In this research, the numerical investigations of the fractional order immune diabetes regulation system by using a competent Bayesian regularization neural network procedure have been provided. The fractional order derivatives are used to get better results in comparison with the integer order. The division of the mathematical system is performed in resting and activated macrophages, and the antigen, autolytic, and beta cells. The data generalization is accessible by using the traditional Adam scheme in order to decrease the mean square error, while the data is separated into testing 16%, training 70%, and substantiation 14%. The designed neural network structure is updated by using the optimization tests through Bayesian regularization, a single layer sigmoid activation function, and twenty-five neurons. As conventional modeling schemes depend on shortening traditions or linear calculations, while the stochastic BRNN can perform complicated data patterns and deliver precise calculations of system performance. The correctness of the designed optimizer is obtained through the overlapping of the outcomes and lesser absolute error for each class of the model. Moreover, few curves based on state transitions, regression, error histograms provide the competences of the proposed solver.

The purpose of this work is to solve the fractional-order model of chaotic virotherapy dynamics by executing a neural network scheme. The chaotic virotherapy dynamics is divided into four categories: uninfected tumor cells, infected tumor cells, immune cells, and virus-free cells. The implementation of fractional derivatives permits the unification of memory properties and long-range dependencies in mathematical systems. The designed computing structure is performed by using a single layer and applying a radial basis activation function in the hidden layer with 12 neurons. Optimization is performed using the resilient backpropagation algorithm, which is one of the reliable schemes for the nonlinear models. The Adam optimizer is used to generate the dataset, which is divided into training as 77%, testing as 12%, and validation as 11%. The results of the fractional-order model of chaotic virotherapy dynamics are presented for solving three variations of the fractional-order values, while the accuracy of the results is validated through solution matching and best/optimal training values. In addition, the consistency of the designed solver is observed through the different states of transition, the regression coefficient, and the error histogram.

Waste-to-Energy (WtE) is one of the modern solutions to landfill problems in this century worldwide. The WtE invention is utilized to manage municipal and industrial waste while producing energy. Several key factors are involved in improving the quality, effectiveness and efficiency of those technologies. The purpose of this study is to identify the efficient critical criteria for upgrading WtE technologies. Through the evaluation of the literature review, case studies and comparative analysis, we identified some major criteria for adapting the WtE technologies. The Decision-Making Trial and Evaluation Laboratory (DEMATEL) method is a widely used Multi-Criteria Decision Making (MCDM) approach for evaluating the importance of criteria. Furthermore, evaluates the degree of significance and relation between these criteria and draws the environmental footprint of WtE technologies. Additionally, the threshold values for the criteria are provided for clarity. Data are obtained from two Decision Makers (DMs) using Dense Neutrosophic Numbers (DNNs) to capture uncertainty and vagueness. Based on the evaluated results, energy efficiency is the most important criterion, followed by environmental impact and is described in more detail in the results section. Finally, sensitivity analysis and comparative analysis are conducted to assess the system’s robustness.

Ribbed channel geometries are widely recognized for their ability to modify flow structures and influence thermal transport. In this study, the nanoscale thermal behavior of nano-enhanced phase change materials (NePCMs) confined within a ribbed nanochannel was investigated using molecular dynamics simulations. The model consisted of a confined domain (50 × 150 × 50 Å3) with non-connected rotating ribs, and the effect of rib number (1–4) on atomic-level structural and thermal properties was systematically analyzed over a 10 ns simulation period. The results show that increasing the number of ribs altered local atomic arrangements, enhanced fluid–structure interactions, and intensified velocity fluctuations within the confined region. These effects led to measurable, statistically significant improvements in thermal transport. Specifically, heat flux increased from 5.19 ± 0.02 to 5.54 ± 0.01 W/m2 (approximately 6.7%), while thermal conductivity increased from 0.65 ± 0.01 to 0.72 ± 0.02 W/m·K (approximately 10.8%) as the rib number increased from 1 to 4. In addition, the phase transition time was slightly reduced, indicating faster energy absorption and release dynamics under enhanced mixing and interfacial interaction conditions. It should be noted that the findings provide atomistic-level insight into how internal geometric features influence heat transfer and phase transition mechanisms. These results contribute to the fundamental understanding of nanoscale transport phenomena and may inform future multiscale design strategies for advanced thermal management systems.

This study developed and trained two optimized Support Vector Regression (SVR) models, with hyperparameters tuned by Particle Swarm Optimization (PSO), to accurately predict the viscosity and thermal conductivity of ZnO-MWCNT/deionized water (DIW) hybrid nanofluids. These nanofluids were prepared at a fixed total volume concentration of ϕ=0.1 %, with varying ZnO: MWCNT mass ratios (20:80 to 80:20), and tested over eight temperatures (20–55 °C). The SVR models demonstrated excellent performance, with mean relative errors of 0.4160 % and 0.2178 % for viscosity and thermal conductivity, respectively, on test data. Subsequently, a multi-objective optimization problem was formulated to simultaneously minimize viscosity and maximize thermal conductivity, and solved using the Non-dominated Sorting Genetic Algorithm II (NSGA-II). This optimization yielded optimal operating conditions (temperature and ZnO: MWCNT mass ratio) within the tested domain (ϕ=0.1 % fixed total concentration, 20–55 °C, mass ratio 20:80 to 80:20) and the corresponding Pareto front, illustrating the trade-offs between the two objectives.

This paper aim to proposes a novel approach to the site selection problem by utilizing the fuzzy distance of Generalized Trapezoidal Fuzzy Numbers (GTrFNs). The study defines a new distance measure for GTrFNs that considers the point of intersection, left spread, right spread, and their weights. This measure also works with Generalized Triangular Fuzzy Numbers (GTFNs) and crisp numbers. Based on the proposed distance measure, the paper then presents a similarity measure for GTrFNs. The presented method is compared with those existing methods to show the advantage of the proposed method. The application potential of these methods is discussed, highlighting their usefulness in various decision-making processes and risk analysis. The key contributions of this work are the development of a comprehensive distance measure for GTrFNs and the derivation of a corresponding similarity measure. Using these measure a site selection problem is discussed to select the study center as a problem and also risk analysis is carried out as a application of similarity measure of the GTrFNs. The sensitivity analysis and comparative analysis for the examples is performed to validate the results.

The objective of this research was to investigate the effects of external electric fields and heat flux on the structural stability of the SARS-CoV-2 main protease (Mpro) in the vicinity of a water/silver nanofluid using molecular dynamics (MD) simulation. The study focused on key dynamical and energetic parameters, including mean-squared displacement, diffusion coefficient, and interaction energy, to evaluate the response of the protease–nanofluid system under different external conditions. The results indicated that the applied electric field strongly affected the protease's dynamical behavior and structural destabilization. Numerically, as the electric field amplitude increased from 0.1 to 0.5 V/Å, the diffusion coefficient and interaction energy increased from 0.65 Ų/ps and -1888.19 kcal/mol to 6.446 Ų/ps and 5650.44 kcal/mol, respectively. In addition, the MD results showed that external heat flux also played a significant role in modulating biomolecular stability. By increasing the heat flux from 1 to 2 W/m², atomic fluctuations within the protease structure increased, thereby enhancing structural destabilization. Under these conditions, the diffusion coefficient increased from 0.885 to 1.044 nm²/ns. Overall, the findings demonstrate that both electric field and heat flux can significantly alter the mobility, interaction behavior, and stability of the SARS-CoV-2 main protease in a water/silver nanofluid environment. These results provide molecular-level insights into how viral protein structures respond to external physical stimuli and may inform the future design of antiviral nanofluid-based systems.

This study investigated the rheological behavior of a hybrid nanofluid composed of 20% ethylene glycol, 80% water, and copper oxide nanoparticles using a Group Method of Data Handling (GMDH) artificial neural network trained on an experimental dataset collected at different temperatures, nanoparticle volume fractions, and shear rates. The primary objective of the present study was to develop an interpretable predictive framework capable of estimating the viscosity behavior of the investigated hybrid nanofluid through explicit quadratic transfer functions rather than conventional black-box predictive models. The polynomial coefficients and network structure were determined using least-squares optimization, and the predictive capability of the developed framework was evaluated using several statistical and graphical validation methods. The results demonstrated that the developed predictive model achieved high accuracy in estimating nanofluid viscosity, with root mean square error, mean absolute error, mean error, and coefficient of determination values of 0.0636, 0.0507, 0.0042, and 0.99157, respectively. The graphical comparisons and error distribution analyses also confirmed strong agreement between the predicted outputs and the experimental measurements throughout the investigated operating conditions. The rheological analysis revealed that temperature was the dominant parameter affecting the viscosity behavior of the hybrid nanofluid. Increasing temperature significantly reduced viscosity, whereas increasing nanoparticle volume fraction increased viscosity. In contrast, a slight increase in shear rate reduced viscosity under the investigated conditions. Furthermore, the influence of nanoparticle concentration on viscosity decreased at elevated temperatures. More specifically, at 10 °C, increasing the nanoparticle volume fraction (NP-φ) from 0 to 1% increased viscosity by approximately 40%, whereas this effect decreased to nearly 5% at 50 °C.

Accurate prediction of the thermophysical and physicochemical properties of hybrid nanofluids is essential for their reliable use in thermal management systems, while extensive experimental characterization is often costly and time-consuming. In this study, a feedforward artificial neural network was developed to simultaneously predict the dynamic viscosity, electrical conductivity, thermal conductivity, and pH of Fe₃O₄/TiO₂ hybrid nanofluids using nanoparticle volume fraction and temperature as inputs. The optimized network contained two input neurons, seven hidden neurons, and four output neurons. Five-fold cross-validation confirmed the model's stability and generalization, yielding low prediction errors across all four properties. Independent testing produced mean relative errors of 2.78% for dynamic viscosity, 2.11% for electrical conductivity, 0.11% for thermal conductivity, and 0.43% for pH. The corresponding absolute-error analysis also confirmed close agreement between the experimental and predicted values throughout the investigated operating domain. More importantly, the model provided physically meaningful insight into the governing behavior of the hybrid nanofluid. Variance-based Sobol sensitivity analysis showed that temperature was the dominant factor controlling dynamic viscosity and thermal conductivity, with first-order sensitivity indices of 0.6402 and 0.5170, respectively. In contrast, nanoparticle volume fraction predominantly governed electrical conductivity and pH, with first-order sensitivity indices of 0.9342 and 0.9750. These results reflect the strong influence of temperature on molecular mobility and heat transport, as well as the dominant role of nanoparticle loading in forming conductive pathways and in surface-related physicochemical processes. The small interaction contributions and narrow 95% bootstrap confidence intervals confirmed the statistical robustness of sensitivity rankings. The proposed framework therefore provided a rapid, accurate, and physically interpretable tool for analyzing and optimizing Fe₃O₄/TiO₂ hybrid nanofluids under the investigated conditions.

This study examined the prediction of viscosity (mu nf) in binary nanofluid mixtures of water and ethylene glycol (EG) containing iron (Fe) and copper oxide (CuO) using machine learning (ML) models. Eight regression techniques were employed in this research: linear regression (Linreg), decision tree regression (D-Treereg), generalized linear regression (genLin), support vector machine (SVM), artificial neural network (ANN), least-squares boosting (LSBoost), bagging regression, and Gaussian process regression (GPR). To assess the performance of each method, 1000 repetitions were performed for each model. The resulting data were evaluated using five performance metrics: Pearson's Linear Correlation Coefficient (PLCC), Spearman's Rank Order Correlation Coefficient (SROCC), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Maximum Absolute Error (ME). The findings reveal that the GPR method outperformed all other techniques, achieving higher correlation and lower error values. Specifically, the GPR model with the ARD Squared Exponential kernel achieved the best performance, with PLCC, RMSE, and MAE values of 0.9991, 0.1903, and 0.1239, respectively. Additionally, GPR models employing Ard Rational Quadratic and ArdMatern32 kernels produced the highest SROCC (0.9983) and ME (0.5339). The superior predictive capability of the GPR method was further corroborated by additional analyses, including scatter diagrams that compared actual and predicted mu nf values. The efficacy of the GPR approach was further confirmed by a 20-bin error histogram illustrating the discrepancies between actual and predicted values. Ultimately, surface plots generated using shear rate (SR), temperature (Temp), and solid volume fraction (phi) demonstrated the model's capacity to reliably predict both observed and unobserved data throughout the testing process.

The influence of solution velocity on the transport and interaction behavior of a carbon nanotube (CNT) nanocarrier loaded with doxorubicin (DOX) was investigated using molecular dynamics simulations. Imposed velocities ranging from 0.001 to 0.005 Å/fs (approximately 100–500 m/s) were used as computational accelerations to examine how flow intensity modifies nanoscale thermodynamic and mechanical responses of the CNT–DOX system. Rather than directly simulating physiological release kinetics, the study evaluates mobility indicators and trends in interaction energy that reflect release tendency. Increasing velocity reduced the maximum local atomic density from 0.0035 to 0.0030 atoms/ų, indicating enhanced molecular dispersion. A moderate temperature rise (380.65–390.28 K) and a slight increase in shear stress (3.16–3.29 Pa) were observed due to kinetic-to-thermal energy conversion. The mean-squared displacement and root-mean-square deviation increased by approximately 9.8% and 5.1%, respectively, confirming enhanced translational mobility and structural rearrangement under stronger flow conditions. The center-of-mass separation between DOX and CNT increased from 9.35 to 10.41 Å, while binding energy became less negative (−1.05 to −0.88 kcal/mol), indicating weakened intermolecular attraction. These findings demonstrate that elevated flow intensity enhances DOX mobility and reduces effective drug–carrier interactions at the molecular scale. Although scaled velocities were employed to accelerate transport processes within atomistic time limits, the observed trends provide mechanistic insight into how hydrodynamic effects influence drug–nanocarrier interaction behavior rather than establishing quantitative in vivo release rates.

The effect of simultaneously using nanofluid (NF) and spring turbulators on heat transfer in straight tubes has been repeatedly studied, whereas this effect in helical tubes has received little attention. Since the quality and quantity of the impact of these turbulators in spiral tubes and straight tubes are naturally different due to the presence of centrifugal forces and vortices, this study experimentally investigates the thermal performance of iron oxide nanofluid in a helical coil tube equipped with spring-wire inserts under a constant heat flux of 1000 W. Experiments were conducted with nanoparticle volume fractions ranging from 0.1 to 0.5% and wire pitches of 0.003, 0.006 and 0.009 m. Results indicated that increasing the nanoparticle concentration and decreasing the wire pitch significantly enhanced the Nusselt number. A maximum heat transfer improvement of approximately 40% was observed compared to water. Two artificial neural network (ANN) models, namely Multi-Layer Perceptron (MLP) and Self-Organizing Map (SOM), were employed to predict thermal behavior. The MLP model outperformed SOM, achieving an R2 greater than 0.99 and lower error rates. To predict the Nu number with a self-organizing map (SOM) ANN with the number of 21 winning neurons with a 3-21-1 topology (including three inputs of Reynolds number, volume fraction, turbulator pitch, and one Nu number output), the obtained data were evaluated. According to the findings, at a pitch of 0.003 m and with a Reynolds number of 10,594, the convection heat transfer coefficient and the Nusselt number are 8200 (W/m2/K) and 110, respectively. This results in the optimal mode of increase for the helical tube. It should be noted that the circular motion of the fluid around the tube axis in spiral tubes is the result of centrifugal force, which causes the flow to transform from laminar to transient and then into turbulent. The experimental results showed that increasing the nanoparticle volume fraction from 0.1% to 0.5% and reducing the turbulator pitch from 0.009 m to 0.003 m significantly enhanced the Nu number by up to 38%, although the pressure drop also increased. The thermal performance evaluation criterion (PEC) reached a maximum value of 1.38 under optimal conditions. Furthermore, an ANN model with a 3-21-1 architecture and a sigmoid activation function was trained, achieving high predictive accuracy with an R-squared value (R2) of 0.989 and a mean square error (MSE) of 7.2434. Using the known enhancement techniques, this study's contribution lies in its systematic integration and multi-objective optimization within a helical coil system. The development of a high-precision ANN model provides a practical framework for designing compact heat exchangers.

The accumulation of wax and asphaltene in surface tanks and transmission lines poses a major challenge for oil extraction and production. Consequently, it is essential to mitigate this issue to ensure the smooth flow of petroleum during both production and transportation. Such deposits can lead to significant operational challenges and financial losses. Methods: This study uses molecular dynamics simulation to assess the effectiveness of EVA copolymer inhibitors and Fe3O4@SiO2 nanoparticles in minimizing aggregation in Fe3O4@SiO2/wax/asphaltene systems. After 10 ns, the simulated sample reached approximately 300 K, indicating thermal equilibrium. The total energy of the examined structure stabilized at 32.338 kcal/mol during the structural equilibrium phase, confirming that the system had reached equilibrium. The agglomeration time was reduced from 8.59 to 8.18 ns, while viscosity increased from 1108 to 1405 mPa & sdot;s as the size of the nanoparticles increased from 15 to 25 & Aring;. This indicates that larger nanoparticle sizes led to shorter aggregation times, whereas smaller nanoparticle sizes were associated with higher viscosity. Conversely, when the inhibitor concentration was increased from 10 to 100 ppm, the agglomeration time increased from 8.59 to 9.06 ns, and the viscosity decreased from 1108 to 1022 mPa & sdot;s. This suggests that higher doses of the inhibitor resulted in reduced viscosity and extended agglomeration time. These results are expected to enhance flow efficiency while simultaneously reducing maintenance costs associated with the buildup of asphaltene and wax in tanks and pipelines. Most importantly, this will provide a more cost-effective and efficient operation within the hydrocarbons sector. Future studies may focus on optimizing nanoparticle characteristics and inhibitor formulations, and on integrating multiscale modeling to improve predictive accuracy and industrial applicability further.

This study explores the effects of nanofluids, used as a dense discrete two-phase system with nanoparticle volume fractions (phi) ranging from 0 to 3 %, on heat transfer in a ribbed micro-channel with a porous medium. Key parameters such as rib angle, Darcy number, and Reynolds number were analyzed for their effect on heat transfer and particle migration. Results indicate that increasing the Darcy number from 0 to 1.883e-4 at a 30 degrees angle and phi = 3 % raised the Nusselt number from 1.8235 to 2.0376 while increasing the Reynolds number from 10 to 1000 at a 30 degrees angle and the same phi raised the Nusselt number from 2.1030 to 3.7519. The maximum Nusselt number observed was 3.9047 for a microchannel with 90 degrees ribs, Reynolds number of Re = 1000, phi = 3 %, and a Darcy number of 7.533e-4. Conversely, the results show that increasing the phi also increases fluid density and relative viscosity, leading to higher kinetic energy and maximum flow velocity in the microchannel. Finally, the results revealed that in the presence of a porous medium with a Darcy number of 1.883e-4, for micro-ribs with an angle of 90 degrees, Re = 10, and phi = 1 %, the value of the friction factor increases from 0.5956 to 0.9495.

This study investigates gas-liquid separation and transport selectivity in a ZSM-5/Ni-MOF-74 hybrid membrane using molecular dynamics simulations under controlled thermodynamic conditions. The simulation domain (50 & times; 50 & times; 250 & Aring;3) is modeled with periodic boundary conditions, using the NVT and NVE ensembles with a time step of 0.1 fs to accurately capture molecular transport behavior. Two governing parameters are systematically varied: the nitrogen fraction in a multicomponent flue gas (0.1-0.5) and the impurity-to-water ratio (0.01-0.05) in aqueous systems containing heavy-metal ions (Pb2+, Cd2+, Hg2+) and inorganic anions (Cl-, SO42-). The novelty of this work lies in the unified molecular-scale analysis of gas-phase diffusion and liquid-phase contaminant rejection within a single zeolite/MOF hybrid membrane, enabling direct comparison of phase-dependent transport mechanisms. The results reveal stronger solid-liquid interactions and greater thermodynamic stability in aqueous systems compared with gas mixtures. After 10 ns, the potential and total energies of the liquid system reached 233.50 and 234.40 kcal mol-1, respectively, whereas the gas phase exhibited significantly lower values (16.44 and 17.33 kcal mol-1). Increasing the N2 fraction enhanced molecular mobility, with the mean-squared displacement increasing from 311.96 to 406.83 & Aring;2 and the diffusion coefficient increasing from 2.01 & times; 10-5 to 2.22 & times; 10-5 m2/s, indicating improved gas transport. In contrast, increasing impurity concentration reduced water flux while increasing salt adsorption, highlighting intensified ion-framework interactions and fouling effects. These findings provide molecular-level insight into permeability-selectivity tradeoffs, offering design guidelines for advanced hybrid membranes in gas separation and water purification.

This paper introduces a weighted -deformed Gram matrix framework for quantum-inspired learning systems, with particular emphasis on applications in biomedical signal analysis. The proposed construction is based on -orthogonal basis functions combined with weighted Jacobi-type kernels, enabling feature representations on nonuniform and memory-dependent domains. We establish fundamental structural properties of the resulting Gram matrix, including symmetry, positive semi-definiteness, and, under mild conditions, strict positive definiteness, ensuring stability, invertibility, and robustness in kernel-based algorithms. A Mercer-type characterization is further derived, confirming the validity of the associated kernel within a reproducing kernel Hilbert space. The roles of the deformation parameters are explicitly interpreted, where governs structural heterogeneity and discretization effects, while encodes temporal memory and scaling behavior. Numerical experiments, including heatmap visualizations and Mercer spectral decompositions, demonstrate the effectiveness of the proposed framework in capturing long-range dependencies and improving kernel conditioning. The results indicate that the -Gram matrix provides a flexible and physically meaningful tool for advancing quantum-inspired and data-driven methodologies in engineering and biomedical applications.

ABSTRACT A fractional order mathematical model of the saturated rate of incidence is solved numerically by applying a neural network scheme. The mathematical fractional order saturated rate of incidence system is classified into four classes of individuals: susceptible, infected, vaccinated, and recovered. The solution of the model is presented in three cases based on the fractional order values of the saturated rate of incidence system to authenticate better performance closer to 0 or 1. The solutions of the model are presented by designing a neural network construction containing Levenberg–Marquardt Backpropagation neural network, a single hidden layer with 10 neurons, and a sigmoid activation function. An Adam numerical scheme is used to get the dataset, which is divided into training, testing, and validation with the ratio of 70%, 20%, and 10%. The capability of the proposed neural network is perceived by the overlapping of the outcomes, small absolute error, and best training values. To validate the solver's reliability, different tests like regression, transition state, and error histogram have also been performed.

Accurate prediction of the thermal conductivity of hybrid nanofluids is essential for the design and optimization of advanced thermal management systems. In the present study, an artificial neural network framework was developed to predict the thermal conductivity of magnesium oxide–graphene oxide/water–ethylene glycol hybrid nanofluids using experimentally measured data. A total of 45 experimental datasets were generated by varying the temperature from 20 to 60 °C and the nanoparticle volume fraction from 0 to 0.20 vol.%. A feedforward multilayer perceptron network was constructed, and ten backpropagation training algorithms were systematically evaluated to identify the optimum predictive model. Among the investigated algorithms, the Levenberg–Marquardt algorithm exhibited the highest predictive performance, achieving a mean squared error of 1.976 × 10⁻⁶, a root mean square error of 1.395 × 10⁻³ W/m·K, a correlation coefficient of 0.9965, and a coefficient of determination of 0.9920. The robustness and generalization capability of the developed model were further confirmed through regression analysis, residual analysis, and 5-fold cross-validation, which yielded root mean square errors ranging from 8.38 × 10⁻⁴ to 4.73 × 10⁻³ W/m·K. A comparison with support vector regression, random forest, and Gaussian process regression demonstrated that the proposed model achieved highly competitive predictive accuracy while maintaining stable performance across different validation datasets. Furthermore, global Sobol sensitivity analysis identified nanoparticle volume fraction as the dominant governing parameter, whereas temperature exerted a considerably smaller influence on thermal conductivity. The observed enhancement in thermal conductivity was primarily attributed to the formation of conductive particle networks and improved interfacial heat transport associated with increasing nanoparticle loading. The proposed framework provided an accurate, robust, and computationally efficient methodology for predicting the thermophysical behavior of hybrid nanofluids and can be readily extended to estimate other thermophysical properties using appropriate experimental datasets.