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

383 Pages·2008·5.077 MB·English

by  Dialla Konaté (ed.)

Mathematical Modeling, Simulation,
Visualization and e-Learning
Dialla Konaté
Editor
Mathematical Modeling,
Simulation, Visualization
and e-Learning
Proceedings of an International Workshop
held at Rockefeller Foundation’s Bellagio
Conference Center, Milan, Italy, 2006
ABC
DiallaKonaté
DepartmentofMathematics
VirginiaTech
McBrydeHall#460
Blacksburg,VA24060
USA
[email protected]
ISBN:978-3-540-74338-5 e-ISBN:978-3-540-74339-2
LibraryofCongressControlNumber:2007938161
MathematicsSubjectClassificationNumbers(2000):34,35,41,42,47,49,65,68,70,74,76,92,97
(cid:1)c 2008Springer-VerlagBerlinHeidelberg
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Preface
The Bellagio International Conference on Mathematical Modeling,
Simulation,Visualizationande-LearningwasheldfromNovember20to
November26,2006,withprimaryfinancialsupportfromtheRockefellerFoun-
dation. It also benefited from the financial and material support of Virginia
Tech and Winston-Salem State University.
Takentogethermathematicalmodeling,simulation,andvisualizationhave
become a major tool in scientific investigation. They are also a growing inter-
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 exper-
imentation may not be possible.
TheBellagio Initiative,whichwastheunderlyingideabehindtheBellagio
InternationalConference,consistsincreatingaforumwhereexcellentmathe-
maticians from underserved countries and communities and the world’s lead-
ing scientists can meet, work together and build networks in order to share
scientific knowledge. This requires that all contributions presented in such a
forum have a high scientific level and a self-contained style. The objective of
this forum is that skilled scientists from all groups and countries be incorpo-
rated within the mainstream of scientific discovery.
It is our goal that scientists from all around the world be welcomed to
aid in investigating the great challenges our world is facing. These challenges
include, among others, the spread of infectious diseases, the management of
water resources, and efforts to reduce air and water pollution. Mathematical
modeling and simulation is among the paths which may lead to a better un-
derstandingofcomplexphenomenalikethoseknownbutnotfullyunderstood
in biological and chemical processes.
In this volume the reader will find excellent contributions from some very
wellknownandotherlessknownscientists.Wehavemadeaconsciousdecision
not to focus on one specific area but to open the forum to a wider set of
problems. This provides an opportunity for more scientists to come in and
VI Preface
be part of the network. An important condition we have imposed on all the
contributionstothisvolumeisthateachpresentsacollectionofopenquestions
which can fuel undergraduate or graduate research activities, even in smaller
or more isolated scientific communities.
This volume is divided into four main sections devoted to:
– numerical methods and problem solving;
– modeling and control of phenomena;
– simulation and visualization of processes and phenomena;
– e-learning.
The dispersion of the different contributions between these four sections is
purely arbitrary. The strong link between these four sections is the power
they can, together, provide to scientific investigation.
Weare very grateful to Springer-Verlag, which has agreed to partner with
the Bellagio Initiative to publish the current book and be part of this im-
portant effort. This book is sold at a special discounted price which does not
include any remuneration for authors or institutions. This supports our ob-
jective, which is to allow scientists from all countries to have better access
to scientific knowledge and actively contribute to scientific discovery. This is
why I am honored and proud to introduce to you the present volume which
I hope, as the first of a series of publications to come, belongs on scientists,
applied mathematicians, and engineers’ bookshelves.
Editing a book written by many authors on different continents is a dif-
ficult task. So in closing, I would like to thank everyone who has supported
me while I was coordinating the work of publishing this volume. I would also
like to apologize to my wife and my children for the time I should have spent
and missed spending with them.
Blacksburg, August 2007 Dialla Konat´e
Names of Officers to the Conference
ProfessorDiallaKonate:DirectorandP.I([email protected]@wssu.
edu)
Organizing Committee
ProfessorsWilliamGreenberg(VirginiaTech,USA),DiallaKonate(Winston-
Salem State University, USA); Oluwole Makinde (University of Limpopo,
SouthAfrica);OusseynouNakoulima(UniversityofAntilles&Guiana,France
&theCaribbean);EitanTadmor(UniversityofMaryland,CollegePark);Oleg
I. Yordanov (Bulgarian Academy of Science, Budapest, Bulgaria).
Team Leaders and Invited Speakers
Omrane Abdennebi (University of Antilles & Guiana, France & the
Caribbean); John Georgiadis (University of Illinois at Urbana Champaign,
USA), David Kinderlehrer (Carnegie-Mellon University, USA); Reinhard
Laubenbacher(VirginiaTech,USA),TashakkoriRahman(AppalachianState
University, USA); Roger Temam (University of Indiana, USA); Michael
Renardy (Virginia Tech, USA).

Contents
Part I Numerical Methods and Problem Solving
Quasi-Analytical Computation of Energy Levels and Wave
Functions in a Class of Chaotic Cavities with Inserted Objects
F. Seydou, O.M. Ramahi, and T. Seppa¨nen ......................... 3
Existence Results and Open Problems in the Kinetic Theory
of Dense Gases
W. Greenberg.................................................... 17
The High Performance Asymptotic Method in Numerical
Simulation
D. Konat´e ...................................................... 33
Modelling the Thermal Operation in a Catalytic Converter
of an Automobile’s Exhaust
O.D. Makinde ................................................... 51
Modelling Transmission Dynamics of Childhood Diseases
in the Presence of a Preventive Vaccine: Application
of Adomian Decomposition Technique
O.D. Makinde ................................................... 63
A New MPFA Formulation for Subsurface Flow Problems
on Unstructured Grids: Derivation of the Discrete Problem
A. Njifenjou and I.M. Nguena ..................................... 75
Analysis of a New MPFA Formulation for Flow Problems
in Geologically Complex Media
A. Njifenjou and M. Mbehou ...................................... 91
X Contents
A Small Eddy Correction Algorithm for the Primitive
Equations of the Ocean
T. Tachim Medjo and R. Temam ..................................107
Part II Modeling and Control of Phenomena
Aspects of Modeling Transport in Small Systems with a Look
at Motor Proteins
D. Kinderlehrer..................................................153
Optimal Control of Ill-Posed Parabolic Distributed Systems
A. Omrane......................................................165
A Parametric Study of Low Reynolds Number Blood Flow
in a Porous, Slowly Varying, Stenotic Artery with Heat
Transfer
A. Ogulu........................................................181
Stability of Generalized Convexity and Monotonicity
P.T. An ........................................................193
Are Viscoelastic Flows Under Control or Out of Control?
M. Renardy .....................................................201
On Topological Optimization and Pollution in Porous Media
I. Faye, A. Sy, and D. Seck .......................................209
Dynamical Analysis of Infectious Diseases in Spatially
Heterogeneous Environments
J.M. Tchuenche .................................................239
Approximate Scale-Invariant Random Fields: Review
and Current Developments
O.I. Yordanov ...................................................253
Part III Simulation and Visualization
Non-Stationary Vibrations of Viscoelastic Circular Cylindrical
Thick Shell Under the Influence of Temperature
F.A. Amirkulova.................................................271
Mathematical Vibration Modelling of the Pre-Stressed
Viscoelastic Thick-Walled Cylindrical Shell
Feruza Abdukadirovna Amirkulova .................................291