Twisted topological tangles or: the knot theory of knitting Abstract: Imagine a 1D curve, then use it to fill a 2D manifold that covers an arbitrary 3D object – this computationally intensive materials challenge has been realized in the ancient technology known as knitting. This process for making functional materials 2D materials […]
Packing, geometry & entropy: Crystallization of spheres in a sphere When twelve equally sized spheres are packed around a central sphere, the smallest volume of the resulting cluster and thus the highest packing is obtained for a regular icosahedron, a shape with twenty equilateral triangles as faces and a five-fold […]
Placement and Symmetry of Singularities on Curved Surfaces In various contexts, biological structures resemble regular two-dimensional lattices made from smaller units like macromolecules (on the nanoscale) or cells (on the tissue scale). This regularity carries an inherent elastic energy penalty when the 2D manifold is also required to have intrinsic […]
From viral capsids to self-assembling nanoparticles Abstract: Viruses are examples of biological nanoparticles. They are made of a highly symmetric protein container, the capsid, that contains the nucleic acid and self-assembles from several copies of a single protein. The relative position of the proteins in the capsids is conventionally described […]