Related papers: Textural equilibrium melt geometries around tetrak…
Accretion of mineralized thin wall-like structures via localized growth along their edges is observed in a range of physical and biological systems ranging from molluscan and brachiopod shells to carbonate-silica composite precipitates. To…
The presence of interparticle cohesion can drastically change the behavior of granular materials. For instance, powders are challenging to handle, and one can make a sandcastle using wet grains. In this study, we report experimental results…
Using the formalism of geometrothermodynamics, we investigate the geometric properties of the equilibrium manifold for diverse thermodynamic systems. Starting from Legendre invariant metrics of the phase manifold, we derive thermodynamic…
A continuum dislocation model of formation of grains whose boundaries have a non-vanishing thickness is proposed. For a single crystal deforming in simple shear the lamellar structure of grains with thin layers containing dislocations as…
Grain boundaries are topological defects that often have a disordered character. Disorder implies that understanding general trends is more important than accurate investigations of individual grain boundaries. Here we present trends in the…
More than half a century after the fundamental, spherical shell structure in nuclei has been established, theoretical predictions indicate that the shell-gaps comparable or even stronger than those at spherical shapes may exist.…
Systems as diverse as mechanical structures assembled from elastic components, and photonic metamaterials enjoy a common geometrical feature: a sublattice symmetry. This property realizes a chiral symmetry first introduced to characterize a…
This review reports some theoretical results on the Geometry of membranes. The governing equations to describe equilibrium configurations of lipid vesicles, lipid membranes with free edges, and chiral lipid membranes are derived from the…
By mixing glass beads with a curable polymer we create a well-defined cohesive granular medium, held together by solidified, and hence elastic, capillary bridges. This material has a geometry similar to a wet packing of beads, but with an…
Grain boundaries, the two-dimensional (2D) defects between differently oriented crystals, control mechanical and transport properties of materials. Our fundamental understanding of grain boundaries is still incomplete even after nearly a…
An example of a teleparallel texture is given by an appropriate choice of torsion components in the tetrad frame.In the light cone limit the metric is not globally Euclidean and the spherical angles depend on torsion similarly to what…
Cohesive assemblies of filaments are a common structural motif found in diverse contexts, ranging from biological materials such as fibrous proteins, to artificial materials such as carbon nanotube ropes and micropatterned filament arrays.…
Using X-ray tomography, we experimentally investigate granular segregation phenomena in a mixture of particles with different densities under quasi-static cyclic shear. We quantitatively characterize their height distributions at steady…
Geometrical constructions, such as the tangent construction on the molar free energy for determining whether a particular composition of a solution, is stable, are related to similar tangent constructions on the orientation-dependent…
This paper investigates the rigidity of bordered polyhedral surfaces. Using the variational principle, we show that bordered polyhedral surfaces are determined by boundary value and discrete curvatures on the interior edges. As a corollary,…
We study the equilibrium configuration of a nematic liquid crystal bounded by a rough surface. The wrinkling of the surface induces a partial melting in the degree of orientation. This softened region penetrates the bulk up to a length…
We propose a general formalism to characterize orientational frustration of smectic liquid crystals in confinement by interpreting the emerging networks of grain boundaries as objects with a topological charge. In a formal idealization,…
We introduce a smoothing algorithm for triangle, quadrilateral, tetrahedral and hexahedral meshes whose centerpiece is a simple geometric triangle transformation. The first part focuses on the mathematical properties of the element…
When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…
Constructing well-behaved Laplacian and mass matrices is essential for tetrahedral mesh processing. Unfortunately, the \emph{de facto} standard linear finite elements exhibit bias on tetrahedralized regular grids, motivating the development…