Broadband coherent perfect absorption by cavity coupled to three-level atoms in linear and nonlinear regimes

A broadband coherent perfect absorption (CPA) scheme consisting of an optical resonator coupled with three-level atoms excited by single cavity mode is proposed and analyzed. We show the output light field from the system is completely suppressed under specific conditions when the system is excited in linear and nonlinear regimes by two identical light fields from two ends of optical cavity. An analytical broadband CPA criterion for central and sideband excitations of cavity quantum electrodynamics (CQED) system is derived in linear regime. Moreover, we show the resonant excitation criterion for CPA is greatly extended in nonlinear regime. A new type of bistability behavior is found. The output field intensity and the bistability curve can be well tuned by dynamically adjusting system parameters. Our results demonstrate that the CPA is quite universal, and it should be useful in a variety of applications in optical logic and optical communication devices.

Nonlinear resonant torus oscillations as a model of Keplerian disc warp dynamics

Observations of distorted discs have highlighted the ubiquity of warps in a variety of astrophysical contexts. This has been complemented by theoretical efforts to understand the dynamics of warp evolution. Despite significant efforts to understand the dynamics of warped discs, previous work fails to address arguably the most prevalent regime – nonlinear warps in Keplerian discs for which there is a resonance between the orbital, epicyclic and vertical oscillation frequencies. In this work, we implement a novel nonlinear ring model, developed recently by Fairbairn and Ogilvie, as a framework for understanding such resonant warp dynamics. Here we uncover two distinct nonlinear regimes as the warp amplitude is increased. Initially we find a smooth modulation theory which describes warp evolution in terms of the averaged Lagrangian of the oscillatory vertical motions of the disc. This hints towards the possibility of connecting previous warp theory under a generalised secular framework. Upon the warp amplitude exceeding a critical value, which scales as the square root of the aspect-ratio of our ring, the disc enters into a bouncing regime with extreme vertical compressions twice per orbit. We develop an impulsive theory which predicts special retrograde and prograde precessing warped solutions, which are identified numerically using our full equation set. Such solutions emphasise the essential activation of nonlinear vertical oscillations within the disc and may have important implications for energy and warp dissipation. Future work should search for this behaviour in detailed numerical studies of the internal flow structure of warped discs.

Comparison of Different Numerical Interface Capturing Methods for the Simulation of Faraday Waves

Faraday instability is a classic problem that occurs due to the relative displacement of the interface that separates two immiscible fluids placed in a closed container under oscillating acceleration parallel to gravity. The interface deformation and the induced flow patterns of this two-phase flow are very complex and numerical simulations could allow a deeper understanding of the dynamics of these systems. Some tests have been performed to establish a reference solution, but further validation is needed in order to ensure the validity of these solutions. In this work, we compare some numerical solutions for the linear and nonlinear regimes using the phase field scheme with predictions obtained using different numerical schemes such as Front Tracking, Volume of Fluid, and Element-based Finite Volume Method. The results show that, in both linear and nonlinear regimes, some important differences in the prediction of the interface dynamics between the methods are observed, and the need to provide a reference numerical solution for future benchmarks is highlighted.

Energy-Based Criterion for Testing the Nonlinear Response Strength of Strong Nonlinear Oscillators

This article proposes a simple energy-based criterion developed to characterize four commonly identified responses, namely: linear, weakly nonlinear, moderately nonlinear and strongly nonlinear regimes. The response of the nonlinear simple pendulum was used for benchmarking the boundary conditions for each of the four response regimes and the test criterion was demonstrated using relevant examples. The test presented in this article is important for clarifying the obscurity surrounding the accuracy and range of validity of recent approximate analytical schemes used to investigate strong nonlinear oscillators. Furthermore, it is meant to create awareness of the need to develop more robust testing criteria. Keywords: strong nonlinear oscillation; periodic oscillation; approximate analytical solution

Dynamics and Wave Propagation in Nonlinear Piezoelectric Metastructures

This paper reports dynamical effects in onedimensional locally resonant piezoelectric metastructures that can be leveraged by nonlinear electrical attachments featuring either combined quadratic and quartic, or essentially quartic potentials. The nonlinear electromechanical unit cell is built upon a linear host oscillator coupled to a nonlinear electrical circuit via piezoelectricity. Its dynamical response to prescribed longitudinal harmonic displacements is approached in the frequency and time domains. Semi-analytical harmonic balance (HB)-based dispersion relations are derived to predict the location and edges of the nonlinear attenuation band. Numerical responses show that weakly and moderately nonlinear piezoelectric metastructures (NPMSs) promote a class of nonlinear attenuation band where a bandgap and a wave supratransmission band coexist, while also imparting nonlinear attenuation at the resonances around the underlying linear bandgap. Besides, strongly nonlinear regimes are shown to elicit broadband chaotic attenuation. Negative capacitance (NC)-based essentially cubic piezoelectric attachments are found to potentiate the aforementioned effects over a broader bandwidth. Excellent agreement is found between the predictions of the HB based dispersion relations and the nonlinear transmissibility functions of undamped and weakly damped NPMSs at weakly and moderately nonlinear regimes, even in the presence of NC circuits. This research is expected to pave the way towards fully tunable smart periodic metastructures for vibration control via nonlinear piezoelectric attachments.PACS 05.45.-a . 62.30.+d . 62.65.+kMathematics Subject Classification (2010) 37N15 . 74H45 . 74H65 . 74J30

A nonlinear magnonic nano-ring resonator

The field of magnonics, which aims at using spin waves as carriers in data-processing devices, has attracted increasing interest in recent years. We present and study micromagnetically a nonlinear nanoscale magnonic ring resonator device for enabling implementations of magnonic logic gates and neuromorphic magnonic circuits. In the linear regime, this device efficiently suppresses spin-wave transmission using the phenomenon of critical resonant coupling, thus exhibiting the behavior of a notch filter. By increasing the spin-wave input power, the resonance frequency is shifted, leading to transmission curves, depending on the frequency, reminiscent of the activation functions of neurons, or showing the characteristics of a power limiter. An analytical theory is developed to describe the transmission curve of magnonic ring resonators in the linear and nonlinear regimes, and is validated by a comprehensive micromagnetic study. The proposed magnonic ring resonator provides a multi-functional nonlinear building block for unconventional magnonic circuits.