Related papers: Competing Hexagonal and Square Lattices on a Spher…
We establish spectral rigidity for spherically symmetric manifolds with boundary and interior interfaces determined by discontinuities in the metric under certain conditions. Rather than a single metric, we allow two distinct metrics in…
A simple method to describe spatially dispersive metasurfaces is proposed where the angle-dependent surface susceptibilities are explicitly used to formulate the zero thickness sheet model of practical metasurface structures. It is shown…
Liquid crystals can self-organize into a layered smectic phase. While the smectic layers are typically straight forming a lamellar pattern in bulk, external confinement may drastically distort the layers due to the boundary conditions…
Smectic liquid crystals are charcterized by layers that have a preferred uniform spacing and vanishing curvature in their ground state. Dislocations in the smectics play an important role in phase nucleation, layer reorientation, and…
The behavior of colloidal particles with a hard core and a soft shell has attracted the attention for researchers in the physical-chemistry interface not only due the large number of applications, but due the unique properties of these…
Lattices induced by coverings arise naturally in matroid theory and combinatorial optimization, providing a structured framework for analyzing relationships between independent sets and closures. In this paper, we explore the structural…
Direct design of complex functional materials would revolutionize technologies ranging from printable organs to novel clean energy devices. However, even incremental steps towards designing functional materials have proven challenging. If…
A variational model for epitaxially-strained thin films on rigid substrates is derived both by {\Gamma}-convergence from a transition-layer setting, and by relaxation from a sharp-interface description available in the literature for…
We consider orthogonal polynomials on the surface of a double cone or a hyperboloid of revolution, either finite or infinite in axis direction, and on the solid domain bounded by such a surface and, when the surface is finite, by…
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…
Topological superconductors, such as noncentrosymmetric superconductors with strong spin-orbit coupling, exhibit protected zero-energy surface states, which possess an intricate helical spin structure. We show that this nontrival spin…
In this paper the normal collision of spherical particles is investigated. The particle interaction is modelled in a macroscopic way using the Hertzian contact force with additional linear damping. The goal of the work is to develop an…
If carbon fibre layers are prevented from slipping over one another as they consolidate onto a non-trivial geometry, they can be particularly susceptible to wrinkling/buckling instabilities. A one dimensional model for wrinkling during…
Crystal growth processes produce a diverse array of surface formations, primarily distinguished by their geometric shapes. While some structures strictly adhere to the underlying crystal symmetry, others exhibit universal circular or oval…
Conformal technicolor is a paradigm for new physics at LHC that may solve the problems of strong electroweak symmetry breaking for quark masses and precision electroweak data. We give explicit examples of conformal technicolor theories…
Thin solids often develop elastic instabilities and subsequently complex, multiscale deformation patterns. Revealing the organizing principles of this spatial complexity has ramifications for our understanding of morphogenetic processes in…
Orthogonal surfaces are nice mathematical objects which have interesting connections to various fields, e.g., integer programming, monomial ideals and order dimension. While orthogonal surfaces in one or two dimensions are rather trivial…
Despite recent breakthroughs in understanding how protein sequence relates to structure and function, considerably less attention has been paid to the general features of protein surfaces beyond those regions involved in binding and…
Using a recently introduced formulation of the ground-state inverse design problem for a targeted lattice [Pi\~neros et al., J. Chem. Phys. 144} 084502 (2016)], we discover purely repulsive and isotropic pair interactions that stabilize…
Pattern dynamics on curved surfaces are found everywhere in nature. The geometry of surfaces have been shown to influence dynamics and play a functional role, yet a comprehensive understanding is still elusive. Here, we report for the first…