Linear Adjustment Research Articles

A new improvement to the characteristic equation method applied to different single-effect LiBr-H2O absorption chillers

The characteristic equation method was developed to be applied to absorption machines using characteristic equations to control and predict the thermodynamic performance of these machines. Since the conventional characteristic equation method was established, different approaches have been taken to improve the accuracy of the results of the characteristic equations. The Dühring parameter (B) represents a linear relationship between the internal boiling temperatures at a given concentration of solution and has usually been adopted as a constant fixed value in the characteristic equation method. The influence of the Dühring parameter (B) on the accuracy of the main results is important to the characteristic equation method and has not been analyzed further. This study analyzed this parameter in the characteristic equation method and a new approach to this method was proposed. This analysis gives a better insight into the influence of this parameter on the characteristic equation method and this approach provides a new use of this method to achieve better thermodynamic prediction and control of absorption chillers of different capacities under different operating conditions. The deviations between the fixed B value usually adopted for the LiBr/H2O solution and each value of the B obtained by the model at different concentrations of solution and internal temperatures affected the accuracy of the main results of the characteristic equations. An approach using a linear adjustment between B and the thrust temperature (Δtthrust) was put forward to reduce these deviations. The results of the characteristic equations were more accurate using this adjustment than using the fixed B value. Then, the characteristic equation method was applied to six LiBr/H2O single-effect absorption chillers using the proposed new approach. This approach was compared with the conventional method and with other main approaches. The heat removed (Q̇E) and COP results from the characteristic equations and the thermodynamic modelling were compared. All the average deviations using the proposed approach were less than 2 %, which represents an improvement in the accuracy of the results of the characteristic equations and gives a better prediction and control of absorption chiller performance. Therefore, the proposed approach contributed to improve the accuracy of the characteristic equation method in order to refine its application to absorption chillers.

Fluorescence microscopic image enhancement method based on multi-saliency guided filtering fusion

Abstract Aiming at addressing the issues of colour deviation and clarity reduction in digital pathological imaging systems caused by complex environmental interferences such as uneven slice thickness, sample jitter, and background noise, this paper proposes a multi-saliency-guided filtering fusion enhancement method that combines energy saliency and Gaussian saliency. Firstly, a series of Gamma correction and spatial linear saturation adjustments are applied to enhance the contrast and colour saturation of blurred images, resulting in a sequence of pseudo-exposure images with improved contrast and saturation. Then, the pseudo-exposure images are decomposed into base and detail layers, and the fusion rules of energy saliency and Gaussian saliency-guided filtering are applied to each layer separately. Finally, clear microscopic images are obtained through two-scale reconstruction. This method overcomes the limitations of conventional deblurring algorithms that rely on prior estimation of scene depth and complex depth mapping processes. Experimental results on a dataset of cytological bright-field microscopic imaging samples show that the clarity evaluation metrics, including peak signal-to-noise ratio, root mean square error, and structural similarity index, have significantly improved, indicating that the proposed method can effectively improve the colour fidelity of the samples while eliminating noise interference and enhancing the clarity of cellular texture structures.

Frequency linearization of voltage controlled oscillator (VCO) for 2 µs frequency modulated continuous wave (FMCW) reflectometer.

Frequency modulated continuous wave reflectometers have been widely used to measure plasma density profiles in many magnetic fusion devices. The frequency modulation (FM) time of the KSTAR reflectometer was 20 µs, that is, the FM rate was 50kHz. However, the edge density of the KSTAR tokamak fluctuates typically over the frequency range of 20-50kHz in the ELMy H-mode plasmas. Therefore, the density profile changes significantly during the FM time, causing significant distortion in the density profile measurements. The FM rate must be increased at least ten times faster than the density fluctuation frequency. A new voltage controlled oscillator (VCO) driver is designed based on the AD8067 operational amplifier to achieve a FM time of 2 µs. The VCO output frequency is linearly modulated by predistorting the tuning voltage of VCO using a 400 MSamples/s arbitrary waveform generator. The resulting output frequency of the VCO is measured by mixing the VCO output with a fixed frequency synthesizer signal and measuring the mixer intermediate frequency using a 2.5 GSamples/s digitizer. The tuning voltage is adjusted to minimize the amount by which the measured frequency deviates from the linearly modulated frequency. A simple linear adjustment proportional to the deviation does not effectively suppress the nonlinearity in FM. The response time of the VCO driver and the VCO input interface should be taken into account by solving the entire circuit equation. In this paper, the developed VCO driver circuit and the frequency linearization method are described.

Tropical Pacific trends explain the discrepancy between observed and modelled rainfall change over the Americas

Understanding the causes for discrepancies between modelled and observed regional climate trends is important for improving present-day climate simulation and reducing uncertainties in future climate projections. Here, we analyse the performance of coupled climate models in reproducing regional precipitation trends during the satellite era. We find statistically significant observed drying in southwestern North America and wetting in the Amazon during the period 1979–2014. Historical climate model simulations do not capture these observed precipitation trends. We trace this discrepancy to the inability of coupled simulations to capture the observed Pacific trade wind intensification over this period. A linear adjustment of free running historical simulations, based on the observed strengthening of the Pacific trade winds and modeled ENSO teleconnections, explains the discrepancy in precipitation trends. Furthermore, both the Pacific trade wind trends and regional precipitation trends are reproduced in climate simulations with prescribed observed sea surface temperatures (SST), underscoring the role of the tropical Pacific SST patterns.

Experimental study of DC excitation effect on the performance of moving coil linear compressor

In this paper, a novel Multi-loop Moving Coil Linear Compressor (M-MC-LC) is studied, in which the piston is driven by the Co-core Bilateral Reverse Coil (CBRC) in a reciprocating motion within the magnetic array. The DC excitation technique is introduced to address the phenomenon that the piston is axially offset under the influence of gas force. In order to clarify the effect of DC excitation on the performance of the moving-coil linear compressor, the compressor prototype is developed, and the dynamic performance testing test-bed and the refrigeration performance test-bed are built to qualitatively and quantitatively analyze the relevant performance parameters of the compressor from theoretical and experimental aspects. The results show that when the DC excitation accounts for less than 20% of the total input voltage, the pressure ratio increases with the increase of DC excitation; when the percentage is at 22.9%, a sudden drop in the volumetric efficiency of compressor occurs. Mass flow and COP increases first and then decreases with the increase of DC voltage excitation. The study results provide a guideline for the stable and reliable operation of the system and provide a valuable reference for the linear compressor piston offset adjustment.

TiN/TiOx/WOx/Pt heterojunction memristor for sensory and neuromorphic computing

The advancement of artificial intelligence (AI) has spurred increasing demands for efficiency, as AI technologies require rapid processing and large-scale data handling to perform complex tasks and enable real-time decision-making. By incorporating biological nociceptor functions, memristors have become instrumental in E-Skin applications, aiding robotics in assessing potential danger. Moreover, in pursuit of energy-efficient data processing, researchers have turned their attention to neuromorphic computing, mimicking the operations of the human brain. In this context, the multifunctional capabilities of individual memristors are pivotal for their utility across diverse conditions. To enhance efficiency, this study investigated the observation of both synaptic and nociceptive behaviors within a heterojunction memristor comprising a TiN/TiOx/WOx/Pt stack. By employing a controlled pulse scheme, advanced sensing capabilities were discovered within our memristor, mimicking key functions of nociceptors such as threshold detection, lack of adaptation, relaxation, and sensitization. Additionally, the processes of potentiation and depression were leveraged to demonstrate the linear adjustment of synaptic weights based on applied pulse schemes, exhibiting various synapse-like behaviors, and enabling advanced computing functions. Consequently, both sensing and computing functionalities of the memristor were achieved using a singular TiN/TiOx/WOx/Pt memristor.

Disentangling Forced Trends in the North Atlantic Jet From Natural Variability Using Deep Learning

AbstractRegional weather variability and extremes over Europe are strongly linked to variations in the North Atlantic jet stream, especially during the winter season. Projections of the evolution of the North Atlantic jet are essential for estimating the regional impacts of climate change. Therefore, separating forced trends in the North Atlantic jet from its natural variability is an extremely relevant task. Here, a deep learning based method, the Latent Linear Adjustment Autoencoder (LLAE), is used for this purpose on an ensemble of fully‐coupled climate simulations. The LLAE is based on a variational autoencoder and an additional linear component. The model uses detrended temperature and geopotential to predict the component of the zonal wind associated with natural variability. The residual between this prediction and the original wind field is interpreted as the forced component of the jet. The method is first tested for the geostrophic wind for which the forced trend can be obtained analytically from the difference between geostrophic wind computed from detrended and full geopotential. Despite the large variability of the total trends, the LLAE is shown to be effective in extracting the forced component of the trend for each individual ensemble member in both geostrophic and full wind fields. The LLAE‐derived forced trend shows an increase in the upper‐level zonal wind speed along a southwest–northeast oriented band over the ocean and a jet extension toward Europe. These are common characteristics over different periods and show some similarities to the upper‐level zonal wind speed trend obtained from the ERA5 reanalysis.

Soil carbon storage under different types of arid land use in Algeria

This study aims to assess the amount of organic carbon stored in soils, as it is an intention of knowing the sustainable soil management, by using two common methods for determining soil organic matter (SOM), namely oxidation with acidified wet dichromate (Walkley–Black method-WB) and loss on ignition (LOI). The study was carried with soil samples collected from a depth of 0 to 30 cm in the Saharan arid region of Ghardaïa (Algeria), with different land uses: agricultural, forest and pastoral. The results obtained from the LOI and WB methods were subjected to statistical analysis, and the relations between both methods were tested to investigate their relationship. The mean percentage of SOM values were 1.86, 2.42, 1.54 by using LOI, but, lower values of 0.34, 0.33, 0.36 were determined by using WB method, for agricultural, forest and pastoral soils respectively. A weak linear relationship between the two analytical procedures was obtained (R2 of 0.19 and 0.13 for agricultural and forest soils), while a medium relationship (R2 = 0.65) was found for pastoral soils when using linear adjustment. However, the opposite behaviour was found when we use the logarithmic adjustment. The study outcomes indicated discrepancies in the measurements of SOM values between the two methods, been higher those estimated with LOI. Finally, in order to identify the best methodology to measure soil organic matter in arid soils, more research is required in these extreme arid regions as they are a gap in world soil organic matter maps.

Addressing multi-attribute large-scale group decision making with overlapping subgroups: A bidirectional adjustment consensus reaching method for heterogeneous decision makers

Due to the rapid development of internet technology, multi-attribute large-scale group decision making (MALSGDM) becomes a research hotspot of multi-attribute group decision making. An interesting phenomenon is that decision makers (DMs) may assume multiple roles across various interest groups, thereby naturally forming overlapping subgroups. Aiming at the MALSGDM problem with overlapping subgroups, this paper proposes an overlapping subgroup-based consensus reaching method considering heterogeneous DMs. Firstly, a novel overlapping clustering method is proposed to decompose the large-scale group into several overlapping subgroups characterized by low evaluation conflict and stable trust relationship, thereby identify ordinary and key DMs. Secondly, a two-criteria consensus reaching judgment method is devised as the termination condition for the consensus reaching process. Thirdly, a novel bidirectional adjustment method considering heterogeneous DMs is constructed, which focuses on key DMs belonging to multiple subgroups simultaneously. The adjusted evaluation values are obtained through linear uncertain minimum adjustment consensus models under two different cases. Finally, a numerical example is provided to demonstrate the feasibility of the proposed method, and the comparative and sensitivity analyses are carried out to verify the superiority of the proposed method.

Atrial fibrillation is perpetuated by human heart secretome in ex-vivo langendorff-perfused hearts

Abstract Introduction Atrial fibrillation (AF) confers high morbidity and mortality, yet parts of the underlying pathophysiology remain elusive. Left atrial (LA) pressure is altered by the presence of AF and vice-versa. The cardiac secretome might be influenced by LA pressure and potentially alters the susceptibility of the atria to AF. We investigated the effect of the human cardiac secretome on atrial electrophysiology in a translational ex-vivo setting. Methods We obtained venous (coronary sinus) serum samples during AF and in sinus rhythm (SR) in patients hospitalized for pulmonary vein isolation (PVI). Moreover, LA tissue was collected from patients undergoing cardiac surgery and coronary sinus serum samples were collected before (CTRL) and after intraoperative volume challenge (VC). Single cardiomyocytes were isolated from human LA tissue and Ca2+ dependent excitation-contraction coupling (ECC) was studied using confocal line-scan imaging with CTRL or VC. Moreover, a modified Langendorff-Setup with the ability to monitor and control intra-cardiac pressure was utilized to perfuse mouse hearts with AF and SR serum. A multielectrode array (MEA) was placed on the epicardial aspect of the left atrium to measure electrical signals in a spatiotemporal fashion. External bipolar burst pacing protocols were applied to test AF inducibility. Results Ca2+ dependent ECC (i.e. Ca2+ amplitude and release) in human cardiomyocytes was unaltered with exposure to VC serum. Upon introducing a modified version of the Langendorff setup with the ability of linear pressure adjustment, a burst pacing protocol to test for AF inducibility was successfully implemented in mice atria. Atria perfused with human AF serum showed significantly increased AF inducibility as compared to SR serum. Moreover, both, total AF duration as well as number of AF episodes (i.e. AF burden) were increased in AF vs. SR serum upon several different pacing protocols. Conclusion Cardiac secretome during increased LA pressure had no significant effect on Ca2+ dependent ECC in human cardiomyocytes. However, secretome during AF conferred pro-arrhythmogenic properties as compared to SR, further strengthening the concept of "AF begets AF". Ongoing experiments test the hypothesis of potential differences in the multi-level omics profile of AF serum as the underlying mechanism.

FABRICATION AND ANALYSIS OF AUTOMATIC LINEAR DISTANCE ADJUSTER

The Automatic linear distance adjustment system tailored for robotics arms, capitalizing on ultrasonic sensor technology. The system's design, implementation, and evaluation are comprehensively explored, highlighting its ability to facilitate precise and autonomous adjustments of linear positions within the robotic arm's operational envelope. Real-time feedback mechanisms are integrated, enabling dynamic regulation of the distance between the end-effector and target objects or surfaces. This ensures optimal positioning and operational efficiency during various tasks such as pick-and-place operations, assembly processes, and object manipulation. By reducing reliance on manual adjustments, the system enhances automation and augments robotics arms' capabilities across diverse industrial and research applications. The seamless integration of the proposed system empowers robotics arms with heightened flexibility, accuracy, and adaptability, thereby fostering advancements in robotic automation and control. This innovation holds promise for streamlining manufacturing processes, enhancing productivity, and facilitating intricate tasks that demand precision and efficiency in robotic operations. Through rigorous evaluation and validation, the system demonstrates its potential to revolutionize robotic arm functionalities and pave the way for future developments in automation technologies Keywords: Arduino Uno , Ultrasonic sensor,Stepper Motor, Linear guide rail .

A simple, accurate, and explicit form of the Green–Ampt model to estimate infiltration, sorptivity, and hydraulic conductivity

AbstractFinding an explicit solution to the widely used Green–Ampt (G–A) one‐dimensional infiltration model has been subject of efforts for more than half a century. We derived an explicit semiempirical approach that combines accuracy with simplicity, a concept that has been generally neglected in previous studies. The equation is , with F (L), Ks (L/T), S (L/T0.5) and t (T) being cumulative infiltration, saturated hydraulic conductivity, sorptivity, and time, respectively. Relative errors (ɛ) by the application of this equation generally do not exceed ±0.3% in most applied infiltration problems faced by water resources engineering today. We show both numerically and mathematically that │ɛ│> 0.3% could only occur if Kst/F > 0.904, a criterion that could apply to sand and loamy sand soils (i.e., coarse texture) and if they experience infiltration rates for over 6 h and 19 h, respectively. Hence, we also derived a simple linear adjustment in the model as Fadj ≅ 0.9796 F + 0.335 S2/Ks to address these longer infiltration rates, and to assure that ɛ remains within the expected ±0.3% range of uncertainty. A linearized regression technique was also developed to accurately estimate S and Ks when the G–A model is used. We numerically demonstrated that our fitting method could be used even when the G–A approach is less valid (diffusive soils), provided that the actual value of the capillary length (λ) is initially known. An added benefit of our approach is that by setting λ equal to 1/3 and 2/3, it can significantly limit the range of initializing, unknown, a priori values of S and Ks, as these two parameters are estimated through the inverse solution of implicit infiltration models. Due to the model's simplicity and accuracy, our solution should find application among hydrologists, natural resource scientists, and engineers who wish to easily derive accurate estimations from the G–A infiltration approach and/or estimate sorptivity and hydraulic conductivity without encountering divergence problems.

Covariate adjustment in experiments with matched pairs

This paper studies inference for the average treatment effect (ATE) in experiments in which treatment status is determined according to “matched pairs” and it is additionally desired to adjust for observed, baseline covariates to gain further precision. By a “matched pairs” design, we mean that units are sampled i.i.d. from the population of interest, paired according to observed, baseline covariates, and finally, within each pair, one unit is selected at random for treatment. Importantly, we presume that not all observed, baseline covariates are used in determining treatment assignment. We study a broad class of estimators based on a “doubly robust” moment condition that permits us to study estimators with both finite-dimensional and high-dimensional forms of covariate adjustment. We find that estimators with finite-dimensional, linear adjustments need not lead to improvements in precision relative to the unadjusted difference-in-means estimator. This phenomenon persists even if the adjustments interact with treatment; in fact, doing so leads to no changes in precision. However, gains in precision can be ensured by including fixed effects for each of the pairs. Indeed, we show that this adjustment leads to the minimum asymptotic variance of the corresponding ATE estimator among all finite-dimensional, linear adjustments. We additionally study an estimator with a regularized adjustment, which can accommodate high-dimensional covariates. We show that this estimator leads to improvements in precision relative to the unadjusted difference-in-means estimator and also provides conditions under which it leads to the “optimal” nonparametric, covariate adjustment. A simulation study confirms the practical relevance of our theoretical analysis, and the methods are employed to reanalyze data from an experiment using a “matched pairs” design to study the effect of macroinsurance on microenterprise.

Automatic Extraction of Martian Subsurface Layer from Radargrams Based on PDE Denoising and KL Filter

The polar regions of Mars, including the South and North Poles, are crucial for studying Martian climate and geological history, as they contain the largest reservoir of subsurface water ice. This study introduces a new approach for reflector detection, which includes radargram denoising to effectively enhance the signal of underground reflectors, peak detection to extract the positions of subsurface stratification from the radar echoes, and peak points connection to form continuous layers. The mapped enhancement denoising process involves a linear brightness adjustment and a fourth-order diffusion equation to enhance the signal of the subsurface layers for effective detection. The subsurface detection extracts the surface and subsurface peak points based on a peak detection algorithm, while using locally window-enhanced peak filtering and Kullback–Leibler (KL) divergence mapping to filter out non-stratified peak points. Finally, the layered connection process uses the proximity parameter to connect peak points in the same layer. Applied to multiple SHARAD (Shallow Radar) images at the Martian poles, this algorithm demonstrated a false detection rate below 5%. Compared to other methods, this method has a missed detection rate of less than 5% and, additionally, exhibits fewer discontinuities in layer connectivity. Therefore, this algorithm shows exceptional proficiency and applicability in analyzing the complex subsurface structures of the Martian polar regions.

Kinematic Analysis and Simulation of a Linear Adjustment Pipe Reproduction Robot

Kinematic Analysis and Simulation of a Linear Adjustment Pipe Reproduction Robot

Improving Estimation Efficiency via Regression-Adjustment in Covariate-Adaptive Randomizations with Imperfect Compliance

Abstract We investigate how to improve efficiency using regression adjustments with covariates in covariate-adaptive randomizations (CARs) with imperfect subject compliance. Our regression-adjusted estimators, which are based on the doubly robust moment for local average treatment effects, are consistent and asymptotically normal even with heterogeneous probabilities of assignment and misspecified regression adjustments. We propose an optimal but potentially misspecified linear adjustment and its further improvement via a nonlinear adjustment, both of which lead to more efficient estimators than the one without adjustments. We also provide conditions for nonparametric and regularized adjustments to achieve the semiparametric efficiency bound under CARs.

Using low-cost air quality sensors to estimate wildfire smoke infiltration into childcare facilities in British Columbia, Canada

The health risks associated with wildfires are expected to increase due to climate change. Children are susceptible to wildfire smoke, but little is known about indoor smoke exposure at childcare facilities. The objective of this analysis was to estimate the effects of outdoor PM2.5 and wildfire smoke episodes on indoor PM2.5 at childcare facilities across British Columbia, Canada. We installed low-cost air-quality sensors inside and outside 45 childcare facilities and focused our analysis on operational hours (Monday–Friday, 08:00–18:00) during the 2022 wildfire season (01 August–31 October). Using random-slope random-intercept linear mixed effects regression, we estimated the overall and facility-specific effects of outdoor PM2.5 on indoor PM2.5, while accounting for covariates. We examined how wildfire smoke affected this relationship by separately analyzing days with and without wildfire smoke. Average indoor PM2.5 increased by 235% on wildfire days across facilities. There was a positive relationship between outdoor and indoor PM2.5 that was not strongly influenced by linear adjustment for meteorological and area-based socio-economic factors. A 1.0 μg m−3 increase in outdoor PM2.5 was associated with a 0.55 μg m−3 [95% CI: 0.47, 0.63] increase indoors on non-wildfire smoke days and 0.51 μg m−3 [95% CI: 0.44, 0.58] on wildfire-smoke days. Facility-specific regression coefficients of the effect of outdoor PM2.5 on indoor PM2.5 was variable between facilities on wildfire (0.18–0.79 μg m−3) and non-wildfire days (0.11–1.03 μg m−3). Indoor PM2.5 responded almost immediately to increased outdoor PM2.5 concentrations. Across facilities, 89% and 93% of the total PM2.5 infiltration over 60 min occurred within the first 10 min following an increase in outdoor PM2.5 on non-wildfire and wildfire days, respectively. We found that indoor PM2.5 in childcare facilities increased with outdoor PM2.5. This effect varied between facilities and between wildfire-smoke and non-wildfire smoke days. These findings highlight the importance of air quality monitoring at childcare facilities for informed decision-making.

Study of adsorption of Congo red on ferric oxide@straw magnetic composites

In this paper, citric acid-modified corn stalk and Fe3O4 were used to make magnetic straw adsorbent to realize rapid separation of adsorbent and wastewater. The influences of pH, dosage, reaction time, and initial stress on the Congo red adsorption rate were investigated. Then, we used adsorption kinetics and isothermal linear adsorption adjustment to explore the adsorption mechanism. Studies have shown the increasing doses of magnetic adsorbents on straw. When the dose was 8 g/L, the commercial adsorption rate was 95%. The adsorption process of magnetic straw adsorbent for Congo red was exothermic. Adsorption was mainly chemisorption, and the adsorption process was relatively fast, reaching adsorption equilibrium after about 90 min.

Mobile robot path planning based on bi-population particle swarm optimization with random perturbation strategy

Path planning for mobile robots poses a challenging optimization problem, requiring the discovery of a near-optimal path within diverse constraints. Conventional particle swarm optimization (PSO) algorithms encounter limitations in solving constrained problems, vulnerability to local optima, and premature convergence. To address these challenges, this paper proposes a bi-population PSO algorithm with a random perturbation strategy (BPPSO), which divides particles into two subpopulations. The first subpopulation enhances global search capabilities by considering the quality of particles and the optimal solution of a randomly selected particle when updating velocities. The second subpopulation strengthens local search using a linear cognitive coefficient adjustment strategy. Moreover, a counter tracks iteration without improvement in the global best position. Upon reaching a predefined threshold, random perturbation is added to the positions of all particles in both subpopulations, increasing diversity and enhancing the ability to escape local optima. The performance of BPPSO was experimentally validated across three benchmark functions and four environment models. The results have demonstrated that the proposed BPPSO outperforms existing PSO algorithms and other established path planning algorithms in terms of path quality and running time, highlighting the feasibility of BPPSO in resolving the challenge of mobile robot path planning.

Comparative dynamics analysis of the environmental policy efficacy in a nonlinear Cournot duopoly with differentiated goods and emission charges

The price and the exchanged quantity volatility observed in real-world markets may be explained, according to the existing empirical literature, in terms of the endogenous fluctuations generated by the presence of nonlinearities. We then replace with a sigmoid adaptive best response mechanism the linear partial adjustment best response rule considered in Mamada and Perrings (2020), where the effect produced by quadratic emission charges on the dynamics of a Cournot duopoly model with homogeneous goods was investigated. Moreover, the sigmoid nonlinearity, in addition to being well suited to describe the bounded output variations caused by physical, historical and institutional constraints, makes the model able to generate interesting, non-divergent dynamic outcomes, despite the linearity of the demand function and of marginal costs. Additionally, following the suggestion in Mamada and Perrings (2020), we deal with the more general case of differentiated products. Beyond analytically studying the stability of the unique steady state, coinciding with the Nash equilibrium, and the effect produced by the main parameters on the stability region, we perform two comparative dynamics investigations which allow to evaluate the environmental policy efficacy when the Nash equilibrium is not stable and thus the standard comparative statics technique does not fit for the purpose. In particular, the former analysis, which is based on a comparison of emissions for different levels of charges, shows that, also in case the Nash equilibrium is not stable, the considered environmental policy may be effective both with complements and with substitutes. The latter investigation, consisting in a comparison of emissions along non-stationary trajectories and along the equilibrium path, in the proposed experiments highlights that emissions are larger along non-stationary trajectories. This gives us the opportunity to show how to act on the level of the asymptotes of the sigmoid adjustment mechanism to reduce output variations, reaching at one time a complete stabilization of the system and limiting pollution.