Past

The seminar will address issues related to numerical simulation

of non-linear behaviour of solid materials to impact loading.

The kinematic and constitutive aspects of the transition from

continuum to discontinuum will be presented as utilised

within an explicit finite element development framework.

Material softening, mesh sensitivity and regularisation of

solutions will be discussed.

At the leading order, the low-energy effective field equations in string

theory admit solutions of the form of products of Minkowski spacetime and a

Ricci-flat Calabi-Yau space. The equations of motion receive corrections at

higher orders in \alpha', which imply that the Ricci-flat Calabi-Yau space is

modified. In an appropriate choice of scheme, the Calabi-Yau space remains

Kahler, but is no longer Ricci-flat. We discuss the nature of these

corrections at order {\alpha'}^3, and consider the deformations of all the

known cohomogeneity one non-compact Kahler metrics in six and eight

dimensions. We do this by deriving the first-order equations associated with

the modified Killing-spinor conditions, and we thereby obtain the modified

supersymmetric solutions. We also give a detailed discussion of the boundary

terms for the Euler complex in six and eight dimensions, and apply the

results to all the cohomogeneity one examples. Additional material will be

presented concerning the case of holonomy G_2.

In this talk, we consider a class of non-linear stochastic partial

differential equations. We represent its solutions as the weighted

empirical measures of interacting particle systems. As a consequence,

a simulation scheme for this class of SPDEs is proposed. There are two

sources of error in the scheme, one due to finite sampling of the

infinite collection of particles and the other due to the Euler scheme

used in the simulation of the individual particle motions. The error

bound, taking into account both sources of error, is derived. A

functional limit theorem is also derived. The results are applied to

nonlinear filtering problems.

This talk is based on joint research with Kurtz.