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Dynamic Mode Decomposition (DMD) is a powerful tool for extracting spatial and temporal patterns from multi-dimensional time series, and it has been used successfully in a wide range of fields, including fluid mechanics, robotics, and…
The introduction of structural defects in otherwise periodic media is well known to grant exceptional space control and localization of waves in various physical fields, including elasticity. Despite the variety of designs proposed so far,…
The nature of the pseudogap state is widely believed as a key to understanding the pairing mechanism underlying unconventional superconductivity. Over the past two decades, significant efforts have been devoted to searching for spontaneous…
Coherent, optically dressed media composed of two-level molecular systems without inversion symmetry are considered as all-optically tunable sources of coherent radiation in the microwave domain. A theoretical model and a numerical toolbox…
Spatially periodic modulation of the intersite coupling in two-dimensional (2D) nonlinear lattices modifies the eigenvalue spectrum by opening mini-gaps in it. This work aims to build stable localized modes in the new bandgaps. Numerical…
Metasurfaces allow tailored control over electromagnetic wavefronts. However, due to the local conservation of power flow, a passive, lossless, and reflectionless metasurface is limited to imparting phase discontinuities -- and not power…
We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…
Verifying closed-loop vision-based control systems remains a fundamental challenge due to the high dimensionality of images and the difficulty of modeling visual environments. While generative models are increasingly used as camera…
Efficient, low-loss, and versatile optical modulators are a critical ingredient for practical integrated photonic systems. Modulators based on micro-electromechanical systems (MEMS) have unique advantages over more traditional thermal,…
Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for…
Out-of-plane gap solitons in 2D photonic crystals are optical beams localized in the plane of periodicity of the medium and delocalized in the orthogonal direction, in which they propagate with a nonzero velocity. We study such gap solitons…
The hybrid plasmonic waveguide consists of a high-permittivity dielectric nanofiber embedded in a low-permittivity dielectric near a metal surface. This architecture is considered as one of the most perspective candidates for long-range…
We consider a modulated discrete nonlinear Schr\"odinger (DNLS) model with alternating on-site potential, having a linear spectrum with two branches separated by a 'forbidden' gap. Nonlinear localized time-periodic solutions with…
The electronic structure of a single-layer graphene with a periodic Fermi velocity modulation is investigated by using an effective Dirac-like Hamiltonian. In a gapless graphene or in a graphene with a constant energy gap the modulation of…
Beam alignment enables efficient, stable transmission and control of optical energy and information, which critically depend on precise monitoring and regulation of the three-dimensional (3D) relative positioning between fibers. This study…
An improved diffuse boundary condition, where the number flux of the incoming real molecules on the wall surface is calculated using the molecular variables rather than the cell's macroscopic variables, is proposed to eliminate the…
Given trajectories with gaps (i.e., missing data), we investigate algorithms to identify abnormal gaps in trajectories which occur when a given moving object did not report its location, but other moving objects in the same geographic…
We consider linear and nonlinear modes pinned to a grating-free (gapless) layer placed between two symmetric or asymmetric semi-infinite Bragg gratings (BGs), with a possible phase shift between them, in a medium with the uniform Kerr…
Dark solitons and localized defect modes against periodic backgrounds are considered in arrays of waveguides with defocusing Kerr nonlinearity constituting a nonlinear lattice. Bright defect modes are supported by local increase of the…
This paper presents a control architecture in which a direct adaptive control technique is used within the model predictive control framework, using the concurrent learning based approach, to compensate for model uncertainties. At each time…