The use of mathematical structures: Modelling real phenomena

Description

“The Use Of Mathematical Structures: Modelling Real Phenomena” is an edited book consisting of 16 contemporaneous open-access articles that are devoted to the mathematical modelling of natural phenomena. To summarize, this book is about the use of applied mathematics and mathematical analysis in the context of its applications to real-world problems. It includes a selection of real-world problems in fluid dynamics, mechanical engineering, biology, and biochemistry. The last chapters include the mathematical modelling of the COVID-19 virus. The intended audience of this book is undergraduate and graduate students, as well as junior researchers. The reader must have a good knowledge of ordinary differential equations, boundary value problems, fractional calculus, stability theory, and wavelets in order to fully understand the real-world problems and their mathematical modelling included in this book. Cover Title Page Copyright DECLARATION ABOUT THE EDITOR TABLE OF CONTENTS List of Contributors List of Abbreviations Preface Chapter 1 Models, Structures, and the Explanatory Role of Mathematics in Empirical Science Abstract Introduction Why Think That Mathematics Does Genuine Explanatory Work? Mathematical Explanations as Structural Explanations From Structural Explanations to Structural Model Explanations Conclusion References Chapter 2 The Real and the Mathematical in Quantum Modeling: From Principles to Models and from Models to Principles Introduction Physical Principles and Mathematical Models in Quantum Mechanics From Models to Principles in Q-Modeling Outside Physics Conflict of Interest Statement Acknowledgments Footnotes References Chapter 3 The Nature and Mathematical Basis for Material Stability in the Chemical and Biological Worlds Abstract Report Discussion Conclusion Endnotes Authors’ Contributions Acknowledgements References Chapter 4 A Riccati-Bernoulli sub-ODE method for Nonlinear Partial Differential Equations and its Application Abstract Introduction Bäcklund transformation of the Riccati-Bernoulli equation Application to the Eckhaus Equation Application to the Nonlinear Fractional Klein-Gordon Equation Application to the Generalized Ostrovsky Equation Application to the generalized ZK-Burgers equation Comparisons and Explanations of the Solutions Conclusions Acknowledgements References Chapter 5 Mathematical Modelling of Mantle Convection at a high Rayleigh number with Variable Viscosity and Viscous Dissipation Abstract Introduction Methods Result and Discussion Conclusion References Chapter 6 Extending the Persistent Primary Variable Algorithm to Simulate Non-Isothermal Two-Phase Two-Component Flow with Phase Change Phenomena Abstract Background Method Numerical Scheme Numerical Solution of the Global Equation System Handling Unphysical Values during the Global Iteration Results and Discussions Nomenclature Authors’ Contributions Acknowledgements References Chapter 7 Modelling and Dynamic Characteristics for a Non-metal Pressurized Reservoir with Variable Volume Abstract Introduction Reservoir Description Modelling and Simulation Experimental Results and Discussion Conclusions Acknowledgements Authors’ Information Author Contributions Funding References Chapter 8 Dynamic Modelling and Natural Characteristic Analysis of Cycloid Ball Transmission Using Lumped Stiffness Method Abstract Introduction Lumped Stiffness Modelling Translational–Torsional Coupling Model Natural Characteristic Analysis Conclusion Authors’ contributions Acknowledgements References Chapter 9 Modelling of Flowslides and Debris Avalanches in Natural and Engineered Slopes: A Review Background Introduction Background Methods Results and Discussion for Natural Slopes Results and Discussion for Engineered Slopes Conclusions Acknowledgements References Chapter 10 On Some Wavelet Solutions of Singular Differential Equations Arising in the Modeling of Chemical and Biochemical Phenomena Abstract Introduction Jacobi Wavelet Bernoulli Wavelet Methods for Solution Error Bounds Numerical Simulation Conclusion Acknowledgements References Chapter 11 A Mathematical Analysis of Hopf-Bifurcation in a Prey-Predator Model with Nonlinear Functional Response Abstract Introduction Mathematical Model Formulation Mathematical Analysis Numerical Experiments and Biological Explanations Conclusion Acknowledgements Funding Authors’ Contributions References Chapter 12 Multiscale Modelling Tool: Mathematical Modelling of Collective Behaviour Without the Maths Abstract Introduction Design and Implementation Results Availability and Future Directions Acknowledgments References Chapter 13 Effects of Greenhouse Gases and Hypoxia on the Population of Aquatic Species: A Fractional Mathematical Model Abstract Introduction Preliminaries Model Dynamics Fractional-Order Analysis on the Proposed Model Experimental Simulations Conclusion Acknowledgements Funding Authors’ Contributions References Index Back Cover