Perturbations due to round-off errors in computer modeling are discontinuous and therefore one cannot use results like KAM theory about smooth perturbations of twist maps. We elaborate a special approximation scheme to construct two smooth periodic on the angle perturbations of the twist map, bounding the discretized map from above and from below. Using the well known Moser’s theorem we prove t...

We derive a material-realistic real-space many-body Hamiltonian for twisted bilayer graphene from first principles, including both single-particle hopping terms $p_z$ electrons and long-range Coulomb interactions. By disentangling low- high-energy subspaces of the electronic dispersion, we are able to utilize state-of-the-art constrained Random Phase Approximation calculations reliably describe...

Twist is a parameter to measure turning of the field lines around axis of the flux tube. Observations show that each active region (AR) has a pronounced overall twist, following hemispheric helicity rule (Pevtsov et al. 1995; Bao & Zhang 1998). etbest, best-fit single value for a whole AR, is used to characterize the overall twist. Writhe is a measure of the spatial turning of the axis of the f...

We studied the effects of wing deformation on the aerodynamic forces of wings of hovering hoverflies by solving the Navier-Stokes equations on a dynamically deforming grid, employing the recently measured wing deformation data of hoverflies in free-flight. Three hoverflies were considered. By taking out the camber deformation and the spanwise twist deformation one by one and by comparing the re...