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-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 371 Seiten

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