Nonlinear Response Research Articles

Empirical approaches for non-linear site response: results for the ESG6-blind test

As a contribution to step 3 of the ESG6 blind prediction exercise, we present an application of two different, purely empirical approaches to estimate the strong ground motion at a soft site ("KUMA") from the observed ground motion at a reference rock site ("SEVO") for the two largest shocks of the Kumamoto 2016 sequence. The two methods estimate the non-linear transfer function between a reference rock and a sedimentary site by modifying the linear transfer function derived from weak motion recordings. The modification is based either on a machine learning tool based on a wide collection of Japanese weak and strong motion recordings and the associated site metadata (method 1), or on an estimate of a site-specific parameter related to an average non-linear site response (method 2). The acceleration time series are then derived at the sedimentary site of interest using an estimation of the time delay between wave arrivals at the rock and site stations, and a minimum phase assumption for the site transfer function. These predictions were made blindly, but after the ESG6 conference they could be compared both with the actual ground motion recorded at KUMA during the two shocks, and the average and range of all other predictions preformed for this benchmark. Both of these purely empirical methods provide an honorable prediction of usual engineering ground motion parameters of the two target events. The performance of these two purely empirical approaches is at least comparable to those of the numerical simulation methods for the foreshock—if not better—and slightly worse for the (largest) mainshock. As the methods required only recordings of weak motions at the target and a referent sites and very simple description of the soil profile. The use of moderate motions to constrain the frequency shift prediction for the second method and the consideration of an alternative phase modification are possible ways to improvement.Graphical

Evaluation of the Nonlinear Response of KCl Solution to High-Amplitude Stimulation Using a Four-Point Cylindrical Gold Electrode.

A four-electrode system and high-voltage amplitude stimulation (with a voltage of more than 1 V) are always used for nonlinear spectroscopy of biological solutions like yeast suspension. Multiple studies indicate that yeast membrane activities are the primary source of the harmonics detected from yeast suspensions. However, other investigations have demonstrated that at least part of the harmonics are mainly due to the nonlinear impedance of the electrode-electrolyte interface. Here, we want to find a mathematical model to analyze the odd harmonics generated by the interface. The KCl solution is the basis of the essential medium used in yeast culture. No study models the nonlinear behavior of the KCl solution using four-electrode. We used a sinusoidal voltage with a low frequency and a high amplitude to test an ionic solution with 1, 30, and 130 mM of potassium chloride. The voltage had no direct current component. Here, we show that the relationship between the amplitude of the excitation voltage and the third harmonic of the current can be accurately represented using the Butler-Volmer equation. Additionally, we analyze the impact of potassium chloride (KCl) concentration on the behavior of the third harmonic. This paper presents a method and model that can be used for nonlinear spectroscopy studies of biological solutions using a four-electrode system with the aim of deriving information from cells without considering the interface effect.

Mitigation of nonlinear responses in POLMUX-based long-haul optical communication system with the duo-binary modulation scheme

Mitigation of nonlinear responses in POLMUX-based long-haul optical communication system with the duo-binary modulation scheme

Effects of Surface Charge Distribution and Electrolyte Ions on the Nonlinear Spectra of Model Solid-Water Interfaces.

Molecular dynamics simulations of model charged solid/water interfaces were carried out to provide insight about the relationship between the second-order nonlinear susceptibility χ(2) and the structure of the interfacial water layer. The results of the calculations reveal that the density fluctuations of water extend to about 12 Å from the surface regardless of the system, while the orientational ordering of molecules is long-ranged and is sensitive to the presence of electrolytes. The charge localization on the surface was found to affect only the high-frequency part of the Im[χ(2)] spectrum, and the addition of salt has very little effect on the spectrum of the first water layer. For solid/neat water interfaces, the spectroscopically active part of the liquid phase has a thickness largely exceeding the region of density fluctuations, and this long-ranged nonlinear activity is mediated by the electric field of the molecules. The electrolyte ions and their hydration shells act in a destructive way on the molecular field. This effect, combined with the screening of the surface charge by ions, drastically reduces the thickness of the spectroscopic diffuse layer. There is an electrolyte concentration at which the nonlinear response of the diffuse layer is suppressed and the χ(2) spectrum of the interface essentially coincides with that of the first water layer.

Hierarchical Modeling of the Nonlinear Optical Response of Composite Materials Based on Tetrathiafulvalene Derivatives.

The presented work concerns computational investigations of the physical properties of composite materials based on polymer matrix and nonlinear optical (NLO) active chromophores. The structural, electronic, and optical properties of selected tetrathiafulvalene (TTF)-based chromophores have been calculated using quantum chemical methods. The polymer matrix changes the physical properties of the inserted chromophores influencing their optical parameters. To explain the mechanism of the NLO signal occurrence from the composites based on poly(methyl methacrylate) (PMMA) matrix and TTF chromophores, their structures are modeled using the classical molecular dynamics. In consequence, the structural properties of the composites are discussed according to the NLO requirements. By developing the theoretical model based on a discrete multipole local field approach, the impact of polymer matrix on the optical properties of chromophores is explained.

Hierarchical Bayesian modeling for calibration and uncertainty quantification of constitutive material models: Application to a uniaxial steel material model

Constitutive material models play an integral role in finite element (FE) modeling of structural components and systems and are governed by a set of parameters. The values of the material model parameters are important for the FE model to be able to predict the real structural behavior as closely as possible. Realistic cyclic material constitutive models well calibrated to experimental data are critical when predicting the nonlinear dynamic response of structural systems to extreme loads (e.g., earthquakes, high winds, blast). Hence, this study focuses on the inference and uncertainty quantification of material model parameters from an experimental dataset consisting of data from experiments on multiple specimens of the same kind, which is a topic of great interest to the structural modeling and simulation community. Traditionally, Bayesian inference is performed by pooling the data from all the specimens, or by considering the data from a single specimen, disregarding the inherent variability (aleatory uncertainty) among specimens of the same kind. Consequently, traditional approaches fail to capture the population distribution of material model parameters, which represents the aleatory specimen-to-specimen variability that is essential for conducting reliability analysis and uncertainty propagation studies. Moreover, these approaches cannot accurately simulate the response of new specimens. To overcome these limitations, this study introduces a novel application of hierarchical Bayesian inference for calibrating material model parameters. By simultaneously considering experimental data from multiple specimens of the same kind, hierarchical Bayesian modeling quantifies both epistemic uncertainty and aleatory specimen-to-specimen variability. In this study, the parameters of the well-known Giuffré-Menegotto-Pinto (GMP) uniaxial material model for reinforcing steel are calibrated and validated based on a dataset of experimental cyclic tests conducted on thirty-six steel specimens, or coupons, originating from three different manufacturing mills, complying to two different manufacturing standards, and subjected to different strain histories. These strain histories are similar to those experienced during seismic events by reinforcing steel bars within reinforced concrete structures. The material model parameters are calibrated using both the traditional and the hierarchical Bayesian approach and the results are compared. Based on the experimental dataset employed in this study, a joint probability distribution of the GMP material model parameters that quantifies both epistemic (due to finite sample size) and aleatory (coupon-to-coupon) variability or uncertainty is provided which can be used for uncertainty propagation in reliability and risk analyses of nonlinear dynamic systems.

Time history seismic response prediction of multiple homogeneous building structures using only one deep learning‐based Structure Temporal Fusion Network

AbstractStructural response prediction under earthquakes is crucial for evaluating the structural performance and subsequent functional restoration. Deep learning provides the potential to rapidly obtain the responses by skipping the time‐consuming nonlinear finite element analysis. However, a single deep learning network may only predict the time history responses of one specific structure, resulting in redundancy and resource waste when building multiple networks for modeling different structures. Thus, this study proposes a Structure Temporal Fusion Network (STFN) that can predict responses of various homogeneous structures using a single network. The key concept is that the seismic waves and the structural characteristics, such as story numbers, are fused together to predict diverse time history responses. Two numeric experiments are conducted, including predicting responses of ideal single‐degree‐of‐freedom (SDOF) structures and regular multistory reinforced concrete frames. Furthermore, a series of ablation analyses are carried out to validate the network architecture. The results indicate that STFN can predict nonlinear time history responses of different structures with mean square errors in the magnitude of and for two experiments, respectively. The solutions also highlight the importance of fusing static characteristics for the modeling of various structures with only one network. The STFN presents a promising solution for time history response prediction across multiple structures in regions.

Nonlinear optical response and application of indirect narrow-bandgap SbTe nanosheets

The nonlinear optical properties of antimony telluride (SbTe) crystal with indirect narrow bandgap are investigated, which exhibits superior performance for nonlinear laser modulation in the infrared band. The nonlinear optical coefficients of SbTe nanosheets are determined to be −3.3 cm/GW, −2.3 cm/GW, −1.9 cm/GW and the modulation depths are 5.5 %, 2.0 %, 1.5 % at 400 nm, 800 nm, 1064 nm, respectively. Based on the SbTe-SA, a Yb:GdScO3 laser centered at 1064 nm is achieved with 633 mW maximum output power, 56 fs pulse width and 104 MHz repetition rate. The damage threshold of the SbTe nanosheets is calculated to be exceed 338 GW/cm2, revealing the great potential in high-power laser modulation. This investigation marks the inaugural theoretical and experimental analysis of SbTe’s optical properties and its application in laser modulation, laying the groundwork for future research into indirect narrow-bandgap materials in laser technology.

Loewner Theory for Stochastic Neuron Model

The nonlinear response of the dynamics of the stochastic neuronal activity based on the leaky integrate-and-fire model was reformulated using the Loewner theory. We observed that the signal-to-noise ratio (SNR), which is an indicator of stochastic resonance (SR), and fluctuation-dissipation relation (FDR) for the neuronal dynamics were newly obtained in the theoretical framework of the Loewner evolution. Particularly, we focus on the role of the Loewner entropy [Formula: see text], defined as the entropy of the Loewner driving force, while showing the efficacy of Loewner time conversion to theorize the nonlinear characteristic of the neuronal dynamics. The present results indicate a possible approach to the novel formulation of biophysical models.

Corrections to Diffusion in Interacting Quantum Systems

The approach to equilibrium in interacting classical and quantum systems is a challenging problem of both theoretical and experimental interest. One useful organizing principle characterizing equilibration is the dissipative universality class, the most prevalent one being diffusion. In this paper, we use the effective field theory (EFT) of diffusion to systematically obtain universal power-law corrections to diffusion. We then employ large-scale simulations of classical and quantum systems to explore their validity. In particular, we find universal scaling functions for the corrections to the dynamical structure factor ⟨n(x,t)n⟩, in the presence of a single U(1) or SU(2) charge in systems with and without particle-hole symmetry, and present the framework to generalize the calculation to multiple charges. Classical simulations show remarkable agreement with EFT predictions for subleading corrections, pushing precision tests of effective theories for thermalizing systems to an unprecedented level. Moving to quantum systems, we perform large-scale tensor-network simulations in unitary and noisy 1D Floquet systems with conserved magnetization. We find a qualitative agreement with EFT, which becomes quantitative in the case of noisy systems. Additionally, we show how the knowledge of EFT corrections allows for fitting methods, which can improve the estimation of transport parameters at the intermediate times accessible by simulations and experiments. Finally, we explore nonlinear response in quantum systems and find that EFT provides an accurate prediction for its behavior. Our results provide a basis for a better understanding of the nonlinear phenomena present in thermalizing systems. Published by the American Physical Society 2024

A method to resolve thermal and electronic contributions to the nolinear optical response

This paper presents the study and implementation of a modified Z-scan technique using a chopper to change the thermal load of the sample, while keeping the input peak irradiance constant. It was verified numerically and experimentally that by changing the frequency of the chopper and keeping the power of the laser beam constant, it is possible to vary the thermal load on the sample. This technique is illustrated under the study of the nonlinear optical (NLO) properties of nucleated Au–Pt metallic nanoparticles (NPs) by ion implantation. The nonlinear optical response was studied using the Z-scan. technique using a Ti:Sapphire laser with femtosecond pulses at a wavelength of 800 nm and a repetition rate of 76 MHz. By scanning the sample using the Z-scan technique it was It is possible to determine the refractive and absorbing contributions to the nonlinear response, in this case as a consequence of a high pulse repetition rate, cumulative pulse-to-pulse thermal effects occurred. Because of this, a modification of the Z-scan technique allowed to separate the resolution of the electronic and thermal contributions on the sample.

Surfactant-Driven Dynamic Changes in Rheology of Activated Carbon Slurry Electrodes.

Carbon black slurry electrodes are an effective means to improve flow battery performance by increasing the active surface area necessary for electrochemical reactions with a cost-effective material. Current challenges with this specific flow battery chemistry include the stability and flowability of the carbon black suspensions, especially in response to formulation choices. Advancing the manufacturing, operation, and performance of these redox flow batteries requires a deeper understanding of how slurry formulation impacts its rheological profile and ultimately battery performance. In response to this need, the linear and nonlinear rheological responses of activated carbon (AC) based slurry electrode materials used in an all-iron flow battery in the presence of a nonionic surfactant (Triton X-100) were measured. Results from these measurements show the slurry is a colloidal gel with elasticity remaining constant despite increasing surfactant concentration until α (= Csurf/CAC) < 0.65. However, at α ≥ 0.65, the slurry abruptly transitions to a fluid with no measurable yield stress. This critical surfactant concentration at which the rheological profile undergoes a dynamic change matches the concentration found previously for gel collapse of this system. Moreover, this transition is accompanied by a complete loss of electrical conductivity. From these data we conclude the site specific adsorption of surfactant molecules often used in slurry formulation has a significant and dramatic impact on the stability and flowability of these suspensions. Work presented herein demonstrates the importance of additive choices when formulating a slurry electrode.

Second Harmonic Generation from exciton-polaritons: Strong coupling between monolayer WS[formula omitted] and multilayer WSe[formula omitted] metasurfaces Quasibound states in the continuum

The second harmonic generation (SHG) from exciton-polaritons, produced by the strong coupling between quantum emitters and cavity photons, can provide a unique insight for controlling nonlinear responses on the nanoscale. Achieving SHG generally depends on phase matching, limited by nonlinear materials and nanostructure fabrication. Here, we demonstrate a novel way to obtain tunable SHG from van der Waals metasurfaces composed of nanostructured multilayer WSe2 strong coupling with monolayer WS2. By breaking symmetry via varying the metasurface unit tilted angle and period, quasibound state in the continuum (q-BIC) mode resonances energy is tuned across the monolayer WS2 exciton resonance energy, enabling anticrossing behavior of strong coupling in both reflection spectrum and SHG spectrum, which means that SHG was successfully observed by strong coupling. Furthermore, the SHG spectrum can be tuned by changing the armchair direction of the monolayer WS2 and pump polarization direction. Moreover, the mechanism of exciton-polaritonic SHG is investigated by a coupled nonlinear oscillator model, which reveals the SHG origin from exciton-polaritons, providing a new rule for fine-tuning the SHG. Our work provides a new strategy and additional freedom in the nonlinear light-matter interaction and coherent control of the SHG in integrated photonic devices.

Second harmonic generation and broad-band photoluminescence in mesoporous Si/SiO2 nanoparticles

Abstract Efficient second harmonic generation and broad-band photoluminescence from deeply subwavelength and nontoxic nanoparticles is essential for nanophotonic applications. Here, we explore nonlinear optical response from mesoporous Si/SiO2, SiO2, and Si nanoparticles, considering various fabrication and treatment procedures. We show that thermal annealing (including femtosecond laser treatment) of mesoporous Si/SiO2 nanoparticles provides the transformation of Si phase from amorphous to crystalline, enhancing the second harmonic and nonlinear photoluminescent response. Notably, the SiO2 mesoporous frame of the considered Si/SiO2 nanoparticles plays a dual positive role for the nonlinear process: it stabilizes the Si material, and SiO2:OH− material has a second-order nonlinearity itself and impacts to the observed second harmonic signal.

Crookedness detection of thrust ball bearing shaft washer based on nonlinear vibration responses

Bearing misalignments are common defects in machinery. One of the most important types of that is the angular misalignment of the bearing rings. In this study, crookedness specific signature related to thrust ball bearing shaft washer is investigated. For this purpose, a vertical structural thrust ball bearing test rig was considered. In the following, effects of rotational shaft speed, crookedness value and axial external force on the shaft washer crookedness signature were studied at several relative positions of sensors. It is shown that crookedness of thrust ball bearing shaft washer has specific frequency and sensor phase difference pattern in the nonlinear vibration responses. Also, the experimental results are applied to validate results of a 4-dof nonlinear dynamical system related to the shaft washer crookedness of thrust ball bearing. In the next step, by comparing input and output amplitude and also existence of flip bifurcation, it is illustrated that this system is a nonlinear dynamical experimental system. It was shown that this nonlinearity makes crooked shaft washer pattern difficult to identify. Finally, by the phase portrait of the sensor response and the relative error value of crookedness signature frequencies, it is clear that the crookedness of shaft washer creates quasi-chaotic behavior supporting crookedness signature frequencies and phase pattern as a supplement property.

Sensitivity analysis of SWAT streamflow and water quality to the uncertainty in soil properties generated by the SoLIM model

Hydrological models are essential tools for understanding natural processes, yet they often encounter with uncertainties due to limited input data and simplified assumptions. Soil data is a crucial input parameter for hydrological models, but it faces cartographic challenges due to lack of standardized soil mapping methods. To explore the applicability of soil datasets derived from the Third Law of Geography in hydrological models, the Soil Landscape Inference Model (SoLIM) based on this principle is used to generate a soil dataset. This dataset is then utilized as input data for a semi-distributed hydrological model (Soil and Water Assessment Tool, SWAT) to assess the impact of soil dataset uncertainty on performance of the hydrological model. This study, utilized the Fengyu River Watershed in Yunnan Province, China as an example, showed that: 1) Although the integration of SoLIM-generated soil data into the SWAT model introduces sensitivity in sediment yield, the overall results remain reliable. This suggests that soil datasets based on the Third Law of Geography can serve as input for semi-distributed hydrological models. 2) Uncertainty introduced by SoLIM-generated soil data affects parameters such as evaporation, total porosity of the soil layer (Φd), and groundwater infiltration coefficient (Ksat). These variations influence the sensitivity of SWAT’s predictions regarding streamflow and water quality. 3) Factors influencing model outcomes include steeper slopes in certain areas, which enhance streamflow velocity and flow rates, resulting in more dynamic and non-linear responses. Additionally, soil water dynamics exhibit higher temporal and spatial variability in forests compared to pasture and rice paddy fields, where vegetation tends to be more uniform, maintaining stable soil water loss pathways and reducing uncertainty in streamflow predictions. The study provides a foundation for studies addressing the difficulties in acquiring high-precision soil datasets for such models.

Exploring the effect of thin film thicknesses on linear and nonlinear optical properties of MoO3 thin film

The structural, morphological, linear, and nonlinear optical properties of MoO3 thin films deposited by thermal deposition were measured. The effect of various thicknesses of films was studied. The structural and morphological parameters of films, determined by x-ray diffraction, field emission scanning electron microscopy, and AFM images, are compared to the linear and nonlinear optical characteristics of these media. The bandgap of the prepared thin films was obtained from the diffuse reflectance spectroscopy spectra. The electron’s effective mass (me*/m0), linear refractive index (n0), and optical static and high frequency dielectric constant (ɛ0, ɛ∞) values were calculated by using the bandgap energy values. Increasing the thicknesses of thin films decreased the bandgap, increased the root mean square, and increased the size of nanoparticles and the nonlinear response of thin films. The high magnitude of n2 and β was because of MoO3 (300 nm-thickness), which were of the order of 10−5 cm2/W and 10−1 cm/W, respectively. The fluctuations in nonlinear responses observed at different thicknesses are attributed to d–d transitions and intraband scattering of equilibrium electrons influenced by laser radiation, as indicated by the nonlinearity data. The considerably elevated refractive nonlinearity values in the analyzed film materials suggest their potential for practical application in optoelectronic devices.

Derivation of elastic and inelastic characteristics of non-periodic masonry using homogenization techniques and micro-modelling approaches

The present study is aimed to develop an ad hoc four-steps procedure, based on the use of Digital Image Processing (DIP) techniques, homogenization methods and micro-modelling approaches, able to provide an effective tool for characterizing the mechanical properties of non-periodic masonry. More in detail, after creating, through a DIP technique and automated procedures, a finite element mesh from the Red-Green-Blue (RGB) image of a real masonry wall with non-periodic texture (Step 1 and Step 2), a homogenization method, which considers the properties of each masonry constituent (stone units and mortar joints), is used to derive the main elastic characteristics of a homogeneous continuum equivalent to the random masonry (Step 3). Specifically, this estimate can be achieved following the test-windows method based on the use of least-sized partitions subjected to boundary conditions in terms of displacements or stresses until a chosen convergence criterion is fulfilled. The non-linear response is then accomplished by means of a micro-modelling approach (Step 4). To this end, a three-dimensional finite element (FE) analysis can be therefore developed to characterize the main inelastic material parameters of the random masonry. Lastly, as a benchmark of the method, the proposed procedure has been validated against the laboratory outcomes obtained from a previous experimental campaign on non-periodic masonry walls.

Multi-year climate memory in shallow lake water levels

Landscape hydrologic memory of meteorological cycles can have an important impact on catchment hydrological responses by propagating clustering of wet or dry conditions into extreme events. The non-linear and hysteretic hydrologic response functions driven by memory are often only studied at shorter temporal scales (event, season) despite larger interannual hydrologic responses evident in some systems. Within the Canadian Boreal, lakes and lake water levels provide an important indicator that can be used to assess the role of landscape memory on catchment hydrological function. Landscape memory has also been hypothesised to control the hydrological dynamics of shallow lake ecosystems that are also important biogeochemically and ecologically. Here we combine measurements of lake water levels in 26 lakes of varying type at varying temporal frequencies within the glaciated sub-humid Boreal Plain, to examine the impact and variability of interdecadal, decadal, multi-year, intra-annual memory on lake water levels. We show multi-annual hysteresis of precipitation-lake water levels with varied characteristics in space and time. These spatial variations in landscape memory are driven by differences in storage capacities controlled by heterogeneity in glacial landforms, wetland-forest landcover and lake properties. Thus, the propensity for drought years or wet years to persist or accumulate into extreme landscape drying or wetting varies significantly between different lake-landscape characteristics. We show how landscape memory is crucial to project lake water levels by defining spatial variability of the impact of periods of meteorological drought and deluge vital for understanding system sensitivity, duration of recovery and in turn infer resilience on Boreal Plain hydrology.

Phenyl-urea chromophores: DFT insights into nonlinear optical enhancement

The present investigation has examined the nonlinear optical (NLO) responses of molecules based on phenyl-urea. The optimized geometries of complexes: (4-nitrophenyl) urea (PU1), 1-methyl-3-(4-nitrophenyl) urea (PU2), and 1,1-dimethyl-3-(4-nitrophenyl) urea (PU3) are extracted using M06–2X/6–311++ g (d, p) level of theory. The estimated nonlinear optical responses (NLO) of the compounds given are based on static and dynamic hyperpolarizabilities, which are reinforced by the dipole moment, polarizabilities, global reactivity parameters, HOMO-LUMO gap, molecular electrostatic potentials (MEP), and βvec. Comparing PU1, PU2, and PU3 to reference substances like urea and p-nitroaniline, a considerably higher NLO activity is estimated. Out of all the compounds, PU3 has the largest NLO response. Such a significant NLO reaction can be attributed to a small HOMO-LUMO gap and high charge transfer. Second-harmonic generation (SHG) and electro-optic Pockel's effect (EOPE) are being explored for dynamic NLO responses. These compounds that are bases of phenyl-urea exhibit a very significant quadratic nonlinear optical response.