Nonlinear Regime Research Articles

Giant tunnel magnetoresistance induced by thermal bias

We analyze the spin-resolved transport and, in particular, the tunnel magnetoresistance of an asymmetric ferromagnetic tunnel junction with an embedded quantum dot or molecule subject to thermal and voltage bias in the nonlinear response regime. We demonstrate that such system exhibits a giant tunnel magnetoresistance effect that can be tuned by gate and bias voltages. Large values of magnetoresistance are associated with the interplay between the Kondo correlations and the ferromagnetic-contact-induced exchange field. In particular, we show that the nonequilibrium current in the parallel and antiparallel magnetic configuration of the system changes sign at different values of the voltage and thermal bias. This gives rise to giant values of magnetoresistance, the sign of which can be controlled by the applied sources.

Data-informed statistical finite element analysis of rail buckling

In this paper, the statistical finite element method is developed further to synthesize distributed rail response data with nonlinear finite element model predictions within and outside the measured loading range. In the data-generating model of the statistical finite element method, the distributed sensing data is decomposed into a finite element model component, a model-reality mismatch component, and a noise component. Each component is considered uncertain and is represented as a Gaussian random vector with a corresponding prior density. The finite element prior density is updated using the Bayesian statistical framework in light of the distributed fiber optic sensing data. The calculated posterior density enables one to infer the true structural response. The required finite element prior density is determined by solving a conventional stochastic forward problem using a polynomial chaos expansion of random fields and a non-intrusive pseudo-spectral projection approach. In this paper, a lab test involving a section of a rail (i.e., a beam-column structural member) instrumented with distributed fiber optic sensors and subjected to axial load causing progressive lateral buckling is considered to demonstrate the use of the statistical finite element method to improve rail response prediction. The results show improved prediction of true rail strain in linear and nonlinear regimes compared with a pure finite element model-based prediction.

Distinguishing the nonlinear propagation regimes of vortex femtosecond pulses in fused silica by evaluating the broadened spectrum.

The nonlinear propagation dynamics of vortex femtosecond laser pulses in optical media is a topic with significant importance in various fields, such as nonlinear optics, micromachining, light bullet generation, vortex air lasing, air waveguide and supercontinuum generation. However, how to distinguish the various regimes of nonlinear propagation of vortex femtosecond pulses remains challenging. This study presents a simple method for distinguishing the regimes of nonlinear propagation of femtosecond pulses in fused silica by evaluating the broadening of the laser spectrum as the input pulse power gradually increases. The linear, self-focusing and mature filamentation regimes for Gaussian and vortex femtosecond pulses in fused silica are distinguished. The critical powers for self-focusing and mature filamentation of both types of laser pulses are obtained. Our work provides a rapid and convenient method for distinguishing different regimes of nonlinear propagation and determining the critical powers for self-focusing and mature filamentation of Gaussian and structured laser pulses in optical media.

Simulations of spin/polarization-resolved laser–plasma interactions in the nonlinear QED regime

Strong-field quantum electrodynamics (SF-QED) plays a crucial role in ultraintense laser–matter interactions and demands sophisticated techniques to understand the related physics with new degrees of freedom, including spin angular momentum. To investigate the impact of SF-QED processes, we have introduced spin/polarization-resolved nonlinear Compton scattering, nonlinear Breit–Wheeler, and vacuum birefringence processes into our particle-in-cell (PIC) code. In this article, we provide details of the implementation of these SF-QED modules and share known results that demonstrate exact agreement with existing single-particle codes. By coupling normal PIC simulations with spin/polarization-resolved SF-QED processes, we create a new theoretical platform to study strong-field physics in currently running or planned petawatt or multi-petawatt laser facilities.

Effect of cone rotation on the nonlinear evolution of Mack modes in supersonic boundary layers

In this paper, we present a systematic study of the nonlinear evolution of the travelling Mack modes in a Mach 3 supersonic boundary layer over a rotating cone with a $7^{\circ }$ half-apex angle using the nonlinear parabolic stability equation (NPSE). To quantify the effect of cone rotation, six cases with different rotation rates are considered, and from the same streamwise position, a pair of oblique Mack modes with the same frequency but opposite circumferential wavenumbers are introduced as the initial perturbations for NPSE calculations. As the angular rotation rate $\varOmega$ increases such that $\bar \varOmega$ (defined as the ratio of the rotation speed of the cone to the streamwise velocity at the boundary-layer edge) varies from 0 to $O(1)$ , three distinguished nonlinear regimes appear, namely the oblique-mode breakdown, the generalised fundamental resonance and the centrifugal-instability-induced transition. For each regime, the mechanisms for the amplifications of the streak mode and the harmonic travelling waves are explained in detail, and the dominant role of the streak mode in triggering the breakdown of the laminar flow is particularly highlighted. Additionally, from the linear stability theory, the dominant travelling mode undergoes the greatest amplification for a moderate $\varOmega$ , which, according to the $e^N$ transition-prediction method, indicates premature transition to turbulence. However, this is in contrast to the NPSE results, in which a delay of the transition onset is observed for a moderate $\varOmega$ . Such a disagreement is attributed to the different nonlinear regimes appearing for different rotation rates. Therefore, the traditional transition-prediction method based on the linear instability should be carefully employed if multiple nonlinear regimes may appear.

Identification of Damage in Planar Multistory Reinforced Concrete Frames Developing a Beam-Sway Plastic Mechanism Using the “M and P” Technique

The effectiveness of a recently proposed methodology for the identification of damage in planar, multistory, reinforced concrete (RC) moment frames, which develop a plastic yield mechanism on their beams, is showcased here via the examining of a group of such existing multistory frames with three or more unequal spans. According to the methodology, the diagram of the instantaneous eigenfrequencies of the frame in the nonlinear regime is drawn as a function of the inelastic seismic roof displacement by the performance of a sequence of pushover and instantaneous modal analyses with gradually increasing target displacement. Using this key diagram, the locations of severe seismic damage in an existing moment frame can be evaluated if the instantaneous fundamental eigenfrequency of the damaged frame, at an analysis step within the nonlinear area, is known in advance by “the monitoring and the identification of frequencies” using a local network of uniaxial accelerometers. This is a hybrid technique because both procedures, the instrumental monitoring of the structure and the pushover analysis on the frame (M and P technique), are combined. A ductile, five-story, planar RC moment frame with three unequal spans is evaluated in this paper by the M and P technique. The results show that the seismic roof displacement, the lateral stiffness matrix, and, finally, the damage image of this existing frame, are fully compatible with the eigenfrequencies identified by the monitoring and are calculated with high accuracy.

Experimental and analytical approaches toward controlling viscous fingering at the interface of two immiscible fluids using the optimal constant piecewise injection rate

Viscous fingering (VF) at the interface of two immiscible fluids can have disruptive effects in many technological applications. Therefore finding methods for reducing it with an effective and simple approach plays a significant role. A proposed solution that restrains the expansion of such complex morphologies, is the time-dependent injection rate. This proposed solution is often done either analytically or by numerical simulations which need to be experimentally proven. In this study, we perform multiple experiments of low viscosity fluid injection into high viscosity fluid in order to study the formation of VF and find injection rates or protocols that reduce VF at the onset of the nonlinear regime and in the fully nonlinear regime by applying several constant piecewise injection rates. Moreover, analytically and numerically studies are done, in which we derive the optimal parameters in piecewise injection profiles to limit the VF and the tip-splitting effect. This optimal constant piecewise injection rate includes specified number of stages as well as the injection time and its rate in each stage. The obtained results revealed that depending on being at the beginning of the nonlinear regime or in the fully nonlinear regime, the optimal constant piecewise injection rate can considerably reduce the length of fingers and the interfacial fingering perturbations. Empirical results show similar trend in terms of instability reduction by applying the same optimal number of piecewise injection rate stages. In addition, evaluating the difference between this piecewise results and the results of linear injection rates, which we have done before, reveals that employing linear injection rates is more effective in controlling the instability in lower injection rates, while for higher injection rates, it is required to utilize a piecewise injection rate.

Wave dynamics of a viscoelastic liquid

A falling film of a weakly viscoelastic liquid (Walters’ liquid B′′) is studied in detail for low to moderate values of the Reynolds number. A linear stability analysis within the framework of the Orr–Sommerfeld-type boundary value problem reveals a destabilizing effect of the viscoelastic parameter near the threshold of instability but a stabilizing effect of the viscoelastic parameter on the primary instability far away from the threshold of instability. The surface equation is derived to decipher the existence of nonlinear waves based on the centre manifold approach. However, it renders an unbounded solution in the short-wave regime. In order to avoid singular behaviour found in the surface equation, a regularized equation, a simplified second-order model, and a full second-order model are proposed. In the linear regime, both the regularized equation and the model equations show excellent agreement with the results of the Orr–Sommerfeld-type boundary value problem, i.e., the viscoelastic parameter demonstrates a dual role in the primary instability. In the nonlinear regime, the results of the regularized equation are verified with those of the simplified second-order model. Both the regularized equation and the simplified second-order model show qualitatively similar characteristics of the nonlinear waves. The speed and maximum amplitude corresponding to the steady-state travelling waves attain fixed values in the drag-inertia regime. Moreover, the speed and maximum amplitude acquired from the regularized equation underestimate the results of the simplified second-order model when the Reynolds number lies in the drag-inertia regime. The time-dependent simulation of the regularized equation displays a train of solitary waves downstream to a monochromatic time periodic forcing at the inlet. The separation distance between the first two solitary pulses is computed, and it seems to approach an asymptotic value when the time is very large. This fact assures the possibility of a bound-state formation among the solitary pulses downstream for the weakly viscoelastic liquid.

Observation of spatial self-phase modulation excited by off-axis integer and fractional vortex beams

Spatial self-phase modulation (SSPM) is widely used to characterize the nonlinear refractive index of two-dimensional layered materials and design passive nonlinear photonic devices. In this work, we investigate the SSPM phenomena of black phosphorus dispersed in agarose solid under the excitation of on-axis and off-axis integer and half-integer vortex beams. It is found that with the increase of the off-axis distance of the Gaussian vortex beam, the pattern of the far-field self-diffraction intensity gradually breaks from the initial ring and finally evolves into a tail outside the self-diffraction ring. Moreover, for half-integer vortex beams, the size of the innermost tail of the self-diffraction ring is nearly half smaller than that of the second outer tail. The underlying mechanism of the observed SSPM phenomenon is also analyzed. Interestingly, the trailing number and rotation direction of the self-diffraction ring pattern quantitatively reflect the magnitude and sign of the topological charge (TC) of the off-axis vortex beam, respectively. This work provides a novel method to measure the TC of off-axis vortex beam in the nonlinear optics regime.

Numerical investigation of optical bistability in a nonlinear plasmonic structure containing a phase change material

In this paper, a controllable nonlinear plasmonic structure is proposed based on a phase change material (PCM) layer to achieve tunable bistability characteristics. To this end, the Ge2Sb2Te5 (GST) layer (as a PCM) is sandwiched between a thin film of Ag and a Kerr material substrate. Then, this multilayered structure is used as a substrate for the ZnSiAs2 grating whose grooves are filled with the Kerr nonlinear material. Next, the grating is covered with a layer of CaF2. In this structure, we first calculate the reflection spectrum for different crystallization fractions using the finite element method (FEM) in the linear regime. The reflectance spectrum shows a dip in the near-infrared region, which is redshifted with increasing the crystallization fraction of the GST layer. This effect results from the movement of surface plasmon resonance to longer wavelengths with increasing the crystallization fraction. Then, we find that the dip in the reflectance spectrum is redshifted with enhancing the input intensity of the incident wave for different crystallization fractions in the nonlinear regime. This behavior confirms the existence of optical bistability through the proposed structure. So, we calculate the bistability curves at a fixed operating wavelength of 1550 nm for different crystallization fractions. Our results demonstrate that as the phase transition from the amorphous to the crystalline state occurs at a fixed operating wavelength, the bistability thresholds reduce while the hysteresis width also decreases and the bistability effect eventually disappears. Therefore, for each crystallization fraction of the GST layer we find a special wavelength at which a reasonable bistability curve with a reasonable hysteresis width is obtained. This operating wavelength is shifted by 33 nm as the crystallization fraction varies from 0.2 to 0.8. Finally, the effects of increasing the thickness of the GST layer on the bistability characteristics are examined. Our results show that stronger tunability of the operating wavelength by 50 nm with variation of crystallization degree from 0.2 to 0.8 is achieved when a thicker GST layer is used instead of a thinner one.

Spatial multiplexing for robust optical vortex transmission with optical nonlinearity

Optical vortex beams, with phase singularity characterized by a topological charge (TC), introduces a new dimension for optical communication, quantum information, and optical light manipulation. However, the evaluation of TCs after beam propagation remains a substantial challenge, impeding practical applications. Here, we introduce vortices in lateral arrays (VOILA), a novel spatial multiplexing approach that enables simultaneous transmission of a lateral array of multiple vortices. Leveraging advanced learning techniques, VOILA effectively decodes TCs, even in the presence of strong optical nonlinearities simulated experimentally. Notably, our approach achieves substantial improvements in single-shot bandwidth, surpassing single-vortex scheme by several orders of magnitude. Furthermore, our system exhibits precise fractional TC recognition in both linear and nonlinear regimes, providing possibilities for high-bandwidth communication. The capabilities of VOILA promise transformative contributions to optical information processing and structured light research, with significant potential for advancements in diverse fields.

Obstruction to ergodicity in nonlinear Schrödinger equationswith resonant potentials.

We identify a class of trapping potentials in cubic nonlinear Schrödinger equations(NLSEs) that make them nonintegrable, but prevent the emergence of power spectra associated with ergodicity. The potentials are characterized by equidistant energy spectra (e.g., the harmonic-oscillator trap), which give rise to a large number of resonances enhancing the nonlinearity. In a broad range of dynamical solutions, spanning the regimes in which the nonlinearity may be either weak or strong in comparison with the linear part of the NLSE, the power spectra are shaped as narrow (quasidiscrete), evenly spaced spikes, unlike generic truly continuous (ergodic) spectra. We develop an analytical explanation for the emergence of these spectral features in the case of weak nonlinearity. In the strongly nonlinear regime, the presence of such structures is tracked numerically by performing simulations with random initial conditions. Some potentials that prevent ergodicity in this manner are of direct relevance to Bose-Einstein condensates: they naturally appear in 1D, 2D, and 3D Gross-Pitaevskii equations(GPEs), the quintic version of these equations, and a two-component GPE system.

Symmetry and Nonlinearity of Spin Wave Resonance Excited by Focused Surface Acoustic Waves

AbstractThe use of a complex ferromagnetic system to manipulate GHz surface acoustic waves (SAWs) is a rich current topic under investigation, but the high‐power nonlinear regime is under‐explored. Focused SAWs are introduced, which provide a way to access this regime with modest equipment. The symmetry of the magneto‐acoustic interaction can be tuned by interdigitated transducer design which can introduce additional strain components. Here, the impact of focused acoustic waves versus standard unidirectional acoustic waves in significantly enhancing the magnon‐phonon coupling behavior is compared. Analytical simulation results based on the modified Landau–Lifshitz–Gilbert theory show good agreement with experimental findings. Nonlinear input power dependence of the transmission through the device is also reported. This experimental observation is supported by the micromagnetic simulation using mumax3 to model the nonlinear dependence. These results pave the way for extending the understanding and design of acoustic wave devices for the exploration of acoustically driven spin wave resonance physics.

Diffusive-thermal instabilities of a planar premixed flame aligned with a shear flow

The stability of a thick planar premixed flame, propagating steadily in a direction transverse to that of unidirectional shear flow, is studied. A linear stability analysis is carried out in the asymptotic limit of infinitely large activation energy, yielding a dispersion relation. The relation characterises the coupling between Taylor dispersion (or shear-enhanced diffusion) and the flame thermo-diffusive instabilities, in terms of two main parameters, namely, the reactant Lewis number L e and the flow Peclet number P e . The implications of the dispersion relation are discussed and various flame instabilities are identified and classified in the L e - P e plane. An important original finding is the demonstration that for values of the Peclet number exceeding a critical value, the classical cellular instability, commonly found for L e < 1 , exists now for L e > 1 but is absent when L e < 1 . In fact, the cellular instability identified for L e > 1 is shown to occur either through a finite-wavelength stationary bifurcation (also known as type-I s ) or through a longwave stationary bifurcation (also known as type-II s ). The latter type-II s bifurcation leads in the weakly nonlinear regime to a Kuramoto-Sivashinsky equation, which is determined. As for the oscillatory instability, usually encountered in the absence of Taylor dispersion in L e > 1 mixtures, it is found to be absent if the Peclet number is large enough. The stability findings, which follow from the dispersion relation derived analytically, are complemented and examined numerically for a finite value of the Zeldovich number. The numerical study involves both computations of the eigenvalues of a linear stability boundary-value problem and numerical simulations of the time-dependent governing partial differential equations. The computations are found to be in good qualitative agreement with the analytical predictions.

Investigating the Effect of Gravity Modulation on Weakly Nonlinear Magnetoconvection in a Nonuniformly Rotating Nanofluid Layer

This paper investigates the impact of gravity modulation on weakly nonlinear magnetoconvection in a nanofluid layer that is nonuniformly rotating. The fundamental equations are obtained for the Cartesian approximation of the Couette flow using the Boussinesq approximation and gravitational modulation. The weakly nonlinear regime is analyzed using the method of perturbations with respect to the small supercritical parameter of the Rayleigh number, considering the effects of Brownian motion and thermophoresis in the nanofluid layer. Heat and mass transfer are evaluated in terms of finite amplitudes and calculated from the Nusselt numbers for the fluid and the volume concentration of nanoparticles. The findings demonstrate that gravitational modulation, nonuniform rotation, and differences in the volume concentration of nanoparticles at the layer boundaries can effectively control heat and mass transfer. Additionally, the negative rotation profile has a destabilizing effect. The study shows that the modulated system conveys more heat and mass than the unmodulated system.

Evaluation of Crosstalk in Nonlinear Regime for Weakly Coupled Multi-Core Fiber With Random Perturbations Using a Split-Step Numerical Model

Evaluation of Crosstalk in Nonlinear Regime for Weakly Coupled Multi-Core Fiber With Random Perturbations Using a Split-Step Numerical Model

Strong-field vacuum polarisation with high energy lasers

When photons propagate in vacuum they may fluctuate into matter pairs thus allowing the vacuum to be polarised. This linear effect leads to charge screening and renormalisation. When exposed to an intense background field a nonlinear effect can arise when the vacuum is polarised by higher powers of the background. This nonlinearity breaks the superposition principle of classical electrodynamics, allowing for light-by-light scattering of probe and background photons mediated through virtual pairs dressed by the background. Vacuum polarisation is a strong-field effect when all orders of interaction between the virtual pair and the background must be taken into account. In this investigation we show that multiple scattering processes of this type may be observed by utilising high-energy laser pulses with long pulse duration, such as are available at facilities like ELI Beamlines. In combination with appropriate sources of high-energy probe photons, multiple probe-background light-by-light scattering allows for testing the genuine nonlinear regime of strong-field quantum electrodynamics. This provides access to the uncharted non-perturbative regime beyond the weak-field limit.

A standard thermodynamic-based extension of the Modified Cam-Clay soil model and its applications

For mechanical behaviours of granular soils considered here (sands, silts and stiff clays), we propose a thermodynamic-based formulation which relies on the Modified Cam-Clay constitutive model. To this end, and in the framework of Generalized Standard Materials (GSM) framework, we introduce a free energy and a yield criterion (or equivalently a dissipation potential) which account for an isotropic nonlinear elastic behaviour and a volumetric hardening law. Based on available works with coupled hardening laws for von Mises plasticity, we propose for pressure-sensitive materials a new nonlinear deviatoric hardening preserving the well-known critical state existence.Taking advantage of the GSM framework, we establish an incremental variational formulation of the model whose solution obeys to a minimization principle. This has required an approximation of the incremental dissipation. The resulting equations are detailed for the use of an implicit resolution scheme with a standard Newton–Raphson algorithm. The constitutive model parameters are calibrated on a pool of experimental data on isotropic, shearing and triaxial tests on loose sand specimen. The investigations of the model responses allow to better predict the nonlinear regimes of soils specimen on monotonic and cyclic loading paths. Numerical finite element simulations finally underline the predictive capabilities of the model on structures.

Quasiperiodicity in the α-Fermi-Pasta-Ulam-Tsingou problem revisited: An approach using ideas from wave turbulence.

The Fermi-Pasta-Ulam-Tsingou (FPUT) problem addresses fundamental questions in statistical physics, and attempts to understand the origin of recurrences in the system have led to many great advances in nonlinear dynamics and mathematical physics. In this work, we revisit the problem and study quasiperiodic recurrences in the weakly nonlinear α-FPUT system in more detail. We aim to reconstruct the quasiperiodic behavior observed in the original paper from the canonical transformation used to remove the three-wave interactions, which is necessary before applying the wave turbulence formalism. We expect the construction to match the observed quasiperiodicity if we are in the weakly nonlinear regime. Surprisingly, in our work, we find that this is not always the case and in particular, the recurrences observed in the original paper cannot be constructed by our method. We attribute this disagreement to the presence of small denominators in the canonical transformation used to remove the three-wave interactions before arriving at the starting point of wave turbulence. We also show that these small denominators are present even in the weakly nonlinear regime, and they become more significant as the system size is increased. We also discuss our results in the context of the problem of equilibration in the α-FPUT system and point out some mathematical challenges when the wave turbulence formalism is applied to explain thermalization in the α-FPUT problem. We argue that certain aspects of the α-FPUT system such as thermalization in the thermodynamic limit and the cause of quasiperiodicity are not clear, and that they require further mathematical and numerical studies.

A non-linear solution to the S8 tension – II. Analysis of DES Year 3 cosmic shear

ABSTRACT Weak galaxy lensing surveys have consistently reported low values of the S8 parameter compared to the Planck lambda cold dark matter (ΛCDM) cosmology. Amon &amp; Efstathiou used KiDS-1000 cosmic shear measurements to propose that this tension can be reconciled if the matter fluctuation spectrum is suppressed more strongly on non-linear scales than assumed in state-of-the-art hydrodynamical simulations. In this paper, we investigate cosmic shear data from the Dark Energy Survey (DES) Year 3. The non-linear suppression of the matter power spectrum required to resolve the S8 tension between DES and the Planck ΛCDM model is not as strong as inferred using KiDS data, but is still more extreme than predictions from recent numerical simulations. An alternative possibility is that non-standard dark matter contributes to the required suppression. We investigate the redshift and scale dependence of the suppression of the matter power spectrum. If our proposed explanation of the S8 tension is correct, the required suppression must extend into the mildly non-linear regime to wavenumbers $k\sim 0.2 \, h\, {\rm Mpc}^{-1}$. In addition, all measures of S8 using linear scales should agree with the Planck ΛCDM cosmology, an expectation that will be testable to high precision in the near future.