Related papers: Geometry of polycrystals and microstructure
The paper investigates two-phase microstructures of optimal 3D composites that store minimal elastic energy in a given strain field. The composite is made of two linear isotropic materials which differ in elastic moduli and self-strains. We…
We introduce trilayer and multilayer moir\'e heterostructures that cannot be viewed from the ``moir\'e-of-moir\'e" perspective of helically-twisted trilayer graphene. These ``intrinsically trilayer" moir\'e systems feature periodic…
Phase transformations can be difficult to characterize at the microscopic level due to the inability to directly observe individual atomic motions. Model colloidal systems, by contrast, permit the direct observation of individual particle…
An isotropic interaction potential for classical particles is devised in such a way that the crystalline ground state of the system changes discontinuously when some parameter of the potential is varied. Using this potential we model…
Mappingsofbi-conformalenergyformthewidestclass of homeomorphisms that one can hope to build a viable extension of Geometric Function Theory with connections to mathematical models of Nonlinear Elasticity. Such mappings are exactly the ones…
Extended one- and two-dimensional defects in crystalline materials are usually metastable. The thermodynamic ground state of the material is presumed to be defect-free. Here, we investigate the conditions under which extended defects, such…
Schrodinger-type wave equations with logarithmic nonlinearity occur in hydrodynamic models of Korteweg-type materials with capillarity and surface tension, which can undergo liquid-solid or liquid-gas phase transitions. One of the…
Many solid materials and liquid crystals exhibit geometric frustration, meaning that they have an ideal local structure that cannot fill up space. For that reason, the global phase must be a compromise between the ideal local structure and…
Anisotropy of interfacial energy is the principal driving force for material microstructure evolution yet its origins remain uncertain and a quantitative description lacking. We present and justify a concise hypothesis on the topography and…
We demonstrate that nascent polymer crystals (i.e., nuclei) are anisotropic entities, with neither spherical nor cylindrical geometry, in contrast to previous assumptions. In fact, cylindrical, spherical, and other high symmetry geometries…
Microstructural evolution in structural materials is known to occur in response to mechanical loading and can often accommodate substantial plastic deformation through the coupled motion of grain boundaries (GBs). This can produce desirable…
The energy-based definition provides a viable resolution to the longstanding confusion on the proper definition of $n$-th order rigidity and flexibility in geometric constraint systems. Applying an energy-based local rigidity analysis to…
It has been long known that numerous halide and oxide perovskites can have non-ideal octahedra, showing tilting, rotation, and metal atom displacements. It has also been known that compounds that have at low temperatures a single structural…
We investigate the geometry of two-dimensional polygonal cracking that forms on the air-exposed surface of dried starch slurries. Two different kinds of starches, made from potato and corn, exhibited distinguished crack evolution, and there…
Crystalline order in dense packings of long polymers with a definite handedness is difficult to reconcile with the tendency of these chiral objects to twist and braid about each other. If the chirality is weak, the state of lowest energy is…
Polycrystalline solids can exhibit material properties that differ significantly from those of equivalent single-crystal samples, in part, because of a spontaneous redistribution of mobile point defects into so-called space-charge regions…
Grain boundaries (GBs), an important constituent of polycrystalline materials, have a wide range of manifestion and significantly affect the properties of materials. Fully understanding the effects of GBs is stalemated due to lack of…
Smectic liquid crystals are remarkable, beautiful examples of materials microstructure, with ordered patterns of geometrically perfect ellipses and hyperbolas. The solution of the complex problem of filling three-dimensional space with…
In the deformation of layered materials such as geological strata, or stacks of paper, mechanical properties compete with the geometry of layering. Smooth, rounded corners lead to voids between the layers, while close packing of the layers…
A novel complex-phase steel alloy is conceived with a deliberately unstable austenite, $\gamma$, phase that enables the deformation-induced martensitic transformations (DIMT) to be explored at low levels of plastic strain. The DIMT was thus…