Asymptotics of the partition function for random matrices via Riemann-Hilbert techniques, and applications to graphical enumeration

We study the partition function from random matrix theory using a well known connection to orthogonal polynomials, and a recently developed Riemann-Hilbert approach to the computation of detailed asymptotics for these orthogonal polynomials. We obtain the first proof of a complete large N expansion for the partition function, for a general class of probability measures on matrices, originally conjectured by Bessis, Itzykson, and Zuber. We prove that the coefficients in the asymptotic expansion are analytic functions of parameters in the original probability measure, and that they are generating functions for the enumeration of labelled maps according to genus and valence. Central to the analysis is a large N expansion for the mean density of eigenvalues, uniformly valid on the entire real axis.Comment: 44 pages, 4 figures. To appear, International Mathematics Research Notice

Turbulence measurements in a swirling confined jet flowfield using a triple hot-wire probe

An axisymmetric swirling confined jet flowfield, similar to that encountered in gas turbine combustors was investigated using a triple hot-wire probe. The raw data from the three sensors were digitized using ADC's and stored on a Tektronix 4051 computer. The data were further reduced on the computer to obtain time-series for the three instantaneous velocity components in the flowfield. The time-mean velocities and the turbulence quantities were deduced. Qualification experiments were performed and where possible results compared with independent measurements. The major qualification experiments involved measurements performed in a non-swirling flow compared with conventional X-wire measurements. In the swirling flowfield, advantages of the triple wire technique over the previously used multi-position single hot-wire method are noted. The measurements obtained provide a data base with which the predictions of turbulence models in a recirculating swirling flowfield can be evaluated

Phase Mixing of Alfvén Waves Near a 2D Magnetic Null Point

The propagation of linear Alfvén wave pulses in an inhomogeneous plasma near a 2D coronal null point is investigated. When a uniform plasma density is considered, it is seen that an initially planar Alfvén wavefront remains planar, despite the varying equilibrium Alfvén speed, and that all the wave collects at the separatrices. Thus, in the non-ideal case, these Alfvénic disturbances preferentially dissipate their energy at these locations. For a non-uniform equilibrium density, it is found that the Alfvén wavefront is significantly distorted away from the initially planar geometry, inviting the possibility of dissipation due to phase mixing. Despite this however, we conclude that for the Alfvén wave, current density accumulation and preferential heating still primarily occur at the separatrices, even when an extremely non-uniform density profile is considered