~ ABSTRACTS ~
Control of Shock Positions with Applications to Sonic
Booms
Olivier Pironneau, University of Paris VI (Pierre et Marie
Curie)
There are many fluid flow problems with discontinuities in
the data or in the flow. Among them two are quite important for
applications:
- transonic and supersonic flow with shocks and buffeting
- acoustics with sonic boom
Optimisation of these systems by standard gradient methods
requires the application of the techniques of the Calculus of
Variations and an implicit assumption that a Taylor expansion
exists with respect to the degrees of freedom of the problem.
Take for example the flow in a transonic nozzle and the
variation of the flow with respect to the inflow conditions;
when these vary the shock moves and the derivative of the flow
variables with respect to inflow conditions is a Dirac measure
and so the Taylor expansion does not exists.
By extending the calculus of variation via the theory of
distribution it is possible to show however that the derivatives
exist. But the result has serious numerical implications; in
particular it favors the mixed finite element methods.
We shall give numerical illustrations using the finite
element method for an inverse problem for Burger's equation, for
the design of a transonic nozzle and for the design of a
business supersonic airplane for sonic boom minimization.
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Post-Fisherian Experimentation
Jeff Wu, School of Industrial and Systems Engineering,
Georgia Institute of Technology, USA
It has been more than 70 years since Fisher’s pioneering work
on experimental design. His impacts on the field of DOE continue
to be felt to these days. In this talk I will review the major
advances in DOE since Fisher and speculate on future
development. A common theme underlying these advances was an
emerging technological development that called for novel ideas
and methods to address these challenges. Fisher's principles of
replication, blocking and randomization arose in the context of
agricultural experiments. Since the 50's attention had turned to
industrial experiments with many factors. Basic principles that
govern the relationships among factorial effects include: effect
hierarchy, effect sparsity, and effect heredity. The minimum
aberration criterion has lately become the primary criterion for
selecting optimal fractional factorial designs. Another
development was Box's response surface methodology, which came
from chemical industries. It emphasized response model fitting
and optimization instead of factorial effect estimation. The
quality movement in the 80's has inspired the development of
robust parameter design (Taguchi). Its central idea is to reduce
variation by exploiting control-by-noise interactions. Factor
asymmetry caused by the differential treatment of control and
noise factors has led to new strategies in design and modeling.
Looking into the future, the current trend in rapid prototyping
through CAD/CAM provides a golden opportunity for research on
computer modeling and experiments. Recent breakthroughs in
biotechnology may call for the development of other novel
techniques.
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Choice of Technique in the Robinson-Solow-Srinivasan Model
M. Ali Khan, Johns Hopkins University
We report results on the optimal "choice of technique" in a model originally
formulated by Robinson, Solow and Srinivasan (henceforth, the RSS model) and
further discussed by Okishio and Stiglitz. By viewing this vintage-capital
model without discounting as a specific instance of the general theory of
intertemporal resource allocation associated with Brock, Gale and McKenzie, we
resolve long-standing conjectures in the form of theorems on the existence and
price support of optimal paths, and of conditions sufficient for the optimality
of a policy first identified by Stiglitz. We dispose of the necessity of these
conditions in surprisingly simple examples of economies in which (i) an optimal
path is periodic, (ii) a path following Stiglitz' policy is bad, and (iii)
there is optimal investment in different vintages at different times.
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Some Problems and Recent Developments in Preference and
Utility Theory
Ghanshyam Mehta, School of Economics, University of
Queensland, Australia
In this talk, the speaker will give an overview from an
economic point of view of some problems and recent developments
in the branch of utility theory that deals with the problem of
representing a preference relation by a utility function. This
topic is very closely related to certain purely mathematical
problems in the fields of topology and order. It also has many
applications in other applied fields such as mathematical
psychology, physics (thermodynamics), ordinal data analysis in
statistics and so on. The talk has been designed to appeal to a
broad group of economists with different interests,
mathematicians, applied scientists in other related fields and
also students at the advanced undergraduate and graduate levels.
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An Introduction to Parallel Computing
Message Passing Interface & Application
Bud Fox,
University of Western Australia
An overview of parallel computing, the Message Passing
Interface (MPI) and its applications, is provided in a
three-part seminar to introduce the relative simplicity of
obtaining the maximum benefit from parallel computing and in
particular on networks of workstations. Part 1 explores the
architectures, models and environments concerning parallel
computation and may allow researchers to identify the
possibility for parallelism in their own work. Part 2 provides
an in-depth look at MPI centred on a practical perspective of
installation, building and running code, and the usage of
supporting tools for debugging and graphical display. Part 3
concerns applications for MPI and includes code excerpts, in a
"show & tell" approach.
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