“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.
Author(s): Olga Moreira
Publisher: Arcler Press
Year: 2022
Language: English
Pages: 430
City: Boston
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
