Related papers: Topological Defect Propagation to Classify Knitted…
We investigate the mechanical behavior of jammed knitted fabrics, where geometric confinement leads to an initially stiff mechanical response that softens into low stiffness behavior with additional applied stress. We show that the jammed…
We study the nucleation and development of crack patterns in thin composite fibers under tension in this work. A fiber comprises an elastic core and an outer layer of a weaker brittle material. In recent tensile experiments on such…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
The classification of materials into insulators and conductors has been shaken up by the discovery of topological insulators that conduct robustly at the edge but not in the bulk. In mechanics, designating a material as insulating or…
Revealing the structural features of a complex system from the observed collective dynamics is a fundamental problem in network science. In order to compute the various topological descriptors commonly used to characterize the structure of…
In this article we investigate the topological changes undergone by trajectory networks as a consequence of progressive geographical infiltration. Trajectory networks, a type of knitted network, are obtained by establishing paths between…
The statistical mechanics of a long knotted collapsed polymer is determined by a free-energy with a knot-dependent subleading term, which is linked to the length of the shortest polymer that can hold such knot. The only other parameter…
Knots are deeply entangled with every branch of science. One of the biggest open challenges in knot theory is to formalise a knot invariant that can unambiguously and efficiently distinguish any two knotted curves. Additionally, the…
Entangled structures such as textiles and architected materials are often doubly periodic. Due to this property and their finite transverse thickness, the symmetries of these materials are described by the crystallographic layer groups.…
Topology is an important determinant of the behavior of a great number of condensed-matter systems, but until recently has played a minor role in elasticity. We develop a theory for the deformations of a class of twisted non-Euclidean…
The high degrees of freedom and complex structure of garments present significant challenges for clothing manipulation. In this paper, we propose a general topological dynamics model to fold complex clothing. By utilizing the visible…
Mechanical metamaterials have continued to offer unprecedented tunability in mechanical properties, but most designs to date have prioritized attaining high stiffness and strength while sacrificing deformability. The emergence of woven…
Rapid progress in additive manufacturing methods has created a new class of ultralight and strong architected metamaterials that resemble periodic truss structures. The mechanical performance of these metamaterials with a very large number…
Knots are entangled structures that cannot be untangled without a cut. Topological stability of knots is one of the many examples of their important properties that can be used in information storage and transfer. Knot dynamics is important…
In this paper the new model of plastic deformation is constructed. For classification of plastic statuses the theory of knot is used.
Proteins are linear molecular chains that often fold to function. The topology of folding is widely believed to define its properties and function, and knot theory has been applied to study protein structure and its implications. More that…
Knots and knotted fields enrich physical phenomena ranging from DNA and molecular chemistry to the vortices of fluid flows and textures of ordered media. Liquid crystals provide an ideal setting for exploring such topological phenomena…
The role of the topology and its relation with the geometry of biopolymers under different physical conditions is a nontrivial and interesting problem. Aiming at understanding this issue for a related simpler system, we use Monte Carlo…
We develop a topological model of knots and links arising from a single (or multiple processive) round(s) of recombination starting with an unknot, unlink, or (2,m)-torus knot or link substrate. We show that all knotted or linked products…
We probe the character of knotting in open, confined polymers, assigning knot types to open curves by identifying their projections as virtual knots. In this sense, virtual knots are transitional, lying in between classical knot types,…