Related papers: Topological Defect Propagation to Classify Knitted…
Structural hierarchy, in which materials possess distinct features on multiple length scales, is ubiquitous in nature; diverse biological materials, such as bone, cellulose, and muscle, have as many as ten hierarchical levels. Structural…
In this work, we investigate the topological properties of knotted defects in smectic liquid crystals. Our story begins with screw dislocations, whose radial surface structure can be smoothly accommodated on $S^3$ for fibred knots by using…
Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber reinforced materials are also common in technology. An important characteristic of such materials is their…
Defects, and in particular topological defects, are architectural motifs that play a crucial role in natural materials. Here we provide a systematic strategy to introduce such defects in mechanical metamaterials. We first present…
Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. The various proposals in the literature are usually motivated by…
Soft elastic filaments that can be stretched, bent and twisted exhibit a range of topologically and geometrically complex morphologies that include plectonemes, solenoids, knot-like and braid-like structures. We combine numerical…
Directional media, such as nematic liquid crystals and ferromagnets, are characterized by their topologically stabilized defects in directional order. In nematics, boundary conditions and surface-treated inclusions often create complex…
Knitted fabrics exhibit high flexibility due to their periodic loop structures formed by bent yarns. Under compressive loading, they develop three-dimensional (3D) wrinkling patterns that reflect nonlinear interactions between yarn…
Physical knot classification is a challenging fine-grained recognition task in which the intended discriminative cue is rope crossing structure; however, high closed-set accuracy may still arise from low-level appearance shortcuts rather…
The humanities, like many other areas of society, are currently undergoing major changes in the wake of digital transformation. However, in order to make collection of digitised material in this area easily accessible, we often still lack…
Consider a knot $K$ in $S^3$ with uniformly distributed electric charge. Whilst solutions to the Laplace equation in terms of Dirichlet integrals are readily available, it is still of theoretical and physical interest to understand the…
Recent studies classify the topology of proteins by analysing the distribution of their projections using knotoids. The approximation of this distribution depends on the number of projection directions that are sampled. Here we investigate…
Mechanical metamaterials are periodic lattice structures with complex unit cell architectures that can achieve extraordinary mechanical properties beyond the capability of bulk materials. A new class of metamaterials is proposed, whose…
The topology of production networks determines the propagation mechanisms of local shocks and thus the co-movement of industries. As a result, we need a more precisely defined production network to model economic growth accurately. In this…
Fractures are a critical process in how materials wear, weaken, and fail whose unpredictable behavior can have dire consequences. While the behavior of smooth cracks in ideal materials is well understood, it is assumed that for real,…
There are two prominent applications of the mathematical concept of topology to the physics of materials: band topology, which classifies different topological insulators and semimetals, and topological defects that represent immutable…
Basket weaving is a traditional craft used to create practical three-dimensional (3D) structures. While the geometry and aesthetics of baskets have received considerable attention, the underlying mechanics and modern engineering potential…
Fracture behavior in architected materials can be influenced by heterogeneities, yet the mechanisms by which imperfections affect crack propagation remain poorly understood. In this study, we introduce well-controlled, localized defects in…
We develop a model characterizing all possible knots and links arising from recombination starting with a twist knot substrate, extending previous work of Buck and Flapan. We show that all knot or link products fall into three…
Knotted molecules occur naturally and are designed by scientists to gain special biological and material properties. Understanding and utilizing knotting require efficient methods to recognize and generate knotted structures, which are…