Nonlinear Regime Research Articles

Characterizing the post-inflationary reheating history. Part II. Multiple interacting daughter fields

We characterize the post-inflationary dynamics of an inflaton ϕ coupled to multiple interacting daughter fields Xn (n = 1, … Nd ) through quadratic-quadratic interactions gn 2 ϕ 2 Xn 2. We assume a monomial inflaton potential V(ϕ) ∝ |ϕ| p (p ≥ 2) around the minimum. By simulating the system in 2+1-dimensional lattices, we study the post-inflationary evolution of the energy distribution and equation of state, from the end of inflation until a stationary regime is achieved. We show that in this scenario, the energy transferred to the daughter field sector can be larger than 50%, surpassing this way the upper bound found previously for single daughter field models. In particular, for p ≥ 4 the energy at very late times is equally distributed between all fields, and only 100/(Nd + 1) % of the energy remains in the inflaton. We also consider scenarios in which the daughter fields have scale-free interactions λnmXn 2 Xm 2, including the case of quartic daughter field self-interactions (for n = m). We show that these interactions trigger a resonance process during the non-linear regime, which in the single daughter field case already allows to deplete more than 50% of the energy from the inflaton for p ≥ 4.

Effect of constitutive law on the erythrocyte membrane response to large strains.

Three constitutive laws, that is the Skalak, neo-Hookean and Yeoh laws, commonly employed for describing the erythrocyte membrane mechanics are theoretically analyzed and numerically investigated to assess their accuracy for capturing erythrocyte deformation characteristics and morphology. Particular emphasis is given to the nonlinear deformation regime, where it is known that the discrepancies between constitutive laws are most prominent. Hence, the experiments of optical tweezers and micropipette aspiration are considered here, for which relationships between the individual shear elastic moduli of the constitutive laws can also be established through analysis of the tension-deformation relationship. All constitutive laws were found to adequately predict the axial and transverse deformations of a red blood cell subjected to stretching with optical tweezers for a constant shear elastic modulus value. As opposed to Skalak law, the neo-Hookean and Yeoh laws replicated the erythrocyte membrane folding, that has been experimentally observed, with the trade-off of sustaining significant area variations. For the micropipette aspiration, the suction pressure-aspiration length relationship could be excellently predicted for a fixed shear elastic modulus value only when Yeoh law was considered. Importantly, the neo-Hookean and Yeoh laws reproduced the membrane wrinkling at suction pressures close to those experimentally measured. None of the constitutive laws suffered from membrane area compressibility in the micropipette aspiration case.

Random walk and non-Gaussianity of the 3D second-quantized Schrödinger–Newton nonlocal soliton

Nonlocal quantum fluids emerge as dark-matter models and tools for quantum simulations and technologies. However, strongly nonlinear regimes, like those involving multi-dimensional self-localized solitary waves, are marginally explored for what concerns quantum features. We study the dynamics of 3D+1 solitons in the second-quantized nonlocal nonlinear Schrödinger–Newton equation. We theoretically investigate the quantum diffusion of the soliton center of mass and other parameters, varying the interaction length. 3D+1 simulations of the Ito partial differential equations arising from the positive P-representation of the density matrix validate the theoretical analysis. The numerical results unveil the onset of non-Gaussian statistics of the soliton, which may signal quantum-gravitational effects and be a resource for quantum computing. The non-Gaussianity arises from the interplay between the soliton parameter quantum diffusion and the stable invariant propagation. The fluctuations and the non-Gaussianity are universal effects expected for any nonlocality and dimensionality.

Intense Whistler-mode Waves at Foreshock Transients: Characteristics and Regimes of Wave−Particle Resonant Interaction

Thermalization and heating of plasma flows at shocks result in unstable charged-particle distributions that generate a wide range of electromagnetic waves. These waves, in turn, can further accelerate and scatter energetic particles. Thus, the properties of the waves and their implication for wave−particle interactions are critically important for modeling energetic particle dynamics in shock environments. Whistler-mode waves, excited by the electron heat flux or a temperature anisotropy, arise naturally near shocks and foreshock transients. As a result, they can often interact with suprathermal electrons. The low background magnetic field typical at the core of such transients and the large wave amplitudes may cause such interactions to enter the nonlinear regime. In this study, we present a statistical characterization of whistler-mode waves at foreshock transients around Earth’s bow shock, as they are observed under a wide range of upstream conditions. We find that a significant portion of them are sufficiently intense and coherent (narrowband) to warrant nonlinear treatment. Copious observations of background magnetic field gradients and intense whistler wave amplitudes suggest that phase trapping, a very effective mechanism for electron acceleration in inhomogeneous plasmas, may be the cause. We discuss the implications of our findings for electron acceleration in planetary and astrophysical shock environments.

Impact of wiggler magnetic field on wakefield generation and electron acceleration by Gaussian, super-Gaussian and Bessel–Gaussian laser pulses propagating in collisionless plasma

In this research, the process of electron acceleration and wakefield generation by Gaussian-like (GL), super-Gaussian (SG) and Bessel–Gaussian (BG) laser pulses through cold collisionless plasma in the presence of a planar magnetostatic wiggler are studied. Three different types of laser spatial profiles, GL, SG and BG, are considered. Additionally, using the hydrodynamics fluid equations, Maxwell's equations as well as the perturbation technique for GL, SG and BG laser pulses in the weakly nonlinear regime and in the presence of a planar magnetostatic wiggler, governing equations for analysing the laser wakefield and electron acceleration have been derived and compared correspondingly. In addition, the effect of some important factors, including the wiggler field strengths, laser intensity, pulse length, plasma electron density and laser frequency on the wakefield and the electron energy gain, have been investigated. Numerical results show that enhancing the wiggler magnetic field results in an increase in the amplitude of the wakefield. Furthermore, it is observed that in comparison with the wakefield amplitude excited by SG and GL laser pulses, the amplitude of the wakefield excited by BG laser pulse is larger when the wiggler field is enhanced. Moreover, it is realized that the type of the laser profile, selected laser parameters and wiggler magnetic field are the most decisive and effective factors in the wakefield amplitude and shape of wakefield generation through cold collisionless plasma. Also, it is seen that as the pulse length declines, the amplitude of the wakefield increases, and correspondingly the resonance positions shift to higher ${({\varOmega _w}/{\varOmega _p})_{max}}$ values.

Physics-aware learning of nonlinear limit cycles and adjoint limit cycles

Thermoacoustic oscillations occur when the heat released by a flame is sufficiently in phase with the acoustic pressure. Under this condition, the linear instability can saturate to a nonlinear self-excited oscillation with a large amplitude. A typical nonlinear regime is a limit cycle, which is characterised by a periodic orbit in the thermoacoustic dynamics. In this paper, we develop a physics-aware data-driven method to predict periodic solutions using forward neural networks. The physics is constrained in two ways. First, the training is informed by a physical residual, which penalises solutions that violate the conservation of mass, momentum, and energy. Second, periodicity is imposed by introducing periodic activation functions in the neural network. We test the algorithm on a nonlinear time-delayed model of a Rijke tube. Adjoint methods offer a cheap and easy way to calculate the gradients with respect to design parameters, hence we extend our study to learning the adjoint variables of the Rijke system, which also settle onto periodic oscillations. We find that (i) periodic solutions of thermoacoustic systems can be accurately learned with this method, (ii) for periodic data, periodic activations outperform conventional activations in terms of prediction capability beyond the training range, and (iii) under the physical constraints, fewer data is sufficient to achieve a good performance. This work opens up possibilities for the prediction of nonlinear thermoacoustics by combining physical knowledge and data.

Gravitational wave inference on a numerical-relativity simulation of a black hole merger beyond general relativity

We apply common gravitational wave inference procedures on binary black hole merger waveforms beyond general relativity. We consider dynamical Chern-Simons gravity, a modified theory of gravity with origins in string theory and loop quantum gravity. This theory introduces an additional parameter $\ell$, corresponding to the length-scale below which beyond-general-relativity effects become important. We simulate data based on numerical relativity waveforms produced under an approximation to this theory, which differ from those of general relativity in the strongly nonlinear merger regime. We consider a system with parameters similar to GW150914 with different values of $\ell$ and signal-to-noise ratios. We perform two analyses of the simulated data. The first is a template-based analysis that uses waveforms derived under general relativity and allows us to identify degeneracies between the two waveform morphologies. The second is a morphology-independent analysis based on BayesWave that does not assume that the signal is consistent with general relativity. The BayesWave analysis faithfully reconstructs the simulated signals. However, waveform models derived under general relativity are unable to fully mimic the simulated modified-gravity signals and such a deviation would be identifiable with existing inference tools. Depending on the magnitude of the deviation, we find that the templated analysis can under perform the morphology-independent analysis in fully recovering simulated beyond-GR waveforms even for achievable signal-to-noise ratios $\gtrsim 20{-}30$.

Nonlinear photonics with metasurfaces

Nonlinear optics is a well-established field of research that traditionally relies on the interaction of light with macroscopic nonlinear media over distances significantly greater than the wavelength of light. However, the recently emerged field of optical metasurfaces provides a novel platform for studying nonlinear phenomena in planar geometries. Nonlinear optical metasurfaces introduce new functionalities to the field of nonlinear optics extending them beyond perturbative regimes of harmonic generation and parametric frequency conversion, being driven by mode-matching, resonances, and relaxed phase-matching conditions. Here we review the very recent advances in the rapidly developing field of nonlinear metasurface photonics, emphasizing multi-frequency and cascading effects, asymmetric and chiral frequency conversion, nonperturbative nonlinear regimes, and nonlinear quantum photonics, empowered by the physics of Mie resonances and optical bound states in the continuum.

Optimizing the placement of numerical relativity simulations using a mismatch predicting neural network

Gravitational wave observations from merging compact objects are becoming commonplace, and as detectors improve and gravitational wave sources become more varied, it is increasingly important to have dense and expansive template banks of predicted gravitational waveforms. Since numerical relativity is the only way to fully solve the nonlinear merger regime of general relativity for comparably massed systems, numerical relativity simulations are critical for gravitational wave detection and analysis. These simulations are computationally expensive, with each simulation placing one point within the high dimensional parameter space of binary black hole coalescences. This makes it important to have a method of placing new simulations in ways that use our computational resources optimally while ensuring sufficient coverage of the parameter space. Accomplishing this requires predicting the impact of a new set of parameters before performing the simulation. To this effect, this paper introduces a neural network to predict the mismatch between the gravitational waves of two binary systems. Using this network, we then show how we can propose new numerical relativity simulations that will provide the most benefit. We also use the network to identify gaps in existing public catalogs and identify degeneracies in the binary black hole parameter space.

Quantum Fluctuation of the Quantum Geometric Tensor and Its Manifestation as Intrinsic Hall Signatures in Time-Reversal Invariant Systems

In time-reversal invariant systems, all charge Hall effects predicted so far are extrinsic effects due to the dependence on the relaxation time. We explore intrinsic Hall signatures by studying the quantum noise spectrum of the Hall current in time-reversal invariant systems, and discover intrinsic thermal Hall noises in both linear and nonlinear regimes. As the band geometric characteristics, quantum geometric tensor and Berry curvature play critical roles in various Hall effects; so do their quantum fluctuations. It is found that the thermal Hall noise in linear order of the electric field is purely intrinsic, and the second-order thermal Hall noise has both intrinsic and extrinsic contributions. In particular, the intrinsic part of the second-order thermal Hall noise is a manifestation of the quantum fluctuation of the quantum geometric tensor, which widely exists as long as Berry curvature is nonzero. These intrinsic thermal Hall noises provide direct measurable means to band geometric information, including Berry curvature related quantities and quantum fluctuation of quantum geometric tensor.

Unconventional photon blockade in four mode coupled optomechanical system

In this study we theoretically and numerically analyze the photon statistics of a weakly driven optomechanical system comprising two optical and two mechanical modes where each mechanical mode is cross-coupled with the two cavity modes by a three-mode optomechanical interaction. We analytically determine the optimal conditions of unconventional photon blockade due to destructive interference between different transition pathways in weak Kerr nonlinear regime. We also numerically evaluate the second order photon correlation function and plot it against different system parameters to find that the numerical results are in agreement with analytical optimal conditions.

Influence of wavelength and accumulated fluence at picosecond laser-induced surface roughening of copper on secondary electron yield

Ultrashort-pulse laser processing of copper is performed in air to reduce the secondary electron yield (SEY). By UV (355 nm), green (532 nm), and IR (1064 nm) laser-light induced surface modification, this study investigates the influence of the most relevant experimental parameters, such as laser power, scanning speed, and scanning line distance (represented as accumulated fluence) on the ablation depth, surface oxidation, topography, and ultimately on the SEY. Increasing the accumulated laser fluence results in a gradual change from a Cu2O to a CuO-dominated surface with deeper micrometer trenches, higher density of redeposited surface particles from the plasma phase, and a reduced SEY. While the surface modifications are less pronounced for IR radiation at low accumulated fluence (<1000 J/cm2), analogous results are obtained for all wavelengths when reaching the nonlinear absorption regime, for which the SEY maximum converges to 0.7. Furthermore, independent of the extent of the structural transformations, an electron-induced surface conditioning at 250 eV allows a reduction of the SEY maximum below unity at doses of 5×10-4 C/mm2. Consequently, optimization of processing parameters for application in particle accelerators can be obtained for a sufficiently low SEY at controlled ablation depth and surface particle density, which are factors that limit the surface impedance and the applicability of the material processing for ultrahigh vacuum systems. The relations between processing parameters and surface features will provide guidance in treating the surface of vacuum components, especially beam screens of selected magnets of the Large Hadron Collider or of future colliders.

Permeability sets the linear path instability of buoyancy-driven disks

The prediction of trajectories of buoyancy-driven objects immersed in a viscous fluid is a key problem in fluid dynamics. Simple-shaped objects, such as disks, present a great variety of trajectories, ranging from zig-zag to tumbling and chaotic motions. Yet, similar studies are lacking when the object is permeable. We perform a linear stability analysis of the steady vertical path of a thin permeable disk, whose flow through the microstructure is modelled via a stress-jump model based on homogenization theory. The relative velocity of the flow associated with the vertical steady path presents a recirculation region detached from the body, which shrinks and eventually disappears as the disk becomes more permeable. In analogy with the solid disk, one non-oscillatory and several oscillatory modes are identified and found to destabilize the fluid–solid coupled system away from its straight trajectory. Permeability progressively filters out the wake dynamics in the instability of the steady vertical path. Modes dominated by wake oscillations are first stabilized, followed by those characterized by weaker, or absent, wake oscillations, in which the wake is typically a tilting induced by the disk inclined trajectory. For sufficiently large permeabilities, the disk first undergoes a non-oscillatory divergence instability, which is expected to lead to a steady oblique path with a constant disk inclination, in the nonlinear regime. A further permeability increase reduces the unstable range of all modes until quenching of all linear instabilities.

On the startup behavior of wormlike micellar networks: The effect of different salts bound to the same surfactant molecule

We report on shear startup data for two wormlike micellar solutions, differing only in concentration and type of two binding aromatic sodium salts. The surfactant molecule is cetylpiridinium chloride at a fixed concentration (100 mM). Sodium salicylate (NaSal) and diclofenac sodium (Diclo) are used as binding salts at concentrations 68 mM NaSal and 52 mM Diclo such that both systems are fully entangled and their linear viscoelastic response is essentially identical. Both systems show the linear response typical of a wormlike micellar solution, with terminal behavior at low frequencies, a well-defined moduli crossover, and a plateau modulus. In the nonlinear regime, however, the behavior of the two systems is totally different, suggesting that the molecular structure difference of the salts and their binding activity to the surfactant molecule are both crucial to determine the fast flow behavior. The NaSal solution shows a very complex rheological response, with strain hardening and very sharp stress peaks, whereas the solution containing Diclo behaves much like ordinary linear polymers, exhibiting pronounced overshoots as well as moderate undershoots in the transient shear viscosity, before approaching the steady state. This polymerlike behavior has also been proved by successfully comparing data with predictions of a constitutive equation recently adopted for both entangled polymers and linear wormlike micelles. As far as NaSal is concerned, a phenomenological model based on rubber network theory is developed, which describes the flow singularities. A physical interpretation of the different behavior in the nonlinear regime is also suggested.

Linear and Nonlinear Optical Field Manipulations with Multifunctional Chiral Coding Metasurfaces

AbstractOptical chirality, which describes the property of asymmetric light–matter interactions for different handedness of polarization, plays an important role in physical photonics, biochemical processes, and molecular recognition. Recently, asymmetric optical responses of chiral nanostructures provide a wide platform for arbitrary and artificial manipulation of optical chirality. Here, a design strategy is theoretically and experimentally introduced to realize a spin‐selective coding metasurface in both linear and third harmonic regimes with giant chirality. Significant chiral transmission and wavefront control are realized by a chiral coding metasurface composed of amorphous silicon (a‐Si) resonators with C2 symmetry. The resonators and the enantiomers are encoded with different transmission amplitude and phase. The information channels are expanded to six‐fold with simultaneous multi‐foci focusing and multi‐vortex generation operating in different polarization and linear/nonlinear channels. The nonlinear chiral high‐contrast imaging is also achieved for spin‐selective pattern information transmission. The study significantly expands the information capacity of coding metasurfaces, and can be readily applied in optical systems for information transmission in both linear and nonlinear regimes.

Characterization of interfacial waves in stratified turbulent gas-liquid pipe flow using Particle Image Velocimetry and controlled disturbances

The work reports an experimental investigation on stratified gas-liquid pipe flow characteristics in the presence of controlled interfacial waves. Studies of this flow regime with controlled interfacial waves are scarce in the literature. Here, the disturbances are excited at the liquid interface by an oscillating paddle. The waves are synchronized with image acquisitions, enabling the utilization of phase-locked measurements and ensemble averaging techniques. Off-axis Particle Image Velocimetry (PIV) and Shadowgraph techniques were applied to provide information about mean and wave-induced modifications on the velocity fields. Results show that mean flow velocities in the liquid and gas phases close to the pipe walls adhere well to the single-phase flow log-law profile. In the liquid layer, this agreement was observed up to half of the water depth. Controlled disturbances enabled the estimation of the wave amplitude thresholds for the appearance of relevant nonlinear wave effects on the flow field. Results suggest that such a threshold can be fairly represented by a constant value of the non-dimensional parameter proposed in the work of Kirby (2008). Within the non-linear wave regimes investigated, noticeable changes in the flow field were observed close to the interface. However, near the wall the flow was weakly affected by the presence of waves, suggesting that interfacial wave effects are weakly coupled with near-wall disturbances and might be modelled independently. Moreover, contributions to interfacial shear stress due to the presence of waves were obtained experimentally. The results presented here are useful for validation and improvement of models used to predict flow characteristics in stratified flows. In addition, they contribute to shed further light on the physical mechanisms involved in the phenomenon.

Fast and accurate predictions of the non-linear matter power spectrum for general models of Dark Energy and Modified Gravity

ABSTRACT We embed linear and non-linear parametrizations of beyond standard cosmological physics in the halo model reaction framework, providing a model-independent prescription for the non-linear matter power spectrum. As an application, we focus on Horndeski theories, using the Effective Field Theory of Dark Energy (EFTofDE) to parametrize linear and quasi-non-linear perturbations. In the non-linear regime, we investigate both a non-linear parametrized post-Friedmann (nPPF) approach as well as a physically motivated and approximate phenomenological model based on the error function (Erf). We compare the parametrized approaches’ predictions of the non-linear matter power spectrum to the exact solutions, as well as state-of-the-art emulators, in an evolving dark energy scenario and two well-studied modified gravity models, finding sub-per cent agreement in the reaction using the Erf model at z ≤ 1 and k ≤ 5 h Mpc−1. This suggests only an additional three free constants, above the background and linear theory parameters, are sufficient to model non-linear, non-standard cosmology in the matter power spectrum at scales down to k ≤ 3h Mpc−1 within $2{{\ \rm per\ cent}}$ accuracy. We implement the parametrizations into ver.2.0 of the ReACT code: ACTio et ReACTio.

Nonlinear wave propagation analysis in architected materials with consideration of extension, shear and bending effects

The current paper deals with the wave dispersion characteristics of two-dimensional architected materials, considering both the linear and nonlinear regimes. We study the full non-linear coupling between the shear, extension, and bending deformation modes on the inner material deformation of the square, triangular, hexagonal, and re-entrant hexagonal unit cells. The dynamical analysis is done at high and low frequencies and for two different wave amplitudes. Based on the Linstedt–Poincare perturbation method, the non-linear correction to the dispersion diagram is evaluated. The relative contribution of each non-linear energy mode on the nonlinear wave dispersion attributes is quantified. The obtained results show that both the wavenumber and lattice design play an important role in the nonlinear wave corrections of the dispersion characteristics. The shear mode is shown to have the highest effect in the non-linear correction for all considered architected materials, compared to the flexural mode, which has the lowest energy contribution. The eigenwaves vectors are used to compare the deformation of hexagonal and re-entrant hexagonal unit cells at low and high frequencies over the entire Brillouin zone. Overall, the present work provides some guideline as to the proper selection of the inner design of architected materials prone to strong nonlinear dynamical effects.

Magnetic potential based formulation for linear and non-linear 3D RF sheath simulation

This paper reports a new numerical scheme to simulate the radio-frequency (RF) induced RF sheath, which is suitable for a large 3D simulation. In the RF sheath boundary model, the tangential component of the electric field () is given by the gradient of a scalar electric field potential. We introduce two additional scalar potentials for the tangential components of the magnetic field, which effectively impose the normal electric displacement (D n ) on the plasma sheath boundary condition via in-homogeneous Neumann boundary condition and constrain the tangential electric field on the surface as curl-free (). In our approach, the non-linear sheath impedance is formulated as a natural extension of the large thickness (or asymptotic) sheath limit (), allowing for handling both asymptotic and non-linear regimes seamlessly. The new scheme is implemented using the Petra-M finite element method analysis framework and is verified with simulations in the literature. The significance of non-linearity is discussed in various plasma conditions. An application of this scheme to asymptotic RF sheath simulation on the WEST ICRF antenna side limiters is also discussed.

Neoclassical toroidal plasma viscosity in bounce-transit and drift resonance regimes in tokamaks

Neoclassical toroidal plasma viscosity in the bounce-transit and drift resonance regimes is calculated using a version of the drift kinetic equation that encompasses the physics of the nonlinear trapping and quasilinear plateau regimes in tokamaks. It is demonstrated that the mirror-force like term controls the transition between these two regimes. When the effective collision frequency is larger than the mirroring or the nonlinear bounce frequency, the quasilinear regime prevails; otherwise, the nonlinear trapping regime reigns. The demonstration is accomplished by using the Eulerian approach and is beyond the grasp of the method of the integration along the unperturbed orbit in solving the drift kinetic equation. The neoclassical toroidal plasma viscosity in the quasilinear plateau regime is calculated. Approximate analytic expressions for the neoclassical toroidal plasma viscosity that include the asymptotic limits of the nonlinear trapping and quasilinear regimes are presented to facilitate thermal and energetic alpha particle transport modeling in tokamaks.