Past

In the first part of the talk I will discuss existence and regularity results for models of complex non-Newtonian fluids containing liquid crystalline polymers. The main technical tool is related to an apriori logarithmic estimate for the 2D Navier-Stokes equations.

In the second part I will consider a simplified version of the system and describe some of its qualitative properties as well as the analytical challenges posed by its study.

The first part is joint work with P Constantin, Ch. Fefferman and E Titi.

\\Common\dfs\htdocs\www\maintainers\reception\enb\abstracts\topology\mt06\tillmann.shtml

\\common\dfs\htdocs\www\maintainers\reception\enb\abstracts\stochastic-analysis\mt06\johansson

\\Common\dfs\htdocs\www\maintainers\reception\enb\abstracts\string-theory\mt06\skinner.shtml

http://www.maths.ox.ac.uk/arg/

The talk starts with a general introduction of the convex

quadratic semidefinite programming problem (QSDP), followed by a number of

interesting examples arising from finance, statistics and computer sciences.

We then discuss the concept of primal nondegeneracy for QSDP and show that

some QSDPs are nondegenerate and others are not even under the linear

independence assumption. The talk then moves on to the algorithmic side by

introducing the dual approach and how it naturally leads to Newton's method,

which is quadratically convergent for degenerate problems. On the

implementation side of the Newton method, we stress that direct methods for

the linear equations in Newton's method are impossible simply because the

equations are quite large in size and dense. Our numerical experiments use

the conjugate gradient method, which works quite well for the nearest

correlation matrix problem. We also discuss difficulties for us to find

appropriate preconditioners for the linear system encountered. The talk

concludes in discussing some other available methods and some future topics.

http://www.maths.ox.ac.uk/oxmos/meetings