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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