Unfolding the Sulcus

Unfolding the Sulcus

Even as we probe physics on ever-smaller scales, materials that can be held and manipulated with our hands often still resist our understanding. Elastic materials, in particular, still confound because of the nonlinear relationship between strain and the displacement of the material needed to maintain the rotational invariance of the elastic energy. The effects of these nonlinearities are often...

Unfolding the sulcus.

Sulci are localized furrows on the surface of soft materials that form by a compression-induced instability. We unfold this instability by breaking its natural scale and translation invariance, and compute a limiting bifurcation diagram for sulcfication showing that it is a scale-free, subcritical nonlinear instability. In contrast with classical nucleation, sulcification is continuous, occurs ...

Unfolding the chaperone story

Protein folding in the cell was originally assumed to be a spontaneous process, based on Anfinsen's discovery that purified proteins can fold on their own after removal from denaturant. Consequently cell biologists showed little interest in the protein folding process. This changed only in the mid and late 1980s, when the chaperone story began to unfold. As a result, we now know that in vivo, p...

Sulcus identification and labelling

Unfolding Orthogonal Polyhedra with Quadratic Refinement: The Delta-Unfolding Algorithm

We show that every orthogonal polyhedron homeomorphic to a sphere can be unfolded without overlap while using only polynomially many (orthogonal) cuts. By contrast, the best previous such result used exponentially many cuts. More precisely, given an orthogonal polyhedron with n vertices, the algorithm cuts the polyhedron only where it is met by the grid of coordinate planes passing through the ...