Nonlinear Characteristics Research Articles

On the study of analytical soliton solutions and interaction aspects to the Estevez-Mansfield-Clarkson equation arising in diversity of fields

Abstract The beta fractional form of the Estevez-Mansfield-Clarkson equation is under consideration and this study is done with the assistance of methods such as modified F-expansion method and the logarithmic transformation. A variety of analytical solutions like bright, dark, mixed, singular, bright-dark, and combined solitons are extracted. Moreover, multi waves structures, interaction with double exponential form, breather waves, mixed type solutions as well as periodic cross kink solutions have been analyzed. The governing equation is converted into an ordinary differential equation by employing an appropriate wave transformation with the β-derivative in order to achieve the desired solutions. The applied approaches have substantial computational capability, enabling them to efficiently address exact solutions with high accuracy in these systems. The results indicate that the equation under investigation theoretically contains a substantial number of soliton solution structures. Additionally, in order to examine the behaviors of the solutions at various parameter values, we plot a variety of graphs that incorporate pertinent parameters. The results of this study have the potential to improve understanding of the nonlinear dynamic characteristics displayed by the specified system and to confirm the effectiveness of the techniques that have been implemented.

Corrosion prediction model for long-distance pipelines based on NLFE-NGO-ELM

Abstract To improve the accuracy of buried pipeline corrosion rate prediction, we developed a Northern Goshawk Optimization-based Extreme Learning Machine (NLFE-NGO-ELM) model enhanced by Non-linear Feature Expansion. Feature selection was used to expand the small dataset and reduce the dimensionality of factors affecting pipeline corrosion. The Northern Goshawk algorithm was used, and 106 sets of pipeline external corrosion detection data were simulated in MATLAB as a case study. The ELM optimizer was analyzed using Grey Wolf Optimization (GWO-ELM), Northern Goshawk Optimization (NGO-ELM), and BP optimization as comparison models. Using NLFE-NGO-ELM significantly improved the model's prediction accuracy and speed. The NGO-ELM model was applied to predict the corrosion rates of 21 pipelines, achieving an absolute error of only 2.40% and an R value of 0.97255, surpassing the predictive performance of NGO-BP and GWO-ELM models. These results indicate that the current model exhibits superior learning performance and stronger fitting capabilities.

Carbon Peak Control Strategies and Pathway Selection in Dalian City: A Hybrid Approach with STIRPAT and GA-BP Neural Networks

Mitigating the rate of global warming is imperative to preserve the natural environment upon which humanity relies for survival; greenhouse gas emissions serve as the principal driver of climate change, rendering the promotion of urban carbon peaking and carbon neutrality a crucial initiative for effectively addressing climate change and attaining sustainable development. This study addresses the inherent uncertainties and complexities associated with carbon dioxide emission accounting by undertaking a scenario prediction analysis of peak carbon emissions in Dalian, utilizing the STIRPAT model in conjunction with a GA-BP neural network model optimized through a genetic algorithm. An analysis of the mechanisms underlying the influencing factors of carbon emissions, along with the identification of the carbon emission peak, is conducted based on carbon emission accounting derived from nighttime lighting data. The GA-BP prediction model exhibits significant advantages in addressing the nonlinear and non-stationary characteristics of carbon emissions, attributable to its robust mapping capabilities and probabilistic analysis proficiency. The findings reveal that energy intensity, tertiary industry value, resident population, and GDP are positively correlated with carbon emissions in Dalian, ranked in order of importance. In contrast, population density significantly reduces emissions. The GA-BP model predicts carbon emissions with 99.33% accuracy, confirming its excellent predictive capability. The recommended strategy for Dalian to achieve its carbon peak at the earliest is to adopt a low-carbon scenario, with a forecasted peak of 191.79 million tons by 2033.

Performance evaluation of fuel cell based on a DC-DC boost converter through optimized MPPT controller

The current electric vehicle domain is increasingly focused on fuel cell technologies due to its flexibility, steady supply of power, low atmospheric pollution, increased startups, and rapid responses. Fuel cells exhibit nonlinear power versus current characteristics, making it challenging to extract maximum peak power from the fuel stack. To address this, this work introduces an adaptive Coati Optimization algorithm combined with a Tilt-integral-derivative (TID) controller (TID-ACOA) to find the maximum power point (MPP) of the fuel stack systems, ensuring maximum power extraction. The proposed MPPT controller is compared with other MPPT controller, including PI, TID, and TID-COA. Comprehensive evaluations are conducted on tracking current, voltage, maximum power extraction, MPPT controller efficiency, converter voltage settling time, and oscillations. The fuel stack’s low output voltages are enhanced using a boost DC-DC converter, and the entire fuel stack-fed boost converter systems is modeled using MATLAB/Simulink. Simulation result show that the TID-ACOA MPPT controller achieves higher MPP tracking efficiency compared to conventional controllers.

Evaluating dynamic models for rigid-foldable origami: unveiling intricate bistable dynamics of stacked-Miura-origami structures as a case study.

Recent advances in origami science and engineering have particularly focused on the challenges of dynamics. While research has primarily focused on statics and kinematics, the need for effective and processable dynamic models has become apparent. This paper evaluates various dynamic modelling techniques for rigid-foldable origami, particularly focusing on their ability to capture nonlinear dynamic behaviours. Two primary methods, the lumped mass-spring-damper approach and the energy-based method, are examined using a bistable stacked Miura-origami (SMO) structure as a case study. Through systematic dynamic experiments, we analyse the effectiveness of these models in predicting bistable dynamic responses, including intra- and interwell oscillations, in different loading conditions. Our findings reveal that the energy-based approach, which considers the structure's inertia and utilizes dynamic experimental data for parameter identification, outperforms other models in terms of validity and accuracy. This model effectively predicts the dynamic response types, the rich and complex nonlinear characteristics and the critical frequency where interwell oscillations occur. Despite its relatively increased complexity in model derivation, it maintains computational efficiency and shows promise for broader applications in origami dynamics. By comparing model predictions with experimental results, this study enhances our understanding of origami dynamics and contributes valuable insights for future research and applications. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Data-model driven probability model of branch power flow for distribution networks and its application to analysis of overload and line loss

The fluctuation of highly penetrated distributed generations (DGs) in distribution networks (DNs) increases branch overload risks, which makes the analysis uncertainty of branch power flow more complex. The probability analysis of branch power can grasp the power flow operation characteristics under uncertain conditions, which supports the power flow optimization management and ensures the safe and economic operation of DNs. Therefore, this paper proposes a data-model driven probability analysis method for branch power flow in DNs. An approximate branch power model is first derived to reveal the analytical relationship between branch power and node power. Then, based on the branch power approximation model and the forecasting error, the datasets of branch apparent power are constructed to capture the complex nonlinear characteristics of the power flow. The non-Gaussian distribution characteristics of branch apparent power and line loss are described by the optimal probability fitting method. Finally, the probability level of branch overload is evaluated and the probability distribution of line loss is analyzed. The case studies demonstrate that the branch power approximation model is highly accurate, and the probability distribution of the branch apparent power presents different characteristics. The proposed method can quickly and accurately calculate the branch overload probability level.

Influence of Spiral Stiffeners’ Symmetric and Asymmetric Angles on Nonlinear Vibration Responses of Multilayer FG Cylindrical Shells

This study utilizes a semi-analytical approach to examine the nonlinear dynamic responses of multilayer functionally graded (MFG) cylindrical shells reinforced by FG spiral stiffeners (FGSSs), which may have symmetric or asymmetric angles, under a thermal condition. It is presumed that the temperature is distributed across the thickness direction. The shell includes three layers: an outer ceramic-rich layer, a middle FG layer, and an inner metal-rich layer. By applying classical shell theory (CST), the smeared stiffeners technique, von Kármán equations, and the Galerkin method, the problem of nonlinear vibrations (NVs) has been addressed. Furthermore, the method of multiple scales (MMSs) is applied to investigate the nonlinear vibrational characteristics of the MFG cylindrical shells reinforced by FGSS, particularly focusing on the 1:2:4 internal resonance and the subharmonic resonance of order 1/2. This study finds that FG spiral stiffeners with symmetric or asymmetric angles and ambient temperature significantly affect the vibrational properties of the MFG cylindrical shells reinforced by spiral stiffeners.

Advances in longitudinal equivalent bending stiffness analysis-novel nonlinear characteristics in the assembly process of prefabricated subway stations

The longitudinal bending stiffness of quasi-rectangular prefabricated subway stations plays a great important role in studying their mechanical behavior and conducting safety assessments. To address the issue of immature stress assumptions for existing prefabricated subway stations, three stress assumptions and five bending modes are proposed while considering the coupling effect between axial force and bending moment. The study investigates novel nonlinear characteristics in the longitudinal equivalent bending stiffness and the influencing factors during the assembly of an existing subway station. An effective method for identifying the longitudinal bending modes suitable for the prefabricated subway station is established, the proposed solution has a good agreement with measured longitudinal bending stiffness efficiency. The study demonstrates that the longitudinal bending mode of the prefabricated subway station shifts from "upward convex" to "downward concave" due to the stepwise assembly method. The longitudinal bending stiffness efficiency displays a significant hysteresis curve, eventually stabilizing at approximately 1 %. Upon completion of the monitoring ring assembly, the concrete bears both longitudinal tensile and compressive stress. When assembling 10 rings from the monitoring ring, the longitudinal reinforcing bars bear tensile stress. The longitudinal bending stiffness of the prefabricated subway station exhibits significant time-variable characteristics throughout the assembly process. The research findings can provide effective references for the analysis of longitudinal mechanics and bending performance during the assembly process.

The haze reduction effect in china under the digital economy

Haze pollution is becoming increasingly serious as it endangers human health and pressurizes economic development. This study incorporates the digital economy and haze pollution management into a unified research framework, and uses the panel data of 285 cities in China from 2011 to 2020 to precisely identify the haze reduction effect of the digital economy, governance mechanisms, and the non-linear and spatial spillover characteristics of the haze reduction effect in China. The findings demonstrate that: First, the digital economy can significantly reduce haze pollution, and this conclusion still holds after considering endogeneity and other robustness tests. Second, the digital economy can inhibit haze pollution by promoting industrial upgrading and improving total factor energy efficiency, and there is a chain mechanism of “industrial green transformation → total factor energy efficiency” and “factor market distortion → total factor energy efficiency.” However, the haze reduction mechanism of digital economy is heterogeneous to cities with different levels of economic development. Independent transmission mechanism plays a complete intermediary role in cities with low level of economic development, while it plays a partial intermediary role in cities with high level of economic development. Chain transmission mechanism only has an impact on cities with high level of economic development. Third, there is an evident threshold effect on the digital economy, and its haze reduction effect has N-type non-linear characteristics. Meanwhile, Digital economy has threshold effect on the mechanism of restraining haze pollution through total factor energy efficiency, industrial green transformation and factor market distortion. With the development of total factor energy efficiency, industrial green transformation and the reduction of factor market distortion, the haze reduction effect of digital economy can produce a qualitative leap. Fourth, Haze pollution in the spatial, temporal, and spatial dimensions has spillover and warning effects, and the haze reduction effect of digital economy shows strong positive externalities. Therefore, the digital economy should be actively developed, and industrial green transformation and factor market reform should be promoted to curb haze pollution by promoting industrial upgrading, improving energy efficiency and strengthening regional joint prevention and control mechanisms.

Generating tyre tread designs using a sensory evaluation regression model and a generative model

This study introduces a method for generating tyre tread images that are highly rated in terms of ‘slip resistance’ sensory evaluations. It involves constructing a regression model to predict ‘slip resistance’ sensory evaluations in tyre tread images and subsequently developing an image generation model informed by this regression model. The regression model was developed using a machine learning framework based on ensemble learning and SHapley Additive exPlanations. The model was then used to filter training data for the image generation process, leading to the creation of a tyre tread image generation model aimed at producing images with high ‘slip resistance’ sensory evaluations, using StyleGAN. The proposed method was applied in a case study using real data, and its effectiveness was validated by comparison with a multiple regression analysis approach. The results revealed that more accurate results were achieved with the random forest (RF) regression model than with the multiple regression model due to the RF regression model’s emphasis on non-linear features. Furthermore, a significant difference was observed between the ‘slip resistance’ sensory evaluation values of the images generated by StyleGAN trained with training data screened by the RF regression model and those from the training data.

Hierarchical MPC-based authority allocation strategy for human–machine shared vehicles considering human–machine conflict

The uncertainty of driver behavior is an important factor affecting the safety of human–machine co-driving vehicles. Traditional rule-based models often fail to capture the nonlinear and complex characteristics of human steering behavior. To overcome this, we propose a data network-driven approach utilizing gated recurrent unit (GRU) neural networks to accurately predict driver steering behavior. The GRU-based driver model is integrated with vehicle dynamics to construct a control-oriented driver–vehicle model. Considering that human–machine conflict may cause vehicle instability, an exponential function combining proportional–integral–derivative is proposed to quantify the human–machine conflict level based on steering difference. To reasonably allocate human–computer permissions based on human–machine interaction, a hierarchical authority allocation framework is proposed. The upper layer provides a reference authority allocation via an exponential function, while the lower layer employs a real-time model predictive control (MPC) optimizer to track this reference, ensuring optimal vehicle path tracking and stability. The proposed system’s effectiveness is validated through driver-in-the-loop testing, demonstrating significant improvements in safety and performance. The results show that in the human–machine conflict scenario, the proposed authority allocation strategy can still ensure the path tracking and safety of the vehicle.

Nonlinear Dynamics Research of Ground Undulatory Fin Robot with Flexible Deformation and Frictional Contact.

The unique rigid-flex connection between the fin-rays and fin-surface in a bionic undulatory fin robot endows the fin-surface with both active flexibility and load-bearing capacity, enabling this robot to perform amphibious motions in underwater, terrestrial, and even marshy environments. However, investigations into dynamic modeling problems for the undulatory fin robot, considering the impact of nonlinear deformation and frictional contact on ground locomotion performance, are scarce. Given this, based on the absolute nodal coordinate formulation (ANCF), this paper presents an efficient and accurate nonlinear dynamic model for this robot to elucidate the fin's flexible deformation and motion law. This model considers material, geometric, and boundary nonlinearities, utilizing ANCF thin plate elements and reference nodes to individually describe the fin-surface and fin-rays of the undulatory fin. Then, by using the master-slave technique, a frictional contact formulation for the fin and the ground is proposed. Furthermore, we conduct in-depth research and analysis on the formation and undulatory motion of the undulatory fin, encompassing its static deformation, static contact deformation, and frictional contact motion, and successfully obtain its responses under various conditions. Research indicates that during fin-surface motion, longitudinal sliding or a tendency for sliding at the contact points results in the undulatory fin moving in a crawling gait. The proposed theoretical model correctly captures the fin's complex nonlinear deformations and frictional characteristics and reveals its ground locomotion mechanism, whose effectiveness and superiority are validated through numerical examples and experiments.

Investigation on nonlinear flutter modes competition of a long-span suspension bridge based on full-bridge aeroelastic model tests

Nonlinear flutter has attracted wide attention due to the bottleneck caused by linear flutter theory on flutter-resistant design of super-long-span bridges. The longer the span, the more closely spaced the natural modes, which may cause competition among flutter-modes in a nonlinear flutter, but it is rarely reported so far. To this end, this study experimentally investigates the 3D nonlinear flutter characteristics of a long-span suspension bridge with closely spaced natural modes based on full-bridge aeroelastic model wind tunnel tests. Since there are two unstable flutter-modes within the interested post-critical regime and thus various complex but interesting flutter-modes competition processes were observed, such as continuous modes competition where the vibration amplitude evolution exhibits various different types of “sawtooth” shapes during stable vibration stages. Meanwhile, the complex nonlinear bifurcation behaviors caused by modes competition were also observed. The evolutionary characteristics of flutter-modes competition are analyzed in detail and relevant mechanisms are discussed. As the wind speed increases, the flutter of the studied bridge mainly undergoes a transition from being dominated by the symmetric mode to being dominated by the antisymmetric mode, accompanied by a continuous modes competition zone in between as a transitional zone. The results show that the continuous modes competition will result in a decrease in the maximum amplitude RMS of the full-span, which is beneficial for the structure. But it may also lead to a transient increase in the maximum amplitude of the full-span due to the coupling vibration shape formed by the two significant flutter-modes, which may be bad for the structure.

An experimental insight into a promising novel organic nonlinear optical single crystal Guanidinium 2,4-dichlorobenzoate (G24DCB)

Guanidinium 2,4-dichlorobenzoate (G24DCB), a new chloro substituted benzoic acid based organic single crystal is synthesized, grown and added to the guanidinium family of single crystals. Such G24DCB crystal was obtained by a versatile slow evaporation solution growth technique. The analysis of single crystal X-ray diffraction examined the phase identification and determination of lattice parameters for the synthesized compound. The G24DCB crystal has monoclinic system and adopts space group P21/c. Powder X-ray diffraction explores the studied crystal's crystalline characteristics. The study of Fourier Transform-Infrared (FTIR) spectroscopy examined the necessary vibrational assignments for the formation of the structure of G24DCB. The UV–Visible-NIR analysis entails the determination of the cut-off wavelength of the G24DCB compound from its transmittance spectrum and the computation of other related optical parameter values. Photoluminescence analysis was employed to investigate the studied crystal's emission characteristics. The thermal stability of the G24DCB crystal was examined through thermogravimetric analysis and differential thermal analysis. The laser-induced damage threshold of the crystal was determined using a Nd:YAG laser. The various mechanical attributes exhibited by the synthesized compound were elucidated by microhardness studies and it corresponds to a soft material type. The various third order nonlinear optical characteristics were probed by Z scan study. The positive results of the aforementioned studies suggest the emerging significance possessed by the novel title crystal Guanidinium 2,4-dichlorobenzoate in nonlinear optical applications.

Data-Driven Control Method Based on Koopman Operator for Suspension System of Maglev Train

The suspension system of the Electromagnetic Suspension (EMS) maglev train is crucial for ensuring safe operation. This article focuses on data-driven modeling and control optimization of the suspension system. By the Extended Dynamic Mode Decomposition (EDMD) method based on the Koopman theory, the state and input data of the suspension system are collected to construct a high-dimensional linearized model of the system without detailed parameters of the system, preserving the nonlinear characteristics. With the data-driven model, the LQR controller and Extended State Observer (ESO) are applied to optimize the suspension control. Compared with baseline feedback methods, the optimization control with data-driven modeling reduces the maximum system fluctuation by 75.0% in total. Furthermore, considering the high-speed operating environment and vertical dynamic response of the maglev train, a rolling-update modeling method is proposed to achieve online modeling optimization of the suspension system. The simulation results show that this method reduces the maximum fluctuation amplitude of the suspension system by 40.0% and the vibration acceleration of the vehicle body by 46.8%, achieving significant optimization of the suspension control.

Bionic Walking Control of a Biped Robot Based on CPG Using an Improved Particle Swarm Algorithm

In the domain of bionic walking control for biped robots, optimizing the parameters of the central pattern generator (CPG) presents a formidable challenge due to its high-dimensional and nonlinear characteristics. The traditional particle swarm optimization (PSO) algorithm often converges to local optima, particularly when addressing CPG parameter optimization issues. To address these challenges, one improved particle swarm optimization algorithm aimed at enhancing the stability of the walking control of biped robots was proposed in this paper. The improved PSO algorithm incorporates a spiral function to generate better particles, alongside optimized inertia weight factors and learning factors. Evaluation results between the proposed algorithm and comparative PSO algorithms were provided, focusing on fitness, computational dimensions, convergence rates, and other metrics. The biped robot walking validation simulations, based on CPG control, were implemented through the integration of the V-REP (V4.1.0) and MATLAB (R2022b) platforms. Results demonstrate that compared with the traditional PSO algorithm and chaotic PSO algorithms, the performance of the proposed algorithm is improved by about 45% (two-dimensional model) and 54% (four-dimensional model), particularly excelling in high-dimensional computations. The novel algorithm exhibits a reduced complexity and improved optimization efficiency, thereby offering an effective strategy to enhance the walking stability of biped robots.

Coupled Richtmyer–Meshkov and Kelvin–Helmholtz instability on a shock-accelerated inclined single-mode interface

The coupling of Richtmyer–Meshkov instability (RMI) and Kelvin–Helmholtz instability (KHI), referred to as RM-KHI, on a shock-accelerated inclined single-mode air–SF $_6$ interface is studied through shock-tube experiments, focusing on the evolution of the perturbation distributed along the inclined interface. To clearly capture the linear (overall linear to nonlinear) evolution of RM-KHI, a series of experiments with a weak (relatively strong) incident shock is conducted. For each series of experiments, various $\theta _{i}$ (angle between incident shock and equilibrium position of the initial interface) are considered. The nonlinear flow features manifest earlier and develop faster when $\theta _{i}$ is larger and/or shock is stronger. In addition, the interface with $\theta _{i}>0^{\circ }$ evolves obliquely along its equilibrium position under the effect of KHI. RMI dominates the early-time amplitude evolution regardless of $\theta _{i}$ and shock intensity, which arises from the discrepancy in the evolution laws between RMI and KHI. KHI promotes the post-early-stage amplitude growth and its contribution is related positively to $\theta _{i}$ . An evident exponential-like amplitude evolution behaviour emerges in RM-KHI with a relatively strong shock and large $\theta _{i}$ . The linear model proposed by Mikaelian (Phys. Fluids, vol. 6, 1994, pp. 1943–1945) is valid for RM-KHI within the linear period. In contrast, the adaptive vortex model (Sohn et al., Phys. Rev. E, vol. 82, 2010, p. 046711) can effectively predict both the interface morphology and overall amplitude evolutions from the linear to nonlinear regimes.

A Multifrequency Data Fusion Deep Learning Model for Carbon Price Prediction

ABSTRACTIn response to the global need for effective management of carbon emissions and alignment with sustainable development goals, predicting carbon trading prices accurately is critical. This study introduces a multifrequency data fusion carbon price prediction model (MFF‐CPPM), addressing the nonlinear characteristics of carbon trading prices and inconsistent feature factor frequencies. The MFF‐CPPM consists of a feature‐extraction frontend, a multifrequency data fusion transformer, and a fusion regression layer, offering a novel methodological approach in forecasting studies. The model's validity was tested in Guangdong, China's largest carbon trading pilot market. The results demonstrated that the MFF‐CPPM outperformed baseline models in terms of carbon price‐prediction accuracy and trend forecasting. Additional trials conducted in Hubei and Beijing confirmed the model's robustness and generalization capabilities, providing valuable evidence of its effectiveness and reliability across varying market contexts. This study presents a novel predictive model for carbon trading prices, with a unique capability to harness data at differing frequencies. The MFF‐CPPM not only enhances forecasting accuracy but also offers an innovative approach to effectively incorporate multifrequency information. This advancement paves the way for flexible forecasting models in any scenario where data arrive at differing frequencies.

Nonlinear characteristics in the cylindrical roller bearing with raceway defects

Cylindrical roller bearings (CRBs) are subjected to significant cyclic stress under extreme operating conditions. This leads to the formation of localized wave defects on the raceway surface, such as burn. Thus, a new mathematical model is proposed to consider the local wave defects on the raceway caused by burns in this paper. Further, a dynamic model of CRB incorporating raceway defects is developed based on the contact relationships between components, and the proposed model is verified by measured acceleration responses. The effects of local wave defects on the nonlinear vibration characteristics of the bearings are studied and the results show that an increase in the number of defect waves reduces the additional displacement of rollers passing through the defect area, obscuring signal characteristics induced by the defect. Moreover, the presence of the defect influences the nonlinear interaction between the roller and raceway, which subsequently affects the cage whirling motion. This study of bearing dynamic behavior in this paper can contribute to the condition monitoring of bearings.

Adaptive control for refrigeration via online identification

Vapor compression refrigeration systems (VCRS) occupy a crucial position in modern society and in the field of thermal sciences. However, the operation of VCRS is subjected to both external disturbances (dynamic-changing environment) and inherent system characteristics (coupling or nonlinear features), leading to issues like reduced refrigeration efficiency and significant fluctuations in cooling capacity. To address these challenges and enhance the adaptability of VCRS in dynamically changing environments, this study establishes a dynamic simulation model for VCRS based on the Switched Moving-Boundary method. The impact of external environmental disturbances on refrigeration performance is investigated, and continuous online identification methods are employed to elucidate its internal coupling characteristics and nonlinear features. The adaptive temperature control method is introduced, benefiting from the developed recursive least squares method with a forgetting factor for online identification, achieving precise model identification which facilities the real-time parameters tuning of adaptive controller. The results indicate that the hybrid paradigm of online identification and adaptive control algorithm not only effectively handles various disturbances but also reduces overshoot and IAE by 2-3 orders of magnitude compared to traditional PID controllers. Adaptive PID control maintains overshoot in the 10-4 order of magnitude and IAE in the 10-5 order of magnitude.