Frontiers in Mathematical Modelling Research

Mathematics Research Developments
Frontiers in MathematicalModelling Research
Contents
Preface
	Some Key Features of the Book
Chapter 1Introduction to MathematicalModelling inApplications
	Abstract
	Introduction
	Types of Mathematical Modelling Approaches
	Applications of Modelling in Science and Engineering
	Analysis of MathematicalModel
		QualitativeAnalysis of a Deterministic Model
		Lypunov Global Stability Theory
		LaSalle’s Invariance Principle
	QualitativeAnalysis of a StochasticModel
		Existence and Uniqueness Theorem
		Stability of Equilibrium Solutions for SDE
		Stochastic Stability Theorem
	Layout of this Book
		Chapter 2: Fault Diagnosis of Rotating Machines Based on the Math-ematicalModel of a Rotor Bearing-Mass System
		Chapter 3: Experimental and Mathematical Modelling to Investigatethe Kinetic Behavior of Plasmid DNA Production by Escherichia ColiDH5
		Chapter 4: MathematicalModelling of Robotic Digitalised Production
		Chapter 5: MathematicalModelling and Simulation of a RobotManipulator
		Chapter 6: Mathematical Modeling Applied to Control the EmergingDeadly Nipah Fever in Bangladesh
		Chapter 7: Mathematical Modeling of the Closed-Loop Performanceof a Continuous Bioreactor under a Feedback Polynomial-TypeController
		Chapter 8: Mathematical Study of Human Movement andTemperature in the Transmission Dynamics ofDengue Disease Between Two Patches
		Chapter 9: A Numerical Model of Malaria Fever Transmission withOrganized Vector Populace and Irregularity
		Chapter 10: MathematicalModeling in Food and Agricultural Areas
		Chapter 11: Mathematical Modelling of Complex Systems usingStochastic Partial Differential Equations: Review and Developmentof Mathematical Concepts
	Conclusion
	References
Chapter 2Fault Diagnosis of Rotating Machines Basedon the MathematicalModel of a RotorBearing-Mass System
	Abstract
	Introduction
	MathematicalModel of the RBMS
		Transfer Functions
		Observability for Unbalance Effects
		Observability under Misalignment
		Observability Due to Unbalance and Misalignment
	RBMS Design
	Validation Results
	Conclusion
	Acknowledgment
	References
Chapter 3Experimental and MathematicalModelling to Investigate the KineticBehavior of Plasmid DNA Production byEscherichia coli DH5
	Abstract
	Introduction
	Methods
		Bacterial Strain and Plasmid
		Medium and Inoculum
		Cultivation
		DCW and Glycerol Determination
		Plasmid DNA Quantification
		NPT II and Organic Acids Quantification
		Model Development
		Thermodynamic Analysis
	Results
		pDNA Production Experiments
		Parametric Identification and Simulations
		Thermodynamics and the Effect of Temperature on theParameters
	Conclusion
	References
Chapter 4Mathematical Modelling inRobotic Digital Production
	Abstract
	Introduction
	Analytical Framework
		Related Work
		Research Purpose and Objectives
	Method
		Section 1. Dynamic and Static Modeling of Processes ofCreation of High-Tech Digital Production Structures
			Setting the Task of Increasing the Enterprise Potential by CreatingHigh-Tech Structures
			Development of a Generalized Economic Mathematical Model
				Prime Cost of Production
			Analysis and Peculiarities of the Implementation of the EconomicMathematical Model
				Modification of the Economic Mathematical Model for a Given ProductInnovation Release Program
				Modification of the Economic Mathematical Model at a Given Level ofAutomation
			Static Modeling of Processes of Creation of High-Tech Structures
		Section 2. Discrete Programming Method in the Strategy ofModeling the Output and Capacity Utilization of High-TechDigital Production Structures
			Optimization of the Production Program of Flexible DigitalManufacturing Organizational and Production Structures
			Management of Processes of Mastering Production Capacities ofthe Developed Highly Automated Organizational and ProductionStructures
		Section 3. Modeling of Processes for Selection of EconomicallyExpedient Limits for Robotics of High-Tech Structures inDigital Production
			Development of an Economic Mathematical Model for DeterminingEconomically Feasible Boundaries for Robotics of Mass Production
			Development of the Economic Mathematical Model for DeterminingEconomically Feasible Boundaries of Robotics of DiversifiedProduction
		Section 4. Mathematical Modeling of Solving theCombinatorial Tasks of Minimizing Costs in the Processof Creating High-Tech Digital Production Structures
			Setting the Task of Modeling the Optimal Composition of HighlyAutomated Production Units
			Algorithm of Creation of Highly Automated Production Units ofthe High-Tech Organizational and Production Structure
			Computational Mechanism of Implementation of the Algorithm ofCreation of Highly Automated Production Units of the High-TechOrganizational and Production Structure
	Results and Discussion
	Conclusion
	References
Chapter 5Mathematical Modelling and Simulation ofa Robot Manipulator
	Abstract
	Introduction
	MathematicalModelling
		Forward Kinematics
		Inverse Kinematics
		Differential Kinematics
		Singularities
		Trajectories
		Numerical Simulation
	Acknowledgment
	Conclusion
	References
Chapter 6MathematicalModeling Appliedto Control the Emerging DeadlyNipah Fever in Bangladesh
	Abstract
	Introduction
	MathematicalModel Formulation
	Analysis of the Model
		Boundedness
		Basic Reproduction Number
	Equilibrium Analysis
		Global Stability of the Endemic Equilibrium Point E
	Incorporating Optimal Control to the Model
		Characterization of Optimal Controls
	Numerical Simulations
	Conclusion
	Acknowledgments
	References
Chapter 7Mathematical Modelling ofthe Closed-Loop Performance ofa Continuous Bioreactor undera Feedback Polynomial-Type Controller
	Abstract
	Introduction
	Methods
		ABE Fermentation Model
		Bifurcation Analysis
		Stability of the Process
		Cubic Control Design
	Results
		Bifurcation Analysis and Open-Loop Stability
		Closed Loop Analysis
		System Stability Analysis
	Conclusion
	References
Chapter 8Mathematical Studyof Human Movement and Temperaturein the Transmission Dynamics ofDengue Disease between Two Patches
	Abstract
	Introduction
	Model Formulation and Analysis
		Existence and Stability of Disease Free Equilibrium Point
		Basic Reproduction Number
	Numerical Results and Discussion
	Conclusion
	References
Chapter 9A Numerical Model of Malaria FeverTransmission with Organized VectorPopulace and Irregularity
	Abstract
	1. Introduction
	2. Mathematical Model
	3. Dynamical Behaviour without Noise
	4. Dynamical Behaviour with Noise
	5. Numerical Simulations
	Conclusion
	Acknowledgments
	Conflict of Interest
	References
Chapter 10MATHEMATICAL MODELLINGIN FOOD AND AGRICULTURAL AREAS
	ABSTRACT
	INTRODUCTION
	MATHEMATICAL MODELING IN THE FOOD AREA
		Heat and Mass Transfer Models
			Heat Transfer
			Mass Transfer
			Diffusive Mass Transfer
				Fick’s Law
				Maxwell-Stefan Theory
			Effective Diffusivity
			Convective Mass Transfer
			Microbial and Enzymatic Inactivation
			Temperature Profiles and Thermal Conductivity Coefficient
			Food Drying
			Other Food-Related Areas
	Mathematical Modeling in the Agricultural Area
		Biochemical Reactions
		Growth Performance
		Plants Processes Dynamic
		Plants Demand Components
		Other Agricultural-Related Areas
		Plant Diseases
		Pest Control
		Animal Care
	Conclusion and Future Outlooks
	References
Chapter 11Mathematical Modelling of ComplexSystems Using Stochastic PartialDifferential Equations: Review andDevelopment of Mathematical Concepts
	ABSTRACT
	Introduction
		Models, Mathematics and Modelling
		Motivation
		SPDEs and Modelling
	Development of Polynomial Chaos Expansion
		One Dimensional PCE
		Multi-Dimensional PCE
	Calculation of PCE
		The Intrusive Projection Method (The GalerkinProjection Method)
		The Non-Intrusive Projection Method
	Implementation of Polynomial Chaos Expansion
		Discretization Scheme in Time and Space
			Example 1: First Order Stochastic Process
				Construction of PCE Model of Example 1
			Example 2: Stochastic Differential Equation
				Simulating Sample Realizations of a Brownian Motion (BM)
				The Euler-Maruyama (EM) Method
			Example 3: The Stochastic Advection Diffusion Equation (SADE)
	The Wick Product
		The Wick Product in Physics
		The Wick Product in Stochastic Analysis
	Conclusion and Discussion
	Appendix A
	References
About the Editors
	M. Haider Ali Biswas, PhD
	M. Humayun Kabir, PhD
Index
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