Progress in Industrial Mathematics at ECMI 2006 (eBook)

Preface 6
Contents 8
Part I Plenary Lectures 22
On the Mean Geometric Densities of Random Closed Sets, and Their Estimation: Application to the Estimation of the Mean Density of Inhomogeneous Fibre Processes 23
Preface [VC] 23
1 Introduction 25
2 Generalized Densities 30
3 Approximation of Mean Densities 34
4 Statistical Methods for Fibre Systems 36
5 Estimators of the Intensity 39
6 Application of the Estimators to the Simulated Inhomogeneous Poisson Segment Process 41
7 Experimental Results 43
References 53
Synthesis of Micro and Nanoparticles from Coaxial Electrified Jets 55
1 Introduction 55
2 Capillary Flows Driven by Electrical Forces 58
3 Core-Shell Nanoparticles 62
4 Conclusions 66
References 67
Numerical Simulation of Induction Furnaces for Silicon Purification 68
1 Introduction 68
2 Statement of the Problem: Mathematical Modelling 71
3 Numerical Approximation 79
4 Numerical Results 80
References 85
Growth and Pattern Formation for Thin Films 86
1 Introduction 86
2 Island Dynamics 87
3 Discrete Elasticity 88
4 Directed Self-Assembly 89
5 Conclusions 91
References 92
On Waves in Fluids: Some Mathematical, Physical and Engineering Aspects 93
1 Introduction 93
2 Sixty Acoustic Wave Equations 94
3 Generation of Magneto-Acoustic-Gravity-Inertial ( MAGI) Waves 102
4 Some Problems in Aeroacoustics 109
5 Conclusion 122
References 123
Quantum Diffusion Models Derived from the Entropy Principle 126
1 Introduction 126
2 Quantum Energy-Transport Model 127
3 Summary and Conclusion 140
References 141
Statistical Aspects of Size Functions for the Description of Random Shapes: Applications to Problems of Lithography in Microelectronics 143
1 Introduction 143
2 Size Functions and Shape Description 144
3 Size Functions and Shape Comparison 146
4 Analysis of Random Shapes Impressed on Integrated Devices 148
References 154
Part II Minisymposia 155
Minisymposium Flow Control in Aircrafts 156
Using Non-Normality for Passive Laminar Flow Control 158
1 Introduction 158
2 Basic Flows 159
3 Linear Stability of the Streaky Basic Flows 160
4 Experimental Results 162
5 Conclusions 163
References 164
On the Catalytic Effect of Resonant Interactions in Boundary Layer Transition 165
1 Introduction 165
2 Experimental Evidence of Catalytic Effect 166
3 Mathematical Formulation 169
4 Subharmonic resonant triad 170
5 Phase-Locked Interaction 171
6 Concluding Remarks 174
References 175
Stabilization of Tollmien–Schlichting Waves by Mode Interaction 176
1 Introduction 176
2 Compressible Navier–Stokes Equations 177
3 Mode Interaction Parametric Forcing
4 Direct Numerical Simulation 182
5 Concluding Remarks 186
References 186
Acoustic Streaming and Lower-than-Laminar Drag in Controlled Channel Flow 188
1 Introduction 188
2 Not Drag but Thrust 191
3 Is the Absence of Reaction on the Walls Counter- Intuitive? 194
4 Conclusion 195
References 196
Recent Progress in the Use of Compliant Walls for Laminar Flow Control 197
1 Introduction 197
2 The Effects of Freestream Turbulence on Transition 198
3 Effects of Wall Compliance on Tollmien–Schlichting Waves 203
4 Effects of Wall Compliance on Velocity Streaks 204
5 Conclusions 205
References 205
Minisymposium Global Flow Instability 207
Summary 207
References 209
Helical Instability and Breakdown of a Batchelor Trailing Vortex 210
1 Introduction 210
2 Numerical Methods 210
3 Vortex Stability and Breakdown 211
4 Influence of Pressure Gradients 212
5 Conclusions 214
References 214
A Finite-Element Alternative for BiGlobal Linear Instability Analysis 215
1 Mathematical Formulation 215
2 Results 216
References 219
Numerical Considerations in Spectral Multidomain Methods for BiGlobal Instability Analysis of Open Cavity Configurations 220
1 Theory 220
2 Results 222
References 225
Minisymposium Analysis of Dynamical Problems in Turbomachinery 226
Modal Identification of Mistuned Bladed Discs 227
1 Introduction 227
2 Mechanical Model 228
3 Identification Algorithm 229
4 Evaluation of the Algorithm 230
5 Conclusion 231
References 232
Aeroelastic Instability of Low-Pressure Rotor Blades 233
1 Introduction 233
2 Analysis Methodology 235
3 Results 237
4 Concluding Remarks 237
References 237
Recent Advances in Numerical Analysis of Nonlinear Vibrations of Complex Structures with Friction Contact Interfaces 239
1 Introduction 239
2 New Friction Constitutive Laws and Modeling of Friction Contact Interfaces 240
3 Methods for Analysis of Nonsmooth Nonlinear Dynamics of Large- Scale Finite Element Models of Structures 241
4 Conclusions 243
References 243
Minisymposium Numerical Methods for Conservation Laws 244
Central Runge–Kutta Schemes for Stiff Balance Laws 245
1 Introduction 245
2 IMEX CRK Schemes 246
References 249
Flow Calculations using Shock Capturing Schemes Based on Power Limiters 250
1 Introduction 250
2 Power Limiters and Weighted PowerENO Method 250
3 Numerical Method 251
References 254
A Comparison Between Relaxation and Kurganov– Tadmor Schemes 255
1 Motivation 255
2 Results 256
3 Concluding Remarks 259
References 259
Minisymposium Multibody Dynamics 260
The Reverse Method of Lines in Flexible Multibody Dynamics 261
1 Introduction 261
2 Equations of Motion 262
3 Time Integration and Reverse Method of Lines 263
4 Simulation Example 265
References 265
Fast Simulation of Quasistatic Rod Deformations for VR Applications 266
1 Introduction 266
2 Cosserat and Kirchhoff Rod Models 267
3 Discrete Rod Models of Mass & Spring Type
References 272
Simulation and Optimization of Suspension Testing Systems 273
1 Introduction 273
2 The Suspension and Test Rig Models 274
3 Improving the Design of the Hexapod 275
4 Summary and Future Work 276
References 277
Minisymposium Some Topics in Astrodynamics and Space Geodesy 278
Optimal Station Keeping for Geostationary Satellites with Electric Propulsion Systems Under Eclipse Constraints 279
1 Introduction 279
2 Problem Specification and Modelling 280
3 Numerical Results 282
References 283
International Reference Systems for Astrodynamics and Space Geodesy 284
1 Introduction 284
2 International Reference Systems in Geodesy and Astrodynamics 285
3 Modelling 286
4 Conclusions 287
References 288
Post-Newtonian Covariant Measurement Formulations in Space Geodesy 289
1 Introduction 289
2 Modelling Assumptions 289
3 Relative Distance 291
4 Local Measurement Procedures 292
5 The Ballistic Problem 293
References 294
Minisymposium Clean Coal Conversion Technologies 295
Mathematical Modelling of Coal Particles Combustion in Pulverised Coal Furnaces 296
1 Introduction 296
2 Mathematical Model 296
3 Numerical Solution 302
References 302
Transport of Particles and Vapors in Flue Gases and Deposition on Cold Surfaces 303
1 Introduction 303
2 Dynamics of Particle in Gases 303
3 Behavior of Particles Near Obstacles Under Strong Temperature Differences 305
4 Monte Carlo Simulation of Deposit Growth Dynamics 306
5 Vapor Deposition 307
6 Final Remarks 307
References 307
A Comprehensive Mathematical Model of Flue- gas Desulfurization 309
1 Flue-gas Desulfurization 309
2 Multiphase, Multidomain Model 310
3 Chemical Model 311
4 Results 312
References 314
Determination of the Kinetic Parameters of a Pulverized Fuel from Drop Tube Experiments 315
1 Introduction 315
2 Char Oxidation Model 316
3 Deconvolution Procedures 316
4 Conclusions and Further Work 319
References 319
Minisymposium Mathematical Problems in Oil Industry 320
An Asphaltene Precipitation Model Using a Lattice Approach 321
1 Introduction 321
2 The Lattice Description 321
3 Enthalpy of Mixing 322
4 The Free Energy of Mixing 323
5 Asphaltene Aggregation 323
6 Results and Conclusions 324
References 325
Formation and Growth of Wax Deposit in the Pipelining of Crude Oils 326
1 The Thermal Field 326
2 The Deposition Equation 327
3 The Deposition Segment 328
4 Ageing 329
5 The Total Mass of Deposit 329
6 Desaturation 329
References 330
Simulations of the Spurt Phenomenon for Suspensions of Rod- Like Molecules 331
1 Introduction 331
2 The Mathematical Model for Suspensions of Rod- Like Molecules in the Dilute Regime 332
3 A Numerical Method for the Smoluchowski Equation 333
References 335
Minisymposium Flow in Porous Media 336
Multiscale Stochastic Homogenization of Convection- Diffusion Equations 337
1 Introduction 337
2 Homogenization of the Convection-Diffusion Equation 338
3 Some Cell Solutions of the Convection Field 340
References 341
Numerical Approximation of Boundary Layers for Rough Boundaries 342
1 Introduction 342
2 The Model Problem 342
3 The Two-Dimensional Case 343
4 Numerical Approximation of the Cell Problems 344
5 Numerical Approximation of cbl 344
6 Numerical Test 345
References 346
Upscaling in Nonlinear Thermal Diffusion Problems in Composite Materials 347
1 Introduction 347
2 Classical Transmission Boundary Conditions 348
3 Diffusion in Partially Fissured Media 350
References 351
Effective Two-Phase Flow Models Including Trapping Effects at the Micro Scale 352
1 Introduction 352
2 The Model 353
Conclusions and Acknowledgment 357
References 357
Minisymposium Shallow Water and Simulation of Environmental Flows 359
ADER DG and FV Schemes for Shallow Water Flows 360
1 Introduction 360
2 The Two-Dimensional Shallow Water System 360
3 Numerical Method 361
4 ADER Schemes 362
5 Convergence Test 363
6 Conclusions and Further Work 364
References 364
Numerical Simulation of Bedload Sediment Transport Using Finite Volume Schemes 365
1 Introduction 365
2 Shallow Water Equations with Sediment Transport 366
3 2D High Order Finite Volume Methods by State Reconstructions 367
4 Numerical Test 368
References 369
New Trends and Applications in Oceanographic Numerical Modelling 370
1 Introduction 370
2 Sinking of the Prestige 370
3 Fish Recruitment 372
4 Coastal Regions 373
5 Conclusions 374
References 374
Study and Development of Numerical Models for the Simulation of Geophysical Flows: The DamFlow Project 375
1 Equations and Numerical Scheme 375
2 A Brief Description of the Implementation 376
3 Numerical Performance of the Matrix Library 377
4 A Brief Description of the Visualization Toolkit 378
5 Numerical Examples 379
References 379
On Variational Data Assimilation for 1D and 2D Fluvial Hydraulics 380
1 Introduction 380
2 Assimilation of Lagrangian Data 381
3 A Joint Assimilation-Coupling Procedure 382
References 384
Minisymposium Multiscale Problems in Materials 385
An Asymptotic Solution of Aggregation Dynamics 387
1 Introduction 387
2 Aggregation Model 388
3 The Signaling Problem and the Three Eras 389
4 Conclusions 393
References 393
Atomistic Simulations of the Incipient Plastic Deformation Mechanisms on Metal Surfaces 395
1 Introduction 395
2 Methodology 395
3 Results 396
4 Conclusions 399
References 399
Critical Thickness for Misfit Dislocation Formation in InAs/ GaAs( 110) Heteroepitaxy 400
1 Introduction 400
2 The Model 401
3 Methodology 402
4 Results and Conclusions 404
References 405
Discrete Dislocation Dynamics in Crystals 406
1 Introduction 406
2 Stored Energy of Discrete Dislocations 406
3 Applications 409
References 410
Interconnection of Continuum and Discrete Models of Dislocation Pile- ups 411
Introduction 411
1 Governing Equations 412
2 The Continuum Approximation 412
3 Dislocation Density in 413
Region 413
4 Conclusions 415
References 415
Simplified PN Models and Natural Convection– Radiation 416
1 Introduction 416
2 The Model for Natural Convection–Radiation 417
3 Numerical Results 419
References 420
Minisymposium Nonlinear Charge and Spin Transport in Semiconductor Nanostructures 421
Electronic Transport in Nanowires at Different Length Scales 423
1 Semiconducting Nanowires 423
2 The Density Functional: Nonequilibrium Green Function Paradigm 428
3 The Density Matrix Renormalization Group Applied to Transport 434
4 Conclusion 438
References 438
SU(4) Kondo Effect in a Mesoscopic Interferometer 440
1 Introduction 440
2 Theoretical Approaches: Scaling Analysis and Numerical Renormalization Group 441
3 Conclusions 444
References 444
Josephson Effect and Magnetic Interactions in Double Quantum Dots 445
1 Exact Diagonalization 446
2 Slave Boson Mean Field 447
References 449
Quantum Shuttle: Physics of a Numerical Challenge 450
1 The Archetypal Model 450
2 The Dynamics: Generalized Master Equation 452
3 Stationary State: A Mathematical Challenge 453
4 The Three Regimes 455
5 Conclusions 457
References 458
Microscopical Model for Hyperfine Interaction in Electronic Transport Through Double Quantum Dots: Spin Blockade Lifting 459
1 Introduction 459
2 Theoretical Model 459
3 Results 461
References 462
Rabi Dynamics in Driven Tunneling Devices 463
1 Model 463
2 Example: Two Interacting Electrons 466
References 467
Quantum-Transmitting-Boundary Algorithm with Local Spin– Orbit Coupling 468
1 Introduction 468
2 Physical System 469
3 The QTBM 469
4 Results 471
5 Conclusions 472
References 472
Spintronic Transport in II–VI Magnetic Semiconductor Resonant Tunneling Devices 473
1 Introduction 473
2 Theoretical Model 474
3 Conclusions 477
References 478
Hysteretic Linear Conductance in Single Electron Transport through a Single Atom Magnet 479
1 Introduction 479
2 Formalism 480
3 Results 481
4 Conclusions 483
References 483
Minisymposium Ferromagnetic Carbon Nanostructures 485
Ferromagnetic Carbon Nanostructures 486
Introduction 486
Nanosized Carbon Structures 486
Intrinsic Magnetic Defects in Nanocarbon 488
Magnetic Properties of Nanocarbon 489
Ferromagnetism in Carbon Nanostructures 491
Conclusions 493
References 493
Looking for Ferromagnetic Signals in Proton- Irradiated Graphite 496
1 Introduction 496
2 Experimental 497
3 Results and Discussion 497
4 Summary and Conclusions 499
References 500
Ferromagnetism and Disorder in Graphene 502
1 Introduction 502
2 Inclusion of Disorder 503
3 Conclusions 506
Acknowledgments 506
References 506
Topological Defects and Electronic Properties in Graphene 507
1 Introduction 507
2 A First Model for the Topological Defects in Graphene 508
3 Generalization of the Model 509
References 511
Transport Through a Graphene Transistor 513
1 Introduction 513
2 The Model 513
3 Results 516
References 516
Minisymposium PDAE Modelling and Multiscale Simulation in Microelectronics and New Technologies 518
Domain Decomposition Techniques for Microelectronic Modeling 519
1 Introduction 519
2 Extra Device Approach 519
3 Intra Device Approach 522
4 Conclusions 524
References 524
A Concept for Classification of Partial Differential Algebraic Equations in Nanoelectronics 525
1 Introduction 525
2 PDAE Models 526
3 Illustrative Example 528
4 Conclusions 529
References 529
Numerical Simulation of a Class of PDAEs with a Separation of Time Scales 531
1 Introduction 531
2 Problem Formulation and QSS Approximation 532
3 Solution of ODEs with IVP-DAEs Embedded 533
4 Application to Micro Power Generation 534
5 Conclusions 535
References 536
Model Order Reduction for Nonlinear Differential Algebraic Equations in Circuit Simulation 537
1 Introduction 537
2 Trajectory Piecewise Linear Model Order Reduction 538
3 Proper Orthogonal Decomposition Combined with Missing Point Estimation 539
4 Numerical Results 540
5 Conclusion and Outlook 542
References 542
Minisymposium Numerical Methods for Semiconductor Kinetic Equations ( COMSON Minisymposium) 543
Comparing Kinetic and MEP Model of Charge Transport in Semiconductors 544
1 Kinetic Model 544
2 The Maximum Entropy System for Electrons in Semiconductors 545
3 Comparison Between the MEP Distribution Function and the Direct Solution of the Boltzmnn Equation 547
References 549
A Deterministic Solver to the Boltzmann- Poisson System Including Quantization Effects for Silicon- MOSFETs 550
1 Introduction 550
2 Boltzmann-Poisson-Schr¨ odinger System 551
3 Numerical Scheme 552
4 Results 553
5 Conclusion 554
References 554
Minisymposium of the ECMI SIG Shape and Size in Medicine, Biotechnology and Material Sciences 556
Size Functions Applied to the Statistical Shape Analysis and Classification of Tumor Cells 557
1 Introduction 557
2 Size Functions and Shape Description 558
3 Application to the Classification of Tumor and Normal Cells 560
References 561
A Mathematical Morphology Approach to Cell Shape Analysis 562
1 Introduction: Context and Motivation 562
2 Multi-Scale Shape Descriptors Using Granulometries 563
3 Radial/Angular Decompositions Using Skeletons in Log- Polar Coordinates 564
References 566
Reconstruction of Transducer Pressure Fields from Schlieren Data 567
1 Schlieren Optical System and Data Acquisition 567
2 A Mathematical Model for Schlieren Tomography 567
3 The Loping Landweber–Kaczmarz Method 569
4 Numerical Experiments 569
References 571
Plant Growth Modeling 572
1 Introduction 572
2 Main Principles and Assumptions (1D Model) 573
3 1D Model with Branching 573
4 2D Model 575
References 577
Minisymposium New Trends in the Analysis of Functional Genomics Data 578
Bayesian Classifiers with Consensus Gene Selection: A Case Study in the Systemic Lupus Erythematosus 579
1 Introduction 579
2 Bayesian Classifiers 579
3 Consensus Gene Selection 580
4 Knowledge Discovery by Means of Bayesian Classifiers 581
5 Results 581
References 583
The Quest for Biological Significance 585
1 Introduction 585
2 From Biological to Statistical Significance: Gene Enrichment Analysis 587
3 Discussion: Drawbacks and Limitations 588
Appendix 589
References 589
Functional Classification of Genes Using Non- Negative Independent Component Analysis 590
1 Introduction 590
2 Methods 591
3 Results 592
4 Discussion and Conclusions 593
References 594
New Trends in the Analysis of Functional Genomic Data 595
1 Replications of the Same Statistical Test 595
2 Blocks of Functional Genes 595
3 The Overall Approach 596
4 Detaching Concepts and Algorithms 597
5 Coda 598
References 598
Minisymposium: Inverse Problems and Applications 600
A Robustness Analysis of the Iterative Multi- Scaling Approach Integrated with Morphological Operations 601
1 Introduction 601
2 Mathematical Formulation 602
3 Numerical Results 604
4 Conclusions 605
References 605
Iterative Microwave Inversion Algorithm Based on the Adjoint- Field Method for Breast Cancer Application 606
1 Introduction 606
2 Shape Reconstruction in Microwave Imaging 607
3 Numerical Experiments 608
References 610
Iterative Microwave Inversion for Breast Cancer Detection Using Level Sets 611
1 Introduction 611
2 Mathematical Model 612
3 Numerical Experiments 614
References 615
Characterization of Reservoirs by Evolving Level Set Functions Obtained from Geostatistics 616
1 Introduction 616
2 Sequential Gaussian Simulation for Constructing Initial Guesses 617
3 Numerical Experiments and Discussion 618
References 621
Reconstruction of Simple Geometric Objects in 3D Optical Tomography Using an Adjoint Technique and a Boundary Element Method 622
1 Introduction 622
2 Solution Strategy for the Inverse Problem 623
3 Calculating Gradient Directions by an Adjoint Scheme 623
4 Results from 3D Simulations 625
5 Conclusion 626
References 626
High Contrast Electrical Impedance Imaging 627
1 Introduction 627
2 The Forward Electrostatic Problem 627
3 The Primal and Dual Inverse Problems 628
4 Primal–Dual Newton Equations 629
5 Numerical Results 630
6 Conclusions 631
References 631
Minisymposium Finance (Oxford) 632
Pricing Exotic Options Using Strong Convergence Properties 633
1 Introduction 633
2 Orthogonal Transformation 635
3 Strong Convergence 636
4 Stochastic Volatility Models 638
5 Pricing Exotic Options Using ML-MC 640
6 Conclusions 647
References 647
Credit Contagion in a Structural Framework 649
1 Introduction 649
2 Two-Firm Model 649
3 Conclusion 654
References 654
The Valuation of Elementary Exotics with Strike Resets 656
1 Introduction 656
2 Background 657
3 Elementary Exotics with Resets 659
References 661
Minisymposium On Optimal Strategies of Multivariate Passport Options 662
Foresight Bias and Suboptimality Correction in Monte– Carlo Pricing of Options with Early Exercise 664
1 Bermudan Option Pricing, Bellman’s Principle 664
2 Conditional Expectation Estimators 665
3 Foresight Bias: Classification, Calculation & Removal
4 Numerical Results 667
References 668
On the American Option Value Near its Exercise Region 669
1 American Options 669
2 Lower Bound for the Value Function Near its Exercise Region 671
3 Application to the Bermudean Approximation of American Options 672
References 673
Free Boundary Problems in Mathematical Finance 674
1 American Put Option 674
2 Credit Default 679
3 Mortgage Prepayment Options 680
References 683
Optimal Strategies of Passport Options 685
1 Multivariate Passport Options 685
2 Two Mean Stochastic Comparison Results 687
3 Optimal Strategies of Multivariate Passport Options 688
References 689
Minisymposium Meshfree Methods for the Solution of PDEs 690
Solving One-Dimensional Moving-Boundary Problems with Meshless Method 691
1 Introduction 691
2 Radial Basis Function Methods 692
3 The Problem 693
4 The Numerical Solution Methods 694
5 Numerical Example 694
6 Discussion and Conclusions 695
References 695
Meshless Simulation of Hele-Shaw Flow 696
1 Introduction 696
2 Asymmetric RBF Collocation 697
3 Non-Newtonian Flow 698
4 Conclusions 700
References 701
Minisymposium: Mathematical Models for the Textile Industry 702
Dynamics of Curved Viscous Fibers 704
1 Motivation 704
2 Systematic Asymptotic Derivation of the Model 705
3 Numerical Results 708
References 708
Modeling and Simulation of Non-Woven Processes 710
1 Introduction 710
2 Fiber Modeling in Euler and Lagrange Description 712
3 Interaction of Fibers and Fluid Flow 713
4 Example: Spinning of Glass Wool Fibers 714
References 715
Asymptotics of Fiber Spinning Equations 716
1 The Problem 716
2 The Stationary, Inviscid Case 717
3 The Instationary, Viscous Case 718
References 721
Three-Dimensional Elastica for Modelling Fibre Assemblies 722
1 Introduction 722
2 Differential Geometry of Centreline of Elastica 722
3 Constitutive Equations 723
4 Equilibrium Equations 723
5 Single Helix Compression Model 724
6 Yarn Compression Model 725
7 Conclusions 726
References 726
Effective Properties of Nonwoven Textiles from Microstructure Simulations 727
1 Introduction 727
2 Nonwoven Model 727
3 Computed Permeability 731
References 731
Minisymposium Approximate Algebraic Techniques for Curves and Surfaces 732
References 732
Computing the Intersection Curve Between a Plane and the Offset of a Parametric Surface 733
1 Introduction 733
2 The Algorithm 734
3 Implementation and Experimentation 735
4 Conclusions and Further Work 737
References 737
Approximating Offsets of Surfaces by using the Support Function Representation 738
1 Introduction 738
2 Support Function Representation of Surfaces 738
3 Approximation of Surfaces 740
References 742
Semantic Modelling for Styling and Design 743
1 Introduction 743
2 Fully Freeform Deformation Features 744
3 Sweep-Like Features 745
4 Conclusions 746
References 747
Minisymposium Web-based Learning Environments in Applied Mathematics 748
An Industrial Application of an Integrated Framework for Production of Interactive Documents 750
1 Introduction 750
2 LATEX2WEB 752
3 An Industrial Application of LATEX2WEB 753
References 754
An e-Learning Platform for Applications of Mathematics to Microelectronic Industry 755
1 Introduction 755
2 The Demonstrator Platform and the e-Learning Platform 755
3 Innovative e-Learning Methods 757
4 Design of the e-Learning Platform 757
5 Conclusions 759
References 759
Web Based System for Graduate Studies: Optimization, Games, and Markets 760
1 Introduction 760
2 Heuristics 761
3 Bayesian Heuristic Approach 761
4 Improving Expert Heuristics 762
5 Distance Studies 762
6 Conclusions 764
References 764
Web-Tool on Differential Equations 765
1 Introduction 765
2 Strategy of e-Study 765
3 Design of the Tool on Differential Equations 767
References 769
Part III Contributed Papers 770
Model and Method to Increase the Thermal Efficiency of Micro- Heat Exchangers for Aerospace Applications 771
1 Introduction 771
2 Problem Description 772
3 Governing Equations and Boundary Conditions 772
4 Results 774
5 Conclusions 775
References 775
Influence of Trailing Jet Instability on the Dynamics of Starting Jets 776
1 Introduction 776
2 Experimental Set-Up 777
3 Numerical Simulation 777
4 Analysis 778
5 Discussion 780
References 780
Modelling and Computational Analysis of the Dynamic Crash Behaviour of Fabric Reinforced Composite Automotive Structures 781
1 Introduction 781
2 Progressive Damage Modelling 781
3 Structural Prototype and Model Development 782
4 Prototype Testing and Model Verification 782
5 Simulation of Impact Loading 783
6 Conclusions 785
References 785
Theoretical Modeling of Flame–Acoustic Interaction 786
1 Introduction 786
2 Flame Model 787
3 Location of the Flame Front 788
4 Transfer Function 789
5 Conclusion 790
References 790
Air-Blown Rivulet Flow of a Perfectly Wetting Fluid on an Inclined Substrate 792
1 Introduction 792
2 Problem Formulation 792
3 Rivulet Solutions 794
4 Classification of Flow Patterns 794
5 Solutions for Prescribed t and Varying a 795
6 Conclusions 796
References 796
The Effect of the Thermal Conductivity of the Substrate on Droplet Evaporation 797
1 Introduction 797
2 Mathematical Model 797
3 Comparison with Experiments 799
4 FurtherWork 801
References 801
The Effect of Particles on Linear and Weakly Nonlinear Instability of a Two- Phase Shallow Flows 802
1 Introduction 802
2 Weakly Nonlinear Spatial Instability of Two- Phase Flows 803
References 806
Water Quality Simulation of a Future Pit Lake 808
1 Introduction 808
2 Model Development 809
3 Model Results 811
References 812
Optimal Management and Design of a Wastewater Purification System 813
1 Introduction 813
2 Optimal Operation and Design: Problem Formulation 814
3 Numerical Solution 816
References 817
Estimation of Fuzzy Anomalies in Water Distribution Systems 819
1 Introduction 819
2 Mathematical Model and State Estimation 820
3 Error Limit Analysis 821
4 The Neural Network 821
5 Conclusions 822
References 823
Investigation of the Evolution and Breakup of Electrically Charged Drops 824
1 Introduction 824
2 The Model Equations 825
3 The Numerical Method 825
4 Results and Conclusions 828
References 829
Homogeneous Nucleation of Dipole Domains and Current Self- Oscillations in Photoexcited Semiconductor Superlattices 830
1 Introduction 830
2 Model Equations 831
3 Numerical Results 833
References 834
Numerical Analysis of a Nickel-Iron Electrodeposition Process 835
1 Introduction 835
2 Existence and Uniqueness Result 836
3 Numerical Methods 837
4 Numerical Result 838
References 839
A Simplified Finite Element Formulation for Spray Transfer GMA Weld Pools 840
1 Introduction 840
2 Mathematical Modelling 840
3 Computational and Numerical Modelling 843
4 Qualitative Behaviour of the Model 843
5 Conclusions and Future Work 844
References 844
Numerical Solution of a Non-Local Elliptic Problem Modeling a Thermistor with a Finite Element and a Finite Volume Method 845
1 Introduction 845
2 Formulation of the Numerical Methods 846
3 Numerical Results and Comparison 848
References 849
Numerical Solution of 3D Magnetostatic Problems in Terms of Scalar Potentials 851
1 Introduction 851
2 Scalar Formulation of the Magnetostatic Problem 851
3 Finite Element Discretization and Numerical Results 853
References 855
Optimization Methods for a Wifi Location System 856
1 Introduction 856
2 The Optimization Method 857
3 Numerical Results 858
4 Conclusions 859
References 860
Flow in the Canal of Schlemm and its Influence on Primary Open Angle Glaucoma 861
1 POAG in Human Eyes 861
2 Governing Equations 861
3 Results 863
4 Conclusions and Further Work 865
References 865
A One-Phase Model for Air-Breathing DMFC Cells with Non- Tafel Kinetics 866
1 Introduction 866
2 Mathematical Model 867
3 Results and Discussions 869
4 Conclusions 870
References 870
Optimising Design Parameters of Enzyme- Channelling Biosensors 871
1 Introduction 871
2 Spatially Extended Model 872
3 Simplified Model 873
4 Numerical Simulations and Discussions 874
References 875
Breast Nodule Ultrasound Segmentation Through Texture- Based Active Contours 876
1 Introduction 876
2 Image Filtering 877
3 Front Propagation 877
4 Active Contours 878
5 Conclusion 880
References 880
A Contrast Invariant Approach to Motion Estimation: Validation and Application to Motion Estimation Improvement 881
1 Introduction 881
2 Motion Estimation and Significance Analysis 882
3 Application: Motion Reassignment 884
4 Results 884
5 Conclusions 885
References 885
A Mathematical Model for Prediction of Recurrence in Bladder Cancer Patients 886
1 Introduction 886
2 Material and Methods 887
3 Results 888
4 Conclusions 890
References 890
Use of the Fourier Transform in the Distributions Sense for Creation Numerical Algorithms for Cone- Beam Tomography 891
References 894
Shapley Value vs. Proportional Rule in Cooperative Affairs 895
1 Introduction 895
2 Cooperative Affairs 895
3 The Proportional Rule 896
4 An Axiomatic Approach to a Value Notion 896
5 Checking the Proportional Rule 897
6 Conclusions 898
References 899
A Wide Family of Solutions Based on Marginal Contributions for Situations of Competence– Cooperation with Structure of a Priori Coalition Blocks 900
1 Introduction and Preliminaries 900
2 Mixed Modified Semivalues 902
3 Computation Procedure of Mixed Modified Semivalues 903
References 904
Time-Varying Grids for Gas Dynamics 905
1 Modeling of the Physical Problem 905
2 Numerical Scheme 906
3 Adaptive Multiresolution 907
References 909
Meshless Poisson Problems in the Finite Pointset Method: Positive Stencils and Multigrid 910
1 Introduction 910
2 Meshless Finite Differences for Poisson Equation 910
3 Least Squares Methods 911
4 Minimal Positive Stencils 912
5 M-Matrices and Multigrid Solvers 913
6 Numerical Results 913
7 Conclusions and Outlook 914
References 914
Basics of a Differential-Geometric Approach to Diffusion: Uniting Lagrangian and Eulerian Models on a Manifold 915
1 Introduction 915
2 The Geometry of Diffusion 916
3 Lagrangian Formalism 917
4 Energy and Mass Conservation 918
5 Conclusion and Outlook 919
References 919
Diagnostic Modelling of Digital Systems with Binary and High- Level Decision Diagrams 920
1 Introduction 920
2 Modelling Digital Systems by Binary Decision Diagrams 920
3 Modelling Systems by a Single DD on Higher Levels 922
4 Experimental Results and Conclusions 924
References 925
Numerical Integration in Bayesian Positioning 926
1 Bayesian Positioning 926
2 Integration Methods 927
3 Numerical Results 928
4 Conclusions 929
References 930
Singular Problems With Quadratic Gradient Term 931
1 Introduction 931
2 Radial Solutions 932
3 Existence Results 933
4 Boundary Estimates 934
References 935
Pattern Matching for Control Chart Monitoring 936
1 Introduction 936
2 Identifying Normal Patterns 938
3 Identifying Decreasing and Increasing Trend Patterns 938
4 Conclusions and Future Works 940
References 940
Index Characterization in DAE Circuit Models Without Passivity Assumptions 941
1 Introduction 941
2 Differential-Algebraic Circuit Models 942
3 Index 1 Configurations 943
4 Concluding Remarks 945
References 945
Fingerprint Classification using Entropy Sensitive Tracing 946
1 Introduction 946
2 Tracer 947
3 Characteristic Lines 947
4 Conclusions 950
References 950
An Invariant Domain Preserving MUSCL Scheme 951
1 Introduction 951
2 Stability of the MUSCL Schemes 952
3 MUSCL Schemes for 2D Unstructured Meshes 954
References 955
A Stable CE–SE Numerical Method for Time- Dependent Advection– Diffusion Equation 957
1 Introduction 957
2 Stability Analysis 959
References 961
A Random Euler Method for Solving Differential Equations with Uncertainties 962
1 Introduction and Preliminaries 962
2 On the Random Euler Method 963
3 Numerical Results 964
References 966
Cubic-Matrix Splines and Second-Order Matrix Models 967
1 Introduction 967
2 Construction of the Method 968
3 Example 970
References 971
Part IV Color Plates 972
Part V Contributor Index 998
List of Contributors 999