Photospheric logarithmic velocity spirals as MHD wave generation mechanisms

Extremal Properties of Logarithmic Spirals

Loxodromic arcs are shown to be the maximizers of inversive arclength, which is invariant under Möbius transformations. Previously, these arcs were known to be extremals. The first result says that at any loxodromic arc, the inversive arclength functional is concave with respect to a non-trivial perturbation that fixes the circle elements at the endpoints. The second result says that among curv...

The triggering of MHD instabilities through photospheric footpoint motions

The results of 3D numerical simulations modelling the twisting of a coronal loop due to photospheric vortex motions are presented. The simulations are carried out using an initial purely axial field and an initial equilibrium configuration with twist, Φ = LBθ/rBz < Φcrit. The non-linear and resistive evolutions of the instability are followed. The magnetic field is twisted by the boundary motio...

The Logarithmic Curvature Graphs of Generalised Cornu Spirals

The Generalized Cornu Spiral (GCS) was first proposed by Ali et al. in 1995 [9]. Due to the monotonocity of its curvature function, the surface generated with GCS segments has been considered as a high quality surface and it has potential applications in surface design [2]. In this paper, the analysis of GCS segment is carried out by determining its aesthetic value using the log curvature Graph...

Stability of General Newton Functional Equations for Logarithmic Spirals

The Logarithmic Curvature Graphs of Generalized Cornu Spirals

The Generalized Cornu Spiral (GCS) was first proposed by Ali et al. in 1995 [1, 9]. Due to the monotonocity of its curvature function, the surface generated with GCS segments has been considered as a high quality surface and it has potential applications in surface design [12]. In this paper, the analysis of GCS segment is carried out by determining its aesthetic value using the log curvature G...