The text covers a wide range of topics such as mathematical modeling of crop pest control management, water resources management, impact of anthropogenic activities on atmospheric carbon dioxide concentrations, impact of climate changes on melting of glaciers and polar bear populations, dynamics of slow–fast predator-prey system and spread and control of HIV epidemic. It emphasizes the use of mathematical modeling to investigate the fluid flow problems including the breaking of viscoelastic jet, instability arising in nanofiber, flow in an annulus channel, and thermal instability in nano-fluids in a comprehensive manner. This book will be a readily accessible source of information for the students, researchers and policymakers interested in the application of mathematical and computational modeling techniques to investigate various biological and engineering phenomena.
Features
- Focuses on the current modeling and computational trends to investigate various ecological, epidemiological, and engineering systems.
- Presents the mathematical modeling of a wide range of ecological and environmental issues including crop pest control management, water resources management, the effect of anthropogenic activities on atmospheric carbon dioxide concentrations, and impact of climate changes on melting of glaciers and polar bear population.
- Covers a wide range of topics including the breaking of viscoelastic jet, instability arising in nanofiber, flow in an annulus channel, and thermal instability in nano-fluids.
- Examines evolutionary models i.e., models of time-varying processes. Highlights the recent developments in the analytical methods to investigate the nonlinear dynamical systems.
- Showcases diversified applications of computational techniques to solve practical biological and engineering problems.
The book focuses on the recent research developments in the mathematical modeling and scientific computing of biological and engineering systems. It will serve as an ideal reference text for senior undergraduate, graduate students, and researchers in diverse fields including ecological engineering, environmental engineering, computer engineering, mechanical engineering, mathematics, and fluid dynamics.
Author(s): Mukesh Kumar Awasthi, Maitri Verma, Mangey Ram
Series: Smart Technologies for Engineers and Scientists
Publisher: CRC Press
Year: 2023
Language: English
Pages: 360
City: Boca Raton
Cover
Half Title
Series Page
Title Page
Copyright Page
Table of Contents
Preface
Editors
Contributors
1 Parameter identification and fuzzy T-S robust static output stabilization for a carbon dioxide model: Moroccan context
Nomenclature
1.1 Introduction: Background and driving forces
1.2 Model presentation
1.3 Carbon dioxide model T-S construction
1.3.1 Model value space
1.3.1.1 Variable C operating subspace
1.3.1.2 Variable N operating subspace
1.3.1.3 Variable F operating subspace
1.3.1.4 Combined value space
1.3.2 Equilibrium points
1.3.2.1 Definition
1.3.2.2 E[sub(4)] equilibrium point
1.3.3 T-S model
1.3.3.1 Change of coordinate
1.3.3.2 T-S model transformation
1.4 Stability analysis
1.4.1 Local stability
1.4.2 Global stability
1.4.3 Attraction domain
1.5 CO[sub(2)] T-S model static output controller
1.5.1 T-S representation
1.5.1.1 Forced system
1.5.1.2 Premise variables
1.5.1.3 T-S rule construction
1.5.2 Static output feedback controller
1.5.3 LMI formulation
1.6 Parameter identification for Moroccan case
1.6.1 Variables background
1.6.1.1 CO[sub(2)] level
1.6.1.2 Human population
1.6.1.3 Forest biomass
1.6.2 Parameters identification
1.6.2.1 Parameter Q[sub(0)]
1.6.2.2 Parameter λ
1.6.2.3 Parameter α
1.6.2.4 Parameter λ[sub(1)]
1.6.2.5 Parameter s
1.6.2.6 Parameter L
1.6.2.7 Parameter θ
1.6.2.8 Parameter ϕ
1.6.2.9 Parameter µ
1.6.2.10 Parameter M
1.6.2.11 Proportion π
1.6.2.12 Proportion π[sub(1)]
1.7 CO[sub(2)] T-S model robust controller synthesis
1.7.1 Forced uncertain model
1.7.2 LMI formulation
1.8 Results and discussion
1.8.1 Parameter identification summary for Morocco
1.8.2 T-S model computation
1.8.3 T-S model behavior
1.8.4 Stability analysis
1.8.5 Forced system control
1.8.5.1 Static output feedback control
1.8.5.2 Robust stabilization
1.9 Conclusion
References
2 Numerical investigation of wave pattern evolution in Gray–Scott model using discontinuous Galerkin finite element method
2.1 Introduction
2.2 Gray–Scott reaction-diffusion model
2.3 Mixed modal DG-FEM scheme
2.4 Results and discussion
2.5 Concluding remarks
Acknowledgments
References
3 Modeling the impact of pre-exposure prophylaxis and male circumcision on HIV/AIDS
Nomenclature
3.1 Introduction
3.2 The mathematical model
3.3 Positivity and boundedness
3.4 The existence of equilibrium points
3.5 Stability analysis
3.5.1 Local stability
3.5.2 Global stability
3.6 Numerical simulation and discussion
3.7 Sensitivity analysis
3.8 Conclusion
Acknowledgements
References
4 Modeling the effect of media awareness campaigns on the spread of HIV/AIDS
4.1 Introduction
4.2 Formulation of mathematical model
4.3 Positivity of solutions
4.4 Invariant region
4.5 Existence of equilibria
4.6 Existence of endemic equilibrium E*(N*, Y*, X*[sub(M)], M*)
4.7 Stability analysis
4.8 Optimal control system
4.9 Characterization of optimal control function
4.10 Numerical simulation and discussion
4.11 Conclusion
Appendix A
Appendix B
References
5 Relaxation oscillation and canard explosion in slow–fast predator–prey systems
5.1 Introduction
5.2 Preliminaries
5.2.1 Slow–fast systems
5.2.2 Geometric singular perturbation theory
5.2.3 The blow-up method for slow–fast systems
5.2.4 Singular Hopf bifurcation, canard cycles, canard explosion and relaxation oscillation
5.2.5 Entry–exit function
5.3 Application in a predator–prey model
5.3.1 Slow–fast analysis
5.3.2 Existence and linearized stability analysis
5.3.3 Bifurcation scenario
5.3.4 Singular Hopf bifurcation and canard cycles
5.3.5 Relaxation oscillation
5.3.6 Bi-stability
5.4 Conclusion
References
6 Impact of periodic farming awareness campaign through media for crop pest control management: A mathematical study
6.1 Introduction
6.2 Mathematical model formulation
6.3 System without periodic campaign (with local awareness only i. e., model 6.1)
6.3.1 Boundedness
6.4 Equilibria and stability
6.5 Stability analysis
6.6 Dynamics of the system with periodic campaign (with local and global periodic campaign)
6.6.1 Stability of periodic orbits
6.7 Numerical simulation
6.8 Discussion and conclusion
References
7 Mathematical modeling and analysis of the impact of global warming on the dynamics of polar bear population
7.1 Introduction
7.2 Mathematical model
7.3 Equilibrium states and stability analysis
7.3.1 Equilibrium states
7.3.2 Local stability analysis
7.3.3 Global stability of S*
7.4 Numerical simulations
7.4.1 Parameters estimation
7.4.2 Effect of variations in parameters
7.5 Conclusions
Acknowledgement
References
8 Rainfall-runoff modeling using SWAT model: A case study of middle Godavari basin, Telangana State, India
8.1 Introduction
8.2 Study area
8.3 Materials and methods
8.3.1 SWAT model inputs
8.3.1.1 Temporal data
8.3.1.2 Spatial data
8.4 Methodology
8.4.1 SWAT model description
8.4.2 Sequential uncertainty fitting (SUFI)-2 algorithm description
8.5 Performance evaluation criteria
8.5.1 Coefficient of determination (R[sup(2)])
8.6 Results and discussion
8.6.1 Land use/land cover (LULLC) statistics and trend patterns for precipitation, temperature
8.6.2 Sensitivity analysis
8.6.2.1 Sensitivity analysis for streamflow
8.6.3 Calibration and validation of streamflow
8.7 Conclusions
Acknowledgments
References
9 Mach number impact on Richtmyer-Meshkov instability in shock-refrigerant-22 bubble interaction
9.1 Introduction
9.2 Numerical method and validation
9.2.1 Governing equations
9.2.2 Validation study
9.2.3 Computational setup
9.2.4 Mesh refinement analysis
9.3 Results and discussion
9.4 Concluding remarks
References
10 One-dimensional weak shock wave in generalized magnetogasdynamics
10.1 Introduction
10.2 Mathematical model and shock-jump boundary conditions
10.3 Exact solution to weak shock wave problem in non-ideal magneto-gasdynamics flow
10.4 Results and discussion
10.5 Conclusion
References
11 Investigation of the boundary layer flow using glass box testing scheme
11.1 Introduction
11.2 Material and methods
11.2.1 Experimental set-up
11.2.2 Numerical methodology
11.3 Results and discussion
11.3.1 Hydrodynamic analysis of the air
11.3.2 Heat analysis of the flat plate collector
11.4 Conclusion
Notation
References
12 Mixing of methanol and water in a micro wavy channel
12.1 Introduction
12.2 Methodology
12.2.1 Governing equations
12.2.2 Mixing index
12.2.3 Parametric sweep
12.2.4 Geometric details
12.3 Result and discussion
12.3.1 Mesh build-up
12.3.2 Mixing of two species
12.3.3 Parametric sweep analysis
12.4 Conclusion
Acknowledgement
References
13 Heat transfer and pressure drop penalty study in flattened micro-finned tubes
Nomenclature
13.1 Introduction
13.2 Numerical models and data reduction
13.3 Mesh-sensitive study
13.4 Results and discussions
13.5 Conclusions
References
14 Heat and mass transfer in convective flow of nanofluid
Nomenclature
14.1 Introduction
14.2 Mathematical formulation
14.2.1 Transformation of Lie group and similarity solutions
14.3 Results and discussion
14.4 Conclusions
References
15 Flow of a second-order fluid due to disk rotation
Nomenclature
15.1 Introduction
15.2 Flow analysis and mathematical formulation
15.3 Analysis of the homotopy perturbation method
15.3.1 Implementation of the method
15.4 Results and discussions
15.5 Conclusion
References
16 Resonance in water pipeline due to transient
Nomenclature
16.1 Introduction
16.2 Mathematical modeling
16.3 Result and discussion
16.4 Conclusion
References
Index
