Surface patterning of low-dimensional systems: the chirality of charged fibres.

Charged surfaces are interesting for their ability to have long-range correlations and their ability to be dynamically tuned. While the configurations of charged planar surfaces have been thoroughly mapped and studied, charged cylindrical surfaces show novel features. The surface patterning of cylindrically confined charges is discussed with emphasis on the role of chiral configurations. The origins of surface patterns due to competing interactions in charged monolayers are summarized along with their associated theoretical models. The electrostatically induced patterns described in this paper are important in many low-dimensional biological systems such as plasma membrane organization, filamentous virus capsid structure or microtubule interactions. A simple model effectively predicting some features of chiral patterns in biological systems is presented. We extend our model from helical lamellar patterns to elliptical patterns to consider asymmetrical patterns in assemblies of filamentous aggregates.

Brane world generated dynamically from string type IIB matrices

We have recently proposed a dynamical mechanism that may realize a flat four-dimensional space-time as a brane in type IIB superstring theory. A crucial role is played by the phase of the chiral fermion integral associated with the IKKT (Ishibashi-Kawai-Kitazawa-Tsuchiya) matrix theory, which is conjectured to be a nonperturbative definition of type IIB superstring theory. We demonstrate our mechanism by studying a simplified model, in which we find that a lower-dimensional brane indeed appears dynamically. We also comment on some implications of our mechanism on model building of the brane world.

Nonuniversality of compact support probability distributions in random matrix theory.

The two-point resolvent is calculated in the large-n limit for the generalized fixed and bounded trace ensembles. It is shown to disagree with that of the canonical Gaussian ensemble by a nonuniversal part that is given explicitly for all monomial potentials V(M)=M(2p). Moreover, we prove that for the generalized fixed and bounded trace ensemble all k-point resolvents agree in the large-n limit, despite their nonuniversality.