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Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of n-component bulk-surface reaction-diffusion systems in a ball, under the assumption of linear kinetics in the bulk and…
We analyze the phenomenon of system size stochastic resonance in a simple spatially extended system by exploiting the knowledge of the nonequilibrium potential. We show that through the analysis of that potential, and particularly its…
We develop a complete stability theory for two-dimensional periodic traveling waves of reaction-diffusion systems. More precisely, we identify a diffusive spectral stability assumption, prove that it implies nonlinear stability and provide…
We introduce a simple model for implementing the concepts of quasi-energy and parametric resonances (PRs) in systems with the $\mathcal{PT}$ symmetry, i.e., a pair of coupled and mutually balanced gain and loss elements. The parametric (ac)…
We present an investigation of the resonance conditions of axisymmetric internal wave sub-harmonics in confined and unconfined domains. In both cases, sub-harmonics can be spontaneously generated from a primary wave field if they satisfy at…
This paper discusses the modeling of acoustic wave fields in microstructured elastic solids within the framework of Riemann-Cartan geometry. We consider a scenario in which microstructural deformations occur significantly faster than those…
Sum-frequency generation (SFG) spectroscopy provides a versatile method for the investigation of non-centrosymmetric media and interfaces. Here, using tunable picosecond infrared (IR) pulses from a free-electron laser, the nonlinear optical…
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…
Based on the reciprocity theorem, we put forward a generalized parametric space for an arbitrary transfer matrix with parity time (PT) symmetry. Through this space, one can extract complete information involving PT phases, reflectances,…
Metasurfaces formed of arrays of subwavelength resonators are often tuned to 'critically couple' with incident radiation, so that at resonance dissipative and radiative damping are balanced and absorption is maximised. Such design criteria…
We consider the generation of longitudinal phonons in an elongated Bose-condensed gas at zero temperature due to parametric resonance as a result of the modulation of the transverse trap frequency. The nonlinear temporal evolution with…
This paper studies pattern formations in coupled elliptic PDE systems governed by transparent boundary conditions. Such systems unify diverse areas, including inverse boundary problems (via a single passive/active boundary measurement),…
The recent surge in popularity of diffusion models for image generation has brought new attention to the potential of these models in other areas of media generation. One area that has yet to be fully explored is the application of…
The processes in nonequilibrium dissipative media caused by coherent structure formation and lead to the complicated dynamics are of interest for nonlinear physics. Here we consider a model of the flow of interacting electronics patterns.…
We address the two-dimensional band-structure of graphene above the vacuum level in the context of discrete states immersed in the three-dimensional continuum. Scattering resonances are discovered that originate from the coupling of the…
Plasmon resonance is the resonant oscillation of conduction electrons at the interface between negative and positive permittivity material stimulated by incident light, which forms the fundamental basis of many cutting-edge industrial…
Diffusion models have emerged as powerful deep generative techniques, producing high-quality and diverse samples in applications in various domains including audio. While existing reviews provide overviews, there remains limited in-depth…
This work introduces the concept of parametric Gaussian processes (PGPs), which is built upon the seemingly self-contradictory idea of making Gaussian processes parametric. Parametric Gaussian processes, by construction, are designed to…
Due to the dominant electron capture by positrons from the molecular wall and the spatial dephasing across the wall-width, a powerful diffraction effect universally underlies the positronium (Ps) formation from fullerenes. This results into…
The averaging method is a classical powerful tool in perturbation theory of dynamical systems. There are two major obstacles to applying the averaging method, resonances and separatrices. In this paper we obtain realistic asymptotic…