Locating Lagrangian coherent structures (LCS) for dynamical systems defined on a spatially limited domain present a challenge because trajectory integration must be stopped at the boundary for lack of further velocity data. This effectively turns the domain boundary into an attractor, introduces edge effects resulting in spurious ridges in the associated finite-time Lyapunov exponent (FTLE) field, and causes some of the real ridges of the FTLE field to be suppressed by strong spurious ridges. To address these issues, we develop a finite-domain FTLE method that renders LCS with an accuracy and fidelity that is suitable for automated feature detection. We show the application of this technique to the analysis of velocity data from aircraft landing at the Hong Kong International Airport.

This paper investigates interval estimation methods for discrete-time linear time-invariant systems. We propose a novel interval estimation method by integrating robust observer design with reachability analysis. By introducing H∞ design into interval estimation, the proposed method provides a systematic and effective approach to improve the accuracy of interval estimation. Moreover, the relationships and comparisons between the existing results and the proposed method are discussed in detail. Finally, simulation results are presented to demonstrate the effectiveness of the proposed method.

Mixed Reality (MR) is of increasing interest within technologydriven modern medicine but is not yet used in everyday practice. This situation is changing rapidly, however, and this paper explores the emergence of MR technology and the importance of its utility within medical applications. A classification of medical MR has been obtained by applying an unbiased text mining method to a database of 1,403 relevant research papers published over the last two decades. The classification results reveal a taxonomy for the development of medical MR research during this period as well as suggesting future trends. We then use the classification to analyse the technology and applications developed in the last five years. Our objective is to aid researchers to focus on the areas where technology advancements in medical MR are most needed, as well as providing medical practitioners with a useful source of reference.

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The accurate real-time detection of turbulent airflow patterns near airports is important for safety and comfort in commercial aviation. In this paper, a method is developed to identify Lagrangian coherent structures (LCS) from horizontal lidar scans at Hong Kong International Airport (HKIA) in China. LCS are distinguished frame-independent material structures that create localized attraction, repulsion, or high shear of nearby trajectories in the flow. As such, they are the fundamental structures behind airflow patterns such as updrafts, downdrafts, and wind shear. Based on a recently developed finite-domain-finite-time Lyapunov exponent (FDFTLE) algorithm from Tang et al. and on new Lagrangian diagnostics presented in this paper that are pertinent to the extracted FDFTLE ridges, the authors differentiate LCS extracted from lidar data. It is found that these LCS derived from horizontal lidar scans compare well to convergence and divergence suggested by vertical slice scans. At HKIA, horizontal scans are predominant: they cover much bigger azimuthal ranges as compared with only two azimuthal angles from the vertical scans. LCS extracted from horizontal scans are thus advantageous in providing organizing turbulence structures over the entire observational domain as compared with a single line along the vertical scan direction. In Part II of this study, the authors will analyze the evolution of LCS and their impacts on landing aircraft based on recorded flight data.

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