Related papers: The capture into parametric autoresonance
Field amplification and particle production due to parametric resonance are highly nontrivial predictions of quantum fields that couple to an oscillating source during inflation and reheating. Understanding this two effects is crucial for…
We show bifurcation of localized spike solutions from spatially constant states in systems of nonlocally coupled equations in the whole space. The main assumptions are a generic bifurcation of saddle-node or transcritical type for spatially…
This paper presents an analytical formulation for correcting the diffraction associated to the second harmonic of an acoustic wave, more compact than that usually used. This new formulation, resulting from an approximation of the correction…
We study the long-time asymptotics of the total mass of the solution to the parabolic Anderson model (PAM) on a supercritical Galton-Watson random tree with bounded degrees. We identify the second-order contribution to this asymptotics in…
This paper is concerned with robust preconditioning of wave equations constrained linear inverse problems from boundary observation data. The main result of this paper is a concept for regularization parameter robust preconditioning.…
The author discusses particular solutions of a second order equation designated by source equation. This equation is special because the metric of the space where it is written is influenced by the solution, rendering the equation…
We describe a novel algorithm for solving general parametric (nonlinear) eigenvalue problems. Our method has two steps: first, high-accuracy solutions of non-parametric versions of the problem are gathered at some values of the parameters;…
In this paper we introduce an optical approximation into the theory of impedance calculation, one valid in the limit of high frequencies. This approximation neglects diffraction effects in the radiation process, and is conceptually…
Nonlinear ultrasound imaging leverages harmonic wave generation to enhance contrast and spatial resolution beyond the capabilities of conventional linear techniques. This behavior is commonly modeled by the Westervelt equation, which…
We consider a two-dimensional analogue of Helmholtz resonator with walls of finite thickness in the critical case when there exists an eigenfrequency equalling to the limit of poles generated by both the bounded component of the resonator…
Describing the solutions of inverse problems arising in signal or image processing is an important issue both for theoretical and numerical purposes. We propose a principle which describes the solutions to convex variational problems…
By analogy to the continuous Painlev\'e II equation, we present particular solutions of the discrete Painlev\'e II (d-P$\rm_{II}$) equation. These solutions are of rational and special function (Airy) type. Our analysis is based on the…
We study the Duffing equation and its generalizations with polynomial nonlinearities. Recently, we have demonstrated that metamorphoses of the amplitude response curves, computed by asymptotic methods in implicit form as $F\left( \Omega ,\…
It is shown that a sub-luminal electromagnetic plasma wave, propagating in phase with a background sub-luminal gravitational wave in a dispersive medium, can undergo parametric amplification. For this phenomena to occur, the dispersive…
The Lorenz-96 model is widely used as a test model for various applications, such as data assimilation methods. This symmetric model has the forcing $F\in\mathbb{R}$ and the dimension $n\in\mathbb{N}$ as parameters and is $\mathbb{Z}_n$…
A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned…
A complete kinetic modeling of an ionized gas in contact with a surface requires the knowledge of the electron desorption time and the electron sticking coefficient. We calculate the desorption time for phonon-mediated desorption of an…
We investigate the $1: 2$ resonance in the periodically forced asymmetric Duffing oscillator due to the period-doubling of the primary $1: 1$ resonance or forming independently, coexisting with the primary resonance. We compute the…
Resonances leave prominent signatures in atomic and molecular ionization triggered by the absorption of single or multiple photons. These signatures reveal various aspects of the ionization process, characterizing both the initial and final…
Attosecond photoelectron interferometry based on the combination of an attosecond pulse train and a synchronized infrared field is a fundamental technique for the temporal characterization of attosecond waveforms and for the investigation…