Related papers: Nature's forms are frilly, flexible, and functiona…
Ever since the discovery of graphene and subsequent explosion of interest in single atom thick materials, studying their mechanical properties has been an active area of research. New length scales often necessitate a rethinking of physical…
The mechanism by which a patterned state accommodates the breaking of translational symmetry by a phase boundary or a sample wall has been addressed in the context of Landau branching in type-I superconductors, refinement of magnetic…
Heterogeneous nucleation is a process wherein extrinsic impurities facilitate freezing by lowering nucleation barriers and constitutes the dominant mechanism for crystallization in most systems. Classical nucleation theory (\textsc{Cnt})…
In many physical situations involving diverse length scales, waves or rays representing them travel through media characterized by spatially smooth, random, modest refactive index variations. "Primary" diffraction (by individual…
Complex textured surfaces occur in nature and industry, from fingerprints to lithography-based micropatterns. Wrinkling by confinement to an incompatible substrate is an attractive way of generating reconfigurable patterned topographies,…
We simulate a two dimensional model of self-propelled particles confined by a deformable boundary. The particles tend to accumulate near the boundary and the shape of the boundary deforms upon the collisions. We find that there are two…
The occurrence of coiled or helical morphologies is common in nature, from plant roots to DNA packaging into viral capsids, as well as in applications such as oil drilling processes. In many examples, chiral structures result from the…
Despite the apparent ease with which a sheet of paper is crumpled and tossed away, crumpling dynamics are often considered a paradigm of complexity. This complexity arises from the infinite number of configurations a disordered crumpled…
Recent decades have seen the discovery of numerous complex materials. At the root of the complexity underlying many of these materials lies a large number of possible contending atomic- and larger-scale configurations and the intricate…
In this paper we give two different proofs of Bobenko and Springborn's theorem of circle pattern: there exists a hyperbolic (or Euclidean) circle pattern with proscribed intersection angles and cone angles on a cellular decomposed surface…
A nematic liquid crystal confined to the surface of a sphere exhibits topological defects of total charge $+2$ due to the topological constraint. In equilibrium, the nematic field forms four $+1/2$ defects, located at the corners of a…
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…
We construct an explicit example of family of non-uniformly hyperbolic diffeomorphisms, at the boundary of the set of uniformly hyperbolic systems, with one orbit of cubic heteroclinic tangency. One of the leaves involved in this…
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…
Mechanical fields over thin elastic surfaces can develop singularities at isolated points and curves in response to constrained deformations (e.g., crumpling and folding of paper), singular body forces and couples, distributions of isolated…
Metric anomalies arising from a distribution of point defects (intrinsic interstitials, vacancies, point stacking faults), thermal deformation, biological growth, etc. are well known sources of material inhomogeneity and internal stress. By…
The complex arrangements of atoms near grain boundaries are difficult to understand theoretically. We propose a phenomenological (Ginzburg-Landau-like) description of crystalline phases based on symmetries and fairly general stability…
We consider thin plates whose energy density is a quadratic function of the difference between the second fundamental form of the deformed configuration and a "natural" curvature tensor. This tensor either denotes the second fundamental…
Mechanochemical processes on surfaces such as the cellular cortex or epithelial sheets, play a key role in determining patterns and shape changes of biological systems. To understand the complex interplay of hydrodynamics and material flows…
Structural cellular materials in nature, such as wood, trabecular bone, corals, and dentin combine complex biological functions with structural roles, such as skeletal support and impact protection1,2. They feature complex structural…