Quantitative Set-Based Design for Complex System Development

This dissertation comprises a body of research facilitating decision-making and complex system development with quantitative set-based design (SBD). SBD is concurrent product development methodology, which develops and analyzes many design alternatives for longer time periods enabling design maturation and uncertainty reduction. SBD improves design space exploration, facilitating the identification of resilient and affordable systems. The literature contains numerous qualitative descriptions and quantitative methodologies describing limited aspects of the SBD process. However, there exist no methodologies enabling the quantitative management of SBD programs throughout the entire product development cycle. This research addresses this knowledge gap by developing the process framework and supporting methodologies guiding product development from initial system concepts to a final design solution. This research provides several new research contributions. First, we provide a comprehensive SBD state-of-practice assessment identifying key knowledge and methodology gaps. Second, we demonstrate the physical implementation of the integrated analytics framework in a model-based engineering environment. Third, we develop a quantitative methodology enabling program management decision making in SBD. Fourth, we describe a supporting uncertainty reduction methodology using multiobjective value of information analysis to assess design set maturity and higher-resolution model usefulness. Finally, we describe a quantitative SBD process framework enabling sequential design maturation and uncertainty reduction decisions. Using an unmanned aerial vehicle case study, we demonstrate our methodology’s ability to resolve uncertainty and converge a complex design space onto a set of resilient and affordable design solutions

Electronic structure of turbostratic graphene

We explore the rotational degree of freedom between graphene layers via the simple prototype of the graphene twist bilayer, i.e., two layers rotated by some angle $\theta$. It is shown that, due to the weak interaction between graphene layers, many features of this system can be understood by interference conditions between the quantum states of the two layers, mathematically expressed as Diophantine problems. Based on this general analysis we demonstrate that while the Dirac cones from each layer are always effectively degenerate, the Fermi velocity $v_F$ of the Dirac cones decreases as $\theta\to 0^\circ$; the form we derive for $v_F(\theta)$ agrees with that found via a continuum approximation in Phys. Rev. Lett., 99:256802, 2007. From tight binding calculations for structures with $1.47^\circ \le \theta < 30^\circ$ we find agreement with this formula for $\theta \gtrsim 5^\circ$. In contrast, for $\theta \lesssim 5^\circ$ this formula breaks down and the Dirac bands become strongly warped as the limit $\theta \to 0$ is approached. For an ideal system of twisted layers the limit as $\theta\to0^\circ$ is singular as for $\theta > 0$ the Dirac point is fourfold degenerate, while at $\theta=0$ one has the twofold degeneracy of the $AB$ stacked bilayer. Interestingly, in this limit the electronic properties are in an essential way determined \emph{globally}, in contrast to the 'nearsightedness' [W. Kohn. Phys. Rev. Lett., 76:3168, 1996.] of electronic structure generally found in condensed matter.Comment: Article as to be published in Phys. Rev B. Main changes: K-point mapping tables fixed, several changes to presentation

Spectral density and metal-insulator phase transition in Mott insulators within RDMFT

We present a method for calculating the spectrum of periodic solids within reduced density matrix functional theory. This method is validated by a detailed comparison of the angular momentum projected spectral density with that of well established many-body techniques, in all cases finding an excellent agreement. The physics behind the pressure induced insulator-metal phase transition in MnO is investigated. The driving mechanism of this transition is identified as increased crystal field splitting with pressure, resulting in a charge redistribution between the Mn $e_g$ and $t_2g$ symmetry projected states.Comment: arXiv admin note: text overlap with arXiv:0912.111

On the impact of the Bristol ChemLabS’ outreach programme on admissions to the School of Chemistry

Analysis of the average number of applicants received from schools that engaged in the Bristol ChemLabS Outreach program prior to a student‟s application with those that did not engage, shows a significant increase in applicants from engaged schools. The significance is weaker when just Post 16 students are considered but this is almost certainly due to a smaller sample size. When this analysis was inspected in terms of the distance of the school from the University of Bristol, there was an increase in the number of applicants from engaged schools irrespective of distance. However, a statistically significant increase was observed for schools within 50 miles of the University from an analysis of just Post 16 students. Students who applied to the department from an engaged school were more likely to accept an offer and also to make the department their firm acceptance. A slightly higher number of applications that were rejected came from engaged schools too. There are two possible reasons; first, the engagement may have encouraged more students who did not have the required entry qualifications. Second, during the period of analysis, the overall entry grades went up by one grade each year. Such a dramatic rise was probably the reason for the slightly elevated numbers