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In this paper, we discuss multiscale methods for nonlinear problems. The main idea of these approaches is to use local constraints and solve problems in oversampled regions for constructing macroscopic equations. These techniques are…
It is well known that the classical energetically consistent micropolar model has limits in simulating the frequency band structure of packed granular materials (see Merkel et al., 2011). It is here shown that if a standard continualization…
A system for bunch-by-bunch detection of transverse proton and antiproton coherent oscillations in the Fermilab Tevatron collider is described. It is based on the signal from a single beam-position monitor located in a region of the ring…
Nonlinear interaction of a low density electron beam with a uniform plasma is studied using two-dimensional particle-in-cell (PIC) simulations. We focus on formation of coherent phase space structures in the case, when a wide…
A nonlinear Helmholtz equation (NLH) with high wave number and Sommerfeld radiation condition is approximated by the perfectly matched layer (PML) technique and then discretized by the linear finite element method (FEM).…
The generation of continuous-variable multipartite entangled states is important for several protocols of quantum information processing and communication, such as one-way quantum computation or controlled dense coding. In this article we…
In developing data-driven modeling methodologies, there is an ongoing need to reconcile the strong predictive performance of opaque black-box models with the transparency required for critical applications. This work introduces an…
In this paper the implications of a recently proposed phenomenological model of cosmology, the Asymptotic Cosmological Model (ACM), on the behavior of scalar perturbations are studied. Firstly we discuss new fits of the ACM at the…
We consider the problem of the formation of soliton states from a modulationally unstable initial condition in the framework of the Schr\"odinger-Poisson (or Newton-Schr\"odinger) equation accounting for gravitational interactions. We…
Nonlinear effects could play a crucial role in addressing optical nonreciprocal behaviors in scattering media. Such behaviors are, however, typically observed within a single transmission channel and predominantly in media with fixed…
Fluid-Structure Interaction (FSI) can be investigated by means of non-linear Finite Element Models (FEM), suitable to capture large deflections of structural parts interacting with fluids, and Computational Fluid Dynamics (CFD). High…
The driven, dissipative Bose-Hubbard model (BHM) provides a generic description of collective phases of interacting photons in cavity arrays. In the limit of strong optical nonlinearities (hard-core limit), the BHM maps on the dissipative,…
Dark Matter (DM) models providing possible alternative solutions to the small- scale crisis of standard cosmology are nowadays of growing interest. We consider DM interacting with light hidden fermions via well motivated fundamental…
A high-frequency asymptotic scheme is generated that captures the motion of waves within discrete hexagonal and honeycomb lattices by creating continuum homogenised equations. The accuracy of these effective medium equations in describing…
We introduce a discrete lossy system, into which a double hot spot (HS) is inserted, i.e., two mutually symmetric sites carrying linear gain and cubic nonlinearity. The system can be implemented as an array of optical or plasmonic…
A deep latent variable model is a powerful method for capturing complex distributions. These models assume that underlying structures, but unobserved, are present within the data. In this dissertation, we explore high-dimensional problems…
Symmetries and their associated selection rules are extremely useful in all fields of science. In particular, for system that include electromagnetic (EM) fields interacting with matter, it has been shown that both of symmetries of matter…
In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude-frequency plots of the dynamics on SSMs provide the classic backbone curves…
In this paper, by mapping datasets to a set of non-linear coherent states, the process of encoding inputs in quantum states as a non-linear feature map is re-interpreted. As a result of this fact that the Radial Basis Function is recovered…
Power system coherency refers to the phenomenon that machines in a power network exhibit similar frequency responses after disturbances, and is foundational for model reduction and control design. Despite abundant empirical observations,…