In this research work, we investigate the asymptotic behavior of a nonlinear swelling (also called expansive) soil system with a time delay and nonlinear damping of variable exponents. We should note here that swelling soils contain clay minerals that absorb water, which may lead to increases in pressure. In architectural and civil engineering, swelling soils are considered sources of problems and harm. The presence of the delay is used to create more realistic models since many processes depend on past history, and the delays are frequently added by sensors, actuators, and field networks that travel through feedback loops. The appearance of variable exponents in the delay and damping terms in this system allows for a more flexible and accurate modeling of this physical phenomenon. This can lead to more realistic and precise descriptions of the behavior of fluids in different media. In fact, with the advancements of science and technology, many physical and engineering models require more sophisticated mathematical tools to study and understand. The Lebesgue and Sobolev spaces with variable exponents proved to be efficient tools for studying such problems. By constructing a suitable Lyapunov functional, we establish exponential and polynomial decay results. We noticed that the energy decay of the system depends on the value of the variable exponent. These results improve on some existing results in the literature.
{"title":"Asymptotic Behavior of Solutions to a Nonlinear Swelling Soil System with Time Delay and Variable Exponents","authors":"Mohammad M. Kafini, M. Al-Gharabli, A. Al‐Mahdi","doi":"10.3390/mca28050094","DOIUrl":"https://doi.org/10.3390/mca28050094","url":null,"abstract":"In this research work, we investigate the asymptotic behavior of a nonlinear swelling (also called expansive) soil system with a time delay and nonlinear damping of variable exponents. We should note here that swelling soils contain clay minerals that absorb water, which may lead to increases in pressure. In architectural and civil engineering, swelling soils are considered sources of problems and harm. The presence of the delay is used to create more realistic models since many processes depend on past history, and the delays are frequently added by sensors, actuators, and field networks that travel through feedback loops. The appearance of variable exponents in the delay and damping terms in this system allows for a more flexible and accurate modeling of this physical phenomenon. This can lead to more realistic and precise descriptions of the behavior of fluids in different media. In fact, with the advancements of science and technology, many physical and engineering models require more sophisticated mathematical tools to study and understand. The Lebesgue and Sobolev spaces with variable exponents proved to be efficient tools for studying such problems. By constructing a suitable Lyapunov functional, we establish exponential and polynomial decay results. We noticed that the energy decay of the system depends on the value of the variable exponent. These results improve on some existing results in the literature.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48077588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
C. Páez-Rueda, A. Fajardo, Manuel Pérez, G. Yamhure, G. Perilla
This paper studies and analyzes the approximation of one-dimensional smooth closed-form functions with compact support using a mixed Fourier series (i.e., a combination of partial Fourier series and other forms of partial series). To explore the potential of this approach, we discuss and revise its application in signal processing, especially because it allows us to control the decreasing rate of Fourier coefficients and avoids the Gibbs phenomenon. Therefore, this method improves the signal processing performance in a wide range of scenarios, such as function approximation, interpolation, increased convergence with quasi-spectral accuracy using the time domain or the frequency domain, numerical integration, and solutions of inverse problems such as ordinary differential equations. Moreover, the paper provides comprehensive examples of one-dimensional problems to showcase the advantages of this approach.
{"title":"Exploring the Potential of Mixed Fourier Series in Signal Processing Applications Using One-Dimensional Smooth Closed-Form Functions with Compact Support: A Comprehensive Tutorial","authors":"C. Páez-Rueda, A. Fajardo, Manuel Pérez, G. Yamhure, G. Perilla","doi":"10.3390/mca28050093","DOIUrl":"https://doi.org/10.3390/mca28050093","url":null,"abstract":"This paper studies and analyzes the approximation of one-dimensional smooth closed-form functions with compact support using a mixed Fourier series (i.e., a combination of partial Fourier series and other forms of partial series). To explore the potential of this approach, we discuss and revise its application in signal processing, especially because it allows us to control the decreasing rate of Fourier coefficients and avoids the Gibbs phenomenon. Therefore, this method improves the signal processing performance in a wide range of scenarios, such as function approximation, interpolation, increased convergence with quasi-spectral accuracy using the time domain or the frequency domain, numerical integration, and solutions of inverse problems such as ordinary differential equations. Moreover, the paper provides comprehensive examples of one-dimensional problems to showcase the advantages of this approach.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43242964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study investigates via Lie symmetry analysis the Hunter–Saxton equation, an equation relevant to the theoretical analysis of nematic liquid crystals. We employ the multiplier method to obtain conservation laws of the equation that arise from first-order multipliers. Conservation laws of the equation, combined with the admitted Lie point symmetries, enable us to perform symmetry reductions by employing the double reduction method. The method exploits the relationship between symmetries and conservation laws to reduce both the number of variables and the order of the equation. Five nontrivial conservation laws of the Hunter–Saxton equation are derived, four of which are found to have associated Lie point symmetries. Applying the double reduction method to the equation results in a set of first-order ordinary differential equations, the solutions of which represent invariant solutions for the equation. While the double reduction method may be more complex to implement than the classical method, since it involves finding Lie point symmetries and deriving conservation laws, it has some advantages over the classical method of reducing PDEs. Firstly, it is more efficient in that it can reduce the number of variables and order of the equation in a single step. Secondly, by incorporating conservation laws, physically meaningful solutions that satisfy important physical constraints can be obtained.
{"title":"Conservation Laws and Symmetry Reductions of the Hunter–Saxton Equation via the Double Reduction Method","authors":"Molahlehi Charles Kakuli, W. Sinkala, P. Masemola","doi":"10.3390/mca28050092","DOIUrl":"https://doi.org/10.3390/mca28050092","url":null,"abstract":"This study investigates via Lie symmetry analysis the Hunter–Saxton equation, an equation relevant to the theoretical analysis of nematic liquid crystals. We employ the multiplier method to obtain conservation laws of the equation that arise from first-order multipliers. Conservation laws of the equation, combined with the admitted Lie point symmetries, enable us to perform symmetry reductions by employing the double reduction method. The method exploits the relationship between symmetries and conservation laws to reduce both the number of variables and the order of the equation. Five nontrivial conservation laws of the Hunter–Saxton equation are derived, four of which are found to have associated Lie point symmetries. Applying the double reduction method to the equation results in a set of first-order ordinary differential equations, the solutions of which represent invariant solutions for the equation. While the double reduction method may be more complex to implement than the classical method, since it involves finding Lie point symmetries and deriving conservation laws, it has some advantages over the classical method of reducing PDEs. Firstly, it is more efficient in that it can reduce the number of variables and order of the equation in a single step. Secondly, by incorporating conservation laws, physically meaningful solutions that satisfy important physical constraints can be obtained.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42054145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
H. Eivazi, Jendrik-Alexander Tröger, Stefan H. A. Wittek, S. Hartmann, A. Rausch
Multiscale FE2 computations enable the consideration of the micro-mechanical material structure in macroscopical simulations. However, these computations are very time-consuming because of numerous evaluations of a representative volume element, which represents the microstructure. In contrast, neural networks as machine learning methods are very fast to evaluate once they are trained. Even the DNN-FE2 approach is currently a known procedure, where deep neural networks (DNNs) are applied as a surrogate model of the representative volume element. In this contribution, however, a clear description of the algorithmic FE2 structure and the particular integration of deep neural networks are explained in detail. This comprises a suitable training strategy, where particular knowledge of the material behavior is considered to reduce the required amount of training data, a study of the amount of training data required for reliable FE2 simulations with special focus on the errors compared to conventional FE2 simulations, and the implementation aspect to gain considerable speed-up. As it is known, the Sobolev training and automatic differentiation increase data efficiency, prediction accuracy and speed-up in comparison to using two different neural networks for stress and tangent matrix prediction. To gain a significant speed-up of the FE2 computations, an efficient implementation of the trained neural network in a finite element code is provided. This is achieved by drawing on state-of-the-art high-performance computing libraries and just-in-time compilation yielding a maximum speed-up of a factor of more than 5000 compared to a reference FE2 computation. Moreover, the deep neural network surrogate model is able to overcome load-step size limitations of the RVE computations in step-size controlled computations.
{"title":"FE2 Computations with Deep Neural Networks: Algorithmic Structure, Data Generation, and Implementation","authors":"H. Eivazi, Jendrik-Alexander Tröger, Stefan H. A. Wittek, S. Hartmann, A. Rausch","doi":"10.3390/mca28040091","DOIUrl":"https://doi.org/10.3390/mca28040091","url":null,"abstract":"Multiscale FE2 computations enable the consideration of the micro-mechanical material structure in macroscopical simulations. However, these computations are very time-consuming because of numerous evaluations of a representative volume element, which represents the microstructure. In contrast, neural networks as machine learning methods are very fast to evaluate once they are trained. Even the DNN-FE2 approach is currently a known procedure, where deep neural networks (DNNs) are applied as a surrogate model of the representative volume element. In this contribution, however, a clear description of the algorithmic FE2 structure and the particular integration of deep neural networks are explained in detail. This comprises a suitable training strategy, where particular knowledge of the material behavior is considered to reduce the required amount of training data, a study of the amount of training data required for reliable FE2 simulations with special focus on the errors compared to conventional FE2 simulations, and the implementation aspect to gain considerable speed-up. As it is known, the Sobolev training and automatic differentiation increase data efficiency, prediction accuracy and speed-up in comparison to using two different neural networks for stress and tangent matrix prediction. To gain a significant speed-up of the FE2 computations, an efficient implementation of the trained neural network in a finite element code is provided. This is achieved by drawing on state-of-the-art high-performance computing libraries and just-in-time compilation yielding a maximum speed-up of a factor of more than 5000 compared to a reference FE2 computation. Moreover, the deep neural network surrogate model is able to overcome load-step size limitations of the RVE computations in step-size controlled computations.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42407058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A cerebral aneurysm is a medical condition where a cerebral artery can burst under adverse pressure conditions. A 20% mortality rate and additional 30 to 40% morbidity rate have been reported for patients suffering from the rupture of aneurysms. In addition to wall shear stress, input jets, induced pressure, and complicated and unstable flow patterns are other important parameters associated with a clinical history of aneurysm ruptures. In this study, the anterior cerebral artery (ACA) was modeled using image segmentation and then rebuilt with aneurysms at locations vulnerable to aneurysm growth. To simulate various aneurysm growth stages, five aneurysm sizes and two wall thicknesses were taken into consideration. In order to simulate realistic pressure loading conditions for the anterior cerebral arteries, inlet velocity and outlet pressure were used. The pressure, wall shear stress, and flow velocity distributions were then evaluated in order to predict the risk of rupture. A low-wall shear stress-based rupture scenario was created using a smaller aneurysm and thinner walls, which enhanced pressure, shear stress, and flow velocity. Additionally, aneurysms with a 4 mm diameter and a thin wall had increased rupture risks, particularly at specific boundary conditions. It is believed that the findings of this study will help physicians predict rupture risk according to aneurysm diameters and make early treatment decisions.
{"title":"A Computational Fluid Dynamics-Based Model for Assessing Rupture Risk in Cerebral Arteries with Varying Aneurysm Sizes","authors":"Rohan Singla, Shubham Gupta, A. Chanda","doi":"10.3390/mca28040090","DOIUrl":"https://doi.org/10.3390/mca28040090","url":null,"abstract":"A cerebral aneurysm is a medical condition where a cerebral artery can burst under adverse pressure conditions. A 20% mortality rate and additional 30 to 40% morbidity rate have been reported for patients suffering from the rupture of aneurysms. In addition to wall shear stress, input jets, induced pressure, and complicated and unstable flow patterns are other important parameters associated with a clinical history of aneurysm ruptures. In this study, the anterior cerebral artery (ACA) was modeled using image segmentation and then rebuilt with aneurysms at locations vulnerable to aneurysm growth. To simulate various aneurysm growth stages, five aneurysm sizes and two wall thicknesses were taken into consideration. In order to simulate realistic pressure loading conditions for the anterior cerebral arteries, inlet velocity and outlet pressure were used. The pressure, wall shear stress, and flow velocity distributions were then evaluated in order to predict the risk of rupture. A low-wall shear stress-based rupture scenario was created using a smaller aneurysm and thinner walls, which enhanced pressure, shear stress, and flow velocity. Additionally, aneurysms with a 4 mm diameter and a thin wall had increased rupture risks, particularly at specific boundary conditions. It is believed that the findings of this study will help physicians predict rupture risk according to aneurysm diameters and make early treatment decisions.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42705004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Burn injuries are very common due to heat, accidents, and fire. Split-thickness skin grafting technique is majorly used to recover the burn sites. In this technique, the complete epidermis and partial dermis layer of the skin are used to make grafts. A small amount of skin is passed into the mesher to create an incision pattern for higher expansion. These grafts are transplanted into the burn sites with the help of sutures for recovering large burn areas. Presently, the maximum expansion possible with skin grafting is very less (<3), which is insufficient for covering larger burn area with a small amount of healthy skin. This study aimed to determine the possibility of employing innovative auxetic skin graft patterns and traditional skin graft patterns with three levels of hierarchy. Six different hierarchical skin graft designs were tested to describe the biomechanical properties. The meshing ratio, Poisson’s ratio, expansion, and induced stresses were quantified for each graft model. The computational results indicated that the expansion potential of the 3rd order auxetic skin graft was highest across all the models. These results are expected to improve burn surgeries and promote skin transplantation research.
{"title":"Finite Element Analysis of Hierarchical Metamaterial-Based Patterns for Generating High Expansion in Skin Grafting","authors":"Vivek Gupta, A. Chanda","doi":"10.3390/mca28040089","DOIUrl":"https://doi.org/10.3390/mca28040089","url":null,"abstract":"Burn injuries are very common due to heat, accidents, and fire. Split-thickness skin grafting technique is majorly used to recover the burn sites. In this technique, the complete epidermis and partial dermis layer of the skin are used to make grafts. A small amount of skin is passed into the mesher to create an incision pattern for higher expansion. These grafts are transplanted into the burn sites with the help of sutures for recovering large burn areas. Presently, the maximum expansion possible with skin grafting is very less (<3), which is insufficient for covering larger burn area with a small amount of healthy skin. This study aimed to determine the possibility of employing innovative auxetic skin graft patterns and traditional skin graft patterns with three levels of hierarchy. Six different hierarchical skin graft designs were tested to describe the biomechanical properties. The meshing ratio, Poisson’s ratio, expansion, and induced stresses were quantified for each graft model. The computational results indicated that the expansion potential of the 3rd order auxetic skin graft was highest across all the models. These results are expected to improve burn surgeries and promote skin transplantation research.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42234240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The main objective of this study is to find out the influences of cooperation and intra-specific competition in the prey population on escaping predation through refuge and the effect of the two intra-specific interactions on the dynamics of prey–predator systems. For this purpose, two mathematical models with Holling type II functional response functions were proposed and analyzed. The first model includes cooperation among prey populations, whereas the second one incorporates intra-specific competition. The existence conditions and stability of different equilibrium points for both models were analyzed to determine the qualitative behaviors of the systems. Refuge through intra-specific competition has a stabilizing role, whereas cooperation has a destabilizing role on the system dynamics. Periodic oscillations were observed in both systems through Hopf bifurcation. From the analytical and numerical findings, we conclude that intra-specific competition affects the prey population and continuously controls the refuge class under a critical value, and thus, it never becomes too large to cause predator extinction due to food scarcity. Conversely, cooperation leads the maximal number of individuals to escape predation through the refuge so that predators suffer from low predation success.
{"title":"Impact of Cooperation and Intra-Specific Competition of Prey on the Stability of Prey–Predator Models with Refuge","authors":"Soumyadip Pal, F. Al Basir, Santanu Ray","doi":"10.3390/mca28040088","DOIUrl":"https://doi.org/10.3390/mca28040088","url":null,"abstract":"The main objective of this study is to find out the influences of cooperation and intra-specific competition in the prey population on escaping predation through refuge and the effect of the two intra-specific interactions on the dynamics of prey–predator systems. For this purpose, two mathematical models with Holling type II functional response functions were proposed and analyzed. The first model includes cooperation among prey populations, whereas the second one incorporates intra-specific competition. The existence conditions and stability of different equilibrium points for both models were analyzed to determine the qualitative behaviors of the systems. Refuge through intra-specific competition has a stabilizing role, whereas cooperation has a destabilizing role on the system dynamics. Periodic oscillations were observed in both systems through Hopf bifurcation. From the analytical and numerical findings, we conclude that intra-specific competition affects the prey population and continuously controls the refuge class under a critical value, and thus, it never becomes too large to cause predator extinction due to food scarcity. Conversely, cooperation leads the maximal number of individuals to escape predation through the refuge so that predators suffer from low predation success.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45325254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work analyses the buckling behaviour of cracked Euler–Bernoulli columns immersed in a Winkler elastic medium, obtaining their buckling loads. For this purpose, the beam is modelled as two segments connected in the cracked section by a mass-less rotational spring. Its rotation is proportional to the bending moment transmitted through the cracked section, considering the discontinuity of the rotation due to bending. The differential equations for the buckling behaviour are solved by applying the corresponding boundary conditions, as well as the compatibility and jump conditions of the cracked section. The proposed methodology allows calculating the buckling load as a function of the type of support, the parameter defining the elastic soil, the crack position and the initial length of the crack. The results obtained are compared with those published by other authors in works that deal with the problem in a partial way, showing the interaction and importance of the parameters considered in the buckling loads of the system.
{"title":"Buckling of Cracked Euler–Bernoulli Columns Embedded in a Winkler Elastic Medium","authors":"J. Loya, C. Santiuste, J. Aranda-Ruiz, R. Zaera","doi":"10.3390/mca28040087","DOIUrl":"https://doi.org/10.3390/mca28040087","url":null,"abstract":"This work analyses the buckling behaviour of cracked Euler–Bernoulli columns immersed in a Winkler elastic medium, obtaining their buckling loads. For this purpose, the beam is modelled as two segments connected in the cracked section by a mass-less rotational spring. Its rotation is proportional to the bending moment transmitted through the cracked section, considering the discontinuity of the rotation due to bending. The differential equations for the buckling behaviour are solved by applying the corresponding boundary conditions, as well as the compatibility and jump conditions of the cracked section. The proposed methodology allows calculating the buckling load as a function of the type of support, the parameter defining the elastic soil, the crack position and the initial length of the crack. The results obtained are compared with those published by other authors in works that deal with the problem in a partial way, showing the interaction and importance of the parameters considered in the buckling loads of the system.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43911797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Exploration of solar irradiance can greatly assist in understanding how renewable energy can be better harnessed. It helps in establishing the solar irradiance climate in a particular region for effective and efficient harvesting of solar energy. Understanding the climate provides planners, designers and investors in the solar power generation sector with critical information. However, a detailed exploration of these climatic characteristics has not yet been studied for the Southern African data. Very little exploration is being done through the use of measures of centrality only. These descriptive statistics may be misleading. As a result, we overcome limitations in the currently used deterministic models through the application of distributional modelling through quantile functions. Deterministic and stochastic elements in the data were combined and analysed simultaneously when fitting quantile distributional function models. The fitted models were then used to find population means as explorative parameters that consist of both deterministic and stochastic properties of the data. The application of QFs has been shown to be a practical tool and gives more information than approaches that focus separately on either measures of central tendency or empirical distributions. Seasonal effects were detected in the data from the whole region and can be attributed to the cyclical behaviour exhibited. Daily maximum solar irradiation is taking place within two hours of midday and monthly accumulates in summer months. Windhoek is receiving the best daily total mean, while the maximum monthly accumulated total mean is taking place in Durban. Developing separate solar irradiation models for summer and winter is highly recommended. Though robust and rigorous, quantile distributional function modelling enables exploration and understanding of all components of the behaviour of the data being studied. Therefore, a starting base for understanding Southern Africa’s solar climate was developed in this study.
{"title":"A Quantile Functions-Based Investigation on the Characteristics of Southern African Solar Irradiation Data","authors":"D. Maposa, A. Masache, P. Mdlongwa","doi":"10.3390/mca28040086","DOIUrl":"https://doi.org/10.3390/mca28040086","url":null,"abstract":"Exploration of solar irradiance can greatly assist in understanding how renewable energy can be better harnessed. It helps in establishing the solar irradiance climate in a particular region for effective and efficient harvesting of solar energy. Understanding the climate provides planners, designers and investors in the solar power generation sector with critical information. However, a detailed exploration of these climatic characteristics has not yet been studied for the Southern African data. Very little exploration is being done through the use of measures of centrality only. These descriptive statistics may be misleading. As a result, we overcome limitations in the currently used deterministic models through the application of distributional modelling through quantile functions. Deterministic and stochastic elements in the data were combined and analysed simultaneously when fitting quantile distributional function models. The fitted models were then used to find population means as explorative parameters that consist of both deterministic and stochastic properties of the data. The application of QFs has been shown to be a practical tool and gives more information than approaches that focus separately on either measures of central tendency or empirical distributions. Seasonal effects were detected in the data from the whole region and can be attributed to the cyclical behaviour exhibited. Daily maximum solar irradiation is taking place within two hours of midday and monthly accumulates in summer months. Windhoek is receiving the best daily total mean, while the maximum monthly accumulated total mean is taking place in Durban. Developing separate solar irradiation models for summer and winter is highly recommended. Though robust and rigorous, quantile distributional function modelling enables exploration and understanding of all components of the behaviour of the data being studied. Therefore, a starting base for understanding Southern Africa’s solar climate was developed in this study.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45300683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Carlos Enrique Valencia Murillo, Miguel Gutierrez Rivera, Luis David Celaya Garcia
In this work, a finite element model to perform the thermal–structural analysis of beams made of functionally graded material (FGM) is presented. The formulation is based on the third-order shear deformation theory. The constituents of the FGM are considered to vary only in the thickness direction, and the effective material properties are evaluated by means of the rule of mixtures. The volume distribution of the top constituent is modeled using the power law form. A comparison of the present finite element model with the numerical results available in the literature reveals that they are in good agreement. In addition, a routine to study functionally graded plane models in a commercial finite element code is used to verify the performance of the proposed model. In the present work, displacements for different values of the power law exponent and surface temperatures are presented. Furthermore, the normal stress variation along the thickness is shown for several power law exponents of functionally graded beams subjected to thermal and mechanical loads.
{"title":"Thermal–Structural Linear Static Analysis of Functionally Graded Beams Using Reddy Beam Theory","authors":"Carlos Enrique Valencia Murillo, Miguel Gutierrez Rivera, Luis David Celaya Garcia","doi":"10.3390/mca28040084","DOIUrl":"https://doi.org/10.3390/mca28040084","url":null,"abstract":"In this work, a finite element model to perform the thermal–structural analysis of beams made of functionally graded material (FGM) is presented. The formulation is based on the third-order shear deformation theory. The constituents of the FGM are considered to vary only in the thickness direction, and the effective material properties are evaluated by means of the rule of mixtures. The volume distribution of the top constituent is modeled using the power law form. A comparison of the present finite element model with the numerical results available in the literature reveals that they are in good agreement. In addition, a routine to study functionally graded plane models in a commercial finite element code is used to verify the performance of the proposed model. In the present work, displacements for different values of the power law exponent and surface temperatures are presented. Furthermore, the normal stress variation along the thickness is shown for several power law exponents of functionally graded beams subjected to thermal and mechanical loads.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44165562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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