Advances in Mathematical and Computational Modeling of Engineering Systems

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