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Periodic structures are a type of metamaterials in which their physical properties not only depend on the unit cell materials but also the way unit cells are arranged and interact with each other. Periodic structure have Interesting wave…
Transition waves in mechanical metamaterials manifest themselves as propagating interfaces between different stable states in lattices composed of arrays of coupled, intrinsically bistable elements. Here, we show experimentally and…
Metamaterials are artificial composite structures designed for controlling waves or fields, and exhibit interaction phenomena that are unexpected on the basis of their chemical constituents. These phenomena are encoded in effective material…
In the field of metamaterials, many intriguing phenomena arise from having a structure which is periodic in space. In time-dependent structures, conceptually similar properties can arise, which nevertheless have fundamentally different…
Within periodic materials and structures, wave scattering and dispersion occur across constituent material interfaces leading to a banded frequency response. In an earlier paper, the elastodynamics of one-dimensional periodic materials and…
In recent decades, scientists have developed the means to engineer synthetic periodic arrays with feature sizes below the wavelength of light. When such features are appropriately structured, electromagnetic radiation can be manipulated in…
Electromagnetic properties of periodic two-dimensional sub-wavelength structures consisting of closely-packed inclusions of materials with negative dielectric permittivity $\epsilon$ in a dielectric host with positive $\epsilon_h$ can be…
We study the frequency dependence of the effective electromagnetic parameters of left-handed and related meta-materials of the split ring resonator and wire type. We show that the reduced translational symmetry (periodic structure) inherent…
Periodic structures have interesting acoustic and vibration properties making them suitable for a wide variety of applications. In a periodic structure, the number of frequencies for each wavevector depends on the degree of freedom of the…
Tetrachiral materials are characterized by a cellular microstructure made by a periodic pattern of stiff rings and flexible ligaments. Their mechanical behaviour can be described by a planar lattice of rigid massive bodies and elastic…
Flexible mechanical metamaterials are compliant structures engineered to achieve unique properties via the large deformation of their components. While their static character has been studied extensively, the study of their dynamic…
Mechanical metamaterials leverage geometric design to achieve unconventional properties, such as high strength at low density, efficient wave guiding, and complex shape morphing. The ability to control shape changes builds on the complex…
Many properties of photonic structures rely on band topology characterized by the integer invariants that can change during the topological transitions and give rise to the disorder-robust topological edge, corner, or interface states.…
Dense ceramics are irreplaceable in applications requiring high mechanical stiffness, chemical and temperature resistance and low weight. To improve their toughness, ceramics can be reinforced with elongated inclusions. Recent manufacturing…
Temporal metamaterials are artificial materials whose electromagnetic properties change over time. In analogy with spatial media and metamaterials, where their properties change smoothly or abruptly over space, temporal metamaterials can…
Biological cells in soft materials can be modeled as anisotropic force contraction dipoles. The corresponding elastic interaction potentials are long-ranged ($\sim 1/r^3$ with distance $r$) and depend sensitively on elastic constants,…
The optical properties of periodic electromagnetic metamaterials are considered as functions of their relative unit cell size $d / \lambda$. The reflection $R$ and transmission $T$ coefficients are numerically calculated for some realistic…
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…
Metamaterials are arrangement of basic building blocks that repeat in space, time, or both. These material systems serve as an excellent platform for controlling waves, such as engineering wavenumber band gaps, flat bands, and…
We show how arbitrary unit cells of periodic materials can be represented as graphs whose nodes represent atoms and whose weighted edges represent tunneling connections between atoms. Further, we present methods to calculate the band…