Mathematical Modeling, Simulation, Visualization and E-Learning : Proceedings of an International Workshop Held at Rockefeller Foundation' S Bellagio Conference Center, Milan, Italy, 2006

"This book is a collection of articles written by some of the most prominent leading applied mathematicians, as well as articles from young and promising scientists from Africa, Asia and Europe. 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. One main feature of the series, which the current book exemplifies, is that 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. Another feature of this book is that each article is meant to present a collection of open questions which can fuel undergraduate or graduate research activities even in smaller or more isolated scientific communities."--Jacket The Bellagio International Conference On Mathematical Modeling, Simulation,visualizationande-learning Washeldfromnovember20to November26,2006,withprimary?nancialsupportfromtherockefellerfo- Dation. It Also Bene?ted From The ?nancial And Material Support Of Virginia Tech And Winston-salem State University. Takentogethermathematicalmodeling,simulation,andvisualizationhave Become A Major Tool In Scienti?c Investigation. They Are Also A Growing Int- Disciplinary Subject In Collegiate Curricula, And Are Expected To Attract More Students From Underserved Communities To Science And Technology Because Of Their Universality And Because They Provide A Visual Aspect To What Is Taught And Learned, Even In Environments Where Physical Implementation And Exp- Imentation May Not Be Possible. Thebellagio Initiative, Which Was The Underlying Idea Behind The Bellagio International Conference, Consists In Creating A Forum Where Excellent Mat- Maticians From Underserved Countries And Communities And The World’s Le- Ing Scientists Can Meet, Work Together And Build Networks In Order To Share Scienti?c Knowledge. This Requires That All Contributions Presented In Such A Forum Have A High Scienti?c Level And A Self-contained Style. The Objective Of This Forum Is That Skilled Scientists From All Groups And Countries Be Incor- Rated Within The Mainstream Of Scienti?c Discovery. Numerical Methods And Problem Solving -- Quasi-analytical Computation Of Energy Levels And Wave Functions In A Class Of Chaotic Cavities With Inserted Objects -- Existence Results And Open Problems In The Kinetic Theory Of Dense Gases -- The High Performance Asymptotic Method In Numerical Simulation -- Modelling The Thermal Operation In A Catalytic Converter Of An Automobile's Exhaust -- Modelling Transmission Dynamics Of Childhood Diseases In The Presence Of A Preventive Vaccine: Application Of Adomian Decomposition Technique -- A New Mpfa Formulation For Subsurface Flow Problems On Unstructured Grids: Derivation Of The Discrete Problem -- Analysis Of A New Mpfa Formulation For Flow Problems In Geologically Complex Media -- A Small Eddy Correction Algorithm For The Primitive Equations Of The Ocean -- Modeling And Control Of Phenomena -- Aspects Of Modeling Transport In Small Systems With A Look At Motor Proteins -- Optimal Control Of Ill-posed Parabolic Distributed Systems --^ A Parametric Study Of Low Reynolds Number Blood Flow In A Porous, Slowly Varying, Stenotic Artery With Heat Transfer -- Stability Of Generalized Convexity And Monotonicity -- Are Viscoelastic Flows Under Control Or Out Of Control? -- On Topological Optimization And Pollution In Porous Media -- Dynamical Analysis Of Infectious Diseases In Spatially Heterogeneous Environments -- Approximate Scale-invariant Random Fields: Review And Current Developments -- Simulation And Visualization -- Non-stationary Vibrations Of Viscoelastic Circular Cylindrical Thick Shell Under The Influence Of Temperature -- Mathematical Vibration Modelling Of The Pre-stressed Viscoelastic Thick-walled Cylindrical Shell -- Viscoelastic Fluids In A Thin Domain: A Mathematical Study For A Non-newtonian Lubrication Problem -- From The African Sona Tradition To New Types Of Designs And Matrices -- Finite Dynamical Systems: A Mathematical Framework For Computer Simulation -- E-learning --^ New Pedagogical Models For Instruction In Mathematics. Dialla Konaté, Editor. Includes Bibliographical References. Cover......Page 0 Mathematical Modeling, Simulation, Visualization and e-Learning......Page 3 ISBN: 9783540743385......Page 4 Preface......Page 5 Names of Officers to the Conference......Page 7 Contents......Page 9 Part I Numerical Methods and Problem Solving......Page 13 Quasi-Analytical Computation of Energy Levels and Wave Functions in a Class of Chaotic Cavities with Inserted Objects......Page 15 Existence Results and Open Problems in the Kinetic Theory of Dense Gases......Page 29 The High Performance Asymptotic Method in Numerical Simulation......Page 45 Modelling the Thermal Operation in a Catalytic Converter of an Automobile’s Exhaust......Page 63 Modelling Transmission Dynamics of Childhood Diseases in the Presence of a Preventive Vaccine: Application of Adomian Decomposition Technique......Page 75 A New MPFA Formulation for Subsurface Flow Problems on Unstructured Grids: Derivation of the Discrete Problem......Page 87 Analysis of a New MPFA Formulation for Flow Problems in Geologically Complex Media......Page 103 A Small Eddy Correction Algorithm for the Primitive Equations of the Ocean......Page 119 Part II Modeling and Control of Phenomena......Page 163 Aspects of Modeling Transport in Small Systems with a Look at Motor Proteins......Page 165 Optimal Control of Ill-Posed Parabolic Distributed Systems......Page 177 A Parametric Study of Low Reynolds Number Blood Flow in a Porous, Slowly Varying, Stenotic Artery with Heat Transfer......Page 193 Stability of Generalized Convexity and Monotonicity......Page 205 Are Viscoelastic Flows Under Control or Out of Control?......Page 213 On Topological Optimization and Pollution in Porous Media......Page 221 Dynamical Analysis of Infectious Diseases in Spatially Heterogeneous Environments......Page 251 Approximate Scale-Invariant Random Fields: Review and Current Developments......Page 265 Non-Stationary Vibrations of Viscoelastic Circular Cylindrical Thick Shell Under the Influence of Temperature......Page 283 Mathematical Vibration Modelling of the Pre-Stressed Viscoelastic Thick-Walled Cylindrical Shell......Page 303 Viscoelastic Fluids in a Thin Domain: A Mathematical Study for a Non-Newtonian Lubrication Problem......Page 327 From the African sona Tradition to New Types of Designs and Matrices......Page 335 Finite Dynamical Systems: A Mathematical Framework for Computer Simulation......Page 355 Part IV e-Learning......Page 371 New Pedagogical Models for Instruction in Mathematics......Page 373 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.