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We consider the canonical ensemble of multilayered constrained Erdos-Renyi networks (CERN) and regular random graphs (RRG), where each layer represents graph vertices painted in a specific color. We study the critical behavior in such…
Periodic photonic structures enable precise control over the light-matter interaction through band structure engineering. Certain lattice geometries exhibit dispersionless flat bands, characterized by vanishing group velocity and diverging…
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…
The existence of large nonlinear optical coefficients is one of the preconditions for using nonlinear optical materials in nonlinear optical devices. For a crystal, such large coefficients can be achieved by matching photon energies with…
We motivate and analyze a simple model for the formation of banded vegetation patterns. The model incorporates a minimal number of ingredients for vegetation growth in semi-arid landscapes. It allows for comprehensive analysis and sheds new…
This paper presents two approaches to the precise design of maximally flat antireflection coatings reducing the reflectance of the substrate to near zero in a certain region around the central frequency. The first ideal case concerns…
Refraction, traditionally viewed as a geometric event occurring at material interfaces, is now being re-examined through the lens of coherence. Recent studies in optics and photonics, including coherence tomography, Moire interference, and…
The boundary problem of linear classical optics about the interaction of electromagnetic radiation with a thin dielectric film has been solved under explicit consideration of its discrete structure. The main attention has been paid to the…
Turing patterns are stationary, wave-like structures that emerge from the nonequilibrium assembly of reactive and diffusive components. While they are foundational in biophysics, their classical formulation relies on a single characteristic…
Arrays of nanostructures have emerged as exceptional tools for the manipulation and control of light. Oftentimes, despite the fact that real implementations of nanostructure arrays must be finite, these systems are modeled as perfectly…
While resonant modes do not exist within band gaps in infinite periodic materials, they may appear as in-gap localized edge modes once the material is truncated to form a finite periodic structure. Here, we provide an analysis framework…
Hyperuniformity refers to the suppression of density fluctuations at large scales. Typical for ordered systems, this property also emerges in several disordered physical and biological systems, where it is particularly relevant to…
When waves are propagated through a medium with scatters and these elements are positioned periodically, as in the crystal structures, multiple scattering leads to a phenomenon known as banded structures. This means that waves can propagate…
An emerging and promising vision of wireless networks consists of coating the environmental objects with reconfigurable metasurfaces that are capable of modifying the radio waves impinging upon them according to the generalized law of…
Many real world networks have groups of similar nodes which are vulnerable to the same failure or adversary. Nodes can be colored in such a way that colors encode the shared vulnerabilities. Using multiple paths to avoid these…
It is well known that direct observation of interference and diffraction pattern in the intensity distribution requires a spatially coherent source. Optical waves emitted from portions beyond the coherence area possess statistically…
We demonstrate full selective control over the constructive or destructive character of fourth-order recurring interferences in a modified version of a HOM interferometer using comb-like two-photon states. The comb spectral/temporal…
We study the cyclic color sequences induced at infinity by colored rays with apices being a given balanced finite bichromatic point set. We first study the case in which the rays are required to be pairwise disjoint. We derive a lower bound…
We construct generalized Hofstadter models that possess "color-entangled" flat bands and study interacting many-body states in such bands. For a system with periodic boundary conditions and appropriate interactions, there exist gapped…
We suggest a geometrical framework to discuss periodic layered structures in the unit disk. The band gaps appear when the point representing the system approaches the unit circle. We show that the trace of the matrix describing the basic…