Nonlinear Response Research Articles

Subcycle dynamics of excitons under strong laser fields.

Excitons play a key role in the linear optical response of two-dimensional (2D) materials. However, their role in the nonlinear response to intense, nonresonant, low-frequency light is often overlooked as strong fields are expected to tear the electron-hole pair apart. Using high-harmonic generation as a spectroscopic tool, we theoretically study their formation and role in the nonlinear optical response. We show that the excitonic contribution is prominent and that excitons remain stable even when the driving laser field surpasses the strength of the Coulomb field binding the electron-hole pair. We demonstrate a parallel between the behavior of strongly laser-driven excitons in 2D solids and strongly driven Rydberg states in atoms, including the mechanisms of their formation and stability. Last, we show how the excitonic contribution can be singled out by encapsulating the 2D material in a dielectric, tuning the excitonic energy and its contribution to the high-harmonic spectrum.

Dielectric and Shear-Mechanical "Humps" in the Nonlinear Response of Polar Glassformers.

Many glassformers display electrorheological effects and a pronounced maximum in their frequency dependent nonlinear dielectric response. The latter so-called "hump" feature was often linked to correlated-particle motions and, so far, was not explored in the large-perturbation mechanical response of viscous liquids. To first clarify the electro-viscoelastic coupling in the linear domain, using the modified Gemant, DiMarzio, and Bishop model, it is demonstrated how the small-amplitude shear mechanical response of S-methoxy-PC, a derivative of propylene carbonate, can be related to its complex dielectric permittivity. Then, in the nonlinear regime, a "hump" feature is identified in the rheological third-order shear modulus of S-methoxy-PC and of another polar glassformer, propylene glycol. Thus, the observation of a "hump" in the cubic response of viscous liquids does not necessarily rely on the application of electrical fields.

Exploring the Third-Order Non-linear Optical Responses and Optical Limiting Properties of p-Nitroaniline Picrate: A Theoretical and Experimental Study

Exploring the Third-Order Non-linear Optical Responses and Optical Limiting Properties of p-Nitroaniline Picrate: A Theoretical and Experimental Study

Tunable nonlinear excitonic optical response in biased bilayer graphene

Tunable nonlinear excitonic optical response in biased bilayer graphene

Non-linear Contact Analysis and Response Surface Optimization of Railway Wheel Using ANSYS

Non-linear Contact Analysis and Response Surface Optimization of Railway Wheel Using ANSYS

Ferroelectric nematic fluids as spontaneous polarization field for enhanced orientational-dependent second-harmonic generation

ABSTRACT Second-order nonlinear optical effects have piqued researchers’ interest in fundamental physics and practical perspectives. The ferroelectric nematic liquid crystals (NF LCs) have recently drawn attention to LC nonlinear optical applications due to their relatively high second-harmonic generation output. Further improving the nonlinear optical properties to get closer to the performance of inorganic nonlinear optical materials is challenging. Here, we take a blending strategy to enhance the nonlinear optical response of a prototype NF LC, DIO. We mixed an organic nonlinear optical crystalline material, 3,5,5-trimethyl (cyclohex-2-enylidene) malononitrile (TCM), with DIO and investigated the effects of TCM doping at various concentrations. We quantitatively determined the second-harmonic generation and spontaneous polarization as functions of temperature and concentration. We found that, compared with the pure DIO, the second-harmonic generation performance increased by about 130% at maximum, 93% in maximum for the nonlinear optical coefficient, and 10% in maximum for spontaneous polarization.

Numerical study of the linear and non-linear damping in an acoustically forced cold-flow test rig with coupled cavities

Quantifying the oscillation amplitude of thermoacoustic instabilities remains a critical and challenging issue, as it is a complex balance between driving and damping processes. The New Pressurized Coupled Cavities (NPCCs) setup designed for the study of acoustic damping is analyzed in this work. It is a cold-flow test rig mimicking the geometry of a liquid rocket engine and equipped with an acoustic forcing device. The chamber 1T mode triggers a strong non-linear harmonic response, while the 1T1L and 1T2L exhibit weak non-linearities. Disturbance energy budgets are used in large-eddy simulations to characterize the damping phenomena with the 1T2L and 1T1L forcing. The correct global damping of the system is retrieved, and local damping contributions are extracted. Then, a non-linear term representing the energy transfer to the harmonics is derived from non-linear acoustics theory. Combined with a linear model, this model correctly retrieves the limit-cycle of the 1T mode.

Atmospheric NH3 in urban Beijing: long-term variations and implications for secondary inorganic aerosol control

Abstract. Ammonia (NH3) has major effects on the environment and climate. In situ measurements of NH3 concentrations taken between June 2009 and July 2020 at an urban site in Beijing were analyzed to study its long-term behavior, responses to meteorological conditions, and influences on the formation of secondary inorganic aerosols (SIAs). The 11-year average NH3 mixing ratio was 26.9±19.3 ppb (median 23.5 ppb). The annual average NH3 mixing ratio increased from 2009 to 2017 by 50 % and then decreased by 49 % from 2017 to 2020. Notably, the long-term trend for NH3 at the ground level did not align with the trends derived from satellite observations and emission estimates. The NH3 concentration exhibited a stronger correlation with the daily variation in water vapor (H2O) concentration than with air temperature. Thermodynamic modeling revealed the nonlinear response of SIAs to NH3, with increased sensitivity when its concentration was reduced to 40 % of the initial level. Although reducing NH3 concentrations can improve air quality during winter, controlling acid gas concentrations has a greater effect than controlling NH3 concentrations on reducing SIA concentrations, until NH3 and acidic gas concentrations are reduced below 80 % of their current levels. Nevertheless, the increased mass proportion of ammonium salts in SIAs during the observation period indicates that future control measures for NH3 concentrations may need to be prioritized in Beijing.

Relationships between water quality of a long-distance inter-basin water diversion project and air pollution emissions along the canal: Distributions, lag effects, and nonlinear responses

Understanding and quantifying the influences and contributions of air pollution emissions on water quality variations is critically important for surface water quality protection and management. To address this, we created a five-year daily data matrix of six water quality indicators—permanganate index (CODMn), NH3-N, pH, turbidity, conductivity, and dissolved organic matter (DOM)—and six air pollution indicators—O3, CO, NO2, SO2, 2.5 μm particulate matter (PM2.5), and inhalable particles (PM10)—using data from seven national monitoring stations along the world's longest water-diversion project, the Middle Route of the South-to-North Water Diversion Project in China (MR-SNWD). Multivariate techniques (Mann–Kendall, Spearman's correlation, lag correlation, and Generalized Additive Models [GAMs]) were applied to examine the nonlinear relationships and lag effects of air pollution on water quality. Air pollution and water quality exhibited marked spatial heterogeneity along the MR-SNWD, with all water quality parameters meeting Class I or II national standards and the air pollution indicators exceeding those thresholds. Except for CODMn and DOM, the other water quality and air pollution indicators exhibited significant seasonal differences. Air pollution exhibited significant lag effects on water quality at the northern stations, with NO2, SO2, PM2.5, and PM10 being highly correlated with changes in pH, with an average lag of 17 d. Based on the GAMs, lag effects enhanced the significant nonlinear relationships between air pollution and water quality, increasing the average deviance explained for CODMn, NH3-N, and pH by 93%, 24%, and 41%, respectively. These findings provide a scientific basis for protecting water quality along the long-distance inter-basin water-diversion project under anthropogenic air pollution.

Time-Resolved Circular Dichroism in Molecules: Experimental and Theoretical Advances.

Following changes in chirality can give access to relevant information on the function or reactivity of molecular systems. Time-resolved circular dichroism (TRCD) spectroscopy proves to be a valid tool to achieve this goal. Depending on the class of molecules, different temporal ranges, spanning from seconds to femtoseconds, need to be investigated to observe such chiroptical changes. Therefore, over the years, several approaches have been adopted to cover the timescale of interest, especially based on pump-probe schemes. Moreover, various theoretical approaches have been proposed to simulate and explain TRCD spectra, including linear and non-linear response methods as well as non-adiabatic molecular dynamics. In this review, an overview on both experimental and theoretical advances in the TRCD field is provided, together with selected applications. A discussion on future theoretical developments for TRCD is also given.

Modulational instability and collapse of internal gravity waves in the atmosphere.

Nonlinear two-dimensional (IGWs) in the atmospheres of the Earth and the Sun are studied. The resulting two-dimensional nonlinear equationhas the form of a generalized nonlinear Schrödinger equationwith nonlocal nonlinearity, that is, when the nonlinear response depends on the wave intensity at some spatial domain. The modulation instability of IGWs is predicted, and specific cases for the Earth's atmosphere are considered. In a number of particular cases, the instability thresholds and instability growth rates are analytically found. Despite the nonlocal nonlinearity, we demonstrate the possibility of critical collapse of IGWs due to the scale homogeneity of the nonlinear term in spatial variables.

Study on the seismic wave input method for earth-rock dam on overburden foundation with dynamic nonlinearity based on nonlinear artificial boundary

Accurately obtaining the seismic response of earth-rock dams on overburden foundations is crucial for seismic safety assessment and design, and a reasonable seismic input method is necessary. The seismic wave input method based on artificial boundaries is widely used in elastic foundations. However, the overburden with obvious dynamic nonlinearity is an insurmountable obstacle for the traditional method. In this research, relying on a specific earth-rock dam project, the essence of the seismic wave input method for nonlinear foundations is analyzed in detail from equivalent loads and viscous boundaries, respectively. The mechanism of inapplicability of the traditional seismic wave input method is illustrated, and an effective modified method is validated and presented. The research indicated that equivalent loads for the nonlinear dynamic response of the overburden foundation can be accurately acquired with the shear box model. The dynamic parameters of soil can be captured dynamically by the nonlinear viscous coupling boundary. The states of the lateral boundary of the overburden foundation are consistent with the free field precisely with the modified seismic wave input method by combining the shear box model and the nonlinear viscous coupling boundary. A large error will be caused by neglecting the dynamic nonlinear behavior of the overburden foundation, where the maximum deviation of peak acceleration may be over 55 % or more. A numerical model with a relatively small lateral range of overburden foundation will be obtained when the modified seismic wave input method is engaged. Moreover, the computational accuracy is enhanced remarkably, with a maximum deviation of no more than 5 %. This study provides effective theoretical support for seismic analysis and safety assessment of earth-rock dams on deep overburden foundations.

Engineering novel alkalides with superalkali clusters: Ab initio insights into nonlinear optical responses

ABSTRACT We designed novel alkalides such as FLi2-M-OLi3 and FLi2-M-NLi4 (M = Li, Na, K), along with OLi3-M-NLi4 (M = Li, Na) by interacting alkali metal atoms with heterogeneous superalkali clusters in anionic, neutral and cationic configurations. The stability of these superalkali based alkalides are confirmed by its binding energy (Eb ). Utilising QTAIM method, the bond strength and nature of bond have been analysed. NPA charge analysis is conducted to forecast charge transfer and also to confirm the alkalide character of the complex along with the electron localisation function (ELF) analysis. The HOMO–LUMO gap analysis is performed to analyse electrical conductivity and chemical reactivity. The nonlinear optical (NLO) properties have been investigated by polarisability and first-order static hyperpolarizibilty (β0 ), which is found to be as high as 2.77 × 107 a. u. for (OLi3-Li-NLi4)+ complex. The UV-Vis spectra and electronic transitions are used to explain the enhanced NLO responses. The study not only identifies new alkalide candidates but also presents strategies to significantly improve their NLO properties, which may be useful in nonlinear optics and optoelectronics.

Vibration suppression of a platform by a fractional type electromagnetic damper and inerter-based nonlinear energy sink

The theory of linear and nonlinear dynamic vibration absorbers is a well-established topic for many years. However, many recent contributions paid attention to the nonlinear vibration absorbers and different practical realizations of corresponding devices. Here, we propose a mechanical system constituted of the inerter-based nonlinear energy sink attached to the main body that is resting on an elastic foundation and is grounded through the fractional type electromagnetic damper. The two-degree-of-freedom system is described via two coupled differential equations with one of them having a fractional-order derivative term and the other one containing cubic stiffness nonlinearity. The incremental harmonic balance (IHB) method is employed to solve the equations and studies the strongly nonlinear periodic responses of the system. Applied approximated solution methodology is validated by the numerical Newmark method adapted to deal with the system of nonlinear fractional-order differential equations. The appropriate and necessary number of harmonics used in the IHB solution is commented and validated. This study can be a first step in understanding the dynamics and giving directions for the future design of vibration-isolating platforms based on inerter-based nonlinear vibration absorbers and electromagnetic dampers.

Joint Bayesian estimation of process and measurement noise statistics in nonlinear Kalman filtering

Bayesian filtering aims at sequentially estimating the states and parameters in nonlinear dynamical systems, and finds applications in a variety of engineering fields. Extended and unscented Kalman filter are popular choices for this purpose as they typically achieve a good trade-off between computational complexity and accuracy, while still quantifying posterior uncertainty. However, the accuracy of the identified states and parameters, both in terms of their posterior mean and variance, is heavily influenced by the assumed statistics of both the process and measurement noise terms. Therefore, learning the noise characteristics becomes an essential aspect of Bayesian filtering, but is non-trivial especially in cases where process and measurement noise statistics are jointly non-identifiable. This article proposes a methodology that decomposes measurement and process noise learning in a fully Bayesian setting. For measurement noise estimation, we improve upon a Bayesian method that leverages conjugacy of the inverse-Wishart distribution with respect to the Gaussian likelihood model. For process noise estimation, Bayesian model averaging is coupled with a mutation scheme to compare the performance of competing models while exploring high-probability regions in the space of the unknown process noise variance. The algorithm is first tested on simple numerical models for both state estimation and parameter learning, highlighting the superior accuracy of the proposed measurement noise correction and the benefits of decoupling process and measurement noise learning in non-identifiable settings. Then we demonstrate the usefulness of this algorithm in more challenging problems, namely identification of a multi-degree-of-freedom system under unmeasured excitation, and modeling of the highly nonlinear response of a full-scale bridge pier using experimental data.

Nonlinear vibro-acoustic modulation for microcrack detection of steel strands based on S-transform bispectrum

Fatigue crack detection is an important issue to ensure the safety of steel strands. The key to solve this problem is to extract the nonlinear response generated by fatigue cracks. In this paper, the nonlinear VAM method is used to detect the structural cracks. The structure with fatigue cracks is excited using low-frequency pumping and high-frequency probing, and the power spectrum analysis of the modulated signal is carried out. In view of the shortcomings of spectral analysis, a new method combining S-transform and bispectrum is proposed, which is called S-transform bispectrum. S transform contains the phase factor, which can retain the absolute phase characteristics of each frequency, and has good time–frequency multi-scale focusing performance. The bispectrum can suppress Gaussian noise, retain phase information, and quantitatively describe the quadratic phase coupling in the signal. Then the simulation and experiment of damaged straight rod, helical rod, and steel strands are carried out. The results show that the proposed method can effectively detect the nonlinear features by using the sideband peaks in the S-transform bispectrum three-dimensional plot, and the nonlinear features are important to identify the structure with damage. At the same time, in order to prove the ability of S-transform bispectrum, an S-transform bispectrum detector is used to verify it, which is superior to the spectrum in terms of its ability to localize modulation sidebands. The proposed S-transform bispectrum has a good application prospect and provides a new tool for structural damage detection.

Failure analysis of a helical compression spring with relatively low spring index

Design of helical springs are well defined and studied thoroughly. Generally, behavior of stiffness is considered to be in linear regime with desired dimensions. However, as the spring index which is defined as ratio of helical diameter to wire diameter gets lower a correction to calculated stress values must be performed. Furthermore, collision between coils, non-homogenous pitch heights between coils, end conditions are other factors leading to increase in stress values as compared to intended design values. An unexpected premature crack formation in a fatigue tested helical compression spring was investigated. First, geometry was measured using CMM and compared with design tolerances. After, metallurgical inspections regarding composition, hardness and microstructure of the material were performed. An analytical and numerical study was conducted in order to evaluate the stress state in the spring. A finite element model was created using ABAQUS and stress increase due to end condition was observed. A premature failure in a helical spring was studied regarding dimensions, material and stress state. The factors leading to nonlinear response of the spring is addressed and compared with experimental tests.

The effects of acoustic disturbances and mechanical vibration on laminar premixed flames: A comparative study

The energy conversion between the combustion process and acoustic waves is very complex in high-performance propulsion systems, which may trigger large-amplitude combustion instabilities, potentially leading to severe vibration or structural damage. Both acoustic disturbances and mechanical vibration are found to be able to cause the combustion instability, but their differences on the influence of laminar premixed flames are still unknown. In this paper, a premixed methane flame burner was disturbed by either a loudspeaker or an electromagnetic vibration exciter, and the effects of their forcing frequencies and amplitudes on the dynamic responses of the premixed methane flame were evaluated. Specifically, the unsteady heat release rate was measured by a photomultiplier tube, and the flame dynamic behaviors were captured by a high-speed camera with image intensifier. Furthermore, the acoustic disturbances upstream of the flame was measured by the two-microphone method, and the structure vibration was measured by an accelerometer. Then, the flame transfer functions were obtained at various equivalence ratios and mean flow velocities. The results demonstrated that the premixed flame exhibited obvious band-pass filtering characteristics when subjected to external forcing, whether through a loudspeaker or an electromagnetic vibration exciter. In addition, increasing either acoustic or structure excitation amplitude to a large extent can make the flame respond in a nonlinear manner. However, when the flame was subjected to mechanical vibration, the peak frequency corresponding to the maximum gain of the flame transfer function had minimal sensitivity to variations in equivalence ratios and mean flow velocities. In contrast, the acoustic disturbances were more likely to induce the nonlinear flame responses and flame front wrinkling.

Simulation of soil-structure interaction using inelasticity-separated finite element method

The soil–structure interaction (SSI) effect is nonnegligible during the nonlinear seismic response analysis of large-scale or underground structures. However, the computation of nonlinear response of a structure considering SSI effect usually is a time-consuming process because the numerical model should involve the structure itself, a wide-range soil domain and the soil–structure interface, especially for large-scale structure. This study aims to incorporate the inelasticity-separated finite element method (IS-FEM), which is an algorithm recently developed for efficient structural nonlinear analysis, to improve the efficiency of the soil-structure interaction system. To this end, an inelasticity-separated contact element model for modeling the nonlinear behavior of soil and structure interface is developed in this study. To derive the inelasticity-separated governing equation of this model, a reference elastic stiffness is defined so that the normal and shear deformation of any point pair in the presented contact element is decomposed into reference linear and reference nonlinear parts according to this reference elastic stiffness. As a result, the problem of inconsistency between the requirement of IS-FEM for constant initial linear elastic stiffness and the existence of inflection point for the stress versus relative displacement relationship of contact behavior can be solved. Then, the Goodman element formulation for depicting the nonlinear contact behavior is introduced and an interpolation scheme to establish the reference nonlinear deformation field in an element is incorporated. By combining the proposed model with existing inelasticity-separated elements, a global analytical model of the soil–structure interaction system can be established within the framework of IS-FEM. Because the nonlinearity usually occur in some local regions of the global model and the use of the IS-FEM only require performing these operations for a small scale matrix representing local nonlinearity, the computational efficiency of nonlinear structural response analysis considering SSI effect can be improved significantly. The applicability and efficiency of the proposed method is finally verified by two numerical examples.

Nonlinear static and dynamic response of a metastructure exhibiting quasi-zero-stiffness characteristics for vibration control: an experimental validation

This work introduces a novel metastructure designed for quasi-zero-stiffness (QZS) properties based on the High Static and Low Dynamic Stiffness mechanism. The metastructure consists of four-unit cells arranged in parallel, each incorporating inclined beams and semicircular arches. Under vertical compression, the inclined beams exhibit buckling and snap-through behavior, contributing negative stiffness, while the semicircular arches provide positive stiffness through bending-dominated behavior. The design procedure to achieve QZS is established and validated through finite element analysis and experimental investigations. The static analysis confirms a QZS region for specific displacement. Dynamic behavior is analyzed using a nonlinear dynamic equation solved using the Harmonic Balance Method, validated experimentally with transmissibility curves showing sudden jump down with effective vibration isolation. Parametric studies with varied payload masses and excitation amplitudes further verify the ability to of metastructure to attenuate vibrations effectively in low-frequency ranges.