An Energy-Minimization Finite-Element Approach for the Frank-Oseen Model of Nematic Liquid Crystals: Continuum and Discrete Analysis

This paper outlines an energy-minimization finite-element approach to the computational modeling of equilibrium configurations for nematic liquid crystals under free elastic effects. The method targets minimization of the system free energy based on the Frank-Oseen free-energy model. Solutions to the intermediate discretized free elastic linearizations are shown to exist generally and are unique under certain assumptions. This requires proving continuity, coercivity, and weak coercivity for the accompanying appropriate bilinear forms within a mixed finite-element framework. Error analysis demonstrates that the method constitutes a convergent scheme. Numerical experiments are performed for problems with a range of physical parameters as well as simple and patterned boundary conditions. The resulting algorithm accurately handles heterogeneous constant coefficients and effectively resolves configurations resulting from complicated boundary conditions relevant in ongoing research.Comment: 31 pages, 3 figures, 3 table

An Error Estimator for Electrically Coupled Liquid Crystals

This paper extends an a posteriori error estimator for the elastic, Frank-Oseen model of liquid crystals, derived in [9], to include electric and flexoelectric effects. The problem involves a nonlinear coupled system of equations with a local unit-length constraint imposed via a penalty method. The proposed estimator is proven to be a reliable estimate of global approximation error. The performance of the coupled error estimator as a guide for adaptive refinement is shown in the numerical results, where the adapted grids successfully yield substantial reductions in computational work and comparable or better conformance to important physical laws.Comment: 10 Pages, 2 Figures, Conference: LSSC 2023. arXiv admin note: substantial text overlap with arXiv:1806.0624

Pragmatic Design: A Case Study of Innovation in a Small Software Company

The research question that underpins this paper is ‘What are the novel features of IS design practice ‘in the wild’? In order to help answer this question, a theoretical perspective that focuses on practitioners’ ‘situated practical theory’ in the ‘co-production’ of IS designs is adopted. The context for this study is that firms operating in the IT sector face particular challenges in navigating the complex web of global regulatory requirements. Accordingly, practitioners indicate the need for IT artefacts to informate and help automate compliance processes in organizations. This paper reports on the design of an innovative IT artefact called Compliance-to-Product (C2P), which is argued to be in the vanguard of a new breed of IS called Compliance Knowledge Management Systems (CKMS). The paper describes how this IT artefact was designed by a small-to-medium sized software enterprise, whose design architecture originated in the ‘situated practical theory’ of the company’s founder. However, the findings illustrate that the detailed design was ‘co-produced’ by a network of social actors from collaborating organizations and that this emerged over time. The paper’s concluding observation is that the findings pose a question for design science and the claims for its ability to shape design practice

Randomized benchmarking of single and multi-qubit control in liquid-state NMR quantum information processing

Being able to quantify the level of coherent control in a proposed device implementing a quantum information processor (QIP) is an important task for both comparing different devices and assessing a device's prospects with regards to achieving fault-tolerant quantum control. We implement in a liquid-state nuclear magnetic resonance QIP the randomized benchmarking protocol presented by Knill et al (PRA 77: 012307 (2008)). We report an error per randomized $\frac{\pi}{2}$ pulse of $1.3 \pm 0.1 \times 10^{-4}$ with a single qubit QIP and show an experimentally relevant error model where the randomized benchmarking gives a signature fidelity decay which is not possible to interpret as a single error per gate. We explore and experimentally investigate multi-qubit extensions of this protocol and report an average error rate for one and two qubit gates of $4.7 \pm 0.3 \times 10^{-3}$ for a three qubit QIP. We estimate that these error rates are still not decoherence limited and thus can be improved with modifications to the control hardware and software.Comment: 10 pages, 6 figures, submitted versio

Technology for space shuttle main engine control checkout and diagnosis /GP 70-232/

Electronic control for space shuttle main engin