ABSTRACT Magnetic fields ( B -fields) play a key role in the formation and evolution of protoplanetary disks, but their properties are poorly understood due to the lack of observational constraints. Using CanariCam at the 10.4 m Gran Telescopio Canarias, we have mapped out the mid-infrared polarization of the protoplanetary disk around the Herbig Ae star AB Aur. We detect ∼0.44% polarization at 10.3 μ m from AB Aur's inner disk ( r < 80 au), rising to ∼1.4% at larger radii. Our simulations imply that the mid-infrared polarization of the inner disk arises from dichroic emission of elongated particles aligned in a disk B -field. The field is well ordered on a spatial scale, commensurate with our resolution (∼50 au), and we infer a poloidal shape tilted from the rotational axis of the disk. The disk of AB Aur is optically thick at 10.3 μ m, so polarimetry at this wavelength is probing the B -field near the disk surface. Our observations therefore confirm that this layer, favored by some theoretical studies for developing magneto-rotational instability and its resultant viscosity, is indeed very likely to be magnetized. At radii beyond ∼80 au, the mid-infrared polarization results primarily from scattering by dust grains with sizes up to ∼1 μ m, a size indicating both grain growth and, probably, turbulent lofting of the particles from the disk mid-plane.
Steel and composite structures are traditionally designed through strength based calculations. An alternative approach is to consider deformation capacity. Deformation based design enables a more accurate allowance to be made for the spread of plasticity and allows strain hardening to be considered in a systematic manner. Importantly, the level of deformation required by the structure at ultimate limit state to reach the required design capacity can also be assessed. In composite construction, deformation based design enables a more rigorous assessment to be made of the development of strength in the structural system taking due account of the compatibility between the constituent materials. In this paper, recent developments to the deformation based continuous strength method for steel and composite design are described. Comparisons of capacities obtained from experiments and numerical simulations with those predicted using the continuous strength method are presented and discussed. Recommendations for future work on this topic are also set out.
