The PDF method for turbulent combustion

Probability Density Function (PDF) methods provide a means of calculating the properties of turbulent reacting flows. They have been successfully applied to many turbulent flames, including some with finite rate kinetic effects. Here the methods are reviewed with an emphasis on computational issues and their application to turbulent combustion

The Complete Spectrum of the WNW_N String

We obtain the complete physical spectrum of the $W_N$ string, for arbitrary $N$. The $W_N$ constraints freeze $N-2$ coordinates, while the remaining coordinates appear in the currents only {\it via} their energy-momentum tensor. The spectrum is then effectively described by a set of ordinary Virasoro-like string theories, but with a non-critical value for the central charge and a discrete set of non-standard values for the spin-2 intercepts. In particular, the physical spectrum of the $W_N$ string includes the usual massless states of the Virasoro string. By looking at the norms of low-lying states, we find strong indications that all the $W_N$ strings are unitary.Comment: 28 page

The Interacting W3W_3 String

We present a procedure for computing gauge-invariant scattering amplitudes in the $W_3$ string, and use it to calculate three-point and four-point functions. We show that non-vanishing scattering amplitudes necessarily involve external physical states with excitations of ghosts as well as matter fields. The crossing properties of the four-point functions are studied, and it is shown that the duality of the Virasoro string amplitudes generalises in the $W_3$ string, with different sets of intermediate states being exchanged in different channels. We also exhibit a relation between the scattering amplitudes of the $W_3$ string and the fusion rules of the Ising model.Comment: (Revised version), 26 pages, Plain Tex, CTP TAMU-86/92, KUL-TF-92/4

On Sibling and Exceptional W Strings

We discuss the physical spectrum for $W$ strings based on the algebras $B_n$, $D_n$, $E_6$, $E_7$ and $E_8$. For a simply-laced $W$ string, we find a connection with the $(h,h+1)$ unitary Virasoro minimal model, where $h$ is the dual Coxeter number of the underlying Lie algebra. For the $W$ string based on $B_n$, we find a connection with the $(2h,2h+2)$ unitary $N=1$ super-Virasoro minimal model.Comment: 16 page

Anchoring historical sequences using a new source of astro-chronological tie-points

The discovery of past spikes in atmospheric radiocarbon activity, caused by major solar energetic particle events, has opened up new possibilities for high-precision chronometry. The two spikes, or Miyake Events, have now been widely identified in tree-rings that grew in the years 775 and 994 CE. Furthermore, all other plant material that grew in these years would also have incorporated the anomalously high concentrations of radiocarbon. Crucially, some plant-based artefacts, such as papyrus documents, timber beams and linen garments, can also be allocated to specific positions within long, currently unfixed, historical sequences. Thus, Miyake Events represent a new source of tie-points that could provide the means for anchoring early chronologies to the absolute timescale. Here, we explore this possibility, outlining the most expeditious approaches, the current challenges and obstacles, and how they might best be overcome.Comment: 11 pages, accepted to Royal Society Proc