Mathematical and Computational Applications

15 pages, 1564 KiB

Open AccessCommunication

CyVerse Austria—A Local, Collaborative Cyberinfrastructure

by Konrad Lang, Sarah Stryeck, David Bodruzic, Manfred Stepponat, Slave Trajanoski, Ursula Winkler and Stefanie Lindstaedt

Math. Comput. Appl. 2020, 25(2), 38; https://doi.org/10.3390/mca25020038 - 24 Jun 2020

Cited by 2 | Viewed by 4712

Abstract

Life sciences (LS) are advanced in research data management, since LS have established disciplinary tools for data archiving as well as metadata standards for data reuse. However, there is a lack of tools supporting the active research process in terms of data management [...] Read more.

Life sciences (LS) are advanced in research data management, since LS have established disciplinary tools for data archiving as well as metadata standards for data reuse. However, there is a lack of tools supporting the active research process in terms of data management and data analytics. This leads to tedious and demanding work to ensure that research data before and after publication are FAIR (findable, accessible, interoperable and reusable) and that analyses are reproducible. The initiative CyVerse US from the University of Arizona, US, supports all processes from data generation, management, sharing and collaboration to analytics. Within the presented project, we deployed an independent instance of CyVerse in Graz, Austria (CAT) in frame of the BioTechMed association. CAT helped to enhance and simplify collaborations between the three main universities in Graz. Presuming steps were (i) creating a distributed computational and data management architecture (iRODS-based), (ii) identifying and incorporating relevant data from researchers in LS and (iii) identifying and hosting relevant tools, including analytics software to ensure reproducible analytics using Docker technology for the researchers taking part in the initiative. This initiative supports research-related processes, including data management and analytics for LS researchers. It also holds the potential to serve other disciplines and provides potential for Austrian universities to integrate their infrastructure in the European Open Science Cloud. Full article

(This article belongs to the Special Issue High-Performance Computing 2020)

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15 pages, 550 KiB

Open AccessFeature PaperArticle

Data-Driven Bayesian Network Learning: A Bi-Objective Approach to Address the Bias-Variance Decomposition

by Vicente-Josué Aguilera-Rueda, Nicandro Cruz-Ramírez and Efrén Mezura-Montes

Math. Comput. Appl. 2020, 25(2), 37; https://doi.org/10.3390/mca25020037 - 20 Jun 2020

Cited by 5 | Viewed by 2682

Abstract

We present a novel bi-objective approach to address the data-driven learning problem of Bayesian networks. Both the log-likelihood and the complexity of each candidate Bayesian network are considered as objectives to be optimized by our proposed algorithm named Nondominated Sorting Genetic Algorithm for [...] Read more.

We present a novel bi-objective approach to address the data-driven learning problem of Bayesian networks. Both the log-likelihood and the complexity of each candidate Bayesian network are considered as objectives to be optimized by our proposed algorithm named Nondominated Sorting Genetic Algorithm for learning Bayesian networks (NS2BN) which is based on the well-known NSGA-II algorithm. The core idea is to reduce the implicit selection bias-variance decomposition while identifying a set of competitive models using both objectives. Numerical results suggest that, in stark contrast to the single-objective approach, our bi-objective approach is useful to find competitive Bayesian networks especially in the complexity. Furthermore, our approach presents the end user with a set of solutions by showing different Bayesian network and their respective MDL and classification accuracy results. Full article

(This article belongs to the Special Issue New Trends in Computational Intelligence and Applications)

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21 pages, 3219 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Numerical Approach to a Nonlocal Advection-Reaction-Diffusion Model of Cartilage Pattern Formation

by Tilmann Glimm and Jianying Zhang

Math. Comput. Appl. 2020, 25(2), 36; https://doi.org/10.3390/mca25020036 - 19 Jun 2020

Cited by 3 | Viewed by 3083

Abstract

We propose a numerical approach that combines a radial basis function (RBF) meshless approximation with a finite difference discretization to solve a nonlinear system of integro-differential equations. The equations are of advection-reaction-diffusion type modeling the formation of pre-cartilage condensations in embryonic chicken limbs. [...] Read more.

We propose a numerical approach that combines a radial basis function (RBF) meshless approximation with a finite difference discretization to solve a nonlinear system of integro-differential equations. The equations are of advection-reaction-diffusion type modeling the formation of pre-cartilage condensations in embryonic chicken limbs. The computational domain is four dimensional in the sense that the cell density depends continuously on two spatial variables as well as two structure variables, namely membrane-bound counterreceptor densities. The biologically proper Dirichlet boundary conditions imposed in the semi-infinite structure variable region is in favor of a meshless method with Gaussian basis functions. Coupled with WENO5 finite difference spatial discretization and the method of integrating factors, the time integration via method of lines achieves optimal complexity. In addition, the proposed scheme can be extended to similar models with more general boundary conditions. Numerical results are provided to showcase the validity of the scheme. Full article

(This article belongs to the Section Natural Sciences)

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11 pages, 290 KiB

Open AccessArticle

On a Laminated Timoshenko Beam with Nonlinear Structural Damping

by Tijani A. Apalara, Aminu M. Nass and Hamdan Al Sulaimani

Math. Comput. Appl. 2020, 25(2), 35; https://doi.org/10.3390/mca25020035 - 19 Jun 2020

Cited by 18 | Viewed by 2616

Abstract

In the present work, we study a one-dimensional laminated Timoshenko beam with a single nonlinear structural damping due to interfacial slip. We use the multiplier method and some properties of convex functions to establish an explicit and general decay result. Interestingly, the result [...] Read more.

In the present work, we study a one-dimensional laminated Timoshenko beam with a single nonlinear structural damping due to interfacial slip. We use the multiplier method and some properties of convex functions to establish an explicit and general decay result. Interestingly, the result is established without any additional internal or boundary damping term and without imposing any restrictive growth assumption on the nonlinear term, provided the wave speeds of the first equations of the system are equal. Full article

(This article belongs to the Section Natural Sciences)

16 pages, 263 KiB

Open AccessArticle

The Complementary q-Lidstone Interpolating Polynomials and Applications

by Zeinab Mansour and Maryam Al-Towailb

Math. Comput. Appl. 2020, 25(2), 34; https://doi.org/10.3390/mca25020034 - 19 Jun 2020

Cited by 7 | Viewed by 1962

Abstract

In this paper, we introduce the complementary q-Lidstone interpolating polynomial of degree

2 n

, which involves interpolating data at the odd-order q-derivatives. For this polynomial, we will provide a q-Peano representation of the error function. Next, we use these [...] Read more.

In this paper, we introduce the complementary q-Lidstone interpolating polynomial of degree

2 n

, which involves interpolating data at the odd-order q-derivatives. For this polynomial, we will provide a q-Peano representation of the error function. Next, we use these results to prove the existence of solutions of the complementary q-Lidstone boundary value problems. Some examples are included. Full article

(This article belongs to the Section Natural Sciences)

9 pages, 1125 KiB

Open AccessFeature PaperArticle

Improving Kernel Methods for Density Estimation in Random Differential Equations Problems

by Juan Carlos Cortés López and Marc Jornet Sanz

Math. Comput. Appl. 2020, 25(2), 33; https://doi.org/10.3390/mca25020033 - 18 Jun 2020

Cited by 7 | Viewed by 2674

Abstract

Kernel density estimation is a non-parametric method to estimate the probability density function of a random quantity from a finite data sample. The estimator consists of a kernel function and a smoothing parameter called the bandwidth. Despite its undeniable usefulness, the convergence rate [...] Read more.

Kernel density estimation is a non-parametric method to estimate the probability density function of a random quantity from a finite data sample. The estimator consists of a kernel function and a smoothing parameter called the bandwidth. Despite its undeniable usefulness, the convergence rate may be slow with the number of realizations and the discontinuity and peaked points of the target density may not be correctly captured. In this work, we analyze the applicability of a parametric method based on Monte Carlo simulation for the density estimation of certain random variable transformations. This approach has important applications in the setting of differential equations with input random parameters. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering & Human Behaviour 2019)

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14 pages, 502 KiB

Open AccessArticle

Evolutionary Multi-Objective Energy Production Optimization: An Empirical Comparison

by Gustavo-Adolfo Vargas-Hákim, Efrén Mezura-Montes and Edgar Galván

Math. Comput. Appl. 2020, 25(2), 32; https://doi.org/10.3390/mca25020032 - 16 Jun 2020

Cited by 5 | Viewed by 3017

Abstract

This work presents the assessment of the well-known Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and one of its variants to optimize a proposed electric power production system. Such variant implements a chaotic model to generate the initial population, aiming to get a better [...] Read more.

This work presents the assessment of the well-known Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and one of its variants to optimize a proposed electric power production system. Such variant implements a chaotic model to generate the initial population, aiming to get a better distributed Pareto front. The considered power system is composed of solar, wind and natural gas power sources, being the first two renewable energies. Three conflicting objectives are considered in the problem: (1) power production, (2) production costs and (3) CO₂ emissions. The Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) is also adopted in the comparison so as to enrich the empirical evidence by contrasting the NSGA-II versions against a non-Pareto-based approach. Spacing and Hypervolume are the chosen metrics to compare the performance of the algorithms under study. The obtained results suggest that there is no significant improvement by using the variant of the NSGA-II over the original version. Nonetheless, meaningful performance differences have been found between MOEA/D and the other two algorithms. Full article

(This article belongs to the Special Issue New Trends in Computational Intelligence and Applications)

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15 pages, 345 KiB

Open AccessArticle

Modelling the Process to Access the Spanish Public University System Based on Structural Equation Models

by Antonio Hervás, Pedro Pablo Soriano, Joan Guàrdia i Olmos, Maribel Peró, Roberto Capilla and José Miguel Montañana

Math. Comput. Appl. 2020, 25(2), 31; https://doi.org/10.3390/mca25020031 - 4 Jun 2020

Cited by 1 | Viewed by 2478

Abstract

Currently, one of the challenges of universities is attracting talent in students, researchers, and teachers. The transition from high school to college requires a student to take a succession of decisions that will shape their future. For this reason, knowledge of the motivations [...] Read more.

Currently, one of the challenges of universities is attracting talent in students, researchers, and teachers. The transition from high school to college requires a student to take a succession of decisions that will shape their future. For this reason, knowledge of the motivations of the students, their family, and their personal environment, to choose a particular degree and/or university to pursue their higher studies, would allow universities to efficiently adjust their recruitment strategies. In this article, a study was developed based on a structural equation model of the access to the Spanish Public University System (SUPE), which can help with supply and demand problems, recruitment actions and policies, and other strategic decisions. This was done through an extensive survey of first-year students of Spanish universities. The results allowed us to obtain the parameters of the model, which showed that the fit between the model and the data obtained were excellent at a global level and acceptable as well in all knowledge areas. The objective of the structural model was to provide a general view of the behavior of the students when deciding the degree and university in which they are going to study, and can help in the decision making of university leaders and to understand some behaviors of the Spanish Public University System. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering & Human Behaviour 2019)

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16 pages, 380 KiB

Open AccessArticle

A Hybrid Function Approach to Solving a Class of Fredholm and Volterra Integro-Differential Equations

by Aline Hosry, Roger Nakad and Sachin Bhalekar

Math. Comput. Appl. 2020, 25(2), 30; https://doi.org/10.3390/mca25020030 - 27 May 2020

Cited by 2 | Viewed by 2462

Abstract

In this paper, we use a numerical method that involves hybrid and block-pulse functions to approximate solutions of systems of a class of Fredholm and Volterra integro-differential equations. The key point is to derive a new approximation for the derivatives of the solutions [...] Read more.

In this paper, we use a numerical method that involves hybrid and block-pulse functions to approximate solutions of systems of a class of Fredholm and Volterra integro-differential equations. The key point is to derive a new approximation for the derivatives of the solutions and then reduce the integro-differential equation to a system of algebraic equations that can be solved using classical methods. Some numerical examples are dedicated for showing the efficiency and validity of the method that we introduce. Full article

(This article belongs to the Section Natural Sciences)

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13 pages, 3084 KiB

Open AccessArticle

Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

by Desmond Adair, Aigul Nagimova and Martin Jaeger

Math. Comput. Appl. 2020, 25(2), 29; https://doi.org/10.3390/mca25020029 - 15 May 2020

Cited by 1 | Viewed by 2581

Abstract

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by [...] Read more.

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam. Full article

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2 pages, 211 KiB

Open AccessEditorial

Preface to Numerical and Symbolic Computation: Developments and Applications—2019

by Maria Amélia R. Loja and Joaquim I. Barbosa

Math. Comput. Appl. 2020, 25(2), 28; https://doi.org/10.3390/mca25020028 - 11 May 2020

Viewed by 1807

Abstract

This book constitutes the printed edition of the Special Issue Numerical and Symbolic Computation: Developments and Applications—2019, published by Mathematical and Computational Applications (MCA) and comprises a collection of articles related to works presented at the 4th International Conference in Numerical and [...] Read more.

This book constitutes the printed edition of the Special Issue Numerical and Symbolic Computation: Developments and Applications—2019, published by Mathematical and Computational Applications (MCA) and comprises a collection of articles related to works presented at the 4th International Conference in Numerical and Symbolic Computation—SYMCOMP 2019—that took place in Porto, Portugal, from April 11th to April 12th 2019 [...] Full article

(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications)

30 pages, 658 KiB

Open AccessArticle

A Projection Hestenes–Stiefel Method with Spectral Parameter for Nonlinear Monotone Equations and Signal Processing

by Aliyu Muhammed Awwal, Lin Wang, Poom Kumam, Hassan Mohammad and Wiboonsak Watthayu

Math. Comput. Appl. 2020, 25(2), 27; https://doi.org/10.3390/mca25020027 - 1 May 2020

Cited by 19 | Viewed by 2862

Abstract

A number of practical problems in science and engineering can be converted into a system of nonlinear equations and therefore, it is imperative to develop efficient methods for solving such equations. Due to their nice convergence properties and low storage requirements, conjugate gradient [...] Read more.

A number of practical problems in science and engineering can be converted into a system of nonlinear equations and therefore, it is imperative to develop efficient methods for solving such equations. Due to their nice convergence properties and low storage requirements, conjugate gradient methods are considered among the most efficient for solving large-scale nonlinear equations. In this paper, a modified conjugate gradient method is proposed based on a projection technique and a suitable line search strategy. The proposed method is matrix-free and its sequence of search directions satisfies sufficient descent condition. Under the assumption that the underlying function is monotone and Lipschitzian continuous, the global convergence of the proposed method is established. The method is applied to solve some benchmark monotone nonlinear equations and also extended to solve

ℓ_{1}

-norm regularized problems to reconstruct a sparse signal in compressive sensing. Numerical comparison with some existing methods shows that the proposed method is competitive, efficient and promising. Full article

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26 pages, 1121 KiB

Open AccessArticle

An m-Polar Fuzzy PROMETHEE Approach for AHP-Assisted Group Decision-Making

by Muhammad Akram, Shumaiza and José Carlos R. Alcantud

Math. Comput. Appl. 2020, 25(2), 26; https://doi.org/10.3390/mca25020026 - 1 May 2020

Cited by 21 | Viewed by 3197

Abstract

The Analytical Hierarchy Process (AHP) is arguably the most popular and factual approach for computing the weights of attributes in the multi-attribute decision-making environment. The Preference Ranking Organization Method for Enrichment of Evaluations (PROMETHEE) is an outranking family of multi-criteria decision-making techniques for [...] Read more.

The Analytical Hierarchy Process (AHP) is arguably the most popular and factual approach for computing the weights of attributes in the multi-attribute decision-making environment. The Preference Ranking Organization Method for Enrichment of Evaluations (PROMETHEE) is an outranking family of multi-criteria decision-making techniques for evaluating a finite set of alternatives, that relies on multiple and inconsistent criteria. One of its main advantages is the variety of admissible preference functions that can measure the differences between alternatives, in response to the type and nature of the criteria. This research article studies a version of the PROMETHEE technique that encompasses multipolar assessments of the performance of each alternative (relative to the relevant criteria). As is standard practice, first we resort to the AHP technique in order to quantify the normalized weights of the attributes by the pairwise comparison of criteria. Afterwards the m-polar fuzzy PROMETHEE approach is used to rank the alternatives on the basis of conflicting criteria. Six types of generalized criteria preference functions are used to measure the differences or deviations of every pair of alternatives. A partial ranking of alternatives arises by computing the positive and negative outranking flows of alternatives, which is known as PROMETHEE I. Furthermore, a complete ranking of alternatives is achieved by the inspection of the net flow of alternatives, and this is known as PROMETHEE II. Two comparative analysis are performed. A first study checks the impact of different types of preference functions. It considers the usual criterion preference function for all criteria. In addition, we compare the technique that we develop with existing multi-attribute decision-making methods. Full article

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26 pages, 4339 KiB

Open AccessFeature PaperArticle

Porous Functionally Graded Plates: An Assessment of the Influence of Shear Correction Factor on Static Behavior

by Ana F. Mota, Maria Amélia R. Loja, Joaquim I. Barbosa and José A. Rodrigues

Math. Comput. Appl. 2020, 25(2), 25; https://doi.org/10.3390/mca25020025 - 24 Apr 2020

Cited by 28 | Viewed by 3590

Abstract

The known multifunctional characteristic of porous graded materials makes them very attractive in a number of diversified application fields, which simultaneously poses the need to deepen research efforts in this broad field. The study of functionally graded porous materials is a research topic [...] Read more.

The known multifunctional characteristic of porous graded materials makes them very attractive in a number of diversified application fields, which simultaneously poses the need to deepen research efforts in this broad field. The study of functionally graded porous materials is a research topic of interest, particularly concerning the modeling of porosity distributions and the corresponding estimations of their material properties—in both real situations and from a material modeling perspective. This work aims to assess the influence of different porosity distribution approaches on the shear correction factor, used in the context of the first-order shear deformation theory, which in turn may introduce significant effects in a structure’s behavior. To this purpose, we evaluated porous functionally graded plates with varying composition through their thickness. The bending behavior of these plates was studied using the finite element method with two quadrilateral plate element models. Verification studies were performed to assess the representativeness of the developed and implemented models, namely, considering an alternative higher-order model also employed for this specific purpose. Comparative analyses were developed to assess how porosity distributions influence the shear correction factor, and ultimately the static behavior, of the plates. Full article

(This article belongs to the Special Issue Mesh-Free and Finite Element-Based Methods for Structural Mechanics Applications)

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20 pages, 835 KiB

Open AccessArticle

Existence of Generalized Augmented Lagrange Multipliers for Constrained Optimization Problems

by Yue Wang, Jinchuan Zhou and Jingyong Tang

Math. Comput. Appl. 2020, 25(2), 24; https://doi.org/10.3390/mca25020024 - 24 Apr 2020

Cited by 5 | Viewed by 2828

Abstract

The augmented Lagrange multiplier as an important concept in duality theory for optimization problems is extended in this paper to generalized augmented Lagrange multipliers by allowing a nonlinear support for the augmented perturbation function. The existence of generalized augmented Lagrange multipliers is established [...] Read more.

The augmented Lagrange multiplier as an important concept in duality theory for optimization problems is extended in this paper to generalized augmented Lagrange multipliers by allowing a nonlinear support for the augmented perturbation function. The existence of generalized augmented Lagrange multipliers is established by perturbation analysis. Meanwhile, the relations among generalized augmented Lagrange multipliers, saddle points, and zero duality gap property are developed. Full article

15 pages, 1535 KiB

Open AccessArticle

Nonlinear Analysis for a Type-1 Diabetes Model with Focus on T-Cells and Pancreatic β-Cells Behavior

by Diana Gamboa, Carlos E. Vázquez and Paul J. Campos

Math. Comput. Appl. 2020, 25(2), 23; https://doi.org/10.3390/mca25020023 - 24 Apr 2020

Cited by 6 | Viewed by 2527

Abstract

Type-1 diabetes mellitus (T1DM) is an autoimmune disease that has an impact on mortality due to the destruction of insulin-producing pancreatic

β

-cells in the islets of Langerhans. Over the past few years, the interest in analyzing this type of disease, either in [...] Read more.

Type-1 diabetes mellitus (T1DM) is an autoimmune disease that has an impact on mortality due to the destruction of insulin-producing pancreatic

β

-cells in the islets of Langerhans. Over the past few years, the interest in analyzing this type of disease, either in a biological or mathematical sense, has relied on the search for a treatment that guarantees full control of glucose levels. Mathematical models inspired by natural phenomena, are proposed under the prey–predator scheme. T1DM fits in this scheme due to the complicated relationship between pancreatic

β

-cell population growth and leukocyte population growth via the immune response. In this scenario,

β

-cells represent the prey, and leukocytes the predator. This paper studies the global dynamics of T1DM reported by Magombedze et al. in 2010. This model describes the interaction of resting macrophages, activated macrophages, antigen cells, autolytic T-cells, and

β

-cells. Therefore, the localization of compact invariant sets is applied to provide a bounded positive invariant domain in which one can ensure that once the dynamics of the T1DM enter into this domain, they will remain bounded with a maximum and minimum value. Furthermore, we analyzed this model in a closed-loop scenario based on nonlinear control theory, and proposed bases for possible control inputs, complementing the model with them. These entries are based on the existing relationship between cell–cell interaction and the role that they play in the unchaining of a diabetic condition. The closed-loop analysis aims to give a deeper understanding of the impact of autolytic T-cells and the nature of the

β

-cell population interaction with the innate immune system response. This analysis strengthens the proposal, providing a system free of this illness—that is, a condition wherein the pancreatic

β

-cell population holds and there are no antigen cells labeled by the activated macrophages. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2019)

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14 pages, 17146 KiB

Open AccessEditor’s ChoiceArticle

Mechanism of Coup and Contrecoup Injuries Induced by a Knock-Out Punch

by Milan Toma, Rosalyn Chan-Akeley, Christopher Lipari and Sheng-Han Kuo

Math. Comput. Appl. 2020, 25(2), 22; https://doi.org/10.3390/mca25020022 - 15 Apr 2020

Cited by 16 | Viewed by 10519

Abstract

Primary Objective: The interaction of cerebrospinal fluid with the brain parenchyma in an impact scenario is studied. Research Design: A computational fluid-structure interaction model is used to simulate the interaction of cerebrospinal fluid with a comprehensive brain model. Methods and Procedures: The method [...] Read more.

Primary Objective: The interaction of cerebrospinal fluid with the brain parenchyma in an impact scenario is studied. Research Design: A computational fluid-structure interaction model is used to simulate the interaction of cerebrospinal fluid with a comprehensive brain model. Methods and Procedures: The method of smoothed particle hydrodynamics is used to simulate the fluid flow, induced by the impact, simultaneously with finite element analysis to solve the large deformations in the brain model. Main Outcomes and Results: Mechanism of injury resulting in concussion is demonstrated. The locations with the highest stress values on the brain parenchyma are shown. Conclusions: Our simulations found that the damage to the brain resulting from the contrecoup injury is more severe than that resulting from the coup injury. Additionally, we show that the contrecoup injury does not always appear on the side opposite from where impact occurs. Full article

(This article belongs to the Special Issue Numerical Modelling and Simulation Applied to Head Trauma)

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15 pages, 5931 KiB

Open AccessArticle

The Strain Rates in the Brain, Brainstem, Dura, and Skull under Dynamic Loadings

by Mohammad Hosseini-Farid, MaryamSadat Amiri-Tehrani-Zadeh, Mohammadreza Ramzanpour, Mariusz Ziejewski and Ghodrat Karami

Math. Comput. Appl. 2020, 25(2), 21; https://doi.org/10.3390/mca25020021 - 7 Apr 2020

Cited by 14 | Viewed by 4858

Abstract

Knowing the precise material properties of intracranial head organs is crucial for studying the biomechanics of head injury. It has been shown that these biological tissues are significantly rate-dependent; hence, their material properties should be determined with respect to the range of deformation [...] Read more.

Knowing the precise material properties of intracranial head organs is crucial for studying the biomechanics of head injury. It has been shown that these biological tissues are significantly rate-dependent; hence, their material properties should be determined with respect to the range of deformation rate they experience. In this paper, a validated finite element human head model is used to investigate the biomechanics of the head in impact and blast, leading to traumatic brain injuries (TBI). We simulate the head under various directions and velocities of impacts, as well as helmeted and unhelmeted head under blast shock waves. It is demonstrated that the strain rates for the brain are in the range of 36 to 241 s⁻¹, approximately 1.9 and 0.86 times the resulting head acceleration under impacts and blast scenarios, respectively. The skull was found to experience a rate in the range of 14 to 182 s⁻¹, approximately 0.7 and 0.43 times the head acceleration corresponding to impact and blast cases. The results of these incident simulations indicate that the strain rates for brainstem and dura mater are respectively in the range of 15 to 338 and 8 to 149 s⁻¹. These findings provide a good insight into characterizing the brain tissue, cranial bone, brainstem and dura mater, and also selecting material properties in advance for computational dynamical studies of the human head. Full article

(This article belongs to the Special Issue Numerical Modelling and Simulation Applied to Head Trauma)

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7 pages, 3525 KiB

Open AccessArticle

Structural Stability of a Family of Exponential Polynomial Maps

by Francisco Solis, Silvia Jerez, Roberto Ku-Carrillo and Sandra Delgadillo

Math. Comput. Appl. 2020, 25(2), 20; https://doi.org/10.3390/mca25020020 - 7 Apr 2020

Viewed by 2111

Abstract

We perturbed a family of exponential polynomial maps in order to show both analytically and numerically their unpredictable orbit behavior. Due to the analytical form of the iteration functions the family has numerically different behavior than its correspondent analytical one, which is a [...] Read more.

We perturbed a family of exponential polynomial maps in order to show both analytically and numerically their unpredictable orbit behavior. Due to the analytical form of the iteration functions the family has numerically different behavior than its correspondent analytical one, which is a topic of paramount importance in computer mathematics. We discover an unexpected oscillatory parametrical behavior of the perturbed family. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering & Human Behaviour 2019)

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22 pages, 8799 KiB

Open AccessArticle

Isogeometric Analysis for Fluid Shear Stress in Cancer Cells

by José A. Rodrigues

Math. Comput. Appl. 2020, 25(2), 19; https://doi.org/10.3390/mca25020019 - 3 Apr 2020

Cited by 5 | Viewed by 3170

Abstract

The microenvironment of the tumor is a key factor regulating tumor cell invasion and metastasis. The effects of physical factors in tumorigenesis is unclear. Shear stress, induced by liquid flow, plays a key role in proliferation, apoptosis, invasion, and metastasis of tumor cells. [...] Read more.

The microenvironment of the tumor is a key factor regulating tumor cell invasion and metastasis. The effects of physical factors in tumorigenesis is unclear. Shear stress, induced by liquid flow, plays a key role in proliferation, apoptosis, invasion, and metastasis of tumor cells. The mathematical models have the potential to elucidate the metastatic behavior of the cells’ membrane exposed to these microenvironment forces. Due to the shape configuration of the cancer cells, Non-uniform Rational B-splines (NURBS) lines are very adequate to define its geometric model. The Isogeometric Analysis allows a simplified transition of exact CAD models into the analysis avoiding the geometrical discontinuities of the traditional Galerkin traditional techniques. In this work, we use an isogeometric analysis to model the fluid-generated forces that tumor cells are exposed to in the vascular and tumor microenvironments, in the metastatic process. Using information provided by experimental tests in vitro, we present a suite of numerical experiments which indicate, for standard configurations, the metastatic behavior of cells exposed to such forces. The focus of this paper is strictly on geometrical sensitivities to the shear stress’ exhibition for the cell membrane, this being its innovation. Full article

(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications)

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16 pages, 2901 KiB

Open AccessArticle

Prescribed Performance Adaptive Backstepping Control for Winding Segmented Permanent Magnet Linear Synchronous Motor

by Weiming Zhang, Dapan Li, Xuyang Lou and Dezhi Xu

Math. Comput. Appl. 2020, 25(2), 18; https://doi.org/10.3390/mca25020018 - 27 Mar 2020

Cited by 2 | Viewed by 2394

Abstract

In this paper, a prescribed performance adaptive backstepping control (PPABC) strategy is proposed to control the speed of a winding segmented permanent magnet linear synchronous motor (WS-PMLSM) with variable parameters and an unknown load disturbance. Firstly, a mathematical model of WS-PMLSM is provided. [...] Read more.

In this paper, a prescribed performance adaptive backstepping control (PPABC) strategy is proposed to control the speed of a winding segmented permanent magnet linear synchronous motor (WS-PMLSM) with variable parameters and an unknown load disturbance. Firstly, a mathematical model of WS-PMLSM is provided. Then, the prescribed performance technique is introduced in the adaptive backstepping control to improve the transient performance and ensures the tracking error converges within a predetermined range. In addition, a constrained command filter is introduced to address the problem of differential expansion which exists in the traditional backstepping method, and a filter compensation signal is designed against the filter error. Moreover, the adaptive law is designed based on Lyapunov stability theory to estimate the uncertainties caused by parameter changes and load disturbances. The stability of the proposed control strategy is given and the simulation of the control system is carried out under the proposed PPABC in contrast with another backstepping control and traditional PI control. Finally, the experiment is conducted to further show the effectiveness of the proposed controller. Full article

(This article belongs to the Section Engineering)

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