Top : optimized kernel functions for a glass distribution (Sect. 3.4.1) together with the missing Wendland kernels (CM₀₄, CM₀₅), the Buhmann kernel (BUH), and the Wu kernel (WU₂). Middle : corresponding derivative of these kernel function. Bottom: fourier transform of these kernels, scaled by k/10. The optimized kernels are quite similar, with some small variations being seen in the Fourier transform. The O_glass,32 kernel deviates the most from the other kernel, with less deep troughs in the Fourier transform. These kernel’s generate excellent glass distributions but degrade significantly in dynamical simulations.