Orientation-dependent handedness and chiral design
Handed phenomena are of central importance in fields ranging from biological self-assembly to the design of optical meta-materials. The definition of chirality (Greek for handedness), as given by Kelvin, associates it with the lack of mirror symmetry: the inability to superpose an object on its mirror image. While this definition has guided the classification of chiral objects for over a century, the quantification of handed phenomena based on this definition has proven elusive, if not impossible as manifest in the paradox of chiral connectedness. In this talk I will put forward a quantification schemein which the handedness of an object depends on the direction in which it is viewed and thus best quantified by a pseudo-tensor. While consistent with familiar chiral notions, such as the right hand rule, this framework allows objects to be simultaneously right and left handed. The trace of the suggested handedness tensors recover Kelvin's definition, yet their full structure is richer, and proven to be in quantitative agreement with the direction-dependent handed behavior of phenomena ranging from fluid flow to optical activity. I will review specific examples of handedness tensors, and discuss how the tensorial approach resolves the existing paradoxes and naturally enables the design of handed meta materials from symmetry principles.