Quantum mechanics in finite dimensional Hilbert space

The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with the infinite dimensional case. The construction of an unbiased basis for state determination is discussed.Comment: 14 pages, no figure

Model-Based Control Using Koopman Operators

This paper explores the application of Koopman operator theory to the control of robotic systems. The operator is introduced as a method to generate data-driven models that have utility for model-based control methods. We then motivate the use of the Koopman operator towards augmenting model-based control. Specifically, we illustrate how the operator can be used to obtain a linearizable data-driven model for an unknown dynamical process that is useful for model-based control synthesis. Simulated results show that with increasing complexity in the choice of the basis functions, a closed-loop controller is able to invert and stabilize a cart- and VTOL-pendulum systems. Furthermore, the specification of the basis function are shown to be of importance when generating a Koopman operator for specific robotic systems. Experimental results with the Sphero SPRK robot explore the utility of the Koopman operator in a reduced state representation setting where increased complexity in the basis function improve open- and closed-loop controller performance in various terrains, including sand.Comment: 8 page

Entanglement for all quantum states

It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom, becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is ubiquitous in quantum systems. Simple examples are calculated and a general proof is provided. The physical relevance of the change of tensor product structure is mentioned.Comment: 9 page

In-Flight Cost Index Optimisation Upon Weather Forecast Updates

This paper presents an optimisation framework to compute the altitude and speed profiles of a trajectory in the execution phase of the flight, such that the expected total cost (ETC) of the operation is minimised (i.e., modelling the expected cost of delay and fuel – including arrival uncertainties – at the arrival gate). This is achieved with a two-stage optimisation strategy: a trajectory optimiser that minimises a generalised direct operating cost function, for a given cost index; and an upper-level optimiser, which obtains the best cost index that minimises the ETC. Several case studies are presented for different departure delays, while considering the impact of two different weather forecast updates too: a region with relative high head-winds appearing half way across the flight; and a cold atmosphere scenario, with a tropopause altitude lower than standard conditions

Quantum diffusion on a cyclic one dimensional lattice

The quantum diffusion of a particle in an initially localized state on a cyclic lattice with N sites is studied. Diffusion and reconstruction time are calculated. Strong differences are found for even or odd number of sites and the limit N->infinit is studied. The predictions of the model could be tested with micro - and nanotechnology devices.Comment: 17 pages, 5 figure

Clinkering and hydration study of non-active and active Belite-Alite-Ye'elimite (BAY) cements

The aim of AIM is to promote industry-driven, interdisciplinary research in material science and engineering in order to provide leading-edge, sustainable solutions to the challenges facing engineers in today’s changing society and environment. http://www.ucl.ac.uk/aim/conference-info/37ccsThe manufacturing process of ye'elimite rich cements emit about 15-37% less CO2 to the atmosphere than OPC. Cements that contain belite, ye’elimite and ferrite, known as BYF cements, are promising eco-friendly binders. However, belite, their main phase, shows a slow hydrating behaviour; therefore the corresponding mortars present lower mechanical strengths than OPC at early ages. To solve this problem, BYF clinkers can be activated by: i) forming alite jointly with belite and ye’elimite during clinkering, known as BAY clinkers. The alite and ye’elimite reaction with water should develop high mechanical strengths at early ages, besides, belite contributes to later curing times. ii) A second activation is based on the stabilisation of alpha forms of belite by dopants. The objective of this work is to obtain two types of BAY clinkers (standard and active BAY) using CaF2 as mineraliser and borax as dopant agent to stabilize alpha forms of belite phase. After that, anhydrite was added as sulphate source to obtain the corresponding cements. The hydration behaviour of these cements has been studied through rheological and x-ray diffraction measurements, the latter combined with Rietveld quantitative phase analysis. In addition, mechanical and dimensional properties of BAY mortars are also presented and discussed.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Considering TMA holding uncertinaty into in-flight trajectory optimisation

Aircraft crew are aware of the delay they have experienced at departure. However, uncertainties ahead, and in particular holdings at arrival, can have an impact on the final performance of their operations. When optimising a trajectory the expected cost at the arrival gate should be considered. Consequently, taking into account potential congestion and extra delay at the arrival airspace is paramount to avoid taking sub-optimal decisions at the early stages of the flight. This paper presents a framework to optimise trajectories in the execution phase of the flight considering expected delays at arrival. A flight from Athens (LGAV) to London Heathrow (EGLL) is used as illustrative example, systematically exploring a range of departure delays and expected holdings at arrival