Related papers: Inherent Symmetry and Microstructure Ambiguity in …

Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of…

Microstructural geometry plays a critical role in the response of heterogeneous materials. Consequently, methods for generating microstructural samples are increasingly crucial to advanced numerical analyses. We extend Sonon et al.'s…

Plane wave density functional theory codes generally assume periodicity in all three dimensions. This causes difficulties when studying charged systems, for instance energies per unit cell become infinite, and, even after being renormalised…

In this paper a second-order homogenization approach for periodic material is derived from an appropriate representation of the down-scaling that correlates the microdisplacement field to the macro-displacement field and the macro-strain…

We consider homogeneous coupled cell networks with asymmetric inputs. We obtain general results concerning codimension-one steady-state bifurcations for networks with any number of cells and any number of asymmetric inputs. These results…

Complex periodic structures inherit spectral properties from the constituent parts of their unit cells, chiefly their spectral band gaps. Exploiting this intuitive principle, which is made precise in this work, means spectral features of…

Triply periodic minimal surface (TPMS) metamaterials characterized by mathematically-controlled topologies exhibit better mechanical properties compared to uniform structures. The unit cell topology of such metamaterials can be further…

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…

This work is devoted to the study of the symmetries of (quasi)periodic architectured materials. For this purpose, the weaker symmetry criterion of indistinguishability is used. It relies on a statistical description of the mesostructure and…

Complex nanophotonic structures hold the potential to deliver exquisitely tailored optical responses for a range of applications. Metal-insulator-metal (MIM) metasurfaces arranged in supercells, for instance, can be tailored by geometry and…

A heterogeneous Cauchy elastic material may display micromechanical effects that can be modeled in a homogeneous equivalent material through the introduction of higher-order elastic continua. Asymptotic homogenization techniques provide an…

Hyperuniform materials, characterized by their suppressed density fluctuations and vanishing structure factors as the wave number approaches zero, represent a unique state of matter that straddles the boundary between order and randomness.…

Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made…

Honeycomb-like microstructures have been shown to exhibit local elastic buckling under compression, with three possible geometric buckling modes, or pattern transformations. The individual pattern transformations, and consequently also…

It is sometimes desirable in choiceless constructions of set theory that one iteratively extends some ground model without adding new sets of ordinals after the first extension. Pushing this further, one may wish to have models $V \subseteq…

We undertake a detailed investigation into the structure of permutations in monotone grid classes whose row-column graphs do not contain components with more than one cycle. Central to this investigation is a new decomposition, called the…

Linear error-correcting codes can be used for constructing secret sharing schemes; however finding in general the access structures of these secret sharing schemes and, in particular, determining efficient access structures is difficult.…

Projecting fields between different meshes commonly arises in computational physics. This operation requires a supermesh construction and its computational cost is proportional to the number of cells of the supermesh $n$. Given any two…

We investigate the distribution of cells by dimension in cylindrical algebraic decompositions (CADs). We find that they follow a standard distribution which seems largely independent of the underlying problem or CAD algorithm used. Rather,…

A rigorous homogenization theory is derived to describe the effective admittivity of cell suspensions. A new formula is reported for dilute cases that gives the frequency-dependent effective admittivity with respect to the membrane…