Lag Effect Research Articles

Numerical analysis of double-fractional PDEs in MHD hybrid nanofluid blood flow with slip velocity, heat source, and radiation effects

Abstract The study of blood flow in cylindrical geometries resembling small arteries is crucial for advancing drug delivery systems, cardiovascular health, and treatment methods. However, Conventional models have failed to capture the complex memory effects and non-local behavior inherent in blood flow dynamics, which hinders their accuracy in predicting critical flow and heat transfer properties for medical applications. To overcome these limitations, this research introduces a novel fractional-order magnetohydrodynamic model for blood flow, incorporating a $ZnO$ and $Fe_3O_4$ hybrid nanofluid. The model uniquely integrates boundary slip velocity effects within the double fractional Maxwell model (DFMM) rheology framework and utilizes the dual fractional phase lag bioheat model (DFPLM) applied to a porous cylindrical structure. Fractional-order time derivatives in the thermal and momentum equations are formulated using the Caputo approach, with numerical solutions derived via finite difference methods leveraging L1 and L2 approximations for Caputo fractional derivatives. The study examines the effects of fractional orders, relaxation time, and phase lags for heat and temperature, along with parameters such as thermal radiation, wall slip velocity, and porosity. These factors are analyzed for their impact on velocity, temperature, skin friction, and the Nusselt number. Results indicate that the hybrid nanofluid enhances heat transfer compared to blood or mono-hybrid nanofluids, while also reducing skin friction. Furthermore, fractional-order models provide more reliable and realistic predictions under varying flow conditions. The DFMM shows smoother transitions in velocity and friction, while the DFPLM predicts higher temperatures and greater heat transfer enhancement compared to classical and single-phase lag models. By integrating fractional calculus, this model offers improved simulation of complex transport phenomena in small arteries, contributing to the development of more effective cardiovascular treatments.

Stress distribution and shear lag effect of composite steel plate girder bridges based on spatial fine mesh elements

Stress distribution and shear lag effect of composite steel plate girder bridges based on spatial fine mesh elements

Modeling the impacts of governmental and human responses on COVID-19 spread using statistical machine learning

ABSTRACT Understanding the impacts of governmental and human responses on the pandemic control is imperative for forecasting pandemic spread under various responsive scenarios and guiding localized interventions before pharmaceutical interventions are available. This study analyzed multiple data sets, including social media, mobility, policy evaluations, and COVID-19 infection reports, to delineate the interactions between governmental and human responses and COVID-19 spread in the United States in 2020 when vaccinations were unavailable. The contributions are (1) uncovering the spatiotemporal variations in governmental and human responses during COVID-19; (2) developing a statistical machine learning algorithm that incorporates spatiotemporal dependencies and temporal lag effects to model the relationships between governmental and human responses and the pandemic spread; (3) dissecting the impacts of human responses on the pandemic across space and time. Results reveal that the determinants of COVID-19 health impacts transitioned from human mobility during the initial outbreak phase to both human mobility and stay-at-home policies during the rapid spread phase, and ultimately to the compound of human mobility, stay-at-home policies and the public awareness in the full-blown phase. These findings furnish guidance for policymakers in implementing adaptive and phased strategies.

Regeneration lags and growth trajectories influence passive seismic line recovery in western North American boreal forests

Across the western North American boreal region, networks of narrow clearings called seismic lines from oil and gas exploration fragment forests. Restoration of seismic lines for habitat recovery of threatened woodland caribou has been prioritized, but there is little guidance on temporal and spatial targets for boreal forest recovery. Between 2016 and 2022, we sampled regenerating trees on 344 seismic lines with limited re‐disturbance across the oil sands region of Alberta, Canada. We modeled growth relationships for regenerating trees, including regeneration lags, using field and geospatial data to predict passive forest recovery on seismic lines. Recovery on seismic lines in peatland and transitional forests could take >30 years, due to longer regeneration lags (8–13 years) and slower‐growing tree species (>25 years to reach 3 m). Recovery in xeric and mesic uplands was nearly half that, due to shorter regeneration lags (3–5 years), faster‐growing species (9–13 years to reach 3 m), and recent wildfires. Over half of seismic lines in upland forests had predicted regeneration lags ≤5 years, including many seismic lines that burned after initial seismic line clearing, indicating regeneration was not delayed. However, all seismic lines in transitional and peatland forests were predicted to have regeneration lags >8 years. Slower recovery on seismic lines is associated with the compounding effects of longer regeneration lags and slower growth rates of dominant tree species. Restoration efforts should prioritize seismic lines where active treatment can significantly reduce regeneration lags and expedite growth.

Numerical Investigation of the Shear Lag Effect on a Cable-Stayed Bridge with an Extra-Wide Composite PK Girder

The composite PK (Pasco-Kennewick) girder cable-stayed bridge (CSB) is a trendy structure with a super-wide girder, excellent lateral rigidity, and high wind resistance. However, the shear lag effect (SLE) of the composite PK girder grows severe due to the super-wide deck. Meanwhile, the SLE of the composite PK girder CSB subjected to huge axial forces significantly differs from that of bridges subjected to only bending moment. Therefore, global and local analyses are conducted on a composite PK girder CSB to determine the SLE during construction and after completion. Furthermore, the effective slab width (Beff) of the composite PK girder under combined bending moment and axial force is analyzed. The results can offer guidance and reference for the design and construction of composite PK girder cable-stayed bridges.

Sex-dependent effects of chronic jet lag on circadian rhythm and metabolism in mice

BackgroundThe circadian clock integrates external environmental changes into the internal physiology of organisms. Perturbed circadian clocks due to misaligned light cycles increase the risk of diseases, including metabolic disorders. However, the effects of sex differences in this context remain unclear.MethodsCircadian misalignment was induced by a chronic jet lag (CJL) shift schedule (light-on time advanced by 6 h every 2 days) in C57BL/6N male and female mice. Core body temperature and activity rhythms were recorded using a nano tag, and the gene expression rhythms of clock and clock-controlled genes in the liver and adrenal glands were analyzed using qPCR. Glucose metabolism and insulin response were evaluated using glucose tolerance, insulin sensitivity, and glucose response assays. Castration and testosterone replacement were performed to assess the fundamental role of testosterone in male phenotypes under CJL.ResultsUnder CJL treatment, male mice exhibited increased weight gain, whereas females exhibited decreased weight gain compared to that of the respective controls. CJL treatment induced a lower robustness of circadian rhythms in core body temperature and a weaker rhythm of clock gene expression in the liver and adrenal glands in females, but not in males. Only male mice exhibited glucose intolerance under CJL conditions, without the development of insulin resistance. Castrated mice without testosterone exhibited decreased weight gain and reduced robustness of body temperature rhythm, as observed in intact females. Testosterone replacement in castrated mice recovered the CJL-induced weight gain, robustness of temperature rhythm, and glucose intolerance observed in intact males.ConclusionsSignificant sex-based differences were observed in circadian clock organization and metabolism under CJL. Testosterone plays a crucial role in maintaining the circadian clock and regulating CJL metabolism in males.

Cumulative and Lag Effects of Meteorological Drought on Vegetation Cover in the Yellow River Basin

Cumulative and Lag Effects of Meteorological Drought on Vegetation Cover in the Yellow River Basin

Impact of Dual Phase Lag on Natural Convection Flow in a Porous Vertical Channel in the Presence of Periodic Boundary

ABSTRACTThe dual‐phase‐lag (DPL) heat conduction model is utilized in this research to analyze the fluid flow of viscous fluid passing through a porous vertical channel with periodic boundary conditions. Periodic heating is subjected to the channel boundary. Equations regarding the model, including the momentum and energy equations, in which the DPL term is incorporated, all in dimensional form, are stated and are being transformed to their dimensionless form, then solved analytically by undetermined coefficients and variation of parameters. The actual expressions of temperature and velocity, as well as the heat transfer rate and skin friction, are determined. The effects of the DPL parameters, suction/injection, Prandtl number, heat source/sink, and Strouhal number on the dimensionless temperature and velocity profiles are demonstrated using graphs that are constructed with the aid of MATLAB. It was found during the investigation that the introduction of the DPL model, together with suction/injection in the channel, enhances the velocity and fluid temperature within the channel. Also, the decreasing effect of temperature gradient phase lag on fluid temperature and velocity conversed with that of heat flux phase lag. As an important contribution, the discovery of the effects of the phase‐lag parameters of the DPL model and suction/injection on fluid temperature and velocity would significantly help researchers advance the design of electrical and electronic systems.

Rainfall and Soil Moisture Jointly Drive Differences in Plant Community Composition in Desert Riparian Forests of Northwest China

Extreme rainfall and soil moisture play important roles in the survival, community composition, and ecosystem function of desert plants. This study focused on arid desert riparian forests ecosystems in the Ebinur Lake Basin of Xinjiang, China. We analyzed the effects of rainfall and soil moisture on species composition, indicator species, β diversity, species turnover, and nestedness using three consecutive years of community surveys. A zero-model combined with a Bayesian framework was used to explore the response of species turnover and nestedness to soil moisture and rainfall, and variance decomposition was used to quantify the relative importance of spatial distance, rainfall, and soil factors in determining species composition. The results indicated the following: (1) when rainfall was high, the richness and abundance of annual herbaceous plants increased. The proportion of the community based on richness (32%) and abundance (58.1%) of annual herbaceous plants in 2016 was higher than that in 2015 and 2017. The Jaccard, Bray–Curtis, and Chao indexes of the community in years with higher rainfall were significantly higher than in years with lower rainfall; however, a lag effect was also observed. (2) Soil factors explained 5% of the changes in community composition, rainfall explained 12% of the changes in community composition, and spatial distance, soil factors, and rainfall jointly explained 32% of the changes in community composition. (3) We also showed that high soil moisture leads to greater β diversity than low soil moisture. Rainfall had the greatest explanatory power on the measured values of β diversity (19.6%) and species turnover (38%), and the factor with the greatest explanatory power for species nestedness was the interaction between rainfall and soil moisture (26.2%). Our findings indicate that drought and rainfall drive differences in plant community composition, with rainfall playing a dominant role. These results provide a basis for understanding the impact of extreme rainfall events on arid ecosystem functions.

Association of ambient ozone exposure with early cardiovascular damage among general urban adults: A repeated-measures cohort study in China

Longitudinal evidence of long-term ozone exposure on heart rate variability (HRV, an early indicator of cardiovascular damage) is lacking and the potential mechanism remains largely unclear. Our objectives were to evaluate the cross-sectional and longitudinal associations of ozone exposure with HRV alteration, and the potential roles of protein carbonyl (PC, biomarker of oxidative protein damage) and transforming growth factor (TGF)-β1 in this association. This repeated-measures prospective study included 4138 participants with 6617 observations from the Wuhan-Zhuhai cohort. Ozone concentrations were estimated using a high temporospatial resolution model for each participant. HRV indices, PC, and TGF-β1 were also repeatedly measured. Cross-sectional and longitudinal relationships of ozone exposure with HRV alteration were evaluated by linear mixed model. Cross-sectionally, the strongest lag effect of each 10 ppb increment in short-term ozone exposure showed a 12.40 %, 8.47 %, 4.31 %, 8.03 %, 3.69 %, and 2.41 % decrement on very low frequency (VLF, lag 3 weeks), LF (lag 2 weeks), high frequency (HF, lag 0–7 days), total power (TP, lag 2 weeks), standard deviation of all normal-to-normal intervals (SDNN, lag 3 weeks), and square root of the mean squared difference between adjacent normal-to-normal intervals (lag 2 weeks), respectively. Longitudinally, each 10 ppb increment of annual average ozone was related with an annual change rate of −0.024 ms2/year in VLF, −0.009 ms2/year in LF, −0.013 ms2/year in HF, −0.014 ms2/year in TP, and −0.004 ms/year in SDNN. Mediation analyses indicated that PC mediated 20.77 % and 12.18 % of ozone-associated VLF and TP decline, respectively; TGF-β1 mediated 16.87 % and 27.78 % of ozone-associated VLF and SDNN reduction, respectively. Our study demonstrated that ozone exposure was cross-sectionally and longitudinally related with HRV decline in general Chinese urban adults, and oxidative protein damage and increased TGF-β1 partly mediated ozone exposure-related HRV reduction.

Using machine learning to reveal seasonal nutrient dynamics and their impact on chlorophyll-a levels in lake ecosystems: A focus on nitrogen and phosphorus

Chlorophyll-a (Chl-a) is a pivotal indicator of lake eutrophication. Studies examining nutrients limiting lake eutrophication at large scales have traditionally focused on summer and autumn, potentially limiting the applicability of their findings. This study encompasses 86 state-controlled points in the Eastern China Basin, spanning data collected from January 2020 to July 2023. Furthermore, we focus on the application of three machine-learning models (i.e., eXtreme Gradient Boosting, Support Vector Machines, and Naive Bayes Classifier) to analyze the seasonal nutrient dynamics in lake ecosystems. We categorized the monitoring data by season to eliminate outliers and employed adaptive synthetic sampling to address data imbalance issues. The results reveal that the direct correlations between total nitrogen (TN), total phosphorus (TP), and TP in conjunction with turbidity and Chl-a are broadly weak, possibly because of geographic variations, nutrient lag effects on algae, and differences in algal community composition. However, probabilistic analyses revealed that as TP or TN levels transitioned from oligo-mesotrophic (O) to eutrophic (E), TP exhibited a greater influence on the variation in Chl-a status than TN during spring and winter (p < 0.05). Conversely, the effects of TP and TN on Chl-a (O-E) were comparable during summer and autumn. Seasonal variations in TN and TP thresholds derived from XGBoost modeling for O and E states of Chl-a suggest the need for stricter control measures during periods of high-nutrient levels and cost-effective management strategies to employ during low-nutrient periods. These findings should enhance our understanding of trophic shifts in lakes and provide a foundation for optimizing eutrophication management strategies across all seasons.

Predicting multi-frequency crude oil price dynamics: Based on MIDAS and STL methods

Accurate prediction of crude oil prices is important for national energy security and socioeconomic development. Research on crude oil price forecasting has primarily focused on the overall price, overlooking the differentiated investment needs of different entities. To solve this problem, we introduce the Seasonal and Trend decomposition using Loess (STL) method into the Mixed Data Sampling (MIDAS) model. This enables us to more accurately analyze the predictive capability of predictors for crude oil prices at different frequencies. Selected predictors include the Dow Jones Index, US Dollar exchange rate, economic policy uncertainty, related crude oil and energy prices, carbon asset prices, and investor attention. Empirical results indicate that these predictors significantly enhance the forecasting accuracy across all components, with the strongest impact in the trend component. Interestingly, a lag effect is observed in the predictors' impact on the seasonal and residual components, but not on the trend component. Moreover, we calculate the duration of each predictor's effectiveness for different components of crude oil prices, distinguishing short-term and long-term effective predictors. This research offers novel insights into the design of crude oil price forecasting models, which is crucial for enhancing investor returns and maintaining stability in the energy market.

Association between nighttime and daytime ambient temperature and insomnia using national emergency department database in the capital city of South Korea.

Insomnia is a growing health concern globally, with significant implications for public health. Most studies have primarily focused on the effects of nighttime temperatures on sleep problems. However, there is a lack of studies comparing nighttime temperatures with daytime temperatures, which are more closely related to daily life activities. This study aimed to explore a short-term association of nighttime and daytime ambient temperature with emergency department (ED) visits for insomnia in the capital city of South Korea. A time-stratified case-crossover design was employed using a conditional logistic regression model. A distributed lag non-linear model was utilized to explore potential non-linear and lag effects of ambient temperature on ED visits for insomnia. Odds ratio (OR) for temperature with maximum ED visits for insomnia (MaxIT) and that for temperature with minimum ED visits for insomnia (MinIT) were calculated and compared. We observed significant associations at high temperatures for both nighttime and daytime (nighttime: 25.0℃ (94.1%) [OR: 1.82, 95% CIs: 1.31-2.55], daytime: 30.6℃ (99.0%) [OR: 2.13, 95% CIs: 1.49-3.06]) compared to MinIT (-8.5℃ (2.7%) and - 8.4℃ (1.0%), respectively). Subgroup analyses found significant associations at high temperatures in females, individuals aged 35-49, and those without comorbidities, and during spring, fall, and winter, for both daytime and nighttime. Our findings provide insights for proactive public health strategies for managing insomnia during global temperature rise.

Analytical solution for rainwater infiltration in monolithic soil covers under heavy rainfall and its implications for practice

This study established an analytical solution for rainwater infiltration in MSCs during heavy rainfall assuming that the soil hydraulic properties follow exponential forms. The analytical solution was used to calculate the factor of safety (FOS) of MSCs after the verification with numerical simulations. It is found that the FOS for the potential slip surface at the cover bottom remined the lowest during and after heavy rainfall. The percolation and FOS might present pronounced “lag effects”, meaning that the maximum percolation rate and minimum FOS occurred after heavy rainfall. A parametric study was conducted to reveal the influencing factors on the hydraulic response and slope stability of MSCs based on the analytical solution. Relevant results demonstrate that the hydraulic performance and slope stability could be improved by decreasing soil saturated hydraulic conductivity, increasing soil desaturation coefficient and lowering water level in landfills. The results also reveal the existence of a threshold of soil saturated hydraulic conductivity (1×10&lt;sup&gt;-8&lt;/sup&gt; m/s for this study) for controlling the hydraulic performance and slope stability of MSCs. Furthermore, the analytical solution was applied to determine the rainfall intensity-duration threshold curves of MSCs. The results indicate that the obtained curves of MSCs satisfied exponential forms.

Model of nonlinear dynamics of development of multicomponent manufacturing enterprises, taking into account the effect of investment lag

The published article proposes a generalization of the economic and mathematical model of the dynamics of development of a multi-industry enterprise, the resources of each production of which are restored by introducing internal lagging investments. The model of such a multi-industry enterprise is presented in the form of systems of coupled differential equations with respect to production factors. It is established that the marginal values of production factors are stationary solutions of systems of differential equations. It is shown that the most efficient operation of the considered multi-industry enterprise will be achieved only when the marginal values of production factors coincide with the values of the resources used, which correspond to the maximum values of profit for each production component. For a two-component production enterprise, calculation models of output, costs and profit for each component and for the entire enterprise are constructed. Numerical solutions of the corresponding system of differential equations are given, on the basis of which integral curves are constructed for production factors, output and profit for each component of the enterprise and for the entire enterprise as a whole.

Climate policy and carbon leakage: Evidence from the low-carbon city pilot program in China

The low-carbon city pilot (LCCP) policy, aimed at promoting the transformation of cities towards low-carbon practices, is an important action for China to mitigate climate change. Though this climate policy brings positive effects in many aspects, the issue of potential carbon leakage due to regional disparity has been overlooked. This paper introduces a novel approach by employing the spatial DID model and prefecture-level city data to assess the LCCP policy and its implications for carbon leakage. The innovative aspect lies in its spatially differentiated analysis, which reveals that while the LCCP policy effectively reduces carbon emissions of local pilot cities, it simultaneously triggers carbon leakage to neighboring non-pilot cities, with the leakage effects diminishing with increasing distance. Additionally, this study uncovers that carbon leakage risks are mitigated when multiple pilot cities are geographically clustered, enhancing the overall effectiveness of the policy. Finally, the impact channel analysis uniquely identifies that carbon leakage results from the inter-city relocation of high-carbon industries, such as manufacturing, which exhibits spatial attenuation and temporal lag effects. This study advances the understanding of low-carbon city pilot programs and provides valuable insights for mitigating carbon leakage risks.

Variations over 20 Years in Vegetation Dynamics and Its Coupled Responses to Individual and Compound Meteorological Drivers in Sichuan Province, China

This study presents an innovative investigation into the spatiotemporal dynamics of vegetation growth and its response to both individual and composite climatic factors. The Normalized Difference Vegetation Index (NDVI), derived from SPOT satellite remote sensing data, was employed as a proxy for vegetation growth. Multiple analytical methods, including the coefficient of variation, Mann–Kendall trend analysis, and Hurst index, were applied to characterize the spatiotemporal patterns of the NDVI in Sichuan Province from 2000 to 2020. The Standardized Precipitation Evapotranspiration Index (SPEI) was calculated using monthly precipitation and temperature data from 45 meteorological stations to examine the influence of composite climatic factors on vegetation growth, while the time lag effects between the NDVI and various climatic variables were also explored. Our findings unveil three key insights: (1) Vegetation coverage in Sichuan Province exhibited an overall increasing trend, with the highest NDVI values in summer and the lowest in winter. Significant NDVI fluctuations were observed in spring in the western Sichuan plateau and in winter in northern, eastern, and southern Sichuan. (2) A significant upward trend in the NDVI was detected across Sichuan Province, except for Chengdu Plain, where a downward trend prevailed outside the summer season. (3) On shorter time scales, the NDVI was positively correlated with precipitation, temperature, and the SPEI, with a one-month lag. The response of the NDVI to sunlight duration showed a two-month lag, with the weakest correlation and a five-month lag in western Sichuan. This research advances our understanding of the complex interactions between vegetation dynamics and climatic factors in Sichuan Province and provides valuable insights for predicting future vegetation growth trends.

Evaluation of wastewater percent positive for assessing epidemic trends - A case study of COVID-19 in Shangrao, China

ObjectiveThis study aims to assess the feasibility of evaluating the COVID-19 epidemic trend through monitoring the positive percentage of SARS-CoV-19 RNA in wastewater. MethodThe study collected data from January to August 2023, including the number of reported cases, the positive ratio of nucleic acid samples in sentinel hospitals, the incidence rate of influenza-like symptoms in students, and the positive ratio of wastewater samples in different counties and districts in Shangrao City. Wastewater samples were obtained through grabbing and laboratory testing was completed within 24 h. The data were then normalized using Z-score normalization and analyzed for lag time and correlation using the xcorr function and Spearman correlation coefficient. ResultsA total of 2797 wastewater samples were collected. The wastewater monitoring study, based on sampling point distribution, was divided into two phases. Wuyuan County consistently showed high levels of positive ratio in wastewater samples in both phases, reaching peak values of 91.67% and 100% respectively. The lag time analysis results indicated that the peak positive ratio in all wastewater samples in Shangrao City appeared around 2 weeks later compared to the other three indicators. The correlation analysis revealed a strong linear correlation across all four types of data, with Spearman correlation coefficients ranging from 0.783 to 0.977, all of which were statistically significant. ConclusionThe positive ratio of all wastewater samples in Shangrao City accurately reflected the COVID-19 epidemic trend from January to August 2023. This study confirmed the lag effect of wastewater percent positive and its strong correlation with the reported incidence rate and the positive ratio of nucleic acid samples in sentinel hospitals, supporting the use of wastewater percent positive monitoring as a supplementary tool for infectious disease surveillance in the regions with limited resources.

Optimizing the Use of Flexible Retort Pouches for Production of Ready to Eat Cobia (Rachycentron canadum) Fish Chunks in Curry Medium

Cobia fish chunks in curry medium, a famous North Eastern Indian dish, was developed using Cobia (Rachycentron canadum) fish chunks prepared in a traditional culinary style. The present study was aimed to optimize F0 values for Cobia fish chunks in curry medium using flexible retortable pouches. The product underwent thermal processing at two distinct lethality levels and heat penetration rates, demonstrating equivalent cooling and heating lag effects. The fh values were 15 and 18.5 minutes for the product processed at F0 values of 9.29 and 8.42 minutes, respectively. The total process times were 39.79 and 38.80 minutes, respectively, for the F0 values of 8.42 and 9.29 minutes. Cook values for the processed product were 86.60 minutes for the F0 value of 8.42 minutes and 92.57 minutes for the F0 value of 9.29 minutes. Based on sensory characteristics, the product processed at an F0 value of 8.42 minutes was rated better over a storage period of 90 days.

A Simulation-Assisted Field Investigation on Control System Upgrades for a Sustainable Heat Pump Heating

Heat pump-based renewable energy and waste heat recycling have become a mainstay of sustainable heating. Still, configuring an effective control system for these purposes remains a worthwhile research topic. In this study, a Smith-predictor-based fractional-order PID cascade control system was fitted into an actual clean heating renovation project and an advanced fireworks algorithm was used to tune the structural parameters of the controllers adaptively. Specifically, three improvements in the fireworks algorithm, including the Cauchy mutation strategy, the adaptive explosion radius, and the elite random selection strategy, contributed to the effectiveness of the tuning process. Simulation and field investigation results demonstrated that the fitted control system counters the adverse effects of time lag, reduces overshoot, and shortens the settling time. Further, benefiting from a delicate balance between heating demand and supply, the heating system with upgraded management increases the average exergetic efficiency by 11.4% and decreases the complaint rate by 76.5%. It is worth noting that the advanced fireworks algorithm mitigates the adverse effect of capacity lag and simultaneously accelerates the optimizing and converging processes, exhibiting its comprehensive competitiveness among this study’s three intelligent optimization algorithms. Meanwhile, the forecast and regulation of the return water temperature of the heating system are independent of each other. In the future, an investigation into the implications of such independence on the control strategy and overall efficiency of the heating system, as well as how an integral predictive control structure might address this limitation, will be worthwhile.