Mathematical and Computational Applications

15 pages, 1526 KiB

Open AccessArticle

Dissolution-Driven Convection in a Porous Medium Due to Vertical Axis of Rotation and Magnetic Field

by Gundlapally Shiva Kumar Reddy, Nilam Venkata Koteswararao, Ragoju Ravi, Kiran Kumar Paidipati and Christophe Chesneau

Math. Comput. Appl. 2022, 27(3), 53; https://doi.org/10.3390/mca27030053 - 20 Jun 2022

Cited by 2 | Viewed by 1751

Abstract

This article aims to study the effect of the vertical rotation and magnetic field on the dissolution-driven convection in a saturated porous layer with a first-order chemical reaction. The system’s physical parameters depend on the Vadasz number, the Hartmann number, the Taylor number, [...] Read more.

This article aims to study the effect of the vertical rotation and magnetic field on the dissolution-driven convection in a saturated porous layer with a first-order chemical reaction. The system’s physical parameters depend on the Vadasz number, the Hartmann number, the Taylor number, and the Damkohler number. We analyze them in an in-depth manner. On the other hand, based on an artificial neural network (ANN) technique, the Levenberg–Marquardt backpropagation algorithm is adopted to predict the distribution of the critical Rayleigh number and for the linear stability analysis. The simulated critical Rayleigh numbers obtained by the numerical study and the predicted critical Rayleigh numbers by the ANN are compared and are in good agreement. The system becomes more stable by increasing the Damkohler and Taylor numbers. Full article

(This article belongs to the Special Issue Significance of Mathematical Modelling and Control in Real-World Problems: New Developments and Applications)

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17 pages, 2528 KiB

Open AccessArticle

Exploration of Darcy–Forchheimer Flows of Non-Newtonian Casson and Williamson Conveying Tiny Particles Experiencing Binary Chemical Reaction and Thermal Radiation: Comparative Analysis

by Sheniyappan Eswaramoorthi, S. Thamaraiselvi and Karuppusamy Loganathan

Math. Comput. Appl. 2022, 27(3), 52; https://doi.org/10.3390/mca27030052 - 20 Jun 2022

Cited by 11 | Viewed by 2332

Abstract

This discussion intends to scrutinize the Darcy–Forchheimer flow of Casson–Williamson nanofluid in a stretching surface with non-linear thermal radiation, suction and heat consumption. In addition, this investigation assimilates the influence of the Brownian motion, thermophoresis, activation energy and binary chemical reaction effects. Cattaneo–Christov [...] Read more.

This discussion intends to scrutinize the Darcy–Forchheimer flow of Casson–Williamson nanofluid in a stretching surface with non-linear thermal radiation, suction and heat consumption. In addition, this investigation assimilates the influence of the Brownian motion, thermophoresis, activation energy and binary chemical reaction effects. Cattaneo–Christov heat-mass flux theory is used to frame the energy and nanoparticle concentration equations. The suitable transformation is used to remodel the governing PDE model into an ODE model. The remodeled flow problems are numerically solved via the BVP4C scheme. The effects of various material characteristics on nanofluid velocity, nanofluid temperature and nanofluid concentration, as well as connected engineering aspects such as drag force, heat, and mass transfer gradients, are also calculated and displayed through tables, charts and figures. It is noticed that the nanofluid velocity upsurges when improving the quantity of Richardson number, and it downfalls for larger magnitudes of magnetic field and porosity parameters. The nanofluid temperature grows when enhancing the radiation parameter and Eckert number. The nanoparticle concentration upgrades for larger values of activation energy parameter while it slumps against the reaction rate parameter. The surface shear stress for the Williamson nanofluid is greater than the Casson nanofluid. There are more heat transfer gradient losses the greater the heat generation/absorption parameter and Eckert number. In addition, the local Sherwood number grows when strengthening the Forchheimer number and fitted rate parameter. Full article

(This article belongs to the Special Issue Significance of Mathematical Modelling and Control in Real-World Problems: New Developments and Applications)

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14 pages, 298 KiB

Open AccessArticle

A Note on Gerber–Shiu Function with Delayed Claim Reporting under Constant Force of Interest

by Kokou Essiomle and Franck Adekambi

Math. Comput. Appl. 2022, 27(3), 51; https://doi.org/10.3390/mca27030051 - 20 Jun 2022

Cited by 2 | Viewed by 1625

Abstract

In this paper, we analyze the Gerber–Shiu discounted penalty function for a constant interest rate in delayed claim reporting times. Using the Poisson claim arrival scenario, we derive the differential equation of the Laplace transform of the generalized Gerber–Shiu function and show that [...] Read more.

In this paper, we analyze the Gerber–Shiu discounted penalty function for a constant interest rate in delayed claim reporting times. Using the Poisson claim arrival scenario, we derive the differential equation of the Laplace transform of the generalized Gerber–Shiu function and show that the differential equation can be transformed to a Volterra equation of the second kind with a degenerated kernel. In the case of an exponential claim distribution, a closed-expression for the Gerber–Shiu function is obtained via sequence expansion. This result allows us to calculate the absolute (relative) ruin probability. Additionally, we discuss a method of solving the Volterra equation numerically and provide an illustration of the ruin’s probability to support the finding. Full article

(This article belongs to the Special Issue Computational Mathematics and Applied Statistics)

21 pages, 12344 KiB

Open AccessArticle

Morlet Cross-Wavelet Analysis of Climatic State Variables Expressed as a Function of Latitude, Longitude, and Time: New Light on Extreme Events

by Jean-Louis Pinault

Math. Comput. Appl. 2022, 27(3), 50; https://doi.org/10.3390/mca27030050 - 4 Jun 2022

Cited by 6 | Viewed by 2620

Abstract

This study aims to advance our knowledge in the genesis of extreme climatic events with the dual aim of improving forecasting methods while clarifying the role played by anthropogenic warming. Wavelet analysis is used to highlight the role of coherent Sea Surface Temperature [...] Read more.

This study aims to advance our knowledge in the genesis of extreme climatic events with the dual aim of improving forecasting methods while clarifying the role played by anthropogenic warming. Wavelet analysis is used to highlight the role of coherent Sea Surface Temperature (SST) anomalies produced from short-period oceanic Rossby waves resonantly forced, with two case studies: a Marine Heatwave (MHW) that occurred in the northwestern Pacific with a strong climatic impact in Japan, and an extreme flood event that occurred in Germany. Ocean–atmosphere interactions are evidenced by decomposing state variables into period bands within the cross-wavelet power spectra, namely SST, Sea Surface Height (SSH), and the zonal and meridional modulated geostrophic currents as well as precipitation height, i.e., the thickness of the layer of water produced during a day, with regard to subtropical cyclones. The bands are chosen according to the different harmonic modes of the oceanic Rossby waves. In each period band, the joint analysis of the amplitude and the phase of the state variables allow the estimation of the regionalized intensity of anomalies versus their time lag in relation to the date of occurrence of the extreme event. Regarding MHWs in the northwestern Pacific, it is shown how a warm SST anomaly associated with the northward component of the wind resulting from the low-pression system induces an SST response to latent and sensible heat transfer where the latitudinal SST gradient is steep. The SST anomaly is then shifted to the north as the phase becomes homogenized. As for subtropical cyclones, extreme events are the culmination of exceptional circumstances, some of which are foreseeable due to their relatively long maturation time. This is particularly the case of ocean–atmosphere interactions leading to the homogenization of the phase of SST anomalies that can potentially contribute to the supply of low-pressure systems. The same goes for the coalescence of distinct low-pressure systems during cyclogenesis. Some avenues are developed with the aim of better understanding how anthropogenic warming can modify certain key mechanisms in the evolution of those dynamic systems leading to extreme events. Full article

(This article belongs to the Special Issue Computational Mathematics and Applied Statistics)

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21 pages, 3847 KiB

Open AccessArticle

An Efficient Orthogonal Polynomial Method for Auxetic Structure Analysis with Epistemic Uncertainties

by Shengwen Yin, Haogang Qin and Qiang Gao

Math. Comput. Appl. 2022, 27(3), 49; https://doi.org/10.3390/mca27030049 - 2 Jun 2022

Cited by 1 | Viewed by 2182

Abstract

Traditional approaches used for analyzing the mechanical properties of auxetic structures are commonly based on deterministic techniques, where the effects of uncertainties are neglected. However, uncertainty is widely presented in auxetic structures, which may affect their mechanical properties greatly. The evidence theory has [...] Read more.

Traditional approaches used for analyzing the mechanical properties of auxetic structures are commonly based on deterministic techniques, where the effects of uncertainties are neglected. However, uncertainty is widely presented in auxetic structures, which may affect their mechanical properties greatly. The evidence theory has a strong ability to deal with uncertainties; thus, it is introduced for the modelling of epistemic uncertainties in auxetic structures. For the response analysis of a typical double-V negative Poisson’s ratio (NPR) structure with epistemic uncertainty, a new sequence-sampling-based arbitrary orthogonal polynomial (SS-AOP) expansion is proposed by introducing arbitrary orthogonal polynomial theory and the sequential sampling strategy. In SS-AOP, a sampling technique is developed to calculate the coefficient of AOP expansion. In particular, the candidate points for sampling are generated using the Gauss points associated with the optimal Gauss weight function for each evidence variable, and the sequential-sampling technique is introduced to select the sampling points from candidate points. By using the SS-AOP, the number of sampling points needed for establishing AOP expansion can be effectively reduced; thus, the efficiency of the AOP expansion method can be improved without sacrificing accuracy. The proposed SS-AOP is thoroughly investigated through comparison to the Gaussian quadrature-based AOP method, the Latin-hypercube-sampling-based AOP (LHS-AOP) method and the optimal Latin-hypercube-sampling-based AOP (OLHS-AOP) method. Full article

(This article belongs to the Special Issue Mathematical and Computational Modelling in Mechanics of Materials and Structures)

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37 pages, 3040 KiB

Open AccessFeature PaperArticle

A Bounded Archiver for Hausdorff Approximations of the Pareto Front for Multi-Objective Evolutionary Algorithms

by Carlos Ignacio Hernández Castellanos and Oliver Schütze

Math. Comput. Appl. 2022, 27(3), 48; https://doi.org/10.3390/mca27030048 - 1 Jun 2022

Cited by 3 | Viewed by 2548

Abstract

Multi-objective evolutionary algorithms (MOEAs) have been successfully applied for the numerical treatment of multi-objective optimization problems (MOP) during the last three decades. One important task within MOEAs is the archiving (or selection) of the computed candidate solutions, since one can expect that an [...] Read more.

Multi-objective evolutionary algorithms (MOEAs) have been successfully applied for the numerical treatment of multi-objective optimization problems (MOP) during the last three decades. One important task within MOEAs is the archiving (or selection) of the computed candidate solutions, since one can expect that an MOP has infinitely many solutions. We present and analyze in this work ArchiveUpdateHD, which is a bounded archiver that aims for Hausdorff approximations of the Pareto front. We show that the sequence of archives generated by ArchiveUpdateHD yields under certain (mild) assumptions with a probability of one after finitely many steps a

Δ^{+}

-approximation of the Pareto front, where the value

Δ^{+}

is computed by the archiver within the run of the algorithm without any prior knowledge of the Pareto front. The knowledge of this value is of great importance for the decision maker, since it is a measure for the “completeness” of the Pareto front approximation. Numerical results on several well-known academic test problems as well as the usage of ArchiveUpdateHD as an external archiver within three state-of-the-art MOEAs indicate the benefit of the novel strategy. Full article

(This article belongs to the Special Issue Evolutionary Multi-objective Optimization: An Honorary Issue Dedicated to Professor Kalyanmoy Deb)

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22 pages, 12258 KiB

Open AccessFeature PaperArticle

Integrated Finite Strip Computation for Modelling and Frequency Analysis of Hybrid Laminated FRP Structures

by Hamidreza Naderian, Moe M. S. Cheung, Elena Dragomirescu and Abdolmajid Mohammadian

Math. Comput. Appl. 2022, 27(3), 47; https://doi.org/10.3390/mca27030047 - 27 May 2022

Viewed by 2109

Abstract

This paper proposes an efficient numerical technique for simulating hybrid fiber-reinforced polymer (FRP) bridge systems. An integrated finite strip method (IFSM) is proposed to evaluate the free vibration performance of cable-stayed FRP bridges. The structural performance of the ultra-long span cable-stayed bridge (ULSCSB) [...] Read more.

This paper proposes an efficient numerical technique for simulating hybrid fiber-reinforced polymer (FRP) bridge systems. An integrated finite strip method (IFSM) is proposed to evaluate the free vibration performance of cable-stayed FRP bridges. The structural performance of the ultra-long span cable-stayed bridge (ULSCSB) is totally different than steel and concrete bridge structures due to the complexity of the mechanical behavior of the FRP deck. Herein, the anisotropic nature of the FRP laminated deck is considered in the analysis by introducing so-called laminate spline strips in the integrated finite strip solution. The structural interactions between all the components of the bridge can be handled using the proposed method. Column strips and cable strips are introduced and used to model the towers and cables, respectively. In addition, a straightforward scheme for modeling boundary conditions is developed. A case study is presented through which the accuracy and efficiency of the IFSM in modeling such structures, as well as in performing natural frequency analysis of long-span cable-stayed FRP bridges, are evaluated. The finite strip results are verified against the finite element analysis, and a significant enhancement in efficiency in terms of reduction in computational cost is demonstrated with the same level of accuracy. Full article

(This article belongs to the Special Issue Mathematical and Computational Modelling in Mechanics of Materials and Structures)

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20 pages, 8706 KiB

Open AccessArticle

Magneto Mixed Convection of Williamson Nanofluid Flow through a Double Stratified Porous Medium in Attendance of Activation Energy

by B. M. Tamilzharasan, S. Karthikeyan, Mohammed K. A. Kaabar, Mehmet Yavuz and Fatma Özköse

Math. Comput. Appl. 2022, 27(3), 46; https://doi.org/10.3390/mca27030046 - 26 May 2022

Cited by 9 | Viewed by 2984

Abstract

This article aims to develop a mathematical simulation of the steady mixed convective Darcy–Forchheimer flow of Williamson nanofluid over a linear stretchable surface. In addition, the effects of Cattaneo–Christov heat and mass flux, Brownian motion, activation energy, and thermophoresis are also studied. The [...] Read more.

This article aims to develop a mathematical simulation of the steady mixed convective Darcy–Forchheimer flow of Williamson nanofluid over a linear stretchable surface. In addition, the effects of Cattaneo–Christov heat and mass flux, Brownian motion, activation energy, and thermophoresis are also studied. The novel aspect of this study is that it incorporates thermal radiation to investigate the physical effects of thermal and solutal stratification on mixed convection flow and heat transfer. First, the profiles of velocity and energy equations were transformed toward the ordinary differential equation using the appropriate similarity transformation. Then, the system of equations was modified by first-order ODEs in MATLAB and solved using the bvp4c approach. Graphs and tables imply the impact of physical parameters on concentration, temperature, velocity, skin friction coefficient, mass, and heat transfer rate. The outcomes show that the nanofluid temperature and concentration are reduced with the more significant thermal and mass stratification parameters estimation. Full article

(This article belongs to the Special Issue Significance of Mathematical Modelling and Control in Real-World Problems: New Developments and Applications)

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14 pages, 896 KiB

Open AccessArticle

Solution of a Complex Nonlinear Fractional Biochemical Reaction Model

by Fatima Rabah, Marwan Abukhaled and Suheil A. Khuri

Math. Comput. Appl. 2022, 27(3), 45; https://doi.org/10.3390/mca27030045 - 26 May 2022

Cited by 7 | Viewed by 2121

Abstract

This paper discusses a complex nonlinear fractional model of enzyme inhibitor reaction where reaction memory is taken into account. Analytical expressions of the concentrations of enzyme, substrate, inhibitor, product, and other complex intermediate species are derived using Laplace decomposition and differential transformation methods. [...] Read more.

This paper discusses a complex nonlinear fractional model of enzyme inhibitor reaction where reaction memory is taken into account. Analytical expressions of the concentrations of enzyme, substrate, inhibitor, product, and other complex intermediate species are derived using Laplace decomposition and differential transformation methods. Since different rate constants, large initial concentrations, and large time domains are unavoidable in biochemical reactions, different dynamics will result; hence, the convergence of the approximate concentrations may be lost. In this case, the proposed analytical methods will be coupled with Padé approximation. The validity and accuracy of the derived analytical solutions will be established by direct comparison with numerical simulations. Full article

(This article belongs to the Special Issue Significance of Mathematical Modelling and Control in Real-World Problems: New Developments and Applications)

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16 pages, 758 KiB

Open AccessArticle

Small Area Estimation of Zone-Level Malnutrition among Children under Five in Ethiopia

by Kindie Fentahun Muchie, Anthony Kibira Wanjoya and Samuel Musili Mwalili

Math. Comput. Appl. 2022, 27(3), 44; https://doi.org/10.3390/mca27030044 - 22 May 2022

Cited by 1 | Viewed by 3125

Abstract

Child undernutrition is one of the 10 most significant public health problems worldwide. There is a rapidly growing demand to produce reliable estimates at the micro administrative level with small sample sizes. In this research, the authors employed small area estimation techniques to [...] Read more.

Child undernutrition is one of the 10 most significant public health problems worldwide. There is a rapidly growing demand to produce reliable estimates at the micro administrative level with small sample sizes. In this research, the authors employed small area estimation techniques to estimate the prevalence of malnutrition at the zonal level among children under five in Ethiopia. The small area estimation concept was sought for by linking the most recent possible survey data and census data in Ethiopia. The results show that there is spatial variation of stunting, wasting and being underweight across the zone level, showing different locations facing different challenges or different extents. Full article

(This article belongs to the Special Issue Computational Mathematics and Applied Statistics)

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16 pages, 444 KiB

Open AccessArticle

Applications of the Sine Modified Lindley Distribution to Biomedical Data

by Lishamol Tomy, Veena G and Christophe Chesneau

Math. Comput. Appl. 2022, 27(3), 43; https://doi.org/10.3390/mca27030043 - 16 May 2022

Cited by 3 | Viewed by 2272

Abstract

In this paper, the applicability of the sine modified Lindley distribution, recently introduced in the statistical literature, is highlighted via the goodness-of-fit approach on biological data. In particular, it is shown to be beneficial in estimating and modeling the life periods of growth [...] Read more.

In this paper, the applicability of the sine modified Lindley distribution, recently introduced in the statistical literature, is highlighted via the goodness-of-fit approach on biological data. In particular, it is shown to be beneficial in estimating and modeling the life periods of growth hormone guinea pigs given tubercle bacilli, growth hormone treatment for children, and the size of tumors in cancer patients. We anticipate that our model will be effective in modeling the survival times of diseases related to cancer. The R codes for the figures, as well as information on how the data are processed, are provided. Full article

(This article belongs to the Special Issue Computational Mathematics and Applied Statistics)

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10 pages, 2343 KiB

Open AccessArticle

Finding the Conjectured Sequence of Largest Small n-Polygons by Numerical Optimization

by János D. Pintér, Frank J. Kampas and Ignacio Castillo

Math. Comput. Appl. 2022, 27(3), 42; https://doi.org/10.3390/mca27030042 - 16 May 2022

Cited by 3 | Viewed by 1892

Abstract

L S P (n)

, the largest small polygon with

n

vertices, is a polygon with a unit diameter that has a maximal of area

A (n)

. It is known that for all odd values

n \geq 3

[...] Read more.

L S P (n)

, the largest small polygon with

n

vertices, is a polygon with a unit diameter that has a maximal of area

A (n)

. It is known that for all odd values

n \geq 3

,

L S P (n)

is a regular

n

-polygon; however, this statement is not valid even for values of

n

. Finding the polygon

L S P (n)

and

A (n)

for even values

n \geq 6

has been a long-standing challenge. In this work, we developed high-precision numerical solution estimates of

A (n)

for even values

n \geq 4

, using the Mathematica model development environment and the IPOPT local nonlinear optimization solver engine. First, we present a revised (tightened) LSP model that greatly assists in the efficient numerical solution of the model-class considered. This is followed by results for an illustrative sequence of even values of

n

, up to

n \leq 1000

. Most of the earlier research addressed special cases up to

n \leq 20

, while others obtained numerical optimization results for a range of values from

6 \leq n \leq 100

. The results obtained were used to provide regression model-based estimates of the optimal area sequence

{A (n)}

, for even values

n

of interest, thereby essentially solving the LSP model-class numerically, with demonstrably high precision. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2021)

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14 pages, 3335 KiB

Open AccessArticle

Microwave Characterization and Modelling of PA6/GNPs Composites

by Erika Pittella, Emanuele Piuzzi, Pietro Russo and Francesco Fabbrocino

Math. Comput. Appl. 2022, 27(3), 41; https://doi.org/10.3390/mca27030041 - 11 May 2022

Cited by 1 | Viewed by 2509

Abstract

The interest in composite materials has increased in the last decades since they have the advantages of combining intrinsic properties of each component and offer better performance with respect to the base constituents. In particular, these kinds of materials can have different electrical [...] Read more.

The interest in composite materials has increased in the last decades since they have the advantages of combining intrinsic properties of each component and offer better performance with respect to the base constituents. In particular, these kinds of materials can have different electrical characteristics by varying the filling percentage and, therefore, they can be used in diverse applications. Thus, a detailed study of the microwave response of these composite systems is of great practical importance. In fact, the dielectric constant and loss tangent are key factors in the design of microwave components. In this frame, the outstanding properties of graphene-like fillers may be exploited to develop new very interesting materials to study and characterize. In this paper, microwave characterization of compounds, based on nylon 6 containing different percentages of graphene nanoplatelets, is carried out taking the neat matrix sample processed under the same conditions as benchmark. The measurements were carried out using two microwave systems, operating at two different frequency bands, appropriate to characterize solid and compact material samples. The achieved results, in line with limited data from the literature and from material data sheets, highlight the possibility to use the present polymers as an excellent electromagnetic interference shielding, as confirmed by full wave electromagnetic numerical simulations that were conducted with a numerical electromagnetic software. Full article

(This article belongs to the Special Issue Mathematical and Computational Modelling in Mechanics of Materials and Structures)

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18 pages, 501 KiB

Open AccessFeature PaperArticle

Enhancing Quasi-Newton Acceleration for Fluid-Structure Interaction

by Kyle Davis, Miriam Schulte and Benjamin Uekermann

Math. Comput. Appl. 2022, 27(3), 40; https://doi.org/10.3390/mca27030040 - 6 May 2022

Cited by 7 | Viewed by 2604

Abstract

We propose two enhancements of quasi-Newton methods used to accelerate coupling iterations for partitioned fluid-structure interaction. Quasi-Newton methods have been established as flexible, yet robust, efficient and accurate coupling methods of multi-physics simulations in general. The coupling library preCICE provides several variants, the [...] Read more.

We propose two enhancements of quasi-Newton methods used to accelerate coupling iterations for partitioned fluid-structure interaction. Quasi-Newton methods have been established as flexible, yet robust, efficient and accurate coupling methods of multi-physics simulations in general. The coupling library preCICE provides several variants, the so-called IQN-ILS method being the most commonly used. It uses input and output differences of the coupled solvers collected in previous iterations and time steps to approximate Newton iterations. To make quasi-Newton methods both applicable for parallel coupling (where these differences contain data from different physical fields) and to provide a robust approach for re-using information, a combination of information filtering and scaling for the different physical fields is typically required. This leads to good convergence, but increases the cost per iteration. We propose two new approaches—pre-scaling weight monitoring and a new, so-called QR3 filter, to substantially improve runtime while not affecting convergence quality. We evaluate these for a variety of fluid-structure interaction examples. Results show that we achieve drastic speedups for the pure quasi-Newton update steps. In the future, we intend to apply the methods also to volume-coupled scenarios, where these gains can be decisive for the feasibility of the coupling approach. Full article

(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)

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29 pages, 660 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

A Trust Region Reduced Basis Pascoletti-Serafini Algorithm for Multi-Objective PDE-Constrained Parameter Optimization

by Stefan Banholzer, Luca Mechelli and Stefan Volkwein

Math. Comput. Appl. 2022, 27(3), 39; https://doi.org/10.3390/mca27030039 - 3 May 2022

Cited by 3 | Viewed by 2152

Abstract

In the present paper non-convex multi-objective parameter optimization problems are considered which are governed by elliptic parametrized partial differential equations (PDEs). To solve these problems numerically the Pascoletti-Serafini scalarization is applied and the obtained scalar optimization problems are solved by an augmented Lagrangian [...] Read more.

In the present paper non-convex multi-objective parameter optimization problems are considered which are governed by elliptic parametrized partial differential equations (PDEs). To solve these problems numerically the Pascoletti-Serafini scalarization is applied and the obtained scalar optimization problems are solved by an augmented Lagrangian method. However, due to the PDE constraints, the numerical solution is very expensive so that a model reduction is utilized by using the reduced basis (RB) method. The quality of the RB approximation is ensured by a trust-region strategy which does not require any offline procedure, in which the RB functions are computed in a greedy algorithm. Moreover, convergence of the proposed method is guaranteed and different techniques to prevent the excessive growth of the number of basis functions are explored. Numerical examples illustrate the efficiency of the proposed solution technique. Full article

(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)

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21 pages, 5051 KiB

Open AccessArticle

Interval-Based Computation of the Uncertainty in the Mechanical Properties and the Failure Analysis of Unidirectional Composite Materials

by Dimitris G. Sotiropoulos and Konstantinos Tserpes

Math. Comput. Appl. 2022, 27(3), 38; https://doi.org/10.3390/mca27030038 - 29 Apr 2022

Cited by 3 | Viewed by 2425

Abstract

An interval-based method is presented to evaluate the uncertainty in the computed mechanical properties and the failure assessment of composite unidirectional (UD) laminates. The method was applied to two composite laminates: a carbon/epoxy and a glass/epoxy. The mechanical properties of the UD lamina [...] Read more.

An interval-based method is presented to evaluate the uncertainty in the computed mechanical properties and the failure assessment of composite unidirectional (UD) laminates. The method was applied to two composite laminates: a carbon/epoxy and a glass/epoxy. The mechanical properties of the UD lamina were derived using simplified micromechanical equations. An uncertainty level of ±5% was assumed for the input properties of the constituents. The global minimum and maximum values of the properties were computed using an interval branch-and-bound algorithm. Interval arithmetic operations were used to evaluate the uncertainty in the Hashin-type failure criteria in a closed form. Using the closed-form uncertainties of intervals and sets of stresses obtained by finite element analysis, the uncertainty in the failure assessment was quantified for the two composite laminates. For the assumed uncertainty level of ±5%, the computed uncertainty for the mechanical properties ranges from 6.64% to 10.63% for the carbon/epoxy material and from 6.72% to 12.28% for the glass/epoxy material. For evaluating the uncertainty effect on the efficiency of failure criteria, a probability of failure function, which employs interval boundaries, was defined and proved capable of evaluating the whole spectrum of stresses. Full article

(This article belongs to the Special Issue Mathematical and Computational Modelling in Mechanics of Materials and Structures)

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17 pages, 4595 KiB

Open AccessArticle

Multivariable Panel Data Cluster Analysis of Meteorological Stations in Thailand for ENSO Phenomenon

by Porntip Dechpichai, Nuttawadee Jinapang, Pariyakorn Yamphli, Sakulrat Polamnuay, Sittisak Injan and Usa Humphries

Math. Comput. Appl. 2022, 27(3), 37; https://doi.org/10.3390/mca27030037 - 24 Apr 2022

Cited by 3 | Viewed by 2575

Abstract

The purpose of this research is to study the spatial and temporal groupings of 124 meteorological stations in Thailand under ENSO. The multivariate climate variables are rainfall, relative humidity, temperature, max temperature, min temperature, solar downwelling, and horizontal wind from the conformal cubic [...] Read more.

The purpose of this research is to study the spatial and temporal groupings of 124 meteorological stations in Thailand under ENSO. The multivariate climate variables are rainfall, relative humidity, temperature, max temperature, min temperature, solar downwelling, and horizontal wind from the conformal cubic atmospheric model (CCAM) in years of El Niño (1987, 2004, and 2015) and La Niña (1999, 2000, and 2011). Euclidean distance timed and spaced with average linkage for clustering and silhouette width for cluster validation were employed. Five spatial clusters (SCs) and three temporal clusters (TCs) in each SC with different average precipitation were compared by El Niño and La Niña. The pattern of SCs and TCs was similar for both events except in the case when severe El Niño occurred. This method could be applied using variables forecasted in the future to be used for planning and managing crop cultivation with the climate change in each area. Full article

(This article belongs to the Special Issue Computational Mathematics and Applied Statistics)

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11 pages, 3408 KiB

Open AccessArticle

Challenges in Kinetic-Kinematic Driven Musculoskeletal Subject-Specific Infant Modeling

by Yeram Lim, Tamara Chambers, Christine Walck, Safeer Siddicky, Erin Mannen and Victor Huayamave

Math. Comput. Appl. 2022, 27(3), 36; https://doi.org/10.3390/mca27030036 - 22 Apr 2022

Viewed by 2573

Abstract

Musculoskeletal computational models provide a non-invasive approach to investigate human movement biomechanics. These models could be particularly useful for pediatric applications where in vivo and in vitro biomechanical parameters are difficult or impossible to examine using physical experiments alone. The objective was to [...] Read more.

Musculoskeletal computational models provide a non-invasive approach to investigate human movement biomechanics. These models could be particularly useful for pediatric applications where in vivo and in vitro biomechanical parameters are difficult or impossible to examine using physical experiments alone. The objective was to develop a novel musculoskeletal subject-specific infant model to investigate hip joint biomechanics during cyclic leg movements. Experimental motion-capture marker data of a supine-lying 2-month-old infant were placed on a generic GAIT 2392 OpenSim model. After scaling the model using body segment anthropometric measurements and joint center locations, inverse kinematics and dynamics were used to estimate hip ranges of motion and moments. For the left hip, a maximum moment of 0.975 Nm and a minimum joint moment of 0.031 Nm were estimated at 34.6° and 65.5° of flexion, respectively. For the right hip, a maximum moment of 0.906 Nm and a minimum joint moment of 0.265 Nm were estimated at 23.4° and 66.5° of flexion, respectively. Results showed agreement with reported values from the literature. Further model refinements and validations are needed to develop and establish a normative infant dataset, which will be particularly important when investigating the movement of infants with pathologies such as developmental dysplasia of the hip. This research represents the first step in the longitudinal development of a model that will critically contribute to our understanding of infant growth and development during the first year of life. Full article

(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)

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23 pages, 3275 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Can DtN and GenEO Coarse Spaces Be Sufficiently Robust for Heterogeneous Helmholtz Problems?

by Niall Bootland and Victorita Dolean

Math. Comput. Appl. 2022, 27(3), 35; https://doi.org/10.3390/mca27030035 - 21 Apr 2022

Viewed by 2662

Abstract

Numerical solutions of heterogeneous Helmholtz problems present various computational challenges, with descriptive theory remaining out of reach for many popular approaches. Robustness and scalability are key for practical and reliable solvers in large-scale applications, especially for large wave number problems. In this work, [...] Read more.

Numerical solutions of heterogeneous Helmholtz problems present various computational challenges, with descriptive theory remaining out of reach for many popular approaches. Robustness and scalability are key for practical and reliable solvers in large-scale applications, especially for large wave number problems. In this work, we explore the use of a GenEO-type coarse space to build a two-level additive Schwarz method applicable to highly indefinite Helmholtz problems. Through a range of numerical tests on a 2D model problem, discretised by finite elements on pollution-free meshes, we observe robust convergence, iteration counts that do not increase with the wave number, and good scalability of our approach. We further provide results showing a favourable comparison with the DtN coarse space. Our numerical study shows promise that our solver methodology can be effective for challenging heterogeneous applications. Full article

(This article belongs to the Special Issue Domain Decomposition Methods)

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28 pages, 11190 KiB

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Reduced Order Modeling Using Advection-Aware Autoencoders

by Sourav Dutta, Peter Rivera-Casillas, Brent Styles and Matthew W. Farthing

Math. Comput. Appl. 2022, 27(3), 34; https://doi.org/10.3390/mca27030034 - 21 Apr 2022

Cited by 9 | Viewed by 3516

Abstract

Physical systems governed by advection-dominated partial differential equations (PDEs) are found in applications ranging from engineering design to weather forecasting. They are known to pose severe challenges to both projection-based and non-intrusive reduced order modeling, especially when linear subspace approximations are used. In [...] Read more.

Physical systems governed by advection-dominated partial differential equations (PDEs) are found in applications ranging from engineering design to weather forecasting. They are known to pose severe challenges to both projection-based and non-intrusive reduced order modeling, especially when linear subspace approximations are used. In this work, we develop an advection-aware (AA) autoencoder network that can address some of these limitations by learning efficient, physics-informed, nonlinear embeddings of the high-fidelity system snapshots. A fully non-intrusive reduced order model is developed by mapping the high-fidelity snapshots to a latent space defined by an AA autoencoder, followed by learning the latent space dynamics using a long-short-term memory (LSTM) network. This framework is also extended to parametric problems by explicitly incorporating parameter information into both the high-fidelity snapshots and the encoded latent space. Numerical results obtained with parametric linear and nonlinear advection problems indicate that the proposed framework can reproduce the dominant flow features even for unseen parameter values. Full article

(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)

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14 pages, 1237 KiB

Open AccessArticle

Coupled Neural–Glial Dynamics and the Role of Astrocytes in Alzheimer’s Disease

by Swadesh Pal and Roderick Melnik

Math. Comput. Appl. 2022, 27(3), 33; https://doi.org/10.3390/mca27030033 - 21 Apr 2022

Cited by 3 | Viewed by 2802

Abstract

Neurodegenerative diseases such as Alzheimer’s (AD) are associated with the propagation and aggregation of toxic proteins. In the case of AD, it was Alzheimer himself who showed the importance of both amyloid beta (

A β

) plaques and tau protein neurofibrillary tangles [...] Read more.

Neurodegenerative diseases such as Alzheimer’s (AD) are associated with the propagation and aggregation of toxic proteins. In the case of AD, it was Alzheimer himself who showed the importance of both amyloid beta (

A β

) plaques and tau protein neurofibrillary tangles (NFTs) in what he called the “disease of forgetfulness”. The amyloid beta forms extracellular aggregates and plaques, whereas tau proteins are intracellular proteins that stabilize axons by cross-linking microtubules that can form largely messy tangles. On the other hand, astrocytes and microglial cells constantly clear these plaques and NFTs from the brain. Astrocytes transport nutrients from the blood to neurons. Activated astrocytes produce monocyte chemoattractant protein-1 (MCP-1), which attracts anti-inflammatory macrophages and clears

A β

. At the same time, the microglia cells are poorly phagocytic for

A β

compared to proinflammatory and anti-inflammatory macrophages. In addition to such distinctive neuropathological features of AD as amyloid beta and tau proteins, neuroinflammation has to be brought into the picture as well. Taking advantage of a coupled mathematical modelling framework, we formulate a network model, accounting for the coupling between neurons and astroglia and integrating all three main neuropathological features with the brain connectome data. We provide details on the coupled dynamics involving cytokines, astrocytes, and microglia. Further, we apply the tumour necrosis factor alpha (TNF-

α

) inhibitor and anti-

A β

drug and analyze their influence on the brain cells, suggesting conditions under which the drug can prevent cell damage. The important role of astrocytes and TNF-

α

inhibitors in AD pathophysiology is emphasized, along with potentially promising pathways for developing new AD therapies. Full article

(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)

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Math. Comput. Appl., Volume 27, Issue 3 (June 2022) – 21 articles

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