Singularity theory study of overdetermination in models for L-H transitions

Two dynamical models that have been proposed to describe transitions between low and high confinement states (L-H transitions) in confined plasmas are analysed using singularity theory and stability theory. It is shown that the stationary-state bifurcation sets have qualitative properties identical to standard normal forms for the pitchfork and transcritical bifurcations. The analysis yields the codimension of the highest-order singularities, from which we find that the unperturbed systems are overdetermined bifurcation problems and derive appropriate universal unfoldings. Questions of mutual equivalence and the character of the state transitions are addressed.Comment: Latex (Revtex) source + 13 small postscript figures. Revised versio

Aerothermal modeling program, phase 1

Aerothermal submodels used in analytical combustor models are analyzed. The models described include turbulence and scalar transport, gaseous full combustion, spray evaporation/combustion, soot formation and oxidation, and radiation. The computational scheme is discussed in relation to boundary conditions and convergence criteria. Also presented is the data base for benchmark quality test cases and an analysis of simple flows

Updated analysis of NN elastic scattering to 3 GeV

A partial-wave analysis of NN elastic scattering data has been updated to include a number of recent measurements. Experiments carried out at the Cooler Synchrotron (COSY) by the EDDA Collaboration have had a significant impact above 1 GeV. Results are discussed in terms of the partial-wave and direct-reconstruction amplitudes.Comment: 16 pages, 14 figures, 2 tables; Fig 10 error corrected; Accepted for publication in Physical Review

Bivariate galaxy luminosity functions in the Sloan Digital Sky Survey

Bivariate luminosity functions (LFs) are computed for galaxies in the New York Value-Added Galaxy Catalogue, based on the Sloan Digital Sky Survey Data Release 4. The galaxy properties investigated are the morphological type, inverse concentration index, Sérsic index, absolute effective surface brightness (SB), reference frame colours, absolute radius, eClass spectral type, stellar mass and galaxy environment. The morphological sample is flux limited to galaxies with r < 15.9 and consists of 37 047 classifications to an rms accuracy of ± half a class in the sequence E, S0, Sa, Sb, Sc, Sd, Im. These were assigned by an artificial neural network, based on a training set of 645 eyeball classifications. The other samples use r < 17.77 with a median redshift of z∼ 0.08, and a limiting redshift of z < 0.15 to minimize the effects of evolution. Other cuts, for example in axis ratio, are made to minimize biases. A wealth of detail is seen, with clear variations between the LFs according to absolute magnitude and the second parameter. They are consistent with an early-type, bright, concentrated, red population and a late-type, faint, less concentrated, blue, star-forming population. This bimodality suggests two major underlying physical processes, which in agreement with previous authors we hypothesize to be merger and accretion, associated with the properties of bulges and discs, respectively. The bivariate luminosity–SB distribution is fit with the Chołoniewski function (a Schechter function in absolute magnitude and Gaussian in SB). The fit is found to be poor, as might be expected if there are two underlying processes

In-situ measurements of wall moisture in a historic building in response to the installation of an impermeable floor

When impermeable ground bearing slabs are installed in old buildings without a damp-proof course, it is a common belief of conservation practitioners that ground moisture will be ‘driven’ up adjacent walls by capillary action. However, there is limited evidence to test this hypothesis. An experiment was used to determine if the installation of a vapour-proof barrier above a flagstone floor in a historic building would increase moisture content levels in an adjacent stone rubble wall. This was achieved by undertaking measurements of wall, soil and atmospheric moisture content over a 3-year period. Measurements taken using timber dowels showed that the moisture content within the wall did not vary in response to wall evaporation rates and did not increase following the installation of a vapour-proof barrier above the floor. This indicates that the moisture levels in the rubble wall were not influenced by changes in the vapour-permeability of the floor

The harmonic measure of diffusion-limited aggregates including rare events

We obtain the harmonic measure of diffusion-limited aggregate (DLA) clusters using a biased random-walk sampling technique which allows us to measure probabilities of random walkers hitting sections of clusters with unprecedented accuracy; our results include probabilities as small as 10- 80. We find the multifractal D(q) spectrum including regions of small and negative q. Our algorithm allows us to obtain the harmonic measure for clusters more than an order of magnitude larger than those achieved using the method of iterative conformal maps, which is the previous best method. We find a phase transition in the singularity spectrum f(α) at α≈14 and also find a minimum q of D(q), qmin=0.9±0.05

Lifetimes of Heavy-Flavour Hadrons -- Whence and Whither?

A theoretical treatment for the weak decays of heavy-flavour hadrons has been developed that is genuinely based on QCD. Its methodology as it applies to total lifetimes and the underlying theoretical issues are sketched. Predictions are compared with present data. One discrepancy emerges: the beauty baryon lifetime appears to be significantly shorter than expected. The ramifications of those findings are analyzed in detail.Comment: 15 pages, no figures, LATEX, two references added and new information concerning a lower charm content in B decays incorporate

Effect of Wavefunction Renormalisation in N-Flavour Qed3 at Finite Temperature

A recent study of dynamical chiral symmetry breaking in N-flavour QED$_3$ at finite temperature is extended to include the effect of fermion wavefunction renormalisation in the Schwinger-Dyson equations. The simple ``zero-frequency'' truncation previously used is found to lead to unphysical results, especially as $T \to 0$. A modified set of equations is proposed, whose solutions behave in a way which is qualitatively similar to the $T=0$ solutions of Pennington et al. [5-8] who have made extensive studies of the effect of wavefunction renormalisation in this context, and who concluded that there was no critical $N_c$ (at T=0) above which chiral symmetry was restored. In contrast, we find that our modified equations predict a critical $N_c$ at $T \not= 0$, and an $N-T$ phase diagram very similar to the earlier study neglecting wavefunction renormalisation. The reason for the difference is traced to the different infrared behaviour of the vacuum polarisation at $T=0$ and at $T \not= 0$.Comment: 17 pages + 13 figures (available upon request), Oxford preprint OUTP-93-30P, IFUNAM preprint FT94-39, LaTe

Transverse Ward-Takahashi Identity, Anomaly and Schwinger-Dyson Equation

Based on the path integral formalism, we rederive and extend the transverse Ward-Takahashi identities (which were first derived by Yasushi Takahashi) for the vector and the axial vector currents and simultaneously discuss the possible anomaly for them. Subsequently, we propose a new scheme for writing down and solving the Schwinger-Dyson equation in which the the transverse Ward-Takahashi identity together with the usual (longitudinal) Ward-Takahashi identity are applied to specify the fermion-boson vertex function. Especially, in two dimensional Abelian gauge theory, we show that this scheme leads to the exact and closed Schwinger-Dyson equation for the fermion propagator in the chiral limit (when the bare fermion mass is zero) and that the Schwinger-Dyson equation can be exactly solved.Comment: 22 pages, latex, no figure