Nonlinear Response Research Articles

Gravito-magnetic polarization of Schwarzschild black hole

We determine the gravito-magnetic Love numbers of non-rotating black holes in all spacetime dimensions through a novel and direct derivation. The Ishibashi-Kodama master field and its associated field equation are avoided. The matching to the EFT variables is simple. This method allows us to correct the values in the literature. Moreover, we highlight a parity-based selection rule for nonlinear terms that include both electric-type and magnetic-type gravitational field tensors, enabling us to conclude that many of the nonlinear response coefficients in the Schwarzschild black hole effective action vanish.

Optimizing the Nonlinear Response of Elliptical Tubular Composite Beams Using SVM

Optimizing the Nonlinear Response of Elliptical Tubular Composite Beams Using SVM

Hybrid uncertainty propagation analysis of nonlinear systems in the frequency domain based on multi-scale random interval moment method

To quantify the impact of hybrid uncertainty (random and interval parameters) on the frequency-domain nonlinear dynamic response, the multi-scale method (MSM) and the random interval moment method (RIMM) are combined to establish a new uncertainty propagation analysis method, called the multi-scale random interval moment method (MS-RIMM). RIMM is used to describe the hybrid uncertainty, while MSM is used to determine the frequency-domain nonlinear dynamic response. The statistical characteristics (i.e., the expectation value and variance) of the amplitude-frequency response of the nonlinear system with hybrid uncertainties are derived. Furthermore, the accuracy and effectiveness of the proposed method are verified by comparing the results with those obtained using the multi-scale Monte Carlo simulation method (MS-MCSM). Overall, the results of this study can serve as a useful reference for the hybrid uncertainty propagation analysis of nonlinear systems and for predicting the frequency-domain nonlinear dynamic response.

Self-induced non-synchronous resonance phenomena and stability in reduced aero-elastic system

The paper is aimed at the parametric dynamic analysis of the two degrees of freedom (DoF) phenomenological model of aero-elastic interaction between a friction-damped flexible mounted body and a flowing fluid. A coupled system of a linear structure oscillator and the van der Pol based wake oscillator is introduced. Firstly, the complex eigenvalue problem is used for the comprehensive analysis of frequency lock-in, veering and crossing areas from the structural mode stability point of view. Further, an in-depth analysis of the fully nonlinear model based on the numerical continuation method is presented. The analysis focuses on non-synchronous vibration in the resonance areas. Attention is paid to the investigation of transition mechanisms to frequency lock-in and frequency veering in the structural response. In experimental studies, the amplitude and frequency jumps are observed. Here, we show that the origin of these jump phenomena results from the mutual coexistence of two stable solutions, which form a hysteresis region, which can be found in experimentally gained data. Moreover, the influence of structure friction-damping on nonlinear response is evaluated. The proposed phenomenological model is validated concerning two different experimental-based investigations.

Synthesis of α-Bi/SrTiO3 heterostructure through the Eu-induced reduction of Bi2O2Se/SrTiO3

Thin Bi films, especially noncentrosymmetric α-phase Bi films (α-Bi), have attracted considerable attention in recent years due to their intriguing physical properties such as ferroelectricity, nonlinear optical response, and coherent spin transport. However, the current experimental preparation of α-Bi films still presents substantial challenges, resulting in only isolated α-Bi islands being achieved. In this study, α-Bi/SrTiO3 (α-Bi/STO) was synthesized from a Bi2O2Se/STO (BOS/STO) heterostructure by depositing a Eu layer and reducing a BOS film. The so-formed α-Bi/STO interface features metallic conductivity with electron mobility of 7.7 × 104 cm2/V s and ultralow resistivity of 1 nΩ cm at 2 K, as well as high residual resistance ratios R300 K/R2 K up to 2353. Furthermore, we observed a complex weak antilocalization–weak localization–weak antilocalization crossover with increasing magnetic field at temperatures below 10 K. Our work presents the synthesis of α-Bi films, which could potentially serve as a valuable platform for experimental validation of diverse theoretical predictions associated with α-Bi heterostructures. Furthermore, this special synthesis method provides valuable insights into the preparation of other metastable films.

Hexadecapole Deformation of ^{238}U from Relativistic Heavy-Ion Collisions Using a Nonlinear Response Coefficient.

The hexadecapole deformation (β_{4}) of the ^{238}U nucleus has not been determined because its effect is overwhelmed by those from the nucleus' large quadrupole deformation (β_{2}) in nuclear electric transition measurements. In this Letter, we identify the nonlinear response of the hexadecapole anisotropy to ellipticity in relativistic U+U collisions that is solely sensitive to β_{4} and insensitive to β_{2}. We demonstrate this by state-of-the-art hydrodynamic calculations and discuss the prospects of discovering the β_{4} of ^{238}U in heavy-ion data at the Relativistic Heavy Ion Collider.

Enhanced Optical Limiting of Gold Nanoparticles/Porous Carbon Nanocomposites.

With the wide application of laser weapons, the requirements of laser protection technology are becoming more and more strict. Therefore, it is important to find ideal optical limiting (OL) materials to protect human eyes and detectors. In this work, the nonlinear optical responses of gold nanoparticles/porous carbon (Au NPs/PC) nanocomposites prepared by the reduction method were studied using the nanosecond Z-scan technique. Compared with porous carbon, the Au NPs/PC nanocomposites show a lower damage threshold, a bigger optical limiting index and a wider absorption spectrum. The interaction between gold nanoparticles and porous carbon enhances the nonlinear scattering effect of suspended bubbles. These results indicate that Au NPs composites have potential applications in the protection of human eyes and detectors.

A low-cost bonded scrap tire rubber isolator in rural regions: Experimental, numerical and theoretical analysis on mechanical behavior

The utilization of low-cost scrap tire pads (STP) made from recycled tires presents a promising alternative to traditional rubber isolators (i.e., fiber-reinforced elastomeric isolators) in rural construction. However, the STP was limited in application to practicing structures due to stability with a shear strain level of 100 % and the significant variability of the mechanical behavior at the same parameters. For these issues, this paper presents a bonded scrap tire rubber isolators (BSTRIs), based on earthquake demand parameters for rural area buildings. In addition, a series of vertical compression and horizontal shear tests were conducted to evaluate the dependency of mechanical behavior on surface pressure (σ0), the first and the second shape factor (S1 and S2). Then, a finite element (FE) model of BSTRIs was developed and validated. The experimental and FE results show that the σ0, S1, and S2 overwhelmingly effect on mechanical behavior (i.e., critical pressure, vertical stiffness, horizontal stiffness, and damping ratio). Moreover, the new theoretical formulations on critical pressure, vertical stiffness, and horizontal stiffness were developed to evaluate the stability of BSTRIs. Finally, based on experimental result, a nonlinear dynamic response was conducted including the BSTRIs-supported and based-fixed unreinforced masonry (URM) buildings under 22 far-field and 28 near-field seismic excitations. The results indicated that the base shear of the BSTRIs-supported URM were decreased by 66.5 % and 50.1 % in far- and near-field record, respectively, compared with the response of the fixed-base URM building.

Exploring the impact of end-capped moieties on nonlinear optical response in d-[formula omitted]-a configurated based organoboron derivatives: A DFT/TD-DFT study

A new series of the organic derivatives (BDPTPD1-BDPTPD8) with push–pull architectures (D-π-A) was developed using various efficient acceptors into reference molecule (BDPTPR). To obtain nonlinear optical insights, BDPTPR and its derived compounds were investigated at M06/6-311G(d,p) level. All derivatives (BDPTPD1-BDPTPD8) have a lesser band gap (2.190–1.152 eV) and bathochromic shift (λmax = 713.086–722.350 nm) than that of reference molecule (Egap = 2.270 eV and λmax = 699.212 nm). Global reactivity calculations described that BDPTPD5 displayed smaller values of hardness (1.036 eV) with a larger value of softness (0.482 eV) relative to all studied chromophores. Similarly, it exhibited the highest values of βtot and γtot, as 1.783 × 10-27 and 2.400 × 10-32esu, respectively, among all investigated compounds. This framework elucidates that structural modification involving diverse end-capped acceptor units performs a crucial role in achieving desirable NLO substances for advanced optoelectronic technology.

Nonlinear coupled vibration of an arch-beam structural system

Nonlinear dynamic analysis of a shallow arch coupled with a cantilever beam (resting on Winkler foundation) is investigated by direct perturbation method. Two key parameters, (beam over arch) density ratio and height of beam, recharacterize coupling intensity between arch and beam. Nonlinear dynamic responses of arch-beam coupled model are predicted by asymptotic analysis, which include hardening and softening cases. After numerical verification of arch-beam coupled model, the uncoupled model (i.e., skipping beam-arch coupling) is also investigated for comparison. Besides, two more related but degenerately coupled models, e.g., arch-oscillator coupled model [1] and arch-rigid body coupled model [2] are both compared with the current arch-beam coupled model, revealing one key coupling characteristic of elastic support/foundation, which is however overlooked in previous models, e.g., only partial mass is involved with dynamic coupling.

Redefined background state in the tropical Pacific resolves the entanglement between the background state and ENSO

Understanding the co-variability between the El Niño–Southern Oscillation (ENSO) and the background state in the tropical Pacific is critical for projecting future ENSO. The difficulty is rooted in a circular logic that the background state routinely defined by multi-decadal mean modulates, and is modulated by, ENSO. This circularity arises due to the asymmetry between El Niño and La Niña, resulting in a non-zero mean, referred to as the ENSO rectification effect. Here, we develop a method based on Box-Cox normalization to define the tropical Pacific background state and its associated anomalies, which removes the ENSO rectification effect and is referred to as the normalized mean state. The normalized mean state accurately quantifies ENSO-related anomalies, ENSO asymmetry, and the ENSO rectification effect. It is evident in both observations and model simulations that the normalized mean state has a clear asymmetric impact on the amplitude of ENSO. A warm background state weakens El Niño but strengthens La Niña through two key processes: the nonlinear response of precipitation to SST and oceanic zonal advection feedback. The normalized mean state successfully solves the circular reasoning fallacy resulting from ENSO asymmetry and offers a framework to study ENSO and tropical climate dynamics with far-reaching impacts on global climate.

Revealing Novel Aspects of Light-Matter Coupling by Terahertz Two-Dimensional Coherent Spectroscopy: The Case of the Amplitude Mode in Superconductors.

Recently developed terahertz (THz) two-dimensional coherent spectroscopy (2DCS) is a powerful technique to obtain materials information in a fashion qualitatively different from other spectroscopies. Here, we utilized THz 2DCS to investigate the THz nonlinear response of conventional superconductor NbN. Using broadband THz pulses as light sources, we observed a third-order nonlinear signal whose spectral components are peaked at twice the superconducting gap energy 2Δ. With narrow-band THz pulses, a THz nonlinear signal was identified at the driving frequency Ω and exhibited a resonant enhancement at temperature when Ω=2Δ. General theoretical considerations show that such a resonance can arise only from a disorder-activated paramagnetic coupling between the light and the electronic current. This proves that the nonlinear THz response can access processes distinct from the diamagnetic Raman-like density fluctuations, which are believed to dominate the nonlinear response at optical frequencies in metals. Our numerical simulations reveal that, even for a small amount of disorder, the Ω=2Δ resonance is dominated by the superconducting amplitude mode over the entire investigated disorder range. This is in contrast to other resonances, whose amplitude-mode contribution depends on disorder. Our findings demonstrate the unique ability of THz 2DCS to explore collective excitations inaccessible in other spectroscopies.

Nonlinear dynamic response and damping performance of the viscoelastic composite core-based sandwich plates subjected to blast load

Nonlinear dynamic response and damping performance of the viscoelastic composite core-based sandwich plates subjected to blast load

Comparative Vision of Nonlinear Thermo-Optical Features and Third-Order Susceptibility of Mechanically Flexible Metallosupramolecular Self-Repairing Networks with Isomeric Organic Acids.

Two self-healing-type supramolecular Ni(II)-metallogels are achieved. The choice of proper low-molecular-weight organic gelators such as trans-butenedioic acid (i.e., trans-BDA) and cis-butenedioic acid (i.e., cis-BDA) and triethylamine in N,N'-dimethylformamide solvent facilitates the metallogelation process. Through rheological investigations the mechanical robustness and viscoelastic properties of synthesized metallogels are explored. An in-depth exploration of thixotropic behavior also supports their self-healing features. Notably, distinct variations in morphologies of metallogels are also ascertained through field emission scanning electron microscopy studies. Furthermore, the existence of versatile noncovalent supramolecular interactions operating throughout the metallogel network is clearly revealed via Fourier transform infrared spectroscopy. Electrospray ionization-mass studies also explore the construction protocol of individual Ni(II)-metallogels. The Z-scan measurements with a 532 nm continuous wave laser were employed to unveil the nonlinear thermo-optical response of two synthesized self-healing metallogels, i.e., trans-BDA-TEA@Ni(II) and cis-BDA-TEA@Ni(II). Crucial parameters like the nonlinear refractive index, nonlinear absorption coefficient, thermo-optical coefficient, and third-order susceptibility of these metallogels are obtained. Metallogels show negative signs for the nonlinear refractive index and the nonlinear absorption coefficient. The real parts of the third-order susceptibility for these metallogels are much greater than the imaginary parts (i.e., χR(3) > χI(3)), making such metallogels very promising for all optical-switching applications.

Thermo‐hydro‐mechanical coupled material point method for modeling freezing and thawing of porous media

AbstractClimate warming accelerates permafrost thawing, causing warming‐driven disasters like ground collapse and retrogressive thaw slump (RTS). These phenomena, involving intricate multiphysics interactions, phase transitions, nonlinear mechanical responses, and fluid‐like deformations, and pose increasing risks to geo‐infrastructures in cold regions. This study develops a thermo‐hydro‐mechanical (THM) coupled single‐point three‐phase material point method (MPM) to simulate the time‐dependent phase transition and large deformation behavior arising from the thawing or freezing of ice/water in porous media. The mathematical framework is established based on the multiphase mixture theory in which the ice phase is treated as a solid constituent playing the role of skeleton together with soil grains. The additional strength due to ice cementation is characterized via an ice saturation‐dependent Mohr–Coulomb model. The coupled formulations are solved using a fractional‐step‐based semi‐implicit integration algorithm, which can offer both satisfactory numerical stability and computational efficiency when dealing with nearly incompressible fluids and extremely low permeability conditions in frozen porous media. Two hydro‐thermal coupling cases, that is, frozen inclusion thaw and Talik closure/opening, are first benchmarked to show the method can correctly simulate both conduction‐ and convection‐dominated thermal regimes in frozen porous systems. The fully THM responses are further validated by simulating a 1D thaw consolidation and a 2D rock freezing example. Good agreements with experimental results are achieved, and the impact of hydro‐thermal variations on the mechanical responses, including thaw settlement and frost heave, are successfully captured. Finally, the predictive capability of the multiphysics MPM framework in simulating thawing‐triggered large deformation and failure is demonstrated by modeling an RTS and the settlement of a strip footing on thawing ground.

Nonlinear optical signatures of topological Dirac fermion.

Dirac fermion in topological materials exhibits intriguing nonlinear optical responses. However, their direct correlation with the linearly dispersed band remains elusive experimentally. Here, we take topological semimetal ZrSiS as a paradigm, unveiling three unique nonlinear optical signatures of Dirac fermion. These signatures include strong quadrupolar response, quantum interference effect, and exponential divergent four-wave mixing (FWM), all of which are described by the prominent third-order nonlinear optical susceptibility. Resonantly enhanced by linear bands, quadrupolar second harmonic generation in centrosymmetric bulk overwhelms the electric-dipole contribution at the surface with inherent inversion symmetry breaking. Furthermore, owing to the interference between multiple resonant transition pathways within linear bands, difference-frequency FWM is several orders of magnitude stronger than sum-frequency FWM and third harmonic generation. The difference-frequency FWM further displays an inverse-square divergence toward degenerate excitation, whose scaling law perfectly matches with the long-sought behavior of Dirac fermion. These signatures lay the solid foundation toward the practical applications of topological materials in nonlinear optoelectronics and photonics.

Nonlinear buckling and postbuckling behaviors of porous FG-GPLRC cylindrical shells with stiffeners subjected to external pressure

Buckling and postbuckling behaviors of porous functionally graded graphene platelets-reinforced composite (porous FG-GPLRC) cylindrical shells with stiffeners subjected to external pressures are presented in this paper. Three distribution types of porosity in the shells are considered. The smeared technique for stiffeners is employed to model the mechanical behaviors of the stiffened shells. The mechanical formulations are established by the thin shell theory considering large deflection assumption, and the Ritz method is applied for three deflection amplitudes. The postbuckling formula of the pressure-deflection and the explicit critical buckling pressures can be achieved. The numerical investigations indicate the outstanding effects of stiffeners, porosity distribution, porosity coefficient, and graphene platelet (GPL) mass fraction on the nonlinear buckling responses of the stiffened shells.

Multi-spring model for tubular rocking steel bridge piers subjected to earthquake loading

Recent decades have seen increased interest in using the controlled rocking concept in seismic resisting systems. Unlike conventional systems, where lateral deformation of a member is achieved through the formation of plastic hinges in critical regions, in the rocking systems this is achieved through a gap opening mechanism. Due to gravity load and/or post-tensioning forces, the rocking systems exhibit a self-centering behavior. Conducting a continuum finite element analysis to investigate the seismic response of such a system is quite expensive in terms of computational resources. On the other hand, a simplified macro model using two springs to simulate the gap opening/closing mechanism cannot accurately predict the dynamic response of the system. This study utilizes a multiple-spring model to simulate the nonlinear seismic response of circular tubular steel piers. An efficient optimization procedure based on a genetic algorithm is developed to calibrate the parameters of the springs. The results of continuum finite element analyses are compared with those obtained from the multi-spring model to verify the accuracy of the model. The proposed method is shown to be advantageous for accurately simulating the seismic response of a bridge model subjected to multi-directional ground motions, particularly the hysteretic force-displacement relationship, and dynamic response time history.

Simultaneous Circular Dichroism and Wavefront Manipulation with Generalized Pancharatnam-Berry Phase Metasurfaces.

Simultaneous circular dichroism and wavefront manipulation have gained considerable attention in various applications, such as chiroptical spectroscopy, chiral imaging, sorting and detection of enantiomers, and quantum optics, which can improve the miniaturization and integration of the optical system. Typically, structures with n-fold rotational symmetry (n ≥ 3) are used to improve circular dichroism, as they induce stronger interactions between the electric and magnetic fields. However, manipulating the wavefront with these structures remains challenging because they are commonly considered isotropic and lack a geometric phase response in linear optics. Here, we propose and experimentally demonstrate an approach to achieve simultaneous circular dichroism (with a maximum value of ∼0.62) and wavefront manipulation using a plasmonic metasurface made up of C3 Archimedes spiral nanostructures. The circular dichroism arises from the magnetic dipole-dipole resonance and strong interactions between adjacent meta-atoms. As a proof of concept, two metadevices are fabricated and characterized in the near-infrared regime. This configuration possesses the potential for future applications in photodetection, chiroptical spectroscopy, and the customization of linear and nonlinear optical responses.

A multiaxial multiscale compressive thermo-mechanical damage model for Fiber Reinforced Cementitious Composites (FRCC)

In the current study, a multiaxial multiscale compressive stress-strain model for Fiber Reinforced Cementitious Composites (FRCC) was innovatively developed. The proposed model was on the basis of the theory of thermodynamics, multiscale theory and internal variable theory. The free energy function and dissipation function were established to characterize the elastic and plastic deformation of FRCC, respectively. The multiscale behaviors of FRCC in meso-scale and macro-scale was taken into account. In meso-scale, the energy dissipation functions of fiber in tension and bond-slip deformation in the interface transition zone (ITZ) were established. The resistance to cracking of cementitious matrix through the fiber bond stress were taken into account. In macro-scale, the thermo-mechanical coupling contributions of plastic damage, thermal damage, yield surface and hardening evolution were creatively considered in the potential function within thermodynamics framework. The influence of types and volume fractions of fibers on the reinforcement mechanism was discussed. When the temperature is higher than the melting point of fiber, the fiber influence coefficients was employed. The sensitivity of yield surface was discussed. The numerical predictions of this developed model were carried out for validation. The nonlinear stress-strain responses of concrete were accurately captured at temperatures ranges from 20 °C to 800 °C compared with the experimental data, which indicates the accuracy and applicability of the proposed model.