Applied Mathematics in Engineering

“Applied Mathematics in Engineering” is an edited book comprising 15 contemporaneous open-access articles focused on mathematical modelling, mathematical optimization, and fractal mathematics and their applications in modern engineering and industry. The first part covers a wide range of mathematical models for solving real-world problems in mechanical engineering, biomedicine, fluid dynamics, and other applications. The second part of the book presents various mathematical optimization methods and algorithms (e.g. topology optimization, hybrid arithmetic optimization, and isogeometric topology optimization) for solving engineering problems. The third part of the book is dedicated to the mathematics of fractals and its applications in the engineering of antennas, image compression technology, fracture mechanics, ophthalmology and more. The intended audience of this book is undergraduate and graduate students, as well as junior researchers. Cover Title Page Copyright DECLARATION ABOUT THE EDITOR TABLE OF CONTENTS List of Contributors List of Abbreviations Preface Chapter 1 A Survey of Mathematical Tools in Topology and Performance Integrated Modeling and Design of Robotic Mechanism Abstract Introduction Relationship Between Development of Robotic Mechanism and Motions Matrix Lie Group and Lie Algebra Based Method Dual Quaternion and Pure Dual Quaternion Based Method Finite Screw and Instantaneous Screw Based Method Discussions Conclusions References Chapter 2 A High Accuracy Modeling Scheme for Dynamic Systems: Spacecraft Reaction Wheel Model Abstract Introduction Methods Results and Discussion Conclusions References Chapter 3 Mathematical Modeling of Vaporization during Laser-induced Thermotherapy in Liver Tissue Abstract Introduction Mathematical Model Mathematical Modeling of Vaporization Numerical Methods Results and Discussion Conclusion References Chapter 4 A Novel Mathematical Modeling with Solution for Movement of Fluid through Ciliary caused Metachronal Waves in a Channel Abstract Introduction Modeling of the Rheological Problem Solution Methodology Velocity Profile Analysis of the Physical Problem Conclusion Acknowledgements References Chapter 5 A New Mathematical Modeling Approach for Thermal Exploration Efficiency under different Geothermal Well Layout Conditions Abstract Introduction Conceptual Model of Geothermal Exploitation Basic Assumptions of the Model Example Model Parameters and Content Results and Discussion Conclusion Acknowledgements References Chapter 6 Mathematical Modeling and Thermodynamics of Prandtl–Eyring Fluid with Radiation Effect: a Numerical Approach Abstract Introduction Mathematical Modeling Numerical Scheme Discussion On Graphical Outcomes Conclusion References Chapter 7 A Reverse Logistics Chain Mathematical Model for a Sustainable Production System of Perishable Goods based on Demand Optimization Abstract Introduction Literature Review Problem Statement and Mathematical Formulation Case Study Conclusions References Chapter 8 New Mathematical Modeling for a Location–routing– inventory Problem in a Multi-period Closed-loop Supply Chain in a Car Industry Abstract Introduction Literature Review Problem Definition Proposed Solution Methods Computational Results Conclusion References Chapter 9 Information Sharing Systems and Teamwork between Sub-teams: A Mathematical Modeling Perspective Abstract Introduction The Proposed Model and Problem Statement Conclusion References Chapter 10 Topology Optimisation under Uncertainties with Neural Networks Abstract Introduction Topology Optimisation Under Uncertainties Neural Network Architectures Results Discussion and Conclusions Author Contributions Acknowledgments Appendix A. Bridge Benchmark Problem Appendix B. Finite Element Discretization Appendix C. Additional Experiments References Chapter 11 A Hybrid Arithmetic Optimization and Golden Sine Algorithm for Solving Industrial Engineering Design Problems Abstract Introduction Preliminaries The Proposed Algorithm Experimental Results and Discussion Conclusions and Future Work Author Contributions Acknowledgments References Chapter 12 Modeling and Optimizing the System Reliability Using Bounded Geometric Programming Approach Abstract Introduction Literature Review Geometric Programming Problem: Basic Concepts Computational Study Conclusions Author Contributions Acknowledgments References Chapter 13 A Comprehensive Review of Isogeometric Topology Optimization: Methods, Applications and Prospects Abstract Introduction Isogeometric Topology Optimization (ITO) Methods Applications of ITO Prospects Conclusions References Chapter 14 Analysis and Computations of Optimal Control Problems for Boussinesq Equations Abstract Introduction Notation Optimal Control of Boussinesq Equations Numerical Results Conclusions Author Contributions References Chapter 15 Fractals: An Eclectic Survey, Part II Abstract Introduction Mathematics of Fractals Fractals in Natural and Artificial Landscapes Fractal Antennas Fractals in Image Compression Fractals in Fracture Mechanics Other Fractal Applications and Innovations Conclusions Author Contributions Acknowledgments References Index Back Cover