SU(3)-Goodman-de la Harpe-Jones subfactors and the realisation of SU(3) modular invariants

We complete the realisation by braided subfactors, announced by Ocneanu, of all SU(3)-modular invariant partition functions previously classified by Gannon.Comment: 47 pages, minor changes, to appear in Reviews in Mathematical Physic

Modular invariants and subfactors

In this lecture we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. Our analysis is based on an approach to modular invariants using braided sector induction ("$\alpha$-induction") arising from the treatment of conformal field theory in the Doplicher-Haag-Roberts framework. Many properties of modular invariants which have so far been noticed empirically and considered mysterious can be rigorously derived in a very general setting in the subfactor context. For example, the connection between modular invariants and graphs (cf. the A-D-E classification for $SU(2)_k$) finds a natural explanation and interpretation. We try to give an overview on the current state of affairs concerning the expected equivalence between the classifications of braided subfactors and modular invariant two-dimensional conformal field theories.Comment: 25 pages, AMS LaTeX, epic, eepic, doc-class fic-1.cl

Modular invariants from subfactors

In these lectures we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. A subfactor with a braiding determines a matrix $Z$ which is obtained as a coupling matrix comparing two kinds of braided sector induction ("alpha-induction"). It has non-negative integer entries, is normalized and commutes with the S- and T-matrices arising from the braiding. Thus it is a physical modular invariant in the usual sense of rational conformal field theory. The algebraic treatment of conformal field theory models, e.g. $SU(n)_k$ models, produces subfactors which realize their known modular invariants. Several properties of modular invariants have so far been noticed empirically and considered mysterious such as their intimate relationship to graphs, as for example the A-D-E classification for $SU(2)_k$. In the subfactor context these properties can be rigorously derived in a very general setting. Moreover the fusion rule isomorphism for maximally extended chiral algebras due to Moore-Seiberg, Dijkgraaf-Verlinde finds a clear and very general proof and interpretation through intermediate subfactors, not even referring to modularity of $S$ and $T$. Finally we give an overview on the current state of affairs concerning the relations between the classifications of braided subfactors and two-dimensional conformal field theories. We demonstrate in particular how to realize twisted (type II) descendant modular invariants of conformal inclusions from subfactors and illustrate the method by new examples.Comment: Typos corrected and a few minor changes, 37 pages, AMS LaTeX, epic, eepic, doc-class conm-p-l.cl

Modular Invariants from Subfactors: Type I Coupling Matrices and Intermediate Subfactors

A braided subfactor determines a coupling matrix Z which commutes with the S- and T-matrices arising from the braiding. Such a coupling matrix is not necessarily of "type I", i.e. in general it does not have a block-diagonal structure which can be reinterpreted as the diagonal coupling matrix with respect to a suitable extension. We show that there are always two intermediate subfactors which correspond to left and right maximal extensions and which determine "parent" coupling matrices Z^\pm of type I. Moreover it is shown that if the intermediate subfactors coincide, so that Z^+=Z^-, then Z is related to Z^+ by an automorphism of the extended fusion rules. The intertwining relations of chiral branching coefficients between original and extended S- and T-matrices are also clarified. None of our results depends on non-degeneracy of the braiding, i.e. the S- and T-matrices need not be modular. Examples from SO(n) current algebra models illustrate that the parents can be different, Z^+\neq Z^-, and that Z need not be related to a type I invariant by such an automorphism.Comment: 25 pages, latex, a new Lemma 6.2 added to complete an argument in the proof of the following lemma, minor changes otherwis

Sculplexity: Sculptures of Complexity using 3D printing

We show how to convert models of complex systems such as 2D cellular automata into a 3D printed object. Our method takes into account the limitations inherent to 3D printing processes and materials. Our approach automates the greater part of this task, bypassing the use of CAD software and the need for manual design. As a proof of concept, a physical object representing a modified forest fire model was successfully printed. Automated conversion methods similar to the ones developed here can be used to create objects for research, for demonstration and teaching, for outreach, or simply for aesthetic pleasure. As our outputs can be touched, they may be particularly useful for those with visual disabilities.Comment: Free access to article on European Physics Letter

The VLT-FLAMES Survey of Massive Stars: Observations centered on the Magellanic Cloud clusters NGC 330, NGC 346, NGC 2004, and the N11 region

We present new observations of 470 stars using the Fibre Large Array Multi-Element Spectrograph (FLAMES) instrument in fields centered on the clusters NGC 330 and NGC 346 in the Small Magellanic Cloud (SMC), and NGC 2004 and the N11 region in the Large Magellanic Cloud (LMC). A further 14 stars were observed in the N11 and NGC 330 fields using the Ultraviolet and Visual Echelle Spectrograph (UVES) for a separate programme. Spectral classifications and stellar radial velocities are given for each target, with careful attention to checks for binarity. In particular we have investigated previously unexplored regions around the central LH9/LH10 complex of N11, finding ~25 new O-type stars from our spectroscopy. We have observed a relatively large number of Be-type stars that display permitted Fe II emission lines. These are primarily not in the cluster cores and appear to be associated with classical Be-type stars, rather than pre main-sequence objects. The presence of the Fe II emission, as compared to the equivalent width of H$\alpha$, is not obviously dependent on metallicity. We have also explored the relative fraction of Be- to normal B-type stars in the field-regions near to NGC 330 and NGC 2004, finding no strong evidence of a trend with metallicity when compared to Galactic results. A consequence of service observations is that we have reasonable time-sampling in three of our FLAMES fields. We find lower limits to the binary fraction of O- and early B-type stars of 23 to 36%. One of our targets (NGC346-013) is especially interesting with a massive, apparently hotter, less luminous secondary component.Comment: 35 pages, 17 figures (some reduced in size). Replacement copy, includes an erratum on the final page. A copy with full res. & embedded figures is at http://www.roe.ac.uk/~cje/flamesMC.ps.g

Electric potential distributions at the interface between plasmasheet clouds

At the interface between two plasma clouds with different densities, temperatures, and/or bulk velocities, there are large charge separation electric fields which can be modeled in the framework of a collisionless theory for tangential discontinuities. Two different classes of layers were identified: the first one corresponds to (stable) ion layers which are thicker than one ion Lamor radius; the second one corresponds to (unstable) electron layers which are only a few electron Larmor radii thick. It is suggested that these thin electron layers with large electric potential gradients (up to 400 mV/m) are the regions where large-amplitude electrostatic waves are spontaneously generated. These waves scatter the pitch angles of the ambient plasmasheet electron into the atmospheric loss cone. The unstable electron layers can therefore be considered as the seat of strong pitch angle scattering for the primary auroral electrons

Autoignition test cell Patent

Test chamber for determining decomposition and autoignition of materials used in spacecraft under controlled environmental condition