Complete Mathematical Model Research Articles

Study of thermal and humidity environment and prediction model in impinging jet ventilation rooms based on thermal and moisture coupling

Variations of indoor humidity have significant influence on thermal comfort, calculation accuracy of air-conditioning load and selection of design parameters. As one of the most promising advanced ventilation strategies, impinging jet ventilation (IJV) has received much attention. However, few study concerned its coupled indoor thermal and humidity environment and there is also no complete mathematical model for the IJV to synchronously predict its indoor temperature and humidity distributions. Therefore, this study first simulated the thermal and humidity environment in IJV rooms with considering the coupled thermal and moisture transfer effect. The results demonstrate a significant correlation between temperature and humidity distributions in IJV, with a correlation coefficient of approximately 0.4. Then, a simplified theoretical model for predicting temperature and humidity distributions in the IJV was established based on the theory of nodal model, and the key parameters within the model that are influenced by indoor airflow pattern were also identified. Next, the model results were compared with the simulation ones and showed that the proposed model is with a mean absolute error of 0.4°C for the prediction of temperature distribution and of 0.21g/kg for the prediction of humidity distribution. These discrepancies are sufficiently minor to validate the accuracy of the proposed model. Last, the potential application value of the proposed model was discussed. Overall, the current study contributes to extend the application of the existing coupled thermal and humidity models to IJV scenarios, and provides a robust theoretical foundation for the more rational design and practical application of the IJV.

Human Vision as A Multi-Circuit Mathematical Model of the Automated Control System

Abstract The paper contains a proposal an original, extended mathematical model of an automatic system of human vision reaction to a forcing light pulse. A comprehensive mathematical model of the vision process was proposed in the form of an equation described in the frequency (dynamics) domain. Mathematical modelling of human senses is very important. It enables better integration of automation systems with a human cooperating with them, also as an automation system. This provides the basis for reasoning based on a mathematical model instead of intuitive reasoning about human reactions to visual stimuli. A block diagram of the proposed system with five human reaction paths is given. The following can be distinguished in the scheme: the main track consisting of: the transport delay of the eye reaction, the transport delay of the afferent nerves, the inertia of the brain with a preemptive action, the transport delay of the centrifugal nerves and the inertial and transport delay of the neuromotor system. In addition, the scheme of the system includes four tracks of negative feedback of motor and force reactions: upper eyelid, lower eyelid, pupil and lens. In the proposed model, the components of each path along with their partial mathematical models are given and discussed. For each reaction path, their overall mathematical models are also given. Taking into account the comprehensive models of all five reaction paths, a complete mathematical model of the automatic system of human reaction to a forcing light impulse is proposed. The proposed mathematical model opens up many possibilities for synchronizing it with mathematical models of many mechatronics and automation systems and their research. Optimizing the parameters of this model and its synchronization with specific models of automation systems is difficult and requires many numerical experiments. This approach enables the design of automation systems that are better synchronized with human reactions to existing stimuli and the selection of optimal parameters of their operation already in the design phase. The proposed model allows, for example, accurate determination of difficulty levels in computer games. Another example of the use of the proposed model is the study of human reactions to various situations generated virtually, for example in flight simulators and other similar ones.

Numerical and experimental frequency analysis of damaged fiber‐reinforced metal laminated composite

AbstractThis research numerically evaluated the eigenvalue responses of the damaged fiber metal laminate (FML) structure. The current numerical model is delved into including crack‐type damage effect on the structural integrity/ stiffness via frequency response. In this regard, a complete mathematical model of FML has been derived through higher‐order shear deformation kinematics for computational purposes. The mathematical model is converted to computer code in the MATLAB platform to predict the eigenvalue responses of FML components with and without damage. The damage influences are considered via circular meshing of finite element steps associated with the isoparametric element (nine nodes and nine degrees of freedom for each node). The solution consistency is checked via convergence, and the results are compared with data available in the open domain. Further, an experimental test is carried out to improve confidence using an in‐house test rig. The experiment was conducted by varying the length of the FML in 0.1 m increments. The results showed good agreement between the numerical and experimental data, with the lowest deviation being 0.29% and the highest 8.97%. The developed numerical model is extended to analyze the influences of design parameters such as geometry shape, aspect ratio (a/b), thickness ratio (a/h) ratio, curvature ratio, and fiber layup sequence on the natural frequency response.

Numerical study of multi-phase flow in ultrashort pulse laser processing

Ultrashort pulse laser processing is highly valued due to its enormous potential for high micromachining quality while it comprises complicated physical mechanisms especially when the pulse width falls in the regime about 10 ps. This study presents a complete mathematical modeling on multi-phase phenomena in ultrashort pulse laser processing, such as melting, vaporization, and solidification. The volume of fluid (VOF) technique is used to capture the interface during phase transition. Based on this hybrid model, the transport of energy and mass are investigated to study the influence of laser parameters on the formation of laser ablation hole. This work develops the incompressible multiphase laser ablation solver based on PIMPLE algorithm. The calculation results are validated by different references under different laser processing parameters which emphasize the importance of mechanism on thermal ablation and hydrodynamics in picosecond laser processing. More calculation results about the trends in hole depth over pulse laser width, laser fluence, and the number of pulses show the intricate influence of laser parameters.

Learning fluid physics from highly turbulent data using sparse physics-informed discovery of empirical relations (SPIDER)

We show how a complete mathematical model of a physical process can be learned directly from data via a hybrid approach combining three simple and general ingredients: physical assumptions of smoothness, locality and symmetry, a weak formulation of differential equations and sparse regression. To illustrate this, we extract a complete system of governing equations of fluid dynamics – the Navier–Stokes equation, the continuity equation and the boundary conditions – as well as the pressure-Poisson and energy equations, from numerical data describing a highly turbulent channel flow in three dimensions. Whether they represent known or unknown physics, relations discovered using this approach take the familiar form of partial differential equations, which are easily interpretable and readily provide information about the relative importance of different physical effects. The proposed approach offers insight into the quality of the data, serving as a useful diagnostic tool. It is also remarkably robust, yielding accurate results for very high noise levels, and should thus be well suited for analysis of experimental data.

Research on the influencing factors of housing price based on multiple linear regression and random forest

This paper aims to use multiple linear regression model and random forest models to analyze and study the factors affecting the housing price in Boston. The multiple linear regression model describes the relationship between multiple independent variables and one dependent variable through linear equations, and the random forest improves the accuracy and robustness by constructing multiple decision trees and combining their prediction results. To deal with complex nonlinear relationships and high dimensional data. Housing price is an important index to reflect the level and condition of economic and social development of a region, so it is of theoretical value and practical significance to explore its influencing factors and ways and degrees. Multiple factors are selected to analyze the weight and importance of each influencing factor, so as to help the government and decision makers to formulate more accurate policies, promote the stable development of the market, and provide scientific decision-making support for real estate developers, investors and ordinary buyers. In this study, the random forest model based on decision tree was used to clean, select and reduce the acquired housing price data, and to find out the main factors affecting housing price from the perspective of information gain, so as to obtain a relatively complete mathematical model and provide a reference scheme for future research by scholars.

Research on Mathematical Modeling of Naval Gun Servo System

Abstract Tracking performance of naval gun servo system is very important to the whole combat function of naval gun weapon system. Therefore, it is very important to construct accurate mathematical model to improve the performance of servo system. This paper analyzed the structure of naval gun servo system in detail and established the transfer function of each component according to its working principle. Finally, the complete mathematical model of naval gun servo system is established through the organic combination of all parts. Then the stability of the mathematical model of naval gun servo system is judged by Rouse criterion. When the original servo system is unstable, it is necessary to modify the model of servo system by designing lead-lag correction to achieve stable control of the servo system, which lays a foundation for further research on control performance optimization based on mathematical model of naval gun servo system.

Аналіз впливу на прохідність автобронетанкової техніки конструктивних факторів та методика її збільшення шляхом автоматичного регулювання тиску повітря в шинах коліс

The purpose of the study is to analyze and determine the influence of various factors on the patency of armored vehicles (AMT) operated by the National Guard of Ukraine. Determination of the change in patency during the movement of AMT in different road and climatic conditions. Analysis of static and dynamic loads, which are characteristic of AMT movement over rough terrain, and their impact on the efficiency of the vehicle. The theoretical component of the study was carried out using mathematical modeling of the work process of regulating the air pressure in tires of AMT wheels, using the example of changes in the characteristics of adhesion coefficients with the supporting surface and rolling resistance depending on the change in pressure and load on the tires of the wheels when the AMT is moving off-road. As a result of mathematical modeling, the dependences of air pressure in tires of AMT wheels were obtained, depending on the coefficient of rolling resistance and the load on each of the wheels. Which, in turn, makes it possible to move to a sufficiently complete mathematical modeling of the movement of AMT on off-road, taking into account the reference cross-country ability. In the process of theoretical research, the structural parameters of the impact on the patency of AMT were analyzed quite completely, and a generalized comparative indicator of the patency parameters of vehicles was proposed. When analyzing it, it was found that the AMT tire and, specifically, the change in air pressure in it, have a significant impact on the bearing capacity. The authors propose to use the following evaluation criteria as criteria for assessing the efficiency of the passability when driving on deformable surfaces: a generalized comparative indicator of the parameters of the passability of vehicles. As a result of consideration of which, a significant influence on the patency parameters of the tires and directly the air pressure in them was established. Regulation and change of the air pressure in the tires of the wheels depending on the change in the coefficient of rolling resistance as well as the change in the load on each wheel, which are the ratio of the work that is spent on the traction force when overcoming different degrees of heaviness of the resistance of the supporting surfaces with the effect of deformation. And the load that falls on each of the AMT wheels allowed us to draw conclusions about the improvement of the regular tire pressure regulation system (RPRS) of the wheels.

System Study Review of Electrical Machines under Specific Operating Conditions of Power Installations

The problem of life cycle vulnerability, predetermined by the development stages, operation and modernization of electrical machines due tosize and weight restrictions, dynamic electromagnetic and thermal overloads, possible flooding and changes in ventilation and cooling conditionsis considered. Reducing the weight and size of electric machines implies eliminating passive sections of magnetic circuits and optimizing the ratio of copper and steel. The desire to reduce weight and size indicators and increase energy density entails increased heat generation and temperature loads of structural elements. The increase in operatingtemperatures of modern machines indicates the need to develop mathematical models that account the response of electrical materials and structural elements to the combined thermal and magnetic fieldeffects. Such models are in demand to study the temperature dependence of insulating, magnetic and operating properties of electrical machines when establishing the requiredoperating moderestrictions in order to preserve and extend the life cycle. The criterion for making management decisions aimed at changing operating modes during operation can be maximum loads that limit exceeding the maximum permissible temperatures of the electrical insulationclass used, as well as critical values of induction determined by the temperature dependence of ferromagnetproperties that affect the performance characteristics of electrical machines. Further solution to the problem lies in the creation of digital twins containing complete mathematical and computer simulation models that describe processes in electrical machines, taking into account the temperature dependence of materialphysical properties of structural elements being subjected to thermal, magnetic and electric fields.

Исследование адсорбционного разделения газовых смесей в условиях нестационарности

The influence of the initial concentration, rate and temperature of adsorption on the adsorption separation of gas mixtures (CO2, CH4, N2, H2S) is investigated. Components: N2 – 5%, H2S – 5%, CO2 – 5% and CH4 – 85%. And as an adsorbent granule of clinoptilolite of irregular shape were used. Isothermal adsorption of CO2 was obtained at different temperatures (293, 313, and 323 K). The obtained isotherms of CO2 adsorption showed that with an increase in temperature, the adsorption of CO2 decreased. The type of isotherms corresponds to Langmuir. The output curves of gas mixture adsorption depending on the gas flow rate and various main components of CO2 were also experimentally studied. The output curves of the adsorption of the CO2 component were studied at various gas flow rates of 20, 50, and 80 mL/min. Equilibrium time increases with a decrease in the gas flow rate. Output curves were also obtained depending on the initial CO2 concentrations of 5%, 10% and 20%. It was determined that with a decrease in the initial concentration of CO2, the equilibrium time also increases. Gas mixture components sorbed downwards: H2S→CO2→CH4→N2. The resulting system of model equations describing the adsorption separation of gas mixtures in a fixed adsorbent layer represents a complete mathematical model of the process under unsteady conditions. The obtained regularities of the process of adsorption of gas mixtures testify to the fact that the process takes place under non-stationary conditions. The proposed models for the optimal design of industrial absorbers can be used for adsorption separation of gas mixtures in the conditions of their unsteady flow.

Performance evaluation of standalone new solar energy system of hybrid PV/electrolyzer/fuel cell/MED-MVC with hydrogen production and storage for power and freshwater building demand

To achieve zero carbon emissions, increasing the scale of renewable energy implementation is imperative. Hydrogen is considered the prospective solution for sustainable energy due to its dual nature as a carbon-neutral fuel and an efficient storage medium for renewable energy sources. So, in this work, a standalone new hybrid energy system powered by solar energy for yearly power and freshwater production for building demand in New Borg El-Arab, Egypt. The system comprises photovoltaic (PV) panels, a water electrolyzer, multi-effect mechanical vapor compression desalination (MED-MVC), and fuel cells with hydrogen storage. A complete mathematical system model is built and solved by MATLAB/Simulink to study the daily, monthly, and yearly performance and sizing of the different system components based on the location climate conditions. The results indicate that PV panels of an area of 1824 m2, in conjunction with an electrolyzer, 863 fuel cells, and a storage tank capacity of 3013.4 m3can satisfy the annual building requirements of 255.17 MWh electricity, 766.5 m3 hot water and 876 m3 cold water. The maximum hydrogen storage lies between September and October, with maximum consumption between February and March. The average annual efficiency of PV, electrolyzer, fuel cell, electrolyzer output, fuel cell output, and overall hybrid system is 20.7%, 68.2%, 34.6%, 13.4%, 4.4%, and 16.5%, respectively, and the performance ratio (PR) of MED-MVC is 2.61. The system proves its capability to supply the building with electrical and water requirements with a levelized cost of energy (LCOE) equal to 0.712 $/kWh. Additionally, This system shows the potential to include other activities in remote areas or islands besides its contribution to achieving SDGs 6, 7, and 13.

An asymmetric rotor model under external, parametric, and mixed excitations: Nonlinear bifurcation, active control, and rub-impact effect

This article explores the nonlinear dynamical analysis and control of a [Formula: see text] DOF system that emulates the lateral vibration of an asymmetric rotor model under external, multi-parametric, and mixed excitation. The linear integral resonant controller ([Formula: see text]) has been coupled to the rotor as an active damper through a magnetic actuator. The complete mathematical model, governing the nonlinear interaction among the rotor, controller, and actuator, is derived based on electromagnetic theory and the principle of solid mechanics. This results in a discontinuous [Formula: see text] DOF system coupled with two [Formula: see text] DOF systems, incorporating the rub-impact effect between the rotor and stator. The complicated mathematical model is investigated using analytical techniques, employing the perturbation method, and validated numerically through time response, basins of attraction, bifurcation diagrams, [Formula: see text] chaotic test, and Poincaré return map. The main findings indicate that the asymmetric system model may exhibit nonzero bistable forward whirling motion under external excitation. Additionally, it can whirl either forward or backward under multi-parametric excitation, besides the trivial stable solution. Furthermore, in the case of mixed excitation, the rotor displays nontrivial tristable solutions, with two corresponding to forward whirling orbits and the other one corresponding to backward whirling oscillation. These findings are validated through the establishment of different basins of attraction. Finally, the performance of the [Formula: see text] in mitigating rotor vibrations and averting nonlinear catastrophic bifurcations under various excitation conditions. Furthermore, the rotor’s dynamical behavior and stability are explored in the event of an abrupt failure of one of the connected controllers. The outcomes demonstrate that the proposed [Formula: see text] effectively eliminates dangerous nonlinearities, steering the system to respond akin to a linear system with controllable oscillation amplitudes. However, the sudden controller failure induces a local rub-impact effect, leading to a nonlocal quasiperiodic oscillation and restoring the dominance of the nonlinearities on the system’s response.

Fuzzy‐PID controller based on improved LFPSO for temperature and humidity control in a CA ripening system

AbstractTemperature and humidity as the key factors affecting the storage and ripening of fruits and vegetables directly determine the quality of fruits and vegetables. In this paper, a temperature and humidity model was constructed based on an integrated device of controlled atmosphere storage and ripening. Aiming at the shortcomings of the temperature and humidity model such as large inertia, nonlinearity, and model uncertainty, a fuzzy‐PID controller based on the improved Lévy flight particle swarm algorithm (LFPSO) is proposed. Initially, a mathematical model of temperature and humidity is developed through mechanism research and parameter estimation. Subsequently, a temperature and humidity fuzzy‐PID control strategy is proposed for regulating temperature and humidity. An improved LFPSO is then introduced to optimize the key parameters of the fuzzy‐PID controller, such as the quantization factor and the scale factor. The superiority of the improved LFPSO algorithm is verified by comparing the test functions. Finally, the improved LFPSO‐fuzzy‐PID controller, fuzzy‐PID controller, and Smith‐PID controller are applied to the simulation model for comparison using the MATLAB Simulink simulation platform. The results show that the improved LFPSO‐fuzzy‐PID control algorithm has a good control effect in the temperature and humidity simulation system of controlled atmosphere (CA) ripening container, which provides a reference for solving the optimization problem of actual engineering design.Practical applicationsIn order to reduce the postharvest cold chain losses of fruits and vegetables, this paper proposes a containerized style device that combines fruits and vegetables storage and ripening for simplifying the losses caused by transshipment at cold chain nodes. Since temperature and humidity play a key role in fruits and vegetables storage and ripening, which directly affect the product quality, this paper establishes a complete mathematical model of CA ripening temperature and humidity system by combining mechanism modeling and parameter identification. In order to keep the temperature and humidity within the ideal range, Smith‐PID controller, fuzzy‐PID controller, and fuzzy‐PID control method based on improved Lévy flight particle swarm optimization are proposed to regulate the air conditioner and humidifier. The performance of three different types of controllers was tested on the MATLAB. The simulation results demonstrate that the improved LFPSO‐fuzzy‐PID controller is superior and more effective than Smith‐PID and fuzzy‐PID controllers.

A novel dynamic stiffness matrix for the nonlocal vibration characteristics of porous functionally graded nanoplates on elastic foundation with small-scale effects

The present paper deals with the development of a dynamic stiffness matrix to evaluate the free vibration response of functionally graded nanoplate (FG-nP) resting on the Winkler-Pasternak elastic foundation. The complete mathematical modeling of the dynamic stiffness matrix for nanostructures is given for the first time. The equation of motion for rectangular FG-nP plates supported on an elastic foundation is derived using Hamilton’s principle in conjunction with nonlocal elasticity theory. The non-local theory is incorporated to account for the size effect in the small-scale plate. The effective material property of the porous FG-nP has been calculated using three recently developed models of porosity. The developed dynamic stiffness matrix is solved using the Wittrick-Williams algorithm to extract the natural frequencies of the FG-nP. The variation of natural frequencies with the change of numerical values, such as nonlocal parameter, aspect ratio, elastic foundation parameters, and porosity volume fraction is analyzed. The validity and accuracy of the results are confirmed through comparison with the available literature. The use of non-local theory in dynamic stiffness analysis is shown to be effective in predicting the natural frequency of the FG-nP on a Winkler-Pasternak elastic foundation, providing new insights into the dynamic behavior of small-scale structures.

Dynamic Modelling and Simulation of A Three-Phase Gravity Separator

Many studies have investigated the crude oil separation process’s separation mechanisms, size, and design, employing horizontal 3-Phase Gravity Separators in depth. There are, however, very few articles on their dynamics, modelling, and simulation. Understanding its dynamic behaviour will aid in designing and tuning the device that can manage water level, oil level, and gas pressure in response to feeding variations. This Scientific Paper gives a complete mathematical analysis, modelling, and simulation of a crude oil separation process using a horizontal 3-Phase Gravity Separator using Mathworks Matlab R2016b-x64 and Aspen Hysys V10. Bishoy’s Equations, which were constructed, will assist in operating this gadget, locating various variables, and observing the effect of modifying variables on the system’s variables. The rationale for this study was developed in response to the small number of articles discovered, which may be a covert issue held up by large oil companies, as well as the complicated equations related to this process that remain unsolved, and to monitor what is happening in this complex dynamic process. As a result, this Research Paper is unique and novel, and it can be compared to the work done by some authors who did not solve the obtained differential equations and did not go further in Aspen Hysys Modeling and Simulation, whereas this paper provides everything related to a three-phase gravity separator, including changing of variables and observing the effect on the system when those variables were modified. Furthermore, separators are designed with internal baffles to promote laminar flow and increase separator efficiency. However, it has been assumed that there are no baffles here, which is a significant problem, but with the help of these equations, the horizontal three-phase gravity separator can be operated at its maximum efficiency. The equations determined the following variables: The height of gas, water, oil, the height of oil when it jumped the weir, the pressure of the gas (in and out), water pressure (in and out), oil pressure (in and out), and the effect of increasing (control valve’s stem position) and decreasing Qin (inlet volumetric flowrate) on these variables have all been studied. This article discovered that increasing the control valve stem position and decreasing the inflow volumetric flowrate of both oil and water was highly unsafe and caused significant variations in the system’s heights and pressures using Matlab. The Aspen Hysys analysis optimally separates the oil, gas, and water to determine material, energy streams properties, and compositions. As a result, this complex dynamic behaviour was observed, and no additional articles were discovered that addressed this subject. This process monitoring will determine the best conditions for flawless separation, with the selectivity of the desired product or products as the primary goal. This research can revolutionize the way people think about oil and gas extraction and processing and benefit colossal oil and gas firms in Europe, Asia, and Africa.

Research on obstacle avoidance of multi-AUV cluster formation based on virtual structure and artificial potential field method★

The formation of autonomous underwater vehicle (AUV) in the three-dimensional environment is very important for carrying out complex ocean tasks. During formation sailing, it is necessary to consider avoiding obstacles while maintaining the formation. In this paper, an AUV formation obstacle avoidance method based on virtual structure and artificial potential field method is proposed. Firstly, a complete mathematical modeling of AUV is carried out, and a sliding mode position tracker based on virtual position points is designed based on this model. Then the tracking points of each AUV in the formation are calculated according to the expected trajectory and formation feature structure to ensure that the spacing between AUVs meets the requirements of the formation. Finally, the artificial potential field method is introduced into the position tracker to avoid obstacles between the obstacle and the AUV. Five groups of simulation experiments of parallel formation, vertical formation, cross formation, triangular formation and unknown complex environment are designed. The formation scalability of the algorithm is simulated and compared with the virtual leader method in related references. Finally, KKSwarm platform is used to conduct a real simulation in 2D environment to verify the effectiveness of the proposed algorithm.The experimental results show that the proposed method can effectively realize the formation navigation of multiple underwater vehicles and successfully avoid obstacles, which provides an effective method to solve the problem of the formation obstacle avoidance of underactuated AUV.

Co-optimization of power and water distribution systems for simultaneous hydropower generation and water pressure regulation

Water Distribution Systems (WDSs) are gravitational systems supplying water, mainly. Little research has been conducted on harnessing the great amount of energy that is currently dissipated during water pressure regulation, usually performed with “passive” devices like Pressure Reduction Valves (PRVs). This paper develops a co-optimization framework between Water and Power Distribution Systems (PDS) and introduces the concept of Integrated Power-Water Distribution System (IPWDS). Under this framework, PRVs are replaced by hydro-turbines, which form the interconnecting links between the two systems. They regulate pressure at the WDS while injecting the power resulting from their action to PDS. The complete WDS and PDS mathematical models are adopted and the detailed turbine design and performance model that accounts for turbines feasible operational range is considered. The suggested method optimizes the power generation of the hydro-turbines subject to the hydraulic restrictions and power flow constraints imposed by each network. Optimal Power Flow (OPF) has been extended in order to accommodate turbine’s model and constraints imposed by the varying daily flows of the WDS and PDS. Results taken under the suggested framework from a typical WDS, demonstrated that more than 393 MWh (approximately $40 K) of clean power could be produced per year. However, the violation of the unified set of constraints from the IPWDS may reduce the amount of renewable power generation by a significant 7%. This paper focuses mainly on the technical aspect of such an approach. Future work will focus on the economic assessment and viability of such joint projects, resulting from co-optimization and on social-technical aspects that aim on maximizing the penetration of turbines within existing PDS.

A comparison of Algebraic Multigrid Bidomain solvers on hybrid CPU–GPU architectures

The numerical simulation of cardiac electrophysiology is a highly challenging problem in scientific computing. The Bidomain system is the most complete mathematical model of cardiac bioelectrical activity. It consists of an elliptic and a parabolic partial differential equation (PDE), of reaction–diffusion type, describing the spread of electrical excitation in the cardiac tissue. The two PDEs are coupled with a stiff system of ordinary differential equations (ODEs), representing ionic currents through the cardiac membrane. Developing efficient and scalable preconditioners for the linear systems arising from the discretization of such computationally challenging model is crucial in order to reduce the computational costs required by the numerical simulations of cardiac electrophysiology. In this work, focusing on the Bidomain system as a model problem, we have benchmarked two popular implementations of the Algebraic Multigrid (AMG) preconditioner embedded in the PETSc library and we have studied the performance on the calibration of specific parameters. We have conducted our analysis on modern HPC architectures, performing scalability tests on multi-core and multi-GPUs settings. The results have shown that, for our problem, although scalability is verified on CPUs, GPUs are the optimal choice, since they yield the best performance in terms of solution time.

Entropy generation for thermo-magnetic fractional order convective flow in complex porous enclosures: a numerical study

PurposeThis study aims to analyze the impact of fractional derivatives on heat transfer and entropy generation during transient free convection inside various complex porous enclosures, such as triangle, L-shape and square-containing wavy surfaces. These porous enclosures are saturated with Cu-water nanofluid and subjected to the influence of a uniform magnetic field.Design/methodology/approachIn the present study, Darcy’s model is used for the momentum transport equation in the porous matrix. Additionally, the Caputo time fractional derivative is introduced in the energy equation to assess the heat transfer phenomenon. Furthermore, the total entropy generation has been computed by combining the entropy generation due to fluid friction (Sff), heat transfer (Sht) and magnetic field (Smf). The complete mathematical model is further simulated using the penalty finite element method, and the Caputo time derivative term is approximated using the L1 scheme. The study is conducted for various ranges of the Rayleigh number (102≤Ra≤104), Hartmann number (0≤Ha≤20) and fractional order parameter (0<α<1) with respect to time.FindingsIt has been observed that the fractional order parameter α governs the characteristics of entropy generation and heat transfer within the selected range of parameters. The Bejan number associated with heat transfer (Beht), fluid friction (Beff) and magnetic field (Bemf) further demonstrate the dominance of flow irreversibilities. It becomes evident that the initial evolution state of streamlines, isotherms and local entropy varies according to the choice of α. Additionally, increasing Ra values from 102 to 104 shows that the heat transfer rate increases by 123.8% for a square wavy enclosure, 7.4% for a triangle enclosure and 69.6% for an L-shape enclosure. Moreover, an increase in the value of Ha leads to a reduction in heat transfer rates and entropy generation. In this case, Bemf→1 shows the dominance of the magnetic field irreversibility in the total entropy generation.Practical implicationsRecently, fractional-order models have been widely used to express numerous physical phenomena, such as anomalous diffusion and dispersion in complex viscoelastic porous media. These models offer a more accurate representation of physical reality that classical models fail to capture; this is why they find a broad range of applications in science and engineering.Originality/valueThe fractional derivative model is used to illustrate the flow pattern, heat transfer and entropy-generating characteristics under the influence of a magnetic field. Furthermore, to the best of the author’s knowledge, a fractional-derivative-based mathematical model for the entropy generation phenomenon in complex porous enclosures has not been previously developed or studied.

Artificial Intelligence Techniques based on aquaculture solar thermal water heating system control

The One of the most promising applications of hot water is aquaculture. Temperature is one of the most principle parameters affects aquaculture life. It can cause stress and mortality or superior environment for growth and reproduction. Shrimp is warm water aquaculture type need hot water supply. To increase pond production it is necessary to keep water temperature at 34oC. Artificial intelligence (AI) techniques are becoming useful as alternate approaches to conventional techniques or as components of integrated systems. They have been used to solve complicated practical problems in various areas and are becoming more and more popular nowadays. In this paper a control system using artificial neural network control (NNC) either adaptive fuzzy logic control (AFLC) are design to control the hot water temperature. A comparison study is applied between the performance of FLC and NNC. The performance of NNC is the best because the control design takes into consideration different variables which give an accurate output than FLC. Also this paper introduces a complete mathematical modeling and MATLAB SIMULINK model for the proposed aquaculture heating system.