Integral Methods in Science and Engineering: Applications in Theoretical and Practical Research

Preface
The International Steering Committee of IMSE
Contents
Contributors
1 Approximate Solution for One-Dimensional Compressible Two-Phase Immiscible Flow in Porous Media for Variable Boundary Conditions
1.1 Introduction
1.2 Mathematical Model
1.2.1 Approximation for λTD(xD,tD)
1.2.2 Approximation for qDC(xD,tD)
1.2.2.1 Solution by the Laplace Transform
1.3 Model Validation
1.3.1 Injection Schedule 1
1.3.2 Injection Schedule 2
1.3.3 Compressibility Effect
1.4 Conclusion
References
2 On Pseudo-Cross Sections for Neutron Escape from a Domain by a Physical Monte Carlo Simulation
2.1 Introduction
2.2 The Physical Monte Carlo Simulation
2.3 The Pseudo-Cross Section for Neutron Escape
2.4 Calculation of Σz(r,E) for a Spherical Case
2.5 Properties and Application of Σz(r,E)
2.6 Conclusion
References
3 From a Unitary Symmetry Hypothesis to Dynamical Structures in Quantum Mechanics Models
3.1 Introduction
3.2 The Symmetry Hypothesis
3.3 The Free Particle Lagrange Density
3.4 The Interaction Lagrange Density
3.5 The Interacting Boson Lagrange Density
3.5.1 The n-n Terms
3.5.1.1 Term 1-1
3.5.1.2 Term 2-2
3.5.1.3 Term 3-3
3.5.1.4 Terms 4-4 and 5-5
3.5.1.5 Term 6-6
3.5.2 Terms n-m (n = m) with Vanishing Spin Trace TrS{Ξaμ()} = 0
3.5.2.1 Term 1-2 and Hermitian Conjugate Term 2-1
3.5.2.2 The Terms 1-4, 4-1, 1-5 and 5-1 Vanish Individually
3.5.2.3 Terms 2-3 and 3-2 Vanish Individually
3.5.2.4 Terms 3-4 and 4-3 Vanish Identically
3.5.2.5 Terms 3-5 and 5-3 Do Not Contribute to the Dynamics
3.5.3 Terms n-m (n = m) with Vanishing Spin Trace
3.5.3.1 Term 2-6 and Hermitian Conjugate Term 6-2
3.5.3.2 Term 4-6 and Hermitian Conjugate Term 6-4
3.5.3.3 Term 5-6 and Hermitian Conjugate Term 6-5
3.5.3.4 The Terms 1-6 and 6-1 Vanish Because of the Contraction of Space–Time Asymmetry
3.5.3.5 Terms 2-4, 2-5, 4-2 and 5-2 Vanish
3.5.3.6 The Terms 3-6 and 6-3
3.5.4 Terms n-m (n = m) Which Contribute to the Dynamics
3.5.4.1 Terms 1-3 and 3-1 Are Equal
3.5.4.2 Term 4-5 and 5-4
3.6 The Resulting Dynamical Model Compatible with Unitary and Chiral Symmetries
3.7 Conclusion
References
4 The Traction Boundary Value Problem for Thin Elastic Structures
4.1 Introduction
4.2 The Mathematical Model
4.3 Exterior Neumann Problem
4.4 First Numerical Example
4.5 Graphical Illustrations I
4.6 Second Numerical Example
4.7 Graphical Illustrations II
References
5 Mapping Properties of Potential Operators Related to the 2D Compressible Stokes System in Weighted Sobolev Spaces
5.1 Introduction
5.2 Preliminaries
5.3 Parametrix and Remainder
5.4 Hydrodynamic Potentials
5.4.1 Mapping Properties
5.5 Conclusions
References
6 Stochastic Effects of the Meander on the Dispersion of Pollutants in the Planetary Boundary Layer Under Low Wind Conditions
6.1 Introduction
6.2 The Advection–Diffusion Model
6.2.1 A Time-Dependent Solution
6.2.2 Fluctuations in the Horizontal Wind Velocity Field
6.3 The INEL Experiment
6.4 Results and Discussion
6.5 Conclusion
References
7 Asymptotics for the Spectrum of a Floquet-Parametric Family of Homogenization Problems Associated with a Dirichlet Waveguide
7.1 Introduction
7.1.1 The Parametric Family of Homogenization Spectral Problems
7.1.2 The Homogenized Problem
7.1.3 The Dirichlet Strip and Some Background
7.2 Preliminary Results
7.3 Convergence and Convergence Rates for Eigenvalues
References
8 The Wavelet-Based Integral Formula for the Solutions of the Wave Equation in an Inhomogeneous Medium: Convergence of Integrals
8.1 Introduction
8.2 Preliminary Considerations by the Fourier Transform
8.3 Some Facts from the Poincaré Affine Wavelet Analysis
8.4 Integral Representation of Solutions in the Homogeneous Medium
8.5 Initial-Value Problem for the Wave Equation in a Half-Plane on a Semi-Infinite Time Interval
8.6 Integral Representation for Solutions in the Inhomogeneous Medium
8.7 On Convergence of Integrals
References
9 Modelling the Spread of a Disease in an Epidemic Through a Country Divided into Geographical Regions
9.1 Introduction
9.2 Mathematical Model
9.3 Numerical Results
9.4 Conclusions
References
10 Computing Elastic Interior Transmission Eigenvalues
10.1 Introduction
10.2 Elastic Transmission Eigenvalue Problem
10.3 The Discretization of the Operators 12I+Dω and Sω
10.4 Solving the Nonlinear Eigenvalue Problem
10.5 Numerical Results
10.6 Summary and Outlook
References
11 A Novel Solution of the Multi-Group Neutron Diffusion Equation by the Hankel Transform Formalism
11.1 Introduction
11.2 Problem Formulation
11.3 Solution by the Infinite Hankel Transform
11.4 Results
11.5 Conclusion
References
12 A Simple Numerical Scheme to Obtain Reflectivity and Transmissivity of an Isotropically Scattering Slab
12.1 Introduction
12.2 The Radiative Transfer Equation in Slab Geometry
12.3 Discrete Ordinate Method
12.4 Spatial Discretization
12.5 Numerical Results
12.6 A Convergence Criterion
12.7 Final Remarks and Conclusion
References
13 A Unified Integral Equation Formulation for Linear and Geometrically Nonlinear Analysis of Thick Plates: Derivation of Equations
13.1 Introduction
13.2 Derivation of the Convective Terms
13.3 Summary of the Results
13.4 Conclusions
References
14 On Viscous Fluid Flow in Curvilinear Coordinate Systems
14.1 Introduction
14.2 Transformation of the Coordinate System
14.3 The Transformed Navier–Stokes Equation
14.4 Numerical Solution
14.5 Numerical Simulations
14.6 Conclusions
References
15 Impact Loading of Interface Cracks: Effects of Cracks Closure and Friction
15.1 Introduction
15.2 Statement of the Problem and Boundary Integral Formulation
15.3 Numerical Results and Conclusions
References
16 Periodic Solutions in Rn for Stationary Anisotropic Stokes and Navier-Stokes Systems
16.1 Introduction
16.2 Anisotropic Stokes and Navier-Stokes Systems
16.3 Some Function Spaces on Torus
16.4 Stationary Anisotropic Stokes System on Flat Torus
16.5 Stationary Anisotropic Navier-Stokes System with Constant Coefficients on Torus
16.5.1 Existence of a Weak Solution to Anisotropic Incompressible Navier-Stokes System on Torus
16.5.2 Solution Regularity for the Stationary Anisotropic Navier-Stokes System
16.6 Some Auxiliary Results
References
17 Null-Solutions of Elliptic Partial Differential Equations with Power Growth
17.1 Introduction and Statement of Main Result
17.2 Preliminaries
17.3 Proof of the Main Result
References
18 On the Use of the Adjoint Technique to the Estimation of Neutron Source Distributions in the Context of Subcritical Nuclear Reactors
18.1 Introduction
18.2 Mathematical Basis
18.3 The Source Estimation Through the Adjoint Technique
18.3.1 Boundary Conditions
18.3.2 The Importance Matrix
18.4 An Illustrative Example
18.5 Concluding Remarks
References
19 The Nodal LTSN Solution and a New Approach to Determine the Outgoing Angular Flux at the Boundary in a Rectangular Domain
19.1 Introduction
19.2 The Integrated SN Equations
19.3 The Nodal LTSN Solution
19.4 Numerical Results
19.5 Conclusions
References
20 A Numerical Study of the Convergence of Two Hybrid Convolution Quadrature Schemes for Broadband Wave Problems
20.1 Introduction
20.2 Convolution Quadrature for the Wave Equation: Summary
20.3 Hybrid Methods Framework
20.4 High-Frequency Approximations
20.4.1 DEA Based HFA
20.4.2 Simple HFA
20.5 Numerical Results
20.5.1 Square Domain
20.5.2 L-Shaped Domain
20.6 Conclusion
References
21 Analytical Reconstruction of the Nonlinear Transfer Function for a Wiener–Hammerstein Model
21.1 Introduction
21.2 Preliminaries
21.3 Data Analysis Using the Lissajous Curve
21.4 Amplitudes and Phases
21.5 Numerical Results
21.6 Conclusions and Future Work
References
22 Variation of Zero-Net Liquid Holdup in Gas–Liquid Cylindrical Cyclone (GLCC©)
22.1 Introduction
22.2 Literature Review
22.2.1 GLCC© Experimental Studies
22.2.2 GLCC© Mechanistic Modeling
22.2.3 GLCC© Zero-Net Liquid Holdup in Vertical Pipes
22.3 Experimental Program
22.3.1 Experimental Facility
22.3.1.1 Experimental Flow Loop
22.3.1.2 GLCC©-Test Section
22.3.1.3 Working Fluids
22.3.1.4 Instrumentation and Data Acquisition
22.3.2 Test Matrix
22.3.3 Testing Procedure
22.4 Results and Discussion
22.4.1 Zero-Net Liquid Holdup Variation
22.4.2 ZNLF Churn Region Height
22.4.3 ZNLH Variation Extended Correlation
22.4.4 Comparison Study
References
23 On the Mono-Energetic Neutron Space Kinetics Equation in Cartesian Geometry: An Analytic Solution by a Spectral Method
23.1 Introduction
23.2 What to Look For
23.3 Model and Methodology
23.4 Results
23.4.1 Homogeneous Case
23.4.2 Heterogeneous Case
23.5 Conclusion
References
Index