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In the first part of this thesis we study string corrections to one-loop amplitudes of single-particle half-BPS operators Op in AdS₅ × S⁵. The tree-level correlators (dual to AdS scattering amplitudes via the AdS/CFT correspondence) in supergravity enjoy an accidental 10d conformal symmetry. Consequently, one observes a partial degeneracy in the spectrum of anomalous dimensions of double-trace operators and at the same time equality of many different correlators for different external charges pᵢ=1,2,3,4. The one-loop contribution is expected to lift such bonus properties, and its precise form can be predicted from tree-level data and consistency with the operator product expansion. Here we present a closed-form Mellin space formula for ⟨Op₁ Op₂ Op₃ Op₄ ⟩ at order λ⁻³/² in the expansion around large λ valid for arbitrary external charges pᵢ. Our formula makes explicit the lifting of the bonus degeneracy among different correlators through a feature we refer to as 'sphere splitting'. While tree-level Mellin amplitudes come with a single crossing symmetric kernel, which defines the pole structure of the AdS₅ × S⁵ amplitude, our one-loop amplitude naturally splits the S⁵ part into two separate contributions. The amplitude also exhibits a remarkable consistency with the corresponding flat space IIB amplitude through the large p limit. In the second part of this thesis we study the relation between the branch cut structure of scattering amplitudes in planar N = 4 SYM and Grassmannian cluster algebras using the novel language of Gröbner theory. We detail how to extract the familiar A-coordinates and their respective adjacency conditions from the Gröbner fan of the Plücker ideal. Having established this connection we apply similar techniques to the case of non dual conformal invariant five-point kinematics where we extract the full non-planar symbol alphabet relevant for the construction of five-point integrals/amplitudes. Finally, we continue to study the connection between cluster algebras and scattering amplitudes by considering the family of partial flag cluster algebras F (2, 4, n) in order to extract information on the symbol alphabet for amplitudes with five-point and six-point non dual conformal invariant kinematics.

Propeller flutter can manifest in a variety of ways. This includes classical bending-torsion flutter, stall flutter and whirl flutter. Classical bending-torsion flutter for propeller blades is driven by the coupling, and excitement, of selected modes of motion. Such flutter problems are often a result of structural coupling and in the linear aerodynamic regime. As a result, low-fidelity, fast calculations can be used to determine boundaries and mitigate the effects via changes in the structural design. Whirl flutter is the most complex and involves the coupling of the aircraft wing modes of motion to the gyroscopic and aerodynamic effects of the propeller. This phenomenon can be highly non-linear due to both the structure and flow-field, and any mitigation involves sophisticated modelling efforts with respect to the airframe. Propeller stall flutter is less complex in terms of the structure, however, involves the highly non-linear aerodynamics associated with detached flow. This phenomena, like classical flutter, is driven by the propeller design and conditions, but due to its nature, the stall flutter boundary significantly reduces the overall flutter boundary of a propeller. Hence, the understanding of this limitation must be known to ensure safe operation. The development of modern propeller blades utilising high sweep/taper with thin aerofoil sections can result in a change in the flutter boundary. In addition to this, propellers are coming back into focus due to the development of electrically driven Vertical Take-off/Landing (eVTOL) vehicles and, due to the nature of such a vehicle design, the propellers are being pushed into significantly different operating conditions. This motivation, coupled with the increased computational power available in the modern era, requires the need to reassess what is required to understand the stall flutter boundary associated with a modern, in-service, propeller blade. To this end, a numerical investigation using Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD) was conducted on the Commander propeller blade of Dowty Propellers. This blade was selected from the list of experimentally investigated blades due to the availability of geometry, structural data and applicability in real life applications. A validation procedure was conducted to assess the effects of the computational setup. This included the effects of turbulence, structural modelling and implementation, with a validated process found whilst using Scale-Adaptive-Simulation (SAS) with interpolated structural modes. An attempt was made to extract aerodynamic damping data of the stall flutter phenomenon via the development of a method from the aeroelastic simulations. Such values give an indication of the stability, with links made to typical two-dimensional modelling. The thesis ends on the parametric study of the validated Commander simulation. This was conducted in order to gain greater detail on the effects of key structural and aerodynamic parameters on the blade stall flutter response. The key outcome from this investigation is the need for scale-resolving methods in propeller stall flutter investigations. This study utilises a hybrid RANS/LES model to capture the key detached flow content. This detached flow content results in significant pressure fluctuations, not observed in traditional statistical models, which drive the aeroelastic deformations. In addition, the requirement for a well validated structural model is highlighted including the setup of the structural solver for which an interpolated modal response method is used. It is also found from this investigation that there is a need for a modern experimental test case focusing on propeller stall flutter. The last comprehensive study was conducted in the 1980's and, with improvements in experimental techniques, greater understanding and data can now be extracted. This new data can be used to validate modern CFD efforts. The novelty of this work lies within the derivation of a method for the extraction of the aerodynamic damping data from three-dimensional simulations. This had previously not be done before and the extracted results correlated with equivalent two-dimensional aerodynamic damping data. Additionally, the development and application of three-dimensional Navier-Stokes based CFD, with a coupled structural model, had not been conducted on propeller stall flutter.