Related papers: Small-World Disordered Lattices: Spectral Gaps and…
We study analytically the dynamics of two-dimensional rectangular lattices with periodic boundary conditions. We consider anisotropic initial data supported on one low-frequency Fourier mode. We show that, in the continuous approximation,…
We seek the possibility of a disorder driven transition in a tight-binding lattice with a flat band using complexity parameter approach. Our results indicate the existence of a localized to extended states transition with increasing…
We study numerically the transport and localization properties of waves in ordered and disordered ladder-shaped lattices with local $\mathcal{PT}$ symmetry. Using a transfer matrix method, we calculate the transmittance and the reflectance…
Topic of the thesis is a theoretical description of the ultracold atomic gases in one- and two-dimensional optical lattices in the presence of the disorder leading to the Anderson localization. The disorder is created by interaction of the…
We examine a one-dimensional $\mathcal{PT}$-symmetric binary lattice in the presence of diagonal disorder. We focus on the wave transport phenomena of localized and extended input beams for this disordered system. In the pure…
We have studied the peculiarities of electron transport in one-dimensional (1D) disordered chain at the presence of correlations between on-site interaction and tunneling integrals. In the considered models the disorder in host-lattice…
Disordered complex networks are of fundamental interest as stochastic models for information transmission over wireless networks. Well-known networks based on the Poisson point process model have limitations vis-a-vis network efficiency,…
Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples…
Photonic lattices facilitate band structure engineering, supporting both localized and extended modes through their geometric design. However, greater control over these modes can be achieved by taking advantage of the interference effect…
The transport properties of a disordered two-dimensional (2D) honeycomb lattice are examined numerically using the spectral approach to the quantum percolation problem, characterized by an Anderson-type Hamiltonian. In our simulations,…
Flatbands feature the distortion-free storage of compact localized states of tailorable shape. Their reliable storage sojourn is, however, limited by disorder potentials, which generically cause uncontrolled coupling into dispersive bands.…
We examine traveling-wave solutions on a regular ring network with one additional long-range link that spans a distance d. The nodes obey the FitzHugh-Nagumo kinetics in the excitable regime. The additional shortcut induces a plethora of…
The aim of this article is to study the attenuation of transient low-frequency waves in 2D lattices in both plane and antiplane problems. The main idea of this article is that analytical solutions to problems of mechanics of discrete…
Incoherent transport of excitations in one-dimensional disordered lattices with pairs of traps placed at random is studied by numerically solving the corresponding master equation. Results are compared to the case of lattices with the same…
Engineering superlattices (SLs) - which are spatially periodic potential landscapes for electrons - is an emerging approach for the realization of exotic properties, including superconductivity and correlated insulators, in two-dimensional…
Cation-disordered solids offer a rich chemical landscape where local coordination, lattice responses, and configurational disorder collectively, yet often implicitly, govern ion transport. In cation-disordered rocksalt oxides, Li+ diffusion…
Misinformation is pervasive in natural, biological, social, and engineered systems, yet its quantitative characterization remains challenging. We develop a general mathematical framework for quantifying information distortion in distributed…
The present paper deals with the wave propagation in a particular two dimensional structure, obtained from a localized perturbation of a reference periodic medium. This reference medium is a ladder like domain, namely a thin periodic…
We propose a random matrix approach to describe vibrational excitations in disordered systems. The dynamical matrix M is taken in the form M=AA^T where A is some real (not generally symmetric) random matrix. It guaranties that M is a…
A discrete drift-diffusion model is derived from a microscopic sequential tunneling model of charge transport in weakly coupled superlattices provided temperatures are low or high enough. Realistic transport coefficients and novel contact…