Abstract. Standard passive aerodynamic flow control devices such as vortex generators and gurney flaps have a working principle that is well understood. They increase the stall angle and the lift below stall and are mainly applied at the inboard part of wind turbine blades. However, the potential of applying a rigidly fixed leading-edge slat element at inboard blade stations is less well understood but has received some attention in the past decade. This solution may offer advantages not only under steady conditions but also under unsteady inflow conditions such as yaw. This article aims at further clarifying what an optimal two-element configuration with a thick main element would look like and what kind of performance characteristics can be expected from a purely aerodynamic point of view. To accomplish this an aerodynamic shape optimization procedure is used to derive optimal profile designs for different optimization boundary conditions including the optimization of both the slat and the main element. The performance of the optimized designs shows several positive characteristics compared to single-element airfoils, such as a high stall angle, high lift below stall, low roughness sensitivity, and higher aerodynamic efficiency. Furthermore, the results highlight the benefits of an integral design procedure, where both slat and main element are optimized, over an auxiliary one. Nevertheless, the designs also have two caveats, namely a steep drop in lift post-stall and high positive pitching moments.

We explore the possibility that the dark matter (DM) component in galaxies may originate fractional gravity. In such a framework, the standard law of inertia continues to hold, but the gravitational potential associated with a given DM density distribution is determined by a modified Poisson equation including fractional derivatives (i.e., derivatives of noninteger type) that are meant to describe nonlocal effects. We analytically derive the expression of the potential that in fractional gravity corresponds to various spherically symmetric density profiles, including the Navarro–Frenk–White (NFW) distribution that is usually exploited to describe virialized halos of collisionless DM as extracted from N-body cosmological simulations. We show that in fractional gravity, the dynamics of a test particle moving in a cuspy NFW density distribution is substantially altered with respect to the Newtonian case, mirroring what in Newtonian gravity would instead be sourced by a density profile with an inner core. We test the fractional gravity framework on galactic scales, showing that (i) it can provide accurate fits to the stacked rotation curves of spiral galaxies with different properties, including dwarfs; (ii) it can reproduce to reasonable accuracy the observed shape and scatter of the radial acceleration relation over an extended range of galaxy accelerations; and (iii) it can properly account for the universal surface density and the core radius versus disk scale length scaling relations. Finally, we discuss the possible origin of the fractional gravity behavior as a fundamental or emerging property of the elusive DM component.

Abstract. Standard passive aerodynamic flow control devices such as vortex generators and gurney flaps have a working principle that is well understood. They increase the stall angle and the lift below stall and are mainly applied at the inboard part of wind turbine blades. However, the potential of applying a rigidly fixed leading edge slat element at inboard blade stations is less well understood but has received some attention in the past decade. This solution may offer advantages not only under steady conditions but also under unsteady inflow conditions such as yaw. This article aims at further clarifying what an optimal two-element configuration with a thick main element would look like, and what kind of performance characteristics can be expected from a purely aerodynamic point of view. To accomplish this an aerodynamic shape optimization procedure is used to derive optimal profile designs for different optimization boundary conditions including the optimization of both the slat and the main element. The performance of the optimized designs shows several positive characteristics as compared to single element airfoils, such as a high stall angle, high lift below stall, low roughness sensitivity and higher aerodynamic efficiency. Furthermore, the results highlight the benefits of an integral design procedure, where both slat and main element are optimized, over an auxiliary one. Nevertheless, the designs also have two caveats, namely a steep drop in lift post-stall and high positive pitching moments.

Recently, in Benetti et al. (Astrophys. J. 2023, 949, 65), we suggested that the dark matter (DM) component in galaxies may originate fractional gravity. In such a framework, the DM component exists, but the gravitational potential associated to its density distribution is determined by a modified Poisson equation including fractional derivatives (i.e., derivatives of noninteger type), which are meant to describe nonlocal effects; as such, this scenario is different from theories where baryonic matter emulates DM-like effects via modifications of gravity (e.g., MONDian frameworks). In Benetti et al., we showed that fractional gravity worked very well for reproducing the kinematics of disk-dominated galaxies, especially dwarfs; there is also preliminary evidence that the strength of fractional effects tends to weaken toward more massive systems. Here, we aim to test fractional gravity in galaxy clusters, with a twofold aim: (i) perform an independent sanity check that it can accurately describe such large and massive structures; (ii) derive a clear-cut trend for its strength in systems with different DM masses. To this purpose, we forward model the density and pressure distributions of the intracluster medium (ICM), working out the hydrostatic equilibrium equation in fractional gravity. Then, we perform a Bayesian analysis of the X-COP galaxy cluster sample and infer constraints on the fractional gravity parameters, for individual clusters as well as stacked clusters. We find that fractional gravity performs remarkably well in modeling the ICM profiles for the X-COP sample. We also check that the DM concentration vs. mass relation is still consistent with the expectations of N-body simulations in the standard cosmological scenario. Finally, we confirm the weakening of the fractional gravity effects toward more massive systems and derive the overall scaling of the fractional gravity parameters from dwarf galaxies to massive clusters, spanning six orders of magnitude in DM mass. Such an overall trend implies that fractional gravity can substantially alleviate the small-scale issues of the standard DM paradigm, while remaining successful on large cosmological scales.