Energy Input Research Articles

Structure Design and Optimization of MRE Vibration Isolator

As an intelligent component, the high-performance MRE vibration isolator has great advantages, such as a wide vibration isolation frequency range and good performance in semi-active vibration reduction applications. In order to develop high-performance MRE devices, Firstly, this paper makes use of the advantages of real-time tracking/away from external excitation frequency of MRE devices, analyzes the working mode of MRE, and designs a shear MRE vibration isolator based on airborne equipment. Secondly, the material selection and magnetic circuit analysis of the MRE are also completed, and the magnetic field in the MRE region is maximized under the same input energy, thus improving the working efficiency of the MRE isolator. Finally, the relationship between magnetic induction intensity and structural size variables is established by the finite element method and the structural dimensionless method. Based on COMSOL multi-physics simulation software (version 6.0), the global optimization is carried out, the results show that the optimal solution satisfying the comprehensive index of optimal vibration isolation performance of the MRE isolator is obtained, then the structural parameters of the isolator are optimized, and its magnetic control performance is improved. The MRE vibration isolator designed in this paper meets the vibration isolation requirements of airborne optical equipment and has certain engineering application value.

Process parameter optimization in polymer powder bed fusion of final part properties in polyphenylene sulfide through design of experiments

AbstractThe Additive Manufacturing (AM) modality of Laser-Based Powder Bed Fusion of Polymers (PBF-LB/P) is an established method for manufacturing semi-crystalline polymers. Like other AM processes, the selection of PBF-LB/P process parameters is critical as it has direct effect on final part properties. While prior research has been predominantly focused on polyamides (e.g., nylon 12), there exists a gap in exploring how process parameters affect higher performance polymers, such as polyphenylene sulfide (PPS). This work aims to explore the effects of PBF-LB/P process parameters on PPS parts printed via PBF-LB/P. While prior PBF-LB/P parameter research primarily relies on evaluating energy input to the system through a single numerical value of energy density, this study investigates the interplay of the print parameters within the energy density equation. To achieve these goals, an analysis was performed on the influence of the laser power, hatch spacing, and beam velocity on ultimate tensile strength (UTS), modulus, and crystallinity of printed parts. A Taguchi L8 array was used in balancing the print parameter combinations allowing for isolation of variance to the specific factors and interactions. Through this approach, print parameter combinations that improved UTS and modulus were identified. Additionally, the study revealed that numerically equivalent energy densities did not lead to equivalent performance, underscoring the significance for including the constitutive process parameters within the energy density equation when establishing process property relationships in printing with PBF-LB/P.

Enhancing the efficiency of solar-powered water distillation units by utilization of waste heat

ABSTRACT Thermal water desalination is based on the evaporation and condensation of water, and such a process consumes a lot of energy, which lowers the economy of the process for commercial water desalination. The objective of this research is to improve the desalination energy efficiency of a novel domestic water desalination unit, which is based on thermal desalination, and this is done via utilization of the waste heat in the generated steam and reducing the operating costs. The distillation process begins with solar-powered evaporation of the salty water in the evaporator, followed by condensation of the generated water vapor coming from the evaporator over the cross-flow heat exchangers located in the condenser, which preheats the incoming saline water from the saltwater tank before it enters the evaporator. To assess the system's performance, comprehensive measurements are taken, including the electrical energy output from the PV panels and the volume of the output distilled water. Notably, the energy efficiency of the distillation is defined as the ratio of the heat energy gained by the distilled water, i.e. collected at the end of the day, to the electrical energy input to the electric heater, and it is found to be, on average, 82%.

Low Evaporation Enthalpy Ionic Covalent Organic Frameworks for Efficient Atmospheric Water Harvesting at Low Humidity

Herein, we introduce a series of ionic covalent organic frameworks (iCOFs) with a focus on addressing the challenge of water collection at low relative humidity levels below 25%. These iCOFs are characterized by numerous hydrophilic sites and high water stability, enabling efficient water vapor adsorption even at relatively low humidity levels. Through the use of various hygroscopic salt cations and precise control of ion concentration within the pores, the water state within the iCOFs pores can be effectively managed. Among the iCOFs, TB‐COF‐Li stands out with an impressive adsorption capacity of 0.24 g g‐1 from 0 to 22% RH. Notably, due to its ionic porous structure, TB‐COF‐Li exhibits a significantly lower enthalpy of evaporation, measured at 967.04 J g‐1, compared to bulk water with an enthalpy of 2387.4 J g‐1. Moreover, under simulated conditions of 1.5 solar intensity at 60 °C, the majority of the adsorbed water can be rapidly desorbed without the need for additional energy input. This efficient desorption process contributes to a high water collection rate of 0.092 g g‐1 h‐1 in the final atmospheric water harvesting device. The development of these iCOFs offers a promising and cost‐effective solution for obtaining fresh water in arid regions.

Assessing the Spurious Impacts of Ice-Constraining Methods on the Climate Response to Sea Ice Loss Using an Idealized Aquaplanet GCM

Abstract Coupled climate model simulations designed to isolate the effects of Arctic sea ice loss often apply artificial heating, either directly to the ice or through modification of the surface albedo, to constrain sea ice in the absence of other forcings. Recent work has shown that this approach may lead to an overestimation of the climate response to sea ice loss. In this study, we assess the spurious impacts of ice-constraining methods on the climate of an idealized aquaplanet general circulation model (GCM) with thermodynamic sea ice. The true effect of sea ice loss in this model is isolated by inducing ice loss through reduction of the freezing point of water, which does not require additional energy input. We compare the results of freezing point modification experiments with experiments where sea ice loss is induced using traditional ice-constraining methods and confirm the result of previous work that traditional methods induce spurious additional warming. Furthermore, additional warming leads to an overestimation of the circulation response to sea ice loss, which involves a weakening of the zonal wind and storm-track activity in midlatitudes. Our results suggest that coupled model simulations with constrained sea ice should be treated with caution, especially in boreal summer, where the true effect of sea ice loss is weakest, but we find the largest spurious response. Given that our results may be sensitive to the simplicity of the model we use, we suggest that devising methods to quantify the spurious effects of ice-constraining methods in more sophisticated models should be an urgent priority for future work. Significance Statement The potential effects of Arctic sea ice loss on midlatitude weather have been investigated using climate models where sea ice loss is artificially induced, without increasing greenhouse gas concentrations. Recently, this approach has been challenged because the artificial heating used to melt sea ice may also have direct effects on climate, which are not caused by sea ice loss. We run simulations with a simplified climate model that allows us to separate the “spurious” direct effects of the artificial heating from the “true” effect of sea ice loss. In our simulations, the responses of temperature and atmospheric circulation are amplified by spurious effects. Consequently, we argue that previous studies using more complex climate models may overestimate the effect of sea ice loss on climate.

Study of Friction Stir Welding effects on the Microstructure & Mechanical Properties of AA3003 Pipes

Abstract In the present study, similar Aluminum (AA3003) alloy pipes with a thickness of 5 mm were friction stir welded using a high-speed steel (HSS) tool with a cylindrical pin profile. Welding was done at three different rotational speeds and three traverse speeds corresponding to pipes of three different diameters. Six combinations of rotational speed and traverse speed were used to observe the effect of energy input on the properties, specifically tensile strength and microhardness, as well as grain size of the resulting microstructure. This systematic variation in welding parameters was designed to assess how changes in energy input influence both the mechanical performance and microstructural attributes of the welded joints. The tensile test results indicated that an ultimate tensile strength (UTS) of 84% relative to the base metal was achieved at a rotational speed of 900 rotations per minute(rpm) and a traverse speed of 131.94 mm/min. The impact energy corresponding to these parameters was found to be 38% more than base metal which is a remarkable contribution. This combination of welding parameters facilitated optimal material flow and bonding, resulting in improved tensile properties of the welded joint. Additionally, the tensile results showed a consistent pattern in the tensile failure of the welded samples, where the joint failure occurred at the location with the lowest hardness in the welded region. This correlation highlights the critical influence of hardness distribution on the structural integrity of the welds, indicating that areas with reduced hardness are more prone to failure under tensile loading of FSWed joints.

Analysis of water–energy–carbon coupling and influencing factors in food production

ABSTRACT Water, energy, and carbon are important factors that determine crop production efficiency. This paper applies the footprint theory to calculate the water, energy, and carbon footprint of food crops in Sichuan Province from 2011 to 2020, evaluates water–energy–carbon interactions and closeness, and employs path analysis to analyse factors influencing the coupling degree and the coupling coordination degree. The results indicate that (1) the annual average green water footprint (WF) exceeds the combined contribution of blue and grey WFs, accounting for 54.69% of the total. Energy inputs and carbon emissions (CEs) increased by 15.3 and 0.23%, respectively. (2) Food production from 2011 to 2020 is at a relatively high coupling stage, as indicated by the average coupling degree of 0.88; however, the average coupling coordination degree is only 0.37, explaining a mild incoordination. (3) The rural Engel's coefficient and average temperature are the largest contributing and inhibiting factors affecting the coupling degree; the agricultural economic level and agricultural planting structure are the largest contributing and inhibiting factors affecting the coupling coordination degree. This study can provide reference for reducing water and energy consumption and CEs as a response to resource scarcity and climate change.

Bio‐Mass Radiative Cooling Materials: Progress and Prospects

AbstractRadiative cooling (RC) is a passive cooling technology that leverages infrared radiation to reduce temperatures without external energy input, presenting a crucial approach to mitigating global warming and lowering energy consumption. Biomass‐based RC materials, known for their environmental sustainability and abundance, offer a promising alternative for RC applications. This review outlines the fundamental principles of radiative cooling and examines recent advancements in biomass‐based RC materials, such as natural wood, cellulose, chitosan, silk, and bioplastics. Furthermore, it highlights key challenges and explores future development prospects in this field.

Synthesis and characterization of Fe3O4@TiO2@Zeolite nanocomposite adsorbent for the removal of Levoflaxin antibiotic from environmental water matrices

AbstractThe presence of pharmaceuticals in water matrices has been a major problem because of its expected adverse consequences on oceanic biological systems and human well-being. Levofloxacin (Levo), a persistent and widely used antibiotic, has emerged as a significant pollutant in water samples. Its resistance to conventional water treatment processes poses challenges for its removal. This work focuses on preparing and characterizing a magnetic nanocomposite adsorbent (Fe3O4@TiO2@Zeolite) designed to efficiently remove levofloxacin from the water samples, leveraging the Fe₃O₄ properties for easy separation and recovery of the adsorbent, TiO2 for its adsorption capacity, while zeolite’s porous structure and high ion-exchange capacity improve adsorption efficiency. Together, these materials create a robust, multifunctional composite with promising applications for pollutant removal from aqueous environments. The adsorption of Levo antibiotic exhibited excellent fitting to both the pseudo-second-order model (R2 = 1) and the Langmuir isotherm (R2 = 0.9240) together with the Freundlich isotherm (R2 = 0.999). Furthermore, the thermodynamic analysis indicated that the adsorption process of Levo was spontaneous and endothermic. This implies that the interaction between Levo and the Fe3O4@TiO2@Zeolite nanocomposite, developed in this study, is favourable and requires energy input. The Fe3O4@TiO2@Zeolite nanocomposite demonstrated a promising efficacy in the removal of Levo from wastewater samples, with removal percentage ranging between 92.43 and 96.95%. The prepared Fe3O4@TiO2@Zeolite composite material could be regenerated up to the 5th cycle. This highlights the potential of the nanocomposite as an effective remedy for the purification of wastewater contaminated with Levo.

Ultrasound Assisted Hybrid Technologies for Extraction of Bioactive Compounds

The sustainable and efficient extraction of bioactive compounds from natural resources offers a promising alternative to synthetic additives and formulations. These compounds including polyphenols, flavonoids and polysaccharides possess antioxidant, antimicrobial and many therapeutic effects rendering them highly demandable by various industries. Conventional extraction methods often exhibit drawbacks such as high energy consumption, excessive solvent usage, prolonged processing times, low extraction yields, and negative environmental impacts. To address these limitations, innovative extraction technologies have emerged, providing more sustainable and efficient solutions. Ultrasound is a promising technology used for extraction of these beneficial compounds with enhanced yield and quality. It can assist various other extraction technologies including microwave assisted extraction, ohmic heating, enzyme extraction, subcritical water extraction and supercritical fluid extraction to obtain high quality extracts. The cavitation and the resulted effects of ultrasound facilitated the cell wall rupture enhancing the mass transfer making the cell structure more accessible by the other extraction technologies for the efficient extraction. This synergistic approach of ultrasound and other mentioned extraction technologies results in increased extraction yields and improved product quality by reducing extraction time, minimizing solvent consumption, and utilizing moderate energy inputs.

Assessment of the Effects of Intake Temperature and Injector Structure on the Combustion Characteristics of Direct‐Injection Spark‐Ignition Methanol Engines

In this article, to address the issues of slower droplet evaporation and fuel mixing inhomogeneity caused by the high latent heat of vaporization of methanol, the effects of the number of nozzle holes and spray cone angle (θsca) on the combustion characteristics of a direct‐injection spark‐ignition methanol engine are numerically investigated at different intake temperatures (Tint) under constant injection pressures. In the results, it is indicated that the maximum‐indicated thermal efficiency (ITE) is 48.01% at 8 holes and a Tint of 328 K. Although the ITE at 298 K with 8 holes is 1.42% lower than 328 K, NOx emissions and ringing intensity (RI) are reduced by 90.46% and 90.61%, respectively. Simultaneously, emissions of CO, hydrocarbon (HC), Soot, unburned methanol, and formaldehyde remain at a low level. Second, there exists an optimal θsca at different holes, thus obtaining the best fuel economy and emissions. The maximum ITE is 48.1% at 8 holes and a θsca of 26°. Finally, under the same energy input and parameter, compared with the diesel engine of the optimal start of injection, the ITE of the optimized methanol engine is increased by 1.65%, and the RI, NOx, HC, CO, and Soot emissions are reduced by 98.58%, 77.85%, 99.35%, 85.71%, and 78.38%, respectively.

O−O Radical Coupling in Ultrathin Reconstructed Co6.8Se8 Nanosheets for Effective Oxygen Evolution and Zinc‐Air Batteries

AbstractDesigning ultrathin transition metal electrocatalysts with optimal surface chemistry state is crucial for oxygen evolution reaction (OER). However, the structure‐dependent electrochemical performance and the underlying catalytic mechanisms are still not clearly distinguished. Herein, we synthesize ultrathin Co6.8Se8 nanosheets (NSs) with subnanometer thickness by incorporating catalytically inactive selenium (Se) into ultrathin Co(OH)2, thereby switching the OER reaction pathway from adsorbate evolution mechanism (AEM) to oxide path mechanism (OPM). The prepared ultrathin Co6.8Se8 NSs exhibit an overpotential of 253 mV at 10 mA/cm2, outperforming the mostly reported Co‐based electrocatalysts. Advanced operando synchrotron spectroscopies and X‐ray absorption spectroscopy reveal the ultrathin Co6.8Se8 NSs, whose surface is reconstructed into Se‐doped Co(OH)2 during the OER process, could trigger direct O*−O* radical coupling rather than OOH* intermediates within AEM pathway thus lowering the energy input. Density functional theory calculations confirm that Co6.8Se8 NSs with shorter Co−Co bond length and stable Co−Se bond could optimize the rate‐determining step barrier via OPM pathway. Besides, rechargeable zinc‐air batteries based on Co6.8Se8 NSs exhibit excellent stability for more than 500 h of continuous charge–discharge cycles at 4 mA/cm2. The present study highlights the structural‐dependent switch of OER pathways and provides valuable insights for further development of ultrathin OER catalysts.

Laser‐Based Closed‐Loop Controlled Heat Treatment for Residual Stress Relief of Additively Manufactured AlSi10Mg Components

In laser powder bed fusion of metals small melt pools with extremely short solidification times and steep temperature gradients to the surrounding material exist due to the layer‐wise and selective melting process with small areas of energy input compared to the cooler, solid ambient material. This causes high thermally induced residual stresses (RS), which can lead to the immediate rejection of the component due to critical part deformation and inhomogeneous mechanical properties under load. To prevent this, furnace‐based stress relief heat treatments are commonly applied before cutting‐off the part from the built platform. In this study a novel closed‐loop controlled laser‐based heat treatment using temperature feedback through inline pyrometer measurement is investigated, enabling a fast and highly efficient postprocess stress relief. Therefore, a laser beam is guided by a scanner optics in a meandering pattern over the top surface of AlSi10Mg cantilever specimens. It enables a decrease of near‐surface RS from 158 to 5 N mm−2, resulting in a reduction of displacement by over 90% at material affecting depths up to 3 mm and area rates of 8 to 163 mm2 s−1.

Energy Analysis in the Production of Purple Sweet Potato Crackers

The production process of purple sweet potato (PSP) crackers involves several stages, including peeling, washing, boiling, kneading, grinding, cutting, frying, and packaging. This study aims to analyze the energy flow and production costs associated with each stage of processing sweet potatoes into crackers at the Azizah Crackers Production House in Padang City. The types of energy considered in this study included human labor, fuel gas, electricity, and raw materials (PSP, cooking oil, and supporting materials). Results showed that the total input energy for the production of PSP crackers was 784,629.95 kJ with average output energy of PSP crackers 803,880.00 kJ. The energy output of PSP crackers was 1.02 times the energy input. The cutting and frying activity required the largest input energy of 46.18% (362,310.15 kJ), while packaging activity required the smallest energy of 0.38% (2,992.33 kJ). Based on the energy type, raw materials contribute the largest energy, amounted to 85.83% (674,822.86 kJ), and the smallest type of energy was electrical energy, which was 0.74% (5,839.72 kJ). Keywords: Energy consumption. Energy flow, Production costs, Production process, PSP Crackers.

Green Growth Index for India: Drivers, Disparities and Ramifications

This article introduces a novel green growth index, offering a new benchmark for assessing the performance of Indian States in sustainable development. Departing from traditional indices like the HDI and SDG Index, our approach integrates economic, environmental and social factors, providing a comprehensive perspective on sustainable development. The study emphasizes the critical role of energy use and input utilization efficiency as major drivers of green growth disparities, alongside conventional economic growth. The findings suggest that robust governance institutions are also key contributors to green growth. The research reveals that states with higher GDP generally exhibit better performance on the GGI but also underscores the importance of addressing the uneven development across different pillars of green growth .The insights and methodologies presented here are poised to inform targeted policy interventions and contribute to ongoing efforts in promoting inclusive and sustainable green growth, taking into consideration the complex trade-offs between environmental protection and socio-economic inequalities.

Uncertainty in determining carbon dioxide removal potential of biochar

Abstract A quantitative and systematic assessment of uncertainty in life-cycle assessment is critical to informing sustainable development of carbon dioxide removal (CDR) technologies. Biochar is the most commonly sold form of CDR to date, and it can be used in applications ranging from concrete to agricultural soil amendments. Previous analyses of biochar rely on modeled or estimated life-cycle data and suggest a cradle-to-gate range of 0.20–1.3 kg CO2 net removal per kg of biomass feedstock, driven by differences in energy consumption, pyrolysis temperature, and feedstock sourcing. Herein, we quantify the distribution of CDR possible for biochar production with a compositional life-cycle inventory model paired with scenario-aware Monte Carlo simulation in a “best practice” (incorporating lower transportation distances, high pyrolysis temperatures, high energy efficiency, recapture of energy for drying and pyrolysis energy requirements, and co-generation of heat and electricity) and “poor practice” (higher transportation distances, lower pyrolysis temperatures, low energy efficiency, natural gas for energy requirements, and no energy recovery) scenarios. In the best-practice scenario, cradle-to-gate CDR (which is representative of the upper limit of removal across the entire life cycle) is highly certain, with a median removal of 1.4 kg of CO2e / kg biomass and results in net removal across the entire distribution. In contrast, the poor-practice scenario results in median net emissions of 0.090 kg CO2e / kg biomass. Whether this scenario emits (66% likelihood) or removes (34% likelihood) carbon dioxide is highly uncertain. The emission intensity of energy inputs to the pyrolysis process and whether the bio-oil co-product is used as a chemical feedstock or combusted are critical factors impacting the net carbon dioxide emissions of biochar production, together responsible for 98% of the difference between the best- and poor-practice scenarios.

Development of a laser-based process to produce a hermetically sealed contacting interface for the encapsulation of temperature-sensitive electronic components

In the construction of hermetically sealed encapsulations, feedthroughs are commonly required as contacting interfaces. The so-called GTMS (glass-to-metal seal) feedthroughs are often used in the field of sensor technology, acting as an interface between sensor unit and evaluation electronics. GTMS feedthroughs, consisting of a metal mount, a glass body, and contacts, transfer electricity, electrical, or optical signals through a glass-based barrier while protecting the inside of a sensor from the ingress of dust, moisture, or gases. They are mainly used in humidity, temperature, pressure, flow, and vacuum sensors and are actually produced in a furnace process in which the entire components are heated to the melting temperature (>400 °C) of the glass body. Sufficient heat must be applied to reduce the viscosity of the glass body to ensure a reliable wetting of mount and contacts. If temperature-sensitive components are involved, a furnace process is not suitable as the high temperatures damage these components. In this case, a technology with localized energy input is required. A laser-based process enables the reduction of the thermal load. Therefore, investigations on the manufacture of compressed GTMS feedthroughs for multilayer low temperature cofired ceramic with a diode laser have been performed, which are described in the following paper. Depending on the irradiation energy, the melting and wetting behavior of the glass body is determined. Results on the influence of the process parameters on the heat input and the thermal load of the components are discussed and quality-relevant properties such as helium tightness and burst pressure resistance of the laser-produced feedthroughs are evaluated.

A high effectiveness impact‐optimized piezoelectric energy harvesting interface system

AbstractThis paper presents a novel high‐performance impact‐optimized interface system for an impact‐driven piezoelectric energy harvester (PEH) which utilizes two independent parallel harvesting plans, that is, low‐efficiency self‐powered passive path and high‐efficiency active maximum power point tracking (MPPT)‐based path, for different situations based on the characteristics of the input excitation and stored energy content which are evaluated by the mode detection unit. It uses a synchronous electrical charge extraction‐based self‐powered passive circuit as a primary energy extraction strategy. Thus, the proposed structure is self‐sustained with cold start capability. When the determined prerequisites are met, the system switches to the secondary energy extraction strategy, that is, high‐efficiency MPPT‐based path, in which during the maximum power point sensing phase, the PEH is sensed without disconnecting it from the interface and during the maximum power point setting phase, a bidirectional DC/DC converter performs a fully bidirectional energy transfer, increasing the extraction efficiency. The proposed system is designed and simulated using standard 180 nm complementary metal‐oxide semiconductor (CMOS) technology. Post‐layout simulation results show that when the input energy content is around 50 µJ, the FoMMOPIR, periodic harvesting efficiency, shock harvesting efficiency, MPPT efficiency, and effectiveness of the proposed system are 505%, 65%, 80%, 70%, and 56%, respectively.

How Do Energy Input and Carbon Emission Constraints Affect the ESG Performance of Manufacturing Enterprises? Evidence from China

Sustainable development is the key to achieving high-quality growth in the manufacturing industry. The article analyzes the impact of energy inputs and carbon emission constraints on the ESG performance of Chinese manufacturing firms using listed company data from 2011-2022, carbon market emission control firms, and new energy city policies. The study finds the following core conclusions. First, energy input-carbon emission constraints can significantly improve the overall ESG performance of manufacturing firms rather than being limited to improving one aspect of performance. The benchmark regression results remain robust after a series of robustness tests. Second, the mechanism test shows that the energy input-carbon emission constraint can improve the ESG performance of manufacturing firms by promoting public green concern in the source prevention link, corporate green technology innovation in the process control link, and corporate green investment in the end governance link. In addition, enterprises' horizontal competition and vertical cooperation factors have a moderating effect on the direct impact of energy input-carbon emission constraints. Supply chain integration as a vertical cooperation factor positively reinforces the marginal increment. Firm competitiveness as a horizontal competition factor produces a "U" shaped moderating effect that is first weak and then strong. Finally, the heterogeneity analysis finds that the energy input-carbon emission constraint effectively promotes the ESG performance of technology-intensive and mature manufacturing firms and has a "snowball" effect on the ESG performance of manufacturing firms in high-carbon industries. Therefore, the two-end synergistic constraint of energy input-carbon emission can effectively promote the growth of ESG performance of manufacturing enterprises, which brings important insights to the green development of manufacturing industries in other countries.

Economic Growth with Nonrenewable and Sustainable Energy

Optimal depletion of nonrenewable energy added to the neoclassical model dampens economic growth as its price rises at the rate of the capital return. The present paper introduces sustainable energy requiring its own capital with the Inada condition requiring both energy inputs are necessary for production. Production is developed in terms of factor shares and price elasticities. Investment in sustainable energy offers relief from the rising nonrenewable price but lowers consumption or capital growth. Simulations of the U.S. economy foresee a smooth transition with growth paths depending on the two saving rates and factor price substitution.