Related papers: Uniform line fillings
Dense, disordered packings of particles are useful models of low-temperature amorphous phases of matter, biological systems, granular media, and colloidal systems. The study of dense packings of nonspherical particles enables one to…
We construct integer error-correcting codes and covering codes for the limited-magnitude error channel with more than one error. The codes are lattices that pack or cover the space with the appropriate error ball. Some of the constructions…
Machine learning models can assist with metamaterials design by approximating computationally expensive simulators or solving inverse design problems. However, past work has usually relied on black box deep neural networks, whose reasoning…
It is well-known that band gaps, in the frequency domain, can be achieved by using periodic metamaterials. However it has been challenging to design materials with broad band gaps or that have multiple overlapping band gaps. For periodic…
A complete characterization is given of the possible macroscopic deformations of periodic nonlinear affine unimode metamaterials constructed from rigid bars and pivots. The materials are affine in the sense that their macroscopic…
Dense random packings of hard particles are useful models of granular media and are closely related to the structure of nonequilibrium low-temperature amorphous phases of matter. Most work has been done for random jammed packings of…
In this paper, we present a unit cell showing a band-gap in the lower acoustic domain. The corresponding metamaterial is made up of a periodic arrangement of this unit cell. We rigorously show that the relaxed micromorphic model can be used…
In this paper we suggest a simple analytical method for description of electromagnetic properties of a geometrically regular two-dimensional subwavelength arrays (metasurfaces) formed by particles with randomly fluctuating polarizabilities.…
This work develops a dynamic homogenization approach for metamaterials. It finds an approximate macroscopic homogenized equation with constant coefficients posed in space and time; however, the resulting homogenized equation is higher order…
We study the diagonals of two-dimensional tilings generated by direct product substitutions. The properties of these diagonals are primarily determined by the eigenvalues of the substitution matrix, but also the order of the letters in the…
We study the isoperimetric problem for Euclidean space endowed with a continuous density. In dimension one, we characterize isoperimetric regions for a unimodal density. In higher dimensions, we prove existence results and we derive…
Recently, a theory for artificial magnetism in two-dimensional photonic crystals has been developed for large wavelength using homogenization techniques. In this paper we pursue this approach within a rigorous stochastic framework:…
Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated…
Lattice-based mechanical metamaterials are known to exhibit quite a unique mechanical behavior owing to their rational internal architecture. This includes unusual properties such as a negative Poisson's ratio, which can be easily tuned in…
When used in bulk applications, mechanical metamaterials set forth a multiscale problem with many orders of magnitude in scale separation between the micro and macro scales. However, mechanical metamaterials fall outside conventional…
Hyperuniformity characterizes a state of matter that is poised at a critical point at which density or volume-fraction fluctuations are anomalously suppressed at infinite wavelengths. Recently, much attention has been given to the link…
Metamaterials are artificially engineered structures that manipulate electromagnetic waves, having optical properties absent in natural materials. Recently, machine learning for the inverse design of metamaterials has drawn attention.…
We theoretically demonstrate the formation of different kinds of two-dimensional split-ring arrays in both triangular and square lattices by one-step holographic interference. The slit width of the split-ring can be adjusted by proper…
This article discusses electromagnetic properties of volumetric metamaterial samples with essentially discrete structure, that is, assembled as a periodic array of electromagnetic resonators. We develop an efficient numerical procedure for…
A Matlab-based computational procedure is proposed to fill a given volume with spheres whose radii are randomly picked from any specified probability distribution supported by \verb|Matlab|. The general program sequence and examples of…