Konaté Mathematical Modeling, Simulation, Visualization and e-Learning

Proceedings of an International Workshop held at Rockefeller Foundation' s Bellagio Conference Center, Milan, Italy, 2006
1. Auflage 2007
ISBN: 978-3-540-74339-2
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 371 Seiten

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.

Autoren/Hrsg.

Konaté, Dialla

Inhaltsverzeichnis

1;Preface;5
2;Names of Officers to the Conference;7
2.1;Organizing Committee;7
2.2;Team Leaders and Invited Speakers;7
3;Contents;8
4;Part I Numerical Methods and Problem Solving;11
4.1;Quasi-Analytical Computation of Energy Levels and Wave Functions in a Class of Chaotic Cavities with Inserted Objects;12
4.1.1;1 Introduction;12
4.1.2;2 Theory;15
4.1.3;3 The Numerical Results of the Classical Bowtie Cavity Containing Circular Objects;19
4.1.4;4 Conclusion;23
4.1.5;References;23
4.2;Existence Results and Open Problems in the Kinetic Theory of Dense Gases;25
4.2.1;1 Introduction;25
4.2.2;2 Kinetic Equations and Streaming Operator;26
4.2.3;3 Semi-Group and Iterations;31
4.2.4;4 Global Solutions;34
4.2.5;5 Removal of the Cutoff;37
4.2.6;6 Discrete Velocity Model;38
4.2.7;References;40
4.3;The High Performance Asymptotic Method in Numerical Simulation;41
4.3.1;1 The Riemann Integration and the Hp-Asymptotic Method;41
4.3.2;2 The Hp-Asymptotic Method on First Order Differential Equations;43
4.3.3;3 The Hp-Asymptotic Method on Higher Order Ordinary Equations;50
4.3.4;4 The Hp-Asymptotic Method on Elliptic Equations;54
4.3.5;References;58
4.4;Modelling the Thermal Operation in a Catalytic Converter of an Automobile’s Exhaust;59
4.4.1;1 Introduction;59
4.4.2;2 Mathematical Model;61
4.4.3;3 Perturbation Method;63
4.4.4;4 Thermal Criticality and Bifurcation Study;64
4.4.5;5 Results and Discussion;65
4.4.6;6 Conclusion;68
4.4.7;Nomenclature;68
4.4.8;References;68
4.5;Modelling Transmission Dynamics of Childhood Diseases in the Presence of a Preventive Vaccine: Application of Adomian Decomposition Technique;70
4.5.1;1 Introduction;70
4.5.2;2 Qualitative Analysis;73
4.5.3;3 Adomian Decomposition Technique;74
4.5.4;4 Numerical Results and Discussion;76
4.5.5;5 Conclusions;77
4.5.6;Appendix;78
4.5.7;References;81
4.6;A New MPFA Formulation for Subsurface Flow Problems on Unstructured Grids: Derivation of the Discrete Problem;82
4.6.1;1 Introduction and the Model Problem;82
4.6.2;2 Spatial Discretization;84
4.6.3;3 Finite Volume Formulation;84
4.6.4;4 Numerical Experiments;93
4.6.5;5 Conclusions and Perspectives;95
4.6.6;References;96
4.7;Analysis of a New MPFA Formulation for Flow Problems in Geologically Complex Media;97
4.7.1;1 Introduction and the Model Problem;97
4.7.2;2 An MPFA Formulation;99
4.7.3;3 The Approximate Solution in Terms of Piecewise Linear Function;103
4.7.4;4 Stability and Error Estimates for the Solution of the Discrete Problem;105
4.7.5;5 Convergence Results;109
4.7.6;6 Conclusions and Perspectives;110
4.7.7;References;110
4.8;A Small Eddy Correction Algorithm for the Primitive Equations of the Ocean;112
4.8.1;1 Introduction;112
4.8.2;2 A Navier–Stokes Type Equation and its Mathematical Setting;114
4.8.3;3 Existence of Strong Solution to (5);129
4.8.4;4 A Small Eddy Correction Method;138
4.8.5;5 Convergence of the Method;144
4.8.6;6 Numerical Results;148
4.8.7;7 Conclusion;152
4.8.8;References;154
5;Part II Modeling and Control of Phenomena;156
5.1;Aspects of Modeling Transport in Small Systems with a Look at Motor Proteins;157
5.1.1;1 Introduction;157
5.1.2;2 A Dissipation Principle;158
5.1.3;3 A Look at Multiple State Motors;160
5.1.4;References;166
5.2;Optimal Control of Ill-Posed Parabolic Distributed Systems;168
5.2.1;1 Introduction;168
5.2.2;2 Existence Problem;169
5.2.3;3 Optimal Control of the Backward Heat Problem;171
5.2.4;4 The Low-Regret Optimal Control;173
5.2.5;5 The Now-Regret Optimal Control;178
5.2.6;References;181
5.3;A Parametric Study of Low Reynolds Number Blood Flow in a Porous, Slowly Varying, Stenotic Artery with Heat Transfer;183
5.3.1;1 Introduction;183
5.3.2;2 The Problem;184
5.3.3;3 Asymptotic Solutions;185
5.3.4;4 Solutions for the Leading Approximations;186
5.3.5;5 Higher Approximate Solutions;188
5.3.6;6 Shear Stress and Heat Transfer;189
5.3.7;7 Results and Discussion;190
5.3.8;References;193
5.4;Stability of Generalized Convexity and Monotonicity;194
5.4.1;1 Introduction;194
5.4.2;2 S-Quasiconvex Functions;196
5.4.3;3 S-Quasimonotone Maps;197
5.4.4;4 A Use of S-Quasimonotonicity in an Economics Model;198
5.4.5;5 Stability Index of Generalized Convex Functions;199
5.4.6;6 Some Questions and Future Tasks;200
5.4.7;References;201
5.5;Are Viscoelastic Flows Under Control or Out of Control?;202
5.5.1;1 Introduction;202
5.5.2;2 Linear Controllability;204
5.5.3;3 Nonlinear Controllability;206
5.5.4;References;208
5.6;On Topological Optimization and Pollution in Porous Media;210
5.6.1;1 Introduction;210
5.6.2;2 A Model;211
5.6.3;3 Study of Partial Differential Equation (PDE);216
5.6.4;4 Topological Optimization;224
5.6.5;5 Numerical Simulations;235
5.6.6;6 Some Open Problems;238
5.6.7;References;238
5.7;Dynamical Analysis of Infectious Diseases in Spatially Heterogeneous Environments;239
5.7.1;1 Introduction;239
5.7.2;2 The Model;240
5.7.3;3 Stability;248
5.7.4;4 Future Trends;250
5.7.5;References;251
5.8;Approximate Scale-Invariant Random Fields: Review and Current Developments;252
5.8.1;1 Introduction;252
5.8.2;2 Exactly Scale-Invariant Stochastic Fields;255
5.8.3;3 Approximate Scale-Invariant Fields;257
5.8.4;4 Applications: Future Work;260
5.8.5;5 Appendix;263
5.8.6;References;265
6;Part III Simulation and Visualization;267
6.1;Non-Stationary Vibrations of Viscoelastic Circular Cylindrical Thick Shell Under the Influence of Temperature;268
6.1.1;1 Introduction;268
6.1.2;2 Derivation the Refined Equations of Longitudinal- Radial Vibrations of Thermoviscoelastic Cylindrical Shell;269
6.1.3;3 Longitudinal Impact on Viscoelastic Cylindrical Shell;276
6.1.4;4 Analysis of Thermo-Stressed State of Viscoelastic Circular Cylindrical Shell;279
6.1.5;References;286
6.2;Mathematical Vibration Modelling of the Pre- Stressed Viscoelastic Thick- Walled Cylindrical Shell;287
6.2.1;1 Introduction;287
6.2.2;2 The Basic Relations;288
6.2.3;3 Longitudinal-Radial Vibrations of Pre-Stressed Circular Cylindrical Shells;290
6.2.4;4 The Torsional Vibration Equations of Circular Cylindrical Shell with Initial Displacements;297
6.2.5;5 Application of Vibration Equations for Solving Problems;300
6.2.6;References;309
6.3;Viscoelastic Fluids in a Thin Domain: A Mathematical Study for a Non- Newtonian Lubrication Problem;311
6.3.1;1 Mathematical Aspect of Lubrication Problems;311
6.3.2;2 Thin Film Non-Newtonian Fluid;313
6.3.3;3 Thin Film Viscoelastic Fluids;314
6.3.4;References;316
6.4;From the African sona Tradition to New Types of Designs and Matrices;318
6.4.1;Introduction: Mathematics in African History;318
6.4.2;Sona Geometry;321
6.4.3;Mathematical Research Inspired by the Reconstructed Sona Tradition;326
6.4.4;References;335
6.5;Finite Dynamical Systems: A Mathematical Framework for Computer Simulation;338
6.5.1;1 Introduction;338
6.5.2;2 Examples of Interaction-Based Computer Simulations;339
6.5.3;3 Background;342
6.5.4;4 Definitions and Examples;343
6.5.5;5 Mathematical Results;346
6.5.6;6 An Open Problem;349
6.5.7;7 Conclusion;351
6.5.8;References;352
7;Part IV e-Learning;354
7.1;New Pedagogical Models for Instruction in Mathematics;355
7.1.1;1 Setting;355
7.1.2;2 Program Structure;356
7.1.3;3 Hardware Requirements;359
7.1.4;4 Operations;360
7.1.5;5 Test Problems;361
7.1.6;6 An Example Problem;362
7.1.7;7 Economics and Conclusions;364
7.1.8;References;365