, particle size. However, advances in computing power and 3D image acquisition and analysis techniques have resulted in major progress being made in the measurement, description and application of particle shape information in recent years. Because we are now in a digital era, it is fitting that many of these advanced techniques are based on digital technology. This review article aims to trace the development of these new techniques, highlight their contributions to both academic and practical applications, and present a perspective for future developments