Rational design for programmable self-assembly using DNA origami colloids Nature is replete with self-assembled materials with complex geometries that give rise to its functionalities, including shells, tubules, and fibers. Despite significant advances in synthesizing nanometer- and micrometer-scale particles, the programmable assembly of similar architectures from synthetic components has remained largely […]
Arts-and-crafts inspired self-assembly: folding, cutting, and coloring triangulated sheets to make tubules and toroids Self-assembly is one of the most promising strategies for making functional materials at the nanoscale. Typically, synthetic self-assembly has been limited to spatially unbounded periodic lattice structures. In contrast, many biological systems have developed the ability […]
Geometry, pattern, and mechanics of notochords The notochord is a rodlike pneumatic tissue that, early in development, serves to lengthen the embryo and template the spine. The internal cells in early zebrafish and other species’ notochords have been shown to pack in a small number of stereotyped patterns. Mutations or […]
Kinetically Trapped Nanocrystals with Symmetry-Preserving Shapes The shape of nanocrystals is crucial in determining their surface area, reactivity, optical properties, mechanical strength, and self-assembly behavior. Traditionally, shape control has been achieved through empirical methods, highlighting the need for a more refined theoretical framework. A comprehensive model should account for the […]
Geometric origin of particle and dislocation dynamics during grain boundary migration Grain boundary (GB) migration induces significant changes in the structure of polycrystalline solids and has a pronounced effect on the macroscopic properties of these materials [1-3]. On the atomic scale, GB migration is governed a mechanism via which constituent […]
Rationalizing Euclidean Assemblies of Hard Polyhedra from Tessellations in Curved Space Entropic self-assembly is governed by the shape of the constituent particles, yet a prioriprediction of crystal structures from particle shape alone is non-trivial for anything but thesimplest of space-filling shapes. At the same time, most polyhedra are not space fillingdue […]
Circle packing in regular polygons We discuss algorithms that allow one to generate configurations of congruent circles inside a regular polygon and present numerical results for polygons with up to 16 sides. Some general properties of these configurations will be highlighted and the topological charge associated with their Voronoi diagrams […]
Hyperuniformity and Particle Packings The study of hyperuniform states of matter is an emerging multidisciplinary field, influencing and linking developments across the physical sciences, mathematics and biology. A hyperuniform point process in d-dimensional Euclidean space is characterized by an anomalous suppression of large-scale density fluctuations relative to those in typical […]
Arrangements of spheres in transverse confinement Much work has been done on the study of structures formed by both hard and soft spheres held in transverse confining potentials [1, 2, 3]. These structures self-assemble under the action of their confining potentials, forming interesting columnar structures. Here we will present an […]
Geometric Design of Kirigami Metamaterials Kirigami, the traditional art of paper cutting, has recently emerged as a promising paradigm for mechanical metamaterials. While many prior works have studied the geometry and mechanics of certain periodic kirigami tessellations, the computational design of more complex structures is less understood. In this talk, […]
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