Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

Discovering mutual proximity and avoiding collisions is one of the most critical services needed by the next generation of Unmanned Aerial Vehicles (UAVs). However, currently available solutions either rely on sharing mutual locations, neglecting the location privacy of involved parties, or are applicable for fully autonomous vehicles only—leaving unaddressed Remotely-Piloted UAVs’ safety needs. Alternatively, proximity can be discovered by adding sensing capabilities. However, in addition to the cost of the sensors, the complexity of integration, and the toll on the energy budget, the effectiveness of such solutions is usually limited by short detection ranges, making them hardly useful in high-mobility scenarios. In this paper, we propose LPPD (an acronym for Lightweight Privacy-preserving Proximity Discovery), a unique solution for privacy-preserving proximity discovery among remotely piloted UAVs based on the exchange of wireless messages. LPPD integrates two main building blocks: (i) a custom space tessellation technique based on randomized spheres; and, (ii) a lightweight cryptographic primitive for private-set intersection. Another feature enjoyed by LPPD is that it does not require online third parties. LPPD is rooted in sound theoretical results and is supported by an experimental assessment performed on a real drone. In particular, experimental results show that LPPD achieves 100% proximity discovery while taking only 39.66 milliseconds in the most lightweight configuration and draining only the 5 · 10− 6% of the UAV’s battery capacity. In addition, LPPD’s security properties are formally verified.

This thesis investigates a one-dimensional Mean-field Planning problem with interactions through ranking. We build a self-contained text that includes the necessary background material. We mention the basic concepts of Mean-field Games and the related notions. The thesis introduces some notions from the Calculus of Variations and Optimal Control. Then, we discuss the uniqueness of solutions for Mean-field Games. To study the uniqueness, we use monotone operator methods.

A brief account of photonics research activities in the selected countries in the Middle East and Africa is presented in this article. Though not comprehensive, we hope to provide a glimpse of the research landscape in the region, and the collaboration and connection with each other and the international partners.

Gaussian random fields with Matérn covariance functions are popular models in spatial statistics and machine learning. In this work, we develop a spatio-temporal extension of the Gaussian Matérn fields formulated as solutions to a stochastic partial differential equation. The spatially stationary subset of the models have marginal spatial Matérn covariances, and the model also extends to Whittle-Matérn fields on curved manifolds, and to more general non-stationary fields. In addition to the parameters of the spatial dependence (variance, smoothness, and practical correlation range) it additionally has parameters controlling the practical correlation range in time, the smoothness in time, and the type of non-separability of the spatio-temporal covariance. Through the separability parameter, the model also allows for separable covariance functions. We provide a sparse representation based on a finite element approximation, that is well suited for statistical inference and which is implemented in the R-INLA software. The flexibility of the model is illustrated in an application to spatio-temporal modeling of global temperature data.

High-order discretizations coupled with adaptive formulations on unstructured grids are expected to be an essential component of future solvers for high-fidelity flow simulations. This work reports on the numerical properties, solution capabilities, and computational performance of a fully-discrete h/p-adaptive entropy stable discontinuous Galerkin (DG) scheme for the compressible Navier–Stokes equations. The numerical framework used in this study is referred to as SSDC. This work verifies and validates low- and high-order spatial discretizations based on summation-by-parts (SBP) operators with a series of test cases. The numerical simulations presented here demonstrate the competitiveness and fidelity of highorder entropy stable methods. The work also reviews the main components of the spatial and temporal discretization techniques implemented in the SSDC solver and provides an overview of the entropy stability analysis for the compressible flow equations.

The metric terms arising in flow simulations with complex geometries and their approximation for tensor product discretizations are studied in this work. The metric terms are constructed for non-conforming discretization at the cell interfaces by solving a strictly convex quadratic optimization problem. This study aims to show the efficacy of the proposed technique in the context of low and high-order accurate entropy stable schemes. Numerical results provide evidence that computing the metric terms with an optimization-based approach leads to a solution whose accuracy is overall on par and often better than the one obtained using the widely adopted Thomas and Lombard metric terms computation.

The analysis of the numerical errors introduced by the schemes is fundamental in large-eddy simulation (LES) techniques, especially implicit LES, for understanding the properties and solution capabilities of the discretizations. In this work, the dispersion and diffusion properties are analyzed for high-order SBP spatial discretizations of the linear advection-diffusion equation. The study relies on the traditional eigenanalysis technique and the ideas introduced in the non-modal analysis. Insights into the discretization scheme’s robustness and the effects of numerical dissipation on the unresolved scales are highlighted.

Close to the viscous walls, the flow properties that any discretization scheme must capture are crucial to accurately represent the problem’s physics. This work assesses the near-wall solution capabilities of the compressible fully-discrete solver SSDC. For this purpose, several configurations of under-resolved turbulent channel flows are studied. The main goal is to determine the optimal grid parameters for different h/p configurations and show the feasibility of conducting simulations with high-order polynomial solutions on relatively coarse meshes with higher off-wall spacing.

Finally, this work compares the performance of classical explicit and implicit LES models for under-resolved flow simulations using high-order entropy stable schemes. The objective is to evaluate the ability of explicit and implicit LES to obtain accurate solutions according to the grid resolution in the domain, the polynomial degree employed, the flow regime, and the effect of both the standard upwind term and explicit modeling on various test cases. The advantages of the implicit LES model, regarding the accuracy and computational performance, are remarked for different configurations.