Mathematical Modeling, Simulation, Visualization and e-Learning (eBook)

Proceedings of an International Workshop held at Rockefeller Foundation' s Bellagio Conference Center, Milan, Italy, 2006

Dialla Konaté (Herausgeber)

eBook Download: PDF

2007
XI, 371 Seiten
Springer Berlin (Verlag)
978-3-540-74339-2 (ISBN)

Infos

This book features articles written by some of the most prominent leading applied mathematicians as well as young and promising ones. The common objective of these articles is to present an important issue which is currently widely discussed in scientific investigation with major human, economic or ecological implications. Each article is as deep as an expert lecture but is also self-contained, so that even isolated scientists with limited resources can profit greatly from it.

Inhalt

Preface 5
Names of Officers to the Conference 7
Organizing Committee 7
Team Leaders and Invited Speakers 7
Contents 8
Part I Numerical Methods and Problem Solving 11
Quasi-Analytical Computation of Energy Levels and Wave Functions in a Class of Chaotic Cavities with Inserted Objects 12
1 Introduction 12
2 Theory 15
3 The Numerical Results of the Classical Bowtie Cavity Containing Circular Objects 19
4 Conclusion 23
References 23
Existence Results and Open Problems in the Kinetic Theory of Dense Gases 25
1 Introduction 25
2 Kinetic Equations and Streaming Operator 26
3 Semi-Group and Iterations 31
4 Global Solutions 34
5 Removal of the Cutoff 37
6 Discrete Velocity Model 38
References 40
The High Performance Asymptotic Method in Numerical Simulation 41
1 The Riemann Integration and the Hp-Asymptotic Method 41
2 The Hp-Asymptotic Method on First Order Differential Equations 43
3 The Hp-Asymptotic Method on Higher Order Ordinary Equations 50
4 The Hp-Asymptotic Method on Elliptic Equations 54
References 58
Modelling the Thermal Operation in a Catalytic Converter of an Automobile’s Exhaust 59
1 Introduction 59
2 Mathematical Model 61
3 Perturbation Method 63
4 Thermal Criticality and Bifurcation Study 64
5 Results and Discussion 65
6 Conclusion 68
Nomenclature 68
References 68
Modelling Transmission Dynamics of Childhood Diseases in the Presence of a Preventive Vaccine: Application of Adomian Decomposition Technique 70
1 Introduction 70
2 Qualitative Analysis 73
3 Adomian Decomposition Technique 74
4 Numerical Results and Discussion 76
5 Conclusions 77
Appendix 78
References 81
A New MPFA Formulation for Subsurface Flow Problems on Unstructured Grids: Derivation of the Discrete Problem 82
1 Introduction and the Model Problem 82
2 Spatial Discretization 84
3 Finite Volume Formulation 84
4 Numerical Experiments 93
5 Conclusions and Perspectives 95
References 96
Analysis of a New MPFA Formulation for Flow Problems in Geologically Complex Media 97
1 Introduction and the Model Problem 97
2 An MPFA Formulation 99
3 The Approximate Solution in Terms of Piecewise Linear Function 103
4 Stability and Error Estimates for the Solution of the Discrete Problem 105
5 Convergence Results 109
6 Conclusions and Perspectives 110
References 110
A Small Eddy Correction Algorithm for the Primitive Equations of the Ocean 112
1 Introduction 112
2 A Navier–Stokes Type Equation and its Mathematical Setting 114
3 Existence of Strong Solution to (5) 129
4 A Small Eddy Correction Method 138
5 Convergence of the Method 144
6 Numerical Results 148
7 Conclusion 152
References 154
Part II Modeling and Control of Phenomena 156
Aspects of Modeling Transport in Small Systems with a Look at Motor Proteins 157
1 Introduction 157
2 A Dissipation Principle 158
3 A Look at Multiple State Motors 160
References 166
Optimal Control of Ill-Posed Parabolic Distributed Systems 168
1 Introduction 168
2 Existence Problem 169
3 Optimal Control of the Backward Heat Problem 171
4 The Low-Regret Optimal Control 173
5 The Now-Regret Optimal Control 178
References 181
A Parametric Study of Low Reynolds Number Blood Flow in a Porous, Slowly Varying, Stenotic Artery with Heat Transfer 183
1 Introduction 183
2 The Problem 184
3 Asymptotic Solutions 185
4 Solutions for the Leading Approximations 186
5 Higher Approximate Solutions 188
6 Shear Stress and Heat Transfer 189
7 Results and Discussion 190
References 193
Stability of Generalized Convexity and Monotonicity 194
1 Introduction 194
2 S-Quasiconvex Functions 196
3 S-Quasimonotone Maps 197
4 A Use of S-Quasimonotonicity in an Economics Model 198
5 Stability Index of Generalized Convex Functions 199
6 Some Questions and Future Tasks 200
References 201
Are Viscoelastic Flows Under Control or Out of Control? 202
1 Introduction 202
2 Linear Controllability 204
3 Nonlinear Controllability 206
References 208
On Topological Optimization and Pollution in Porous Media 210
1 Introduction 210
2 A Model 211
3 Study of Partial Differential Equation (PDE) 216
4 Topological Optimization 224
5 Numerical Simulations 235
6 Some Open Problems 238
References 238
Dynamical Analysis of Infectious Diseases in Spatially Heterogeneous Environments 239
1 Introduction 239
2 The Model 240
3 Stability 248
4 Future Trends 250
References 251
Approximate Scale-Invariant Random Fields: Review and Current Developments 252
1 Introduction 252
2 Exactly Scale-Invariant Stochastic Fields 255
3 Approximate Scale-Invariant Fields 257
4 Applications: Future Work 260
5 Appendix 263
References 265
Part III Simulation and Visualization 267
Non-Stationary Vibrations of Viscoelastic Circular Cylindrical Thick Shell Under the Influence of Temperature 268
1 Introduction 268
2 Derivation the Refined Equations of Longitudinal- Radial Vibrations of Thermoviscoelastic Cylindrical Shell 269
3 Longitudinal Impact on Viscoelastic Cylindrical Shell 276
4 Analysis of Thermo-Stressed State of Viscoelastic Circular Cylindrical Shell 279
References 286
Mathematical Vibration Modelling of the Pre- Stressed Viscoelastic Thick- Walled Cylindrical Shell 287
1 Introduction 287
2 The Basic Relations 288
3 Longitudinal-Radial Vibrations of Pre-Stressed Circular Cylindrical Shells 290
4 The Torsional Vibration Equations of Circular Cylindrical Shell with Initial Displacements 297
5 Application of Vibration Equations for Solving Problems 300
References 309
Viscoelastic Fluids in a Thin Domain: A Mathematical Study for a Non- Newtonian Lubrication Problem 311
1 Mathematical Aspect of Lubrication Problems 311
2 Thin Film Non-Newtonian Fluid 313
3 Thin Film Viscoelastic Fluids 314
References 316
From the African sona Tradition to New Types of Designs and Matrices 318
Introduction: Mathematics in African History 318
Sona Geometry 321
Mathematical Research Inspired by the Reconstructed Sona Tradition 326
References 335
Finite Dynamical Systems: A Mathematical Framework for Computer Simulation 338
1 Introduction 338
2 Examples of Interaction-Based Computer Simulations 339
3 Background 342
4 Definitions and Examples 343
5 Mathematical Results 346
6 An Open Problem 349
7 Conclusion 351
References 352
Part IV e-Learning 354
New Pedagogical Models for Instruction in Mathematics 355
1 Setting 355
2 Program Structure 356
3 Hardware Requirements 359
4 Operations 360
5 Test Problems 361
6 An Example Problem 362
7 Economics and Conclusions 364
References 365

Produkt-Details

• Erscheint lt. Verlag: 8.12.2007
• Zusatzinfo: XI, 371 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Themenwelt: Wirtschaft
• Schlagworte: algorithm • algorithms • Calculus • computational mathematics • Computer • Distributed Systems • Dynamische Systeme • Mathematical Modeling • Modeling • Numerical Methods • Optimization • Simulation • Transport • Vibration • Visualization
• ISBN-10: 3-540-74339-1 / 3540743391
• ISBN-13: 978-3-540-74339-2 / 9783540743392