Radiative-convective equilibrium models of Uranus and Neptune

The present study of Uranus and Neptune radiative-convective equilibrium models gives emphasis to such aspects of the stratospheric energy balance as the influence of aerosol heating and convective penetration. The results obtained for Uranus imply that a continuum absorber may be a significant factor in the stratosphere despite the great distance from the sun. The results obtained for Neptune show that such a continuum absorber could significantly contribute to the energy balance within a localized stratospheric region, although it probably cannot furnish sufficient power to account for the observed IR spectrum irrespective of its vertical distribution. Attention is accordingly given to the convective penetration that could arise under such rapid vertical mixing that CH4's condensation cannot occur before the gas is carried above the condensation region

A simple construction of complex equiangular lines

A set of vectors of equal norm in $\mathbb{C}^d$ represents equiangular lines if the magnitudes of the inner product of every pair of distinct vectors in the set are equal. The maximum size of such a set is $d^2$, and it is conjectured that sets of this maximum size exist in $\mathbb{C}^d$ for every $d \geq 2$. We describe a new construction for maximum-sized sets of equiangular lines, exposing a previously unrecognized connection with Hadamard matrices. The construction produces a maximum-sized set of equiangular lines in dimensions 2, 3 and 8.Comment: 11 pages; minor revisions and comments added in section 1 describing a link to previously known results; correction to Theorem 1 and updates to reference

The size of the largest fluctuations in a market model with Markovian switching

This paper considers the size of the large fluctuations of a stochastic differential equation with Markovian switching. We concentrate on processes which obey the Law of the Iterated Logarithm, or obey upper and lower iterated logarithm growth bounds on their almost sure partial maxima. The results are applied to financial market models which are subject to random regime shifts. We prove that the security exhibits the same long-run growth properties and deviations from the trend rate of growth as conventional geometric Brownian motion, and also that the returns, which are non-Gaussian, still exhibit the same growth rate in their almost sure large deviations as stationary continuous-time Gaussian processes

On the interpretation of lateral manganin gauge stress measurements in polymers

Encapsulated wire-element stress gauges enable changes in lateral stress during shock loading to be directly monitored. However, there is substantial debate with regards to interpretation of observed changes in stress behind the shock front; a phenomenon attributed both to changes in material strength and shock- dispersion within the gauge-encapsulation. Here, a pair of novel techniques which both modify or remove the embedding medium where such stress gauges are placed within target materials have been used to try and inform this debate. The behavior of three polymeric materials of differing complexity was considered, namely polystyrene, the commercially important resin transfer moulding RTM 6 resin and a commercially available fat lard. Comparison to the response of embedded gauges has suggested a possible slight decrease in the absolute magnitude of stress. However, changing the encapsulation has no detectable effect on the gradient behind the shock in such polymeric systems

An interactive multi-block grid generation system

A grid generation procedure combining interactive and batch grid generation programs was put together to generate multi-block grids for complex aircraft configurations. The interactive section provides the tools for 3D geometry manipulation, surface grid extraction, boundary domain construction for 3D volume grid generation, and block-block relationships and boundary conditions for flow solvers. The procedure improves the flexibility and quality of grid generation to meet the design/analysis requirements