Sensitivity Coefficients Research Articles

Preparation and application of a Cu-doped antimony electrode to improve the performance of pH measurement in seawater.

Antimony-based electrodes are widely used in various fields for pH detection due to their low cost. However, their application in the marine environment is significantly hampered by the significant potential drift observed in seawater pH measurements. This study focuses on enhancing the stability of a pure antimony electrode by doping various amounts of copper without compromising its pH response. A series of electrochemical tests demonstrated that the fabricated alloy electrodes exhibited excellent pH response characteristics, including sensitivity, ion selectivity, response time, reversibility, and temperature coefficients. Moreover, the alloy electrodes were more resistant to corrosion than the pure antimony electrode, thereby guaranteeing the stability. Notably, the alloy electrodes containing 63 at% and 70 at% antimony exhibited superior electrochemical characteristics. The surface analysis elucidated that the alloy electrode had reduced oxidation, surface cracks and antimony peeling compared to the pure antimony electrode. Furthermore, the prepared alloy electrodes exhibited excellent pH response and stability in simulated high-salinity seawater and real seawater. The above results highlight that doping cheap copper into antimony can improve the electrode stability by enhancing the corrosion resistance and slowing down the oxidation rate, thus enabling reliable long-time operation in a relatively stable state. These findings provide experimental support for developing novel pH electrodes based on non-noble metals for use in challenging environments such as seawater.

Establishing the hot working window for the forging of S32906 super duplex stainless steel through considering deformation parameter sensitivities

The evaluation of the hot workability of the super duplex stainless steel (SDSS) material still lacks scientific and theoretical basis, leading to the frequent occurrence of unacceptable defects in its forgings. In this study, a novel method for estimating the hot workability of S32906 SDSS was proposed and verified through forging. Firstly, the flow behavior and microstructural characteristics were demonstrated by conducting isothermal compression tests at the deformation temperature from 1000 °C to 1250 °C and the strain rate from 0.01 s−1 to 10 s−1. The influence of microstructure on flow and work hardening behaviors was correlated and displayed. Then, based on the deformation characteristics presented through the variations of strain rate sensitivity (SRS) and deformation temperature sensitivity (DTS) coefficients, the SRS and DTS maps were constructed and overlaid for obtaining the hot working window. Ultimately, a large plate type forging of S32906 SDSS applied in engineering was used to verify the applicability of the obtained window. The new method can provide an in-depth understanding of hot workability and enable control of the forming and microstructural properties for this unique material.

Удосконалення методики оцінки інвестиційної безпеки держави з урахуванням «кругових» інвестицій

The article discusses the features of «round tripping» investments that come to the country in the form of foreign direct investment (FDI), but in its essence is the return of previously withdrawn domestic capital abroad, mainly to offshore jurisdictions. The author suggests that there is a significant impact of «round tripping» investments on the investment security of the State, taking into account the motives of their formation and a significant illegal component, the absence of additional effects from attracting these investments into the economy. It is proposed to supplement the system of indicators of investment security of the State with the indicator «share of «round tripping» investments in the total volume of FDI (excluding reinvested capital)». To find out the directedness of the relationship between this indicator and the country’s economy, a regression analysis based on the data of 2010–2022 was applied. As a result of the analysis, a direct relationship between GDP in actual prices and GDP per capita, as dependent variables, and the share of «round tripping» investments in total FDI as an independent variable, has been identified. The article assesses the level of investment security of Ukraine in 2015–2021 taking into account the share of «round tripping» investments in the total volume of FDI (excluding reinvested income) based on the calculation of the integral indicator. The results of the calculation of the sensitivity coefficients of the integral indicator to changes in indicators testified to the largest impact of «round tripping» investments on the state of investment security of Ukraine in 2021. The carried out study confirmed the expediency of improving the methodology for assessing the investment security of the State by supplementing the system of indicators with the indicator of the share of «round tripping» investments in the total volume of FDI (excluding reinvested income).

A semi-probabilistic approach for assessing material and model uncertainty in the out-of-plane response of URM structures

A procedure tailored for a practical calibration of partial safety factors (PSF) related to input material properties is presented. The methodology addresses the propagation of material and model uncertainty through a FORM-based calibration, resulting in a noteworthy reduction in computation time compared to full probabilistic approaches. The novelty lies on the introduction of the Star Design with Central Point (SDCP) method for the computation of sensitivity coefficients and corresponding partial safety factors for material uncertainty. A calibration example is reported with reference to unreinforced masonry structures under out-of-plane failure. The effect of considering different geometries, failure modes, and modelling approaches is explored. A comparative analysis involving different approaches to propagate uncertainties emphasize the promising potential of the proposed procedure.

A variable future-time-steps method for solving nonlinear unsteady inverse heat conduction problems

In some non-linear unsteady inverse problems, the inverse solution will oscillate violently in the whole time domain due to the sharp change of the sensitivity coefficients. To deal with this problem, a new sequential function specification method with variable future time steps is proposed in this paper. The future time steps are adjusted by the error amplification coefficients which are defined as the reciprocal of the square sum of the sensitivity coefficients. When the error amplification coefficients are small, a small number of future time steps is used to reduce the deterministic error. While in the period with large error amplification coefficient, a large number of future time steps is used to reduce stochastic error. Finally, the total error of estimated heat flux is reduced. Avoid the sharp fluctuation of estimated heat flux in time domain due to the sharp change of sensitivity coefficients. The variable future-time-steps method is applied to the estimation of 1-D non-linear unsteady heat flux without and with ablation through numerical experiments. Numerical experiments show that the proposed method can not only estimate various forms of heat flux, but also its inversion results are significantly better than those of the fixed future time steps method based on the discrepancy principle, and also better than those of the fixed future time step method based on the minimum relative error of heat flux.

Micromechanism and mathematical model of stress sensitivity in tight reservoirs of binary granular medium

Research on reservoir rock stress sensitivity has traditionally focused on unary granular structures, neglecting the binary nature of real reservoirs, especially tight reservoirs. Understanding the stress-sensitive behavior and mathematical characterization of binary granular media remains a challenging task. In this study, we conducted online-NMR experiments to investigate the permeability and porosity evolution as well as stress-sensitive control mechanisms in tight sandy conglomerate samples. The results revealed stress sensitivity coefficients between 0.042 and 0.098 and permeability damage rates ranging from 65.6% to 90.9%, with an average pore compression coefficient of 0.0168–0.0208 MPa−1. Pore-scale compression occurred in three stages: filling, compression, and compaction, with matrix pores playing a dominant role in pore compression. The stress sensitivity of binary granular media was found to be influenced by the support structure and particle properties. High stress sensitivity was associated with small fine particle size, high fines content, high uniformity coefficient of particle size, high plastic deformation, and low Young's modulus. Matrix-supported samples exhibited a high irreversible permeability damage rate (average = 74.2%) and stress sensitivity coefficients (average = 0.089), with pore spaces more slit-like. In contrast, grain-supported samples showed low stress sensitivity coefficients (average = 0.021) at high stress stages. Based on the experiments, we developed a mathematical model for stress sensitivity in binary granular media, considering binary granular properties and nested interactions using Hertz contact deformation and Poiseuille theory. By describing the change in activity content of fines under stress, we characterized the non-stationary state of compressive deformation in the binary granular structure and classified the reservoir into three categories. The model was applied for production prediction using actual data from the Mahu reservoir in China, showing that the energy retention rates of support-dominated, fill-dominated, and matrix-controlled reservoirs should be higher than 70.1%, 88%, and 90.2%, respectively.

Quantifying the Uncertainty of Sensitivity Coefficients Computed From Uncertain Compound Admittance Matrix and Noisy Grid Measurements

Quantifying the Uncertainty of Sensitivity Coefficients Computed From Uncertain Compound Admittance Matrix and Noisy Grid Measurements

A variance-reduction strategy for the sensitivity of βeff

The Monte Carlo computation of the GPT-based sensitivity of the effective delayed neutron fraction βeff to nuclear data proves to be quite difficult to converge due to the small amount of delayed neutrons that are sampled in k-eigenvalue calculations. This paper describes a variance-reduction method aimed at efficiently computing the sensitivity coefficients of βeff, reducing the associated Monte Carlo uncertainty and increasing the Figure Of Merit. This variance-reduction technique allows also computing the sensitivities of βj eff for a specific precursor family j. Verification and performance evaluation are achieved using simple configurations admitting analytical solutions and several continuousenergy benchmarks.

Unraveling Intrinsic Relationships of Thermal Properties in Thermoreflectance Experiments

Thermoreflectance techniques, particularly Frequency-Domain Thermoreflectance (FDTR), play a crucial role in measuring the thermal properties of bulk and thin-film materials. These methods precisely measure thermal conductivity, specific heat capacity, and interfacial thermal conductance by analyzing the temperature-dependent reflectivity changes in materials. However, the complex interplay among parameters presents challenges in data analysis, where single-variable analysis often fails to accurately capture intra-layer and inter-layer interactions. This paper uses FDTR as a case study and systematically explores the relationships between sensitivity coefficients of various parameters through Singular Value Decomposition (SVD). Specifically, the sensitivity matrix <b><i>S</i></b> of the system's parameters is subjected to SVD to identify smaller singular values and their corresponding right singular vectors, which are the basis vectors of the null space of matrix <b><i>S</i></b> . These vectors reveal the relationships among parameter sensitivities, and by contradiction, these relationships reveal the most fundamental combined parameters that determine the thermoreflectance signal. This approach not only clarifies the dependencies among variables but also identifies the maximum number of parameters that can be experimentally extracted, as well as the parameters that must be known beforehand. To demonstrate the practical value of these combined parameters, this study conducts a detailed analysis of FDTR signals from an aluminum/sapphire sample. Unlike traditional FDTR experiments, which typically fit only substrate thermal conductivity and interfacial thermal conductance, our sensitivity analysis reveals that it is possible to simultaneously determine the thermal conductivity of the metal film, substrate thermal conductivity, substrate specific heat capacity, and interfacial thermal conductance. The fitting results are consistent with reference values from the literature and measurements from other thermoreflectance techniques, validating the effectiveness and reliability of our method. This comprehensive analysis not only deepens the understanding of thermoreflectance phenomena but also provides robust support for advancements in thermal characterization technology and material research, showcasing the significant potential of applying SVD in complex multi-parameter systems.

Validation of the Canadian Institute for Health Information Diagnostic Codes for Benign Gynaecologic Surgery

We investigated the validity of the 10th Revision Canadian modification of International Statistical Classification of Disease and Related Health Problems (ICD-10-CA) diagnostic codes for surgery for benign gynaecologic conditions in the Canadian Institute for Health Information Discharge Abstract Database (CIHI-DAD), the main source of routinely collected data in Canada. Reabstracted data from patient charts was compared to ICD-10-CA codes and measures of validity were calculated with 95% confidence intervals.A total of 1068 procedures were identified. More objective, structural diagnoses (fibroids, prolapse) had higher sensitivity and near-perfect Kappa coefficients, while more subjective, symptomatic diagnoses (abnormal uterine bleeding, pelvic pain) had lower sensitivity and moderate-substantial Kappa coefficients. Specificity, positive predictive values, and negative predictive values were generally high for all diagnoses. These findings support the use of CIHI-DAD data for gynaecologic research.

Study of the influence of the structure of rolled iron on its hardness

Problem. The influence of the structure of cast irons on their hardness was studied using multifractal analysis. The spectrum of statistical dimensions of the cast iron microstructure was calculated using the Renyi formula. Materials and methods. The hardness of chromium-nickel cast iron was determined at three points of the sample. Results of experiments. It was found that the pairwise correlation coefficients for predicting hardness by traditional structure characteristics (length, diameter, area) were R2 = 0.73...0.87. When assessing hardness indicators by multifractal characteristics, the correlation coefficients are 0.78...0.88 for the pearlite structure with flake graphite and 0.81...0.93 for the pearlite structure with spherical graphite. The sensitivity coefficients of the hardness indicators of СПХН-43 rolls to the information and correlation dimensions of carbides, as well as to the fractal and statistical D-100 dimensions of flake graphite were determined. The sensitivity of hardness indicators to the fractal and statistical D100 dimensions of carbides and to the fractal and correlation dimensions of flake graphite was determined for СПХНФ-47 rolls. Conclusions. Based on the results obtained, an approach to assessing the hardness of СПХН-43 and СПХНФ-47 rolls was developed, which includes: 1). Determination of the statistical dimension spectrum of the cast iron structure elements. 2). Determination of the sensitivity coefficients of hardness indicators to the spectrum of dimensions of structural elements. 3). Creation of a mathematical model for predicting the hardness of rolls. The considered approach can be interpreted as an alternative method for assessing the quality criteria of cast irons based on the analysis of their structure.

STUDY OF PHASE VOLTAGE AND LOAD SYMMETRATION IN ACTIVE-ADAPTIVE DISTRIBUTION ELECTRIC NETWORKS

Networks of 0.4 kV are characterized by a large unbalance of loads in phases. Current unbalance leads to voltage unbalance and additional losses of electrical energy. As a result, the voltage at the consumer may not meet the quality standards of electrical energy. In addition, due to unbalance, the service life of electrical equipment is reduced. Since the effect of stress balancing significantly depends on the place of balancing loads on the line, the paper proposes to determine the places of balancing loads by solving a multicriteria optimization problem. The paper proposes an objective function that minimizes active power losses and contains the total index of active power losses and indices of voltage unbalance coefficients in the negative and zero sequence.
 
 The purpose of the study is to obtain an effective objective function for determining the places of balancing loads and voltages in the network, which ensures a minimum of active power losses and the values of the voltage unbalance factors within the required limits; conduct a study of balancing loads and voltages depending on the places of balancing.
 
 Materials and methods. In the work, methods for calculating electrical networks were used, taking into account voltage losses and active power. To study the places of balancing loads and voltages, the method of multicriteria optimization with restrictions was used. The study of the objective function was carried out on a mathematical model of a low voltage overhead line. All calculations were carried out in MATLAB.
 
 Research results. A review and analysis of modern tools and methods for balancing loads and voltages in low voltage networks has been carried out. As a result of the analysis, it was concluded that there is no algorithm for determining the places of load balancing in low-voltage networks that provide minimal active power losses and the values of the voltage unbalance factors within the required limits. The task of finding places for balancing loads and voltages is a multiobjective optimization problem with constraints. Therefore, an objective function was proposed that minimizes active power losses in the network and contains the total index of active power losses and indices of voltage unbalance coefficients for the reverse and zero sequence. To study the proposed objective function, a model overhead line of a 0.4 kV network with specified phase loads and voltages was used. For the model line, the calculation of active power losses and the values of the voltage unbalance coefficients in the initial mode before balancing was carried out. All calculations were carried out for each phase separately. At the first stage, the calculation of the sensitivity coefficients of active power losses and the sensitivity coefficients for the voltage unbalance coefficients was carried out. To study the balancing of loads, nodes were selected that have the maximum values of the sensitivity coefficients. It follows from the calculation results that the best effect from balancing is observed when balancing loads simultaneously in two nodes: in the node with the highest value of the total sensitivity factor of active power losses, and in the node with the maximum value of the phase sensitivity factor of active power losses. When balancing loads in only one of the nodes, the most optimal of the selected ones will be the node most remote from the TS. We also obtained weight coefficients that provide a minimum of the objective function.
 
 Conclusions. The proposed objective function is effective for determining the places of load and voltage balancing in low voltage networks. In this case, the best effect is observed when balancing loads in nodes that have the highest values of the sensitivity coefficients of total active power losses and by phases. The node most remote from the TP will be more optimal. When balancing loads in places determined using the proposed objective function, it is possible to reduce power losses and ensure the values of the unbalance coefficients in the nodes on the line less than the maximum allowable value.

Sensitivity Analysis of Upper Limb Musculoskeletal Models During Isometric and Isokinetic Tasks.

Sensitivity coefficients are used to understand how errors in subject-specific musculoskeletal model parameters influence model predictions. Previous sensitivity studies in the lower limb calculated sensitivity using perturbations that do not fully represent the diversity of the population. Hence, the present study performs sensitivity analysis in the upper limb using a large synthetic dataset to capture greater physiological diversity. The large dataset (n = 401 synthetic subjects) was created by adjusting maximum isometric force, optimal fiber length, pennation angle, and bone mass to induce atrophy, hypertrophy, osteoporosis, and osteopetrosis in two upper limb musculoskeletal models. Simulations of three isometric and two isokinetic upper limb tasks were performed using each synthetic subject to predict muscle activations. Sensitivity coefficients were calculated using three different methods (two point, linear regression, and sensitivity functions) to understand how changes in Hill-type parameters influenced predicted muscle activations. The sensitivity coefficient methods were then compared by evaluating how well the coefficients accounted for measurement uncertainty. This was done by using the sensitivity coefficients to predict the range of muscle activations given known errors in measuring musculoskeletal parameters from medical imaging. Sensitivity functions were found to best account for measurement uncertainty. Simulated muscle activations were most sensitive to optimal fiber length and maximum isometric force during upper limb tasks. Importantly, the level of sensitivity was muscle and task dependent. These findings provide a foundation for how large synthetic datasets can be applied to capture physiologically diverse populations and understand how model parameters influence predictions.

Valence electron concentration and ferromagnetism govern precipitation in NiFeGa magnetic shape memory alloys

Precipitation is one of a few effective ways enabling to reduce the brittleness of NiFeGa magnetic shape memory alloys. However, the physical origin behind precipitation and the key factors deciding precipitation remain unknown. There is still a lack of available methods to control the precipitation of NiFeGa. To this end, the precipitation of Ni2FeGa is systemically studied by combining first-principles calculations and experimental examinations from the following four aspects: the stability of the matrix, the crystal structure and stability of precipitates, the key factors dominating precipitation and the strategy of tailoring precipitation. Results show that the L21 matrix phase possesses weak elastic and dynamic stabilities, which may be linked to the occurrence of precipitation. It is identified theoretically and experimentally that the precipitate has L12 rather than the previously reported FCC structure. The underlying mechanism was clarified from electron density of state and chemical bond. Valence electron concentration e/a and magnetism are found to be the dominant factors affecting the relative stability of precipitate against matrix with sensitivity coefficients of ‒175.1 and 67.4 meV, respectively. The increase of e/a prefers stabilizing the precipitate, but the enhanced magnetism favors the matrix. Conversely, the influence of lattice volume on precipitation is weak from the aspects of both sensitivity and adjustable range. Lastly, an effective strategy of tuning precipitation, i.e., by tailoring e/a and magnetism, is proposed and verified. This work is expected to lay a theoretical foundation for tailoring precipitation and further optimizing the mechanical and functional performances of ferromagnetic Heusler alloys.

Evaluation of Neural Network-based Derivatives for Topology Optimization

Abstract Neural networks have gained popularity for modeling complex non-linear relationships. Their computational efficiency has led to their growing adoption in optimization methods, including topology optimization. Recently, there have been several contributions towards improving derivatives of neural network outputs, which can improve their use in gradient-based optimization. However, a comparative study has yet to be conducted on the different derivative methods for the sensitivity of the input features on the neural network outputs. This paper aims to evaluate four derivative methods: analytical neural network's Jacobian, central finite difference method, complex step method, and automatic differentiation. These methods are implemented into density-based and homogenization-based topology optimization using multilayer perceptrons (MLPs). For density-based topology optimization, the MLP approximates Young's modulus for the solid-isotropic-material-with-penalization (SIMP) model. For homogenization-based topology optimization, the MLP approximates the homogenized stiffness tensor of a representative volume element, e.g., square cell microstructure with a rectangular hole. The comparative study is performed by solving two-dimensional topology optimization problems using the sensitivity coefficients from each derivative method. Evaluation includes initial sensitivity coefficients, convergence plots, and the final topologies, compliance, and design variables. The findings demonstrate that neural network-based sensitivity coefficients are sufficient for density-based and homogenization-based topology optimization. The neural network's Jacobian, complex step method, and automatic differentiation produced identical sensitivity coefficients to working precision. The study's open-source code is provided through an included Python repository.

Combined Radiation and Temperature Effects on Brillouin-Based Optical Fiber Sensors

The combined effects of temperature (from −80 °C to +80 °C) and 100 kV X-ray exposure (up to 108 kGy(SiO2)) on the physical properties of Brillouin scattering and losses in three differently doped silica-based optical fibers, with varying dopant type and concentration (4 wt%(Ge), 10 wt%(Ge) and 1 wt%(F)), are experimentally studied in this work. The dependencies of Brillouin Frequency Shifts (BFS), Radiation-Induced Attenuation (RIA) levels, Brillouin gain attenuation, Brillouin frequency temperature (CT) and strain (Cε) sensitivity coefficients are studied under X-rays in a wide temperature range [−80 °C; +80 °C]. Brillouin sensing capabilities are investigated using a Brillouin Optical Time Domain Analyzer (BOTDA), and several properties are reported: (i) similar behavior of the Brillouin gain amplitude decrease with the increase in the RIA; (ii) the F-doped and heavily Ge-doped fibers do not exhibit a temperature dependence under radiation for their responses in Brillouin gain losses. Increasing Ge dopant concentration also reduces the irradiation temperature effect on RIA. In addition, Radiation-Induced Brillouin Frequency Shift (RI-BFS) manifests a slightly different behavior for lower temperatures than RIA, presenting an opportunity for a comprehensive understanding of RI-BFS origins. Related temperature and strain sensors are designed for harsh environments over an extended irradiation temperature range, which is useful for a wide range of applications.

High-integration optical fiber sensor with Vernier effect based on spatial beam splitting

A highly integrated optical fiber sensor is theoretically and experimentally demonstrated, which can realize optical Vernier effect by spatial beam splitting structure. The split parallel beams could be generated by spliced non-equal-diameter hollow-core fibers (NED-HCFs). By optimizing mode-field distribution and self-imaging effect, the fringe visibility (FV) of the Vernier envelope can be enhanced to 5.11 dB. Experimental results show that the central air-waveguide has a high-pressure sensitivity of 43.42 nm/MPa, while the cladding-waveguide presents the immunity of wavelength to external pressure. The measured temperature sensitivity coefficients are −108.2 pm/℃ for Vernier envelope, 11.5 pm/℃ for cladding-waveguide. Therefore, the simultaneous measurement of pressure and temperature can be realized by using the proposed structure based on dual-parameter sensitivity matrix. Meanwhile, the sensor has a fast pressure response of 0.021 s due to the open-cavity microchannel. The proposed sensor provides a new idea for the design of optical fiber structures based on Vernier effect.

Investigations of Nonlinear Optical Properties of Lithium Niobate Crystals

The article is devoted to nonlinear effects in lithium niobate crystals. The possibility of using digital holographic interferograms obtained with the help of laser radiation of different duration at different moments of time for the reconstruction of dynamic phase changes is shown. Holograms were recorded on lithium niobate crystals doped with iron ions in various concentrations using He-Ne and He-Cd lasers, and the diffraction efficiency was calculated. Also, the effect of gamma radiation on the optical properties of LiNbO3 and LiNbO3:Fe crystals was studied. At the same time, it was determined that the band gap of the samples decreases, as a result of which the refractive index, absorption coefficient and photorefractive sensitivity increase several times.

New algorithm for estimating parameters from interrupted thermal response tests of ground heat exchangers

It is a long-standing challenge to determine soil thermal properties from interrupted thermal response tests (TRTs). To meet this challenge, this study develops a new parameter estimation algorithm by integrating three key elements: a short-time model, a derivative-enhanced objective function, and the zero-order Tikhonov regularization strategy. The algorithm is validated to be reliable by a reference sandbox dataset. Whereas interruption reduces the test duration and the number of available test data, it also increases the independence of sensitivity coefficients, thus resulting in high identifiability. To achieve this identifiability, a reliable short-time temperature response model is the prerequisite. Whereas temperature derivatives can boost the temperature data as a set of independent experimental data, regularization is highly necessary to stabilize the iterative solution process by suppressing the influence of the data noise amplified by the temperature derivatives.

Assessing the Sensitivity of the Heat Transfer Coefficient at the Polymer-Calibrator Interface in Profile Extrusion

One of the major challenges in modeling the cooling stage of the thermoplastic profile extrusion process is defining the heat transfer coefficient at the polymer-calibrator interface (hint), which significantly affects the cooling rate. Accurate values for the hint are essential for improving process efficiency using numerical modeling codes. In the existing literature, values of hint are only available for a limited number of cases, and there are no systematic studies regarding the influence of processing conditions on this parameter. This study focuses on the determination of accurate values for hint and on the influence of processing parameters, namely: cooling fluid temperature, pulling velocity, and vacuum pressure. To accomplish this, a previously developed calibrator prototype, and associated methodology, targeting the measurement of hint for thermoplastic materials, is utilized in a conventional profile extrusion line. The results obtained show hint values in the range of 200–1500 W·m−2·K−1, which is in accordance with the results published in the available literature. The results also reveal that the cooling fluid temperature and the pulling velocity have the most substantial influence on hint, while vacuum pressure has minimal impact within the range of the experiments conducted.