Nonlinear Regime Research Articles

Perturbations of Spinning Black Holes beyond General Relativity: Modified Teukolsky Equation

The detection of gravitational waves from compact binary mergers by the LIGO/Virgo collaboration has, for the first time, allowed for tests of relativistic gravity in the strong, dynamical and nonlinear regime. Outside Einstein's relativity, spinning black holes may be different from their general relativistic counterparts, and their merger may then lead to a modified ringdown. We study the latter and, for the first time, derive a modified Teukolsky equation, i.e., a set of linear, decoupled differential equations that describe dynamical perturbations of non-Kerr black holes for the radiative Newman-Penrose scalars $\Psi_0$ and $\Psi_4$. We first focus on non-Ricci-flat, Petrov type D black hole backgrounds in modified gravity, and derive the modified Teukolsky equation through direct decoupling and through a new approach, proposed by Chandrasekhar, that uses certain gauge conditions. We then extend this analysis to non-Ricci-flat, Petrov type I black hole backgrounds in modified gravity, assuming they can be treated as a linear perturbation of Petrov type D, black hole backgrounds in GR by generalizing Chandrasekhar's approach, and derive the decoupled modified Teukolsky equation. Our work lays the foundation to study the gravitational waves emitted in the ringdown phase of black hole coalescence in modified gravity for black holes of any spin. Our work can also be extended to compute gravitational waves emitted by extreme mass-ratio binary inspirals in modified gravity.

Thermal radiation in asymmetrically driven coupled non-linear photonic cavities

We study thermal radiation from a system of two coupled photonic cavities including the nonlinear Kerr effect, using numerical simulations and analytical methods. The general system, which can be implemented as two cavities in a waveguide, is asymmetrically driven with a monochromatic pumping from a single side. We describe the eigenmodes in the linear and nonlinear regime as well as the transmission of the coupled system. These results are then employed to understand the thermal radiation exhibited from both sides as each part of the system is coupled to a bath at a different temperature. Interestingly, the radiation spectrum is complicated, and can present up to four peaks due to the rich nonlinear coupling features. Furthermore, in certain regimes these spectra can drastically change upon variation of the bath temperatures. In addition, interference between the emitted and reflected radiation can lead to dips in the thermal radiation. Moreover, the system can exhibit self-pulsing, leading to comblike spectra for thermal radiation with peaks of very large amplitude. Our proposed analytical model for thermal radiation in the stable regime fits very well with the numerical results and describes a general class of devices.

Ligand impact on reactive oxygen species generation of Au10 and Au25 nanoclusters upon one- and two-photon excitation

In photodynamic therapy (PDT), light-sensitive photosensitizers produce reactive oxygen species (ROS) after irradiation in the presence of oxygen. Atomically-precise thiolate-protected gold nanoclusters are molecule-like nanostructures with discrete energy levels presenting long lifetimes, surface biofunctionality, and strong near-infrared excitation ideal for ROS generation in PDT. We directly compare thiolate-gold macromolecular complexes (Au10) and atomically-precise gold nanoclusters (Au25), and investigate the influence of ligands on their photoexcitation. With the ability of atomically-precise nanochemistry, we produce Au10SG10, Au10AcCys10, Au25SG18, and Au25AcCys18 (SG: glutathione; AcCys: N-acetyl-cysteine) fully characterized by high-resolution mass spectrometry. Our theoretical investigation reveals key factors (energetics of excited states and structural influence of surface ligands) and their relative importance in singlet oxygen formation upon one- and two-photon excitation. Finally, we explore ROS generation by gold nanoclusters in living cells with one- and two-photon excitation. Our study presents in-depth analyses of events within gold nanoclusters when photo-excited both in the linear and nonlinear optical regimes, and possible biological consequences in cells.

Interaction of two cylinders immersed in a viscous fluid. On the effect of moderate Keulegan–Carpenter numbers on the fluid forces

This work deals with the hydrodynamic interaction of two parallel circular cylinders, with identical radii, immersed in a viscous fluid initially at rest. One cylinder is stationary while the other one is imposed a harmonic motion with a moderate amplitude of vibration. The direction of motion is parallel to the line joining the centers of the two cylinders. The two dimensional fluid–structure problem is numerically solved by the Arbitrary Lagrangian–Eulerian method implemented in the open-source CFD code TrioCFD. First, we show that the fluid forces on the two cylinders are aligned with the direction of the imposed motion. Second, we show that the moderate oscillations of the moving cylinder create nonlinear effects in the fluid that strongly affect the characteristics (Fourier harmonics) of the hydrodynamic force acting on the stationary cylinder. The fluid force on the moving cylinder is shown to be poorly affected by the nonlinear effects, which makes it possible to extend the linear concept of self-added mass and damping coefficients. First, we show that the self-added coefficients decrease as Sk−1/2, with Sk the Stokes number (dimensionless number constructed from the imposed vibration frequency). Second, we show that the self-added mass (resp. damping) decreases (resp. increases) as −KC3 (resp. +KC3), with KC the Keulegan–Carpenter number (ratio between the imposed amplitude vibration and the separation distance between the cylinders). These variations are included in new power laws derived from nonlinear regressions of the numerical results. These new power laws for the self-added coefficients combine the effect of both Sk and KC, covering the viscous (Sk≥500) and weakly nonlinear (KC≤0.3) regimes.

Discrete Breathers of Nonlinear Dimer Lattices: Bridging the Anti-continuous and Continuous Limits

In this work, we study the dynamics of an infinite array of nonlinear dimer oscillators which are linearly coupled as in the classical model of Su, Schrieffer and Heeger (SSH). The ratio of in-cell and out-of-cell couplings of the SSH model defines distinct $\textit{phases}$: topologically trivial and topologically non-trivial. We first consider the case of weak out-of-cell coupling, corresponding to the topologically trivial regime for linear SSH; for any prescribed isolated dimer frequency, $\omega_b$, which satisfies non-resonance and non-degeneracy assumptions, we prove that there are discrete breather solutions for sufficiently small values of the out-of-cell coupling parameter. These states are $2\pi/\omega_b$- periodic in time and exponentially localized in space. We then study the global continuation with respect to this coupling parameter. We first consider the case where $\omega_b$, the seeding discrete breather frequency, is in the (coupling dependent) phonon gap of the underlying linear infinite array. As the coupling is increased, the phonon gap decreases in width and tends to a point (at which the topological transition for linear SSH occurs). In this limit, the spatial scale of the discrete breather grows and its amplitude decreases, indicating the weakly nonlinear long wave regime. Asymptotic analysis shows that in this regime the discrete breather envelope is determined by a vector gap soliton of the limiting envelope equations. We use the envelope theory to describe discrete breathers for SSH- coupling parameters corresponding to topologically trivial and, by exploiting an emergent symmetry, topologically nontrivial regimes, when the spectral gap is small. Our asymptotic theory shows excellent agreement with extensive numerical simulations over a wide range of parameters.

Localized layers of turbulence in stratified horizontally sheared Poiseuille flow

This paper presents a numerical analysis of the instability developing in horizontally sheared Poiseuille flow, when stratification extends along the vertical direction. Our study builds on the previous work that originally detected the linear instability of such a configuration, by means of experiments, theoretical analysis and numerical simulations (Le Gal et al., J. Fluid Mech., vol. 907, 2021, R1). We extend this investigation beyond linear theory, investigating nonlinear regimes with direct numerical simulations. We find that the flow loses its vertical homogeneity through a secondary bifurcation, due to harmonic resonances, and describe this symmetry-breaking mechanism in the vicinity of the instability threshold. When departing from this limit, we observe a series of bursting events that break down the flow into disordered motions driven by localized shear instabilities. This intermittent dynamics leads to the coexistence of horizontal localized layers of stratified turbulence surrounded by quiescent regions of meandering waves.

Simulating bulk viscosity in neutron stars. I. Formalism

The faithful inclusion of the effects of bulk viscosity induced by the presence of chemical reactions is an important issue for simulations of core-collapse supernovae, binary neutron star mergers, and neutron star oscillations, where particle abundances are locally pushed out of chemical equilibrium by rarefaction and compression of the fluid elements. In this work, we discuss three different approaches that can be used to implement bulk viscosity in general relativistic hydrodynamic simulations of neutron stars: the exact multi-component reacting fluid, and two M\"uller-Israel-Stewart theories, namely the second order Hiscock-Lindblom model and its linear limit, the Maxwell-Cattaneo model. After discussing the theory behind the three approaches, we specialize their dynamics equations to spherical symmetry in the radial gauge-polar slicing (i.e., Schwarzschild) coordinates. We also discuss a particular choice for the equation of state of the fluid and the associated neutrino emission rates, which are used in a companion paper for the numerical comparison of the three frameworks, and we obtain the effective sound speed for the Hiscock-Lindblom theory in the non-linear regime.

Global gyrokinetic simulations of electromagnetic turbulence in stellarator plasmas

Global electromagnetic turbulence is simulated in stellarator geometry using the gyrokinetic particle-in-cell code EUTERPE. The evolution of the turbulent electromagnetic field and the plasma profiles is considered at different values of the plasma beta and for different magnetic configurations. It is found that turbulence is linearly driven at relatively high toroidal mode numbers. In the nonlinear regime, lower toroidal mode numbers, including zonal flows, are excited resulting in a quench of the linear instability drive. The turbulent heat flux is outward and leads to the nonlinear relaxation of the plasma temperature profile. The particle flux is inward for the parameters considered. The effect of the parallel perturbation of the magnetic field on the stellarator turbulence is addressed.

An investigation into the nonlinear rheological behavior of modified asphalt binders using large amplitude oscillatory shear rheology

ABSTRACT Asphalt binders have been studied extensively with respect to their linear viscoelastic properties. From these properties, performance metrics have been derived and used for specification purposes. However, these materials are used in asphalt concrete pavements where they may experience time-dependent loads in the nonlinear regime. In the past, the vast majority of asphalt binders exhibited strong correlations between their linear and nonlinear properties and so despite this mismatch in characterization and the actual use phase domains, a system based on linear properties could be reliably deployed. More recently though, novel binders and additives have been introduced with differing relationships between linear and nonlinear behaviors. As such there is a need to characterize the asphalt binder response under large strains and use specifications that more explicitly account for the binder nonlinearity. Here, an attempt has been made to characterize the nonlinear rheological properties of asphalt binder using large amplitude oscillatory shear. The response of a single terminal blend, crumb rubber modified binder under large strains is analyzed using Lissajous-Bowditch plots while the contribution of higher harmonics is evaluated using Fourier-transform rheology. Finally, the elastic and viscous contributions are obtained using stress decomposition to an orthogonal set of Chebyshev polynomials. It is found that the relative nonlinearity increases with increasing strain and frequency under the tested conditions. The asphalt binder evaluated in this study predominantly exhibits shear thinning and either strain stiffening or softening behavior depending upon the test conditions. The applicability of time-temperature superposition in the nonlinear regime for asphalt binders is also evaluated.

Nonlinear corrections of overlap reduction functions for pulsar timing arrays

Recent pulsar timing array experiments have reported a hint of gravitational stochastic background in nHz band frequency. Further confirmation might rely on whether the signature of the signals is consistent with that sketched by overlap reduction functions, known as Hellings-Downs curves. This paper investigates the nonlinear corrections of overlap reduction functions in the presence of non-Gaussianity, in which the self-interaction of gravity is first taken into account. Expanding Einstein field equations and geodesic equations into the nonlinear regime, we obtain nonlinear corrections for the timing residuals of pulsar timing, and theoretically study the overlap reduction functions for pulsar timing arrays. In the event of considerable correction from the three-point correlations of gravitational waves, the shapes of the overlap reduction functions with nonlinear corrections can be differentiated from Hellings-Downs curves.

On collective nature of non-linear torsional Alfvén waves

ABSTRACT Torsional Alfvén waves in coronal plasma loops are usually considered to be non-collective, i.e. consist of cylindrical surfaces evolving independently, which significantly complicates their detection in observations. This non-collective nature, however, can get modified in the non-linear regime. To address this question, the propagation of non-linear torsional Alfvén waves in straight magnetic flux tubes has been investigated numerically using the astrophysical MHD code Athena++ and analytically, to support numerical results, using the perturbation theory up to the second order. Numerical results have revealed that there is radially uniform-induced density perturbation whose uniformity does not depend on the radial structure of the mother Alfvén wave. Our analysis showed that the ponderomotive force leads to the induction of the radial and axial velocity perturbations, while the mechanism for the density perturbation is provided by a non-equal elasticity of a magnetic flux tube in the radial and axial directions. The latter can be qualitatively understood by the interplay between the Alfvén wave perturbations, external medium, and the flux tube boundary conditions. The amplitude of these non-linearly induced density perturbations is found to be determined by the amplitude of the Alfvén driver squared and the plasma parameter β. The existence of the collective and radially uniform density perturbation accompanying non-linear torsional Alfvén waves could be considered as an additional observational signature of Alfvén waves in the upper layers of the solar atmosphere.

On the Nonlinear Shaping Gain With Probabilistic Shaping and Carrier Phase Recovery

The performance of different probabilistic amplitude shaping (PAS)techniques in the nonlinear regime is investigated, highlighting its dependence on the PAS block length and the interaction with carrier phase recovery (CPR). Different PAS implementations are considered, based on different distribution matching (DM) techniques—namely, sphere shaping, shell mapping with different number of shells, and constant composition DM—and amplitude-to-symbol maps. When CPR is not included, PAS with optimal block length provides a nonlinear shaping gain with respect to a linearly optimized PAS (with infinite block length); among the considered DM techniques, the largest gain is obtained with sphere shaping. On the other hand, the nonlinear shaping gain becomes smaller, or completely vanishes, when CPR is included, meaning that in this case all the considered implementations achieve a similar performance for a sufficiently long block length. Similar results are obtained in different link configurations ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1\times 180$</tex-math></inline-formula> km, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$15\times 80$</tex-math></inline-formula> km, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$27\times 80$</tex-math></inline-formula> km single-mode-fiber links), and also including laser phase noise, except when in-line dispersion compensation is used. Furthermore, we define a new metric, the nonlinear phase noise (NPN) metric, which is based on the frequency resolved logarithmic perturbation models and explains the interaction of CPR and PAS. We show that the NPN metric is highly correlated with the performance of the system. Our results suggest that, in general, the optimization of PAS in the nonlinear regime should always account for the presence of a CPR algorithm. In this case, the reduction of the rate loss (obtained by using sphere shaping and increasing the DM block length) turns out to be more important than the mitigation of the nonlinear phase noise (obtained by using constant-energy DMs and reducing the block length), the latter being already granted by the CPR algorithm.

Strongly nonlinear topological phases of cascaded topoelectrical circuits

Circuits provide ideal platforms of topological phases and matter, yet the study of topological circuits in the strongly nonlinear regime, has been lacking. We propose and experimentally demonstrate strongly nonlinear topological phases and transitions in one-dimensional electrical circuits composed of nonlinear capacitors. Nonlinear topological interface modes arise on domain walls of the circuit lattices, whose topological phases are controlled by the amplitudes of nonlinear voltage waves. Experimentally measured topological transition amplitudes are in good agreement with those derived from nonlinear topological band theory. Our prototype paves the way towards flexible metamaterials with amplitude-controlled rich topological phases and is readily extendable to two and three-dimensional systems that allow novel applications.

Single-Beam Room-Temperature Atomic Magnetometer with Large Bandwidth and Dynamic Range

We present a single-beam atomic magnetometer operating at room temperature for the measurement of ac magnetic fields. The magnetometer functions in the nonlinear regime of magneto-optical rotation of ${}^{85}\mathrm{Rb}$ atomic vapor without any buffer gases. We demonstrate a sensitivity of approximately $0.9\phantom{\rule{0.2em}{0ex}}\mathrm{pT}/\sqrt{\mathrm{Hz}}$ at 2 kHz and a large bandwidth of 24 kHz. The dynamic range of measurement is ${10}^{6}$, making the sensor effective even in Earth's field. We present the signal-to-noise and bandwidth characteristics of the system for both shielded and unshielded modes of operation. Moreover, we perform theoretical analysis for the atom-light system for the single-laser-beam configuration. The effect of light intensity and detuning on the magnetometer is studied theoretically as well as experimentally to understand the strengths and limitations of the technique.

Multimode hybrid gold-silicon nanoantennas for tailored nanoscale optical confinement.

High-index dielectric nanoantennas, which provide an interplay between electric and magnetic modes, have been widely used as building blocks for a variety of devices and metasurfaces, both in linear and nonlinear regimes. Here, we investigate hybrid metal-semiconductor nanoantennas, consisting of a multimode silicon nanopillar core coated with a gold layer, that offer an enhanced degree of control over the mode selection and confinement, and emission of light on the nanoscale exploiting high-order electric and magnetic resonances. Cathodoluminescence spectra revealed a multitude of resonant modes supported by the nanoantennas due to hybridization of the Mie resonances of the core and the plasmonic resonances of the shell. Eigenmode analysis revealed the modes that exhibit enhanced field localization at the gold interface, together with high confinement within the nanopillar volume. Consequently, this architecture provides a flexible means of engineering nanoscale components with tailored optical modes and field confinement for a plethora of applications, including sensing, hot-electron photodetection and nanophotonics with cylindrical vector beams.

Nonlinear harmonic vibrations of laminate plates with VE layers using refined zig-zag theory. Part 2 – Numerical solution

The paper is devoted to the numerical analysis of the harmonic vibrations of laminate plates with viscoelastic layers in the von Kàrmàn geometrically non-linear regime. The amplitude equation derived in the prequel paper Part 1 – theoretical background is discretized using the 8-noded bi-quadratic plate finite elements. The response curves are obtained using the continuation method to solve the discretised amplitude equation treated as the equation with the frequency of vibrations as a parameter. The proposed method of solution is verified by comparing the results with those from available literature. Furthermore, several numerical analyses are performed, including testing of FE mesh density, plate aspect ratio, various VE materials, support conditions and layers layout as well as the possibility of simplification of the complex-valued zig-zag function used in the description of plate kinematics. Several results of practical importance are found and discussed in the conclusions.

Non‐Reciprocal Cavity Polariton with Atoms Strongly Coupled to Optical Cavity

AbstractBreaking the time‐reversal symmetry of light is of great importance for fundamental physics and has attracted increasing interest in the study of non‐reciprocal photonic devices. Here, a chiral cavity quantum electrodynamics system with multiple atoms strongly coupled to a Fabry–Pérot cavity is experimentally demonstrated. By polarizing the internal quantum state of the atoms, the time‐reversal symmetry of the atom‐cavity interaction is broken. The strongly coupled atom‐cavity system can be described by non‐reciprocal quasiparticles, that is, the cavity polariton. When it works in the linear regime, the inherent nonreciprocity makes the system work as a single‐photon‐level optical isolator. Benefiting from the collective enhancement of multiple atoms, an isolation ratio exceeding 30 dB on the single‐quanta level (≈ 0.1 photon on average) is achieved. The validity of the non‐reciprocal device under zero magnetic field and the reconfigurability of the isolation direction are also experimentally demonstrated. Moreover, when the cavity polariton works in the nonlinear regime, the quantum interference between polaritons with weak anharmonicity induces non‐reciprocal nonclassical statistics of cavity transmission from coherent probe light.

Shear-Triggered Release of Lipid Nanoparticles from Tissue-Mimetic Hydrogels.

Shear forces are involved in many cellular processes and increase remarkably in the case of cardiovascular diseases in the human body. While various stimuli, such as temperature, pH, light, and electromagnetic fields, have been considered for on-demand release, developing drug delivery systems that are responsive to physiological-level shear stresses remains as a challenge. For this purpose, liposomes embedded in hydrogel matrices are promising as they can dynamically engage with their environment due to their soft and deformable structure. However, for optimal drug delivery systems, the interaction between liposomes and the surrounding hydrogel matrix, and their response to the shear should be unraveled. Here, we used unilamellar DMPG liposomes as drug nanocarriers and polyethylene (glycol) diacrylate (PEGDA) hydrogels having different elasticities, from 1Pa to 180Pa, as extracellular matrix (ECM)-mimetic matrices to understand shear-triggered liposome discharge from hydrogels. The presence of liposomes provides hydrogels with temperature-controlled water uptake which is sensitive to membrane microviscosity. By systematically applying shear deformation from linear to nonlinear deformation regimes, we modulate the liposome release under transient and cyclic stimuli. Considering that shear force is commonly encountered in biofluid flow, these results will provide fundamental basis for rational design of shear-controlled liposomal drug delivery systems. This article is protected by copyright. All rights reserved.

Restoring the reciprocity invariance in nonlinear systems with broken mirror symmetry

Circumventing the reciprocity invariance has posed an interesting challenge in the design of modern devices for wave engineering. In passive devices, operating the device in the nonlinear response regime is a common means for realizing nonreciprocity. Because mirror-symmetric systems are trivially reciprocal, breaking the mirror symmetry is a necessary requirement for nonreciprocal dynamics to exist in nonlinear systems. However, the response of an asymmetric nonlinear system is not necessarily nonreciprocal. In this work, we report on the existence of stable, steady-state nonlinear reciprocal dynamics in coupled asymmetric systems subject to external harmonic excitation. We restore reciprocity in the asymmetric system by tuning two symmetry-breaking parameters simultaneously under certain operating conditions. Specifically, we identify response regimes in the vicinity of the primary resonances of the system where the steady-state left-to-right transmission characteristics are identical to the right-to-left characteristics in terms of frequency, amplitude and phase. We interpret these regimes of reciprocal dynamics in the context of phase nonreciprocity, wherein incident waves undergo a nonreciprocal phase shift depending on their direction of travel. We hope these findings help design devices with new functionalities for controlling and steering of elastic waves.

Adiabatic light propagation in nonlinear waveguide couplers with longitudinally varying detunings via resonance-locked inverse engineering

We investigate the adiabatic evolution of light in nonlinear waveguide couplers via resonance-locked inverse engineering based on stimulated Raman adiabatic passage (STIRAP). The longitudinal varying detunings of the propagation coefficients are designed to eliminate dynamically the nonlinear effect, which induce the non-adiabatic oscillations. We show that different light evolutions such as complete light transfer, light split and light return can be realized adiabatically with appropriate choices of the detunings even in the nonlinear regime. The features open new opportunities for the realization of all-optical nonlinear devices with high fidelity in integrated optics.