We prove that ifm ≥ n−3 then every Sm-invariant F-nef divisor on the moduli space of stable n-pointed curves of genus zero is linearly equivalent to an effective combination of boundary divisors. As an application, we determine the Mori cone of the moduli spaces of stable curves of small genus with few marked points.

In this thesis we study compactifications of type II string theories and M-theory to four dimensions. We construct the four-dimensional N = 2 supergravities that arise from compactifications of type IIA string theory and M-theory on manifolds with SU(3)structure. We then study their potential for moduli stabilisation and give explicit examples where all the moduli are stabilised. We also study ...

We discuss the moduli space approximation for heterotic M-theory, both for the minimal case of two boundary branes only, and when a bulk brane is included. The resulting effective actions may be used to describe the cosmological dynamics in the regime where the branes are moving slowly, away from singularities. We make use of the recently derived colliding branes solution to determine the globa...

We discuss the prepotential describing the effective field theory of N =2 heterotic superstring models. At the one loop-level the prepotential develops logarithmic sin-gularities due to the appearance of charged massless states at particular surfaces in the moduli space of vector multiplets. These singularities modify the classical duality symmetry group which now becomes a representation of th...

The statistical data required for quantitative analysis of the physical properties of composite materials may be obtained using digital image processing techniques. This approach allows accurate quantitative determination of volume fraction data, of interface area per unit volume, and of more sophisticated measures of the microgeometry of material mixtures including the n-point spatial correlat...

In this paper, we develop a mean field Mori-Tanaka model T. Mori and K. Tanaka, Acta. Metall. 21, 571 1973 to calculate the effective magnetoelectroelastic moduli of matrix-based multiferroic composites, emphasizing the effects of shape and orientation distribution of second phase particles that have not been investigated before. Through a systematic study, it is observed that laminated composi...

We investigate the weakening of elastic materials through randomly distributed circles and cracks numerically and compare the results to predictions from homogenization theories. We find a good agreement for the case of randomly oriented cracks of equal length in an isotropic plane-strain medium for lower crack densities; for higher densities the material is weaker than predicted due to precurs...

In the "central" region of moduli space of string theories, which is most likely to describe the "real world," the string coupling is about unity and the volume of compact dimensions is about the string volume. We map this region, assuming that the string coupling and compact volume moduli are chiral superfields of N = 1 supergravity in four dimensions, and requiring that the supersymmetry (SUS...

Nonlinear supersymmetry is used to compute the general form of the effective D-brane action in type I string theory compactified to four dimensions in the presence of internal magnetic fields. In particular, the scalar potential receives three contributions: (1) a nonlinear part of the D-auxiliary component, associated to the Dirac-Born-Infeld action; (2) a Fayet-Iliopoulos (FI) D-term with a m...

Eshelby's theory is the foundation of composite mechanics, allowing calculation of the effective elastic moduli of composites from a knowledge of their microstructure. However, it ignores interfacial stress and only applies to very dilute composites-i.e. where any inclusions are widely spaced apart. Here, within the framework of the Mori-Tanaka multiphase approximation scheme, we extend Eshelby...