Applications of convex analysis and comparison functionals to extremum principles

In many areas of applied mathematics, the govering equations can be expressed as dual equations which are elements in two vector spaces where a given functional defined on a cartesian product space has zero gradients. If this functional has a global saddle structure then the variational principle can be replaced by dual extremum principles of the Noble and Sewell type. The purpose of the present paper is to investigate how comparison functional which have convex, concave or saddle structure can be used to generate upper and lower bounding principles and critical sequences. The methods are illustrated by applications to the periodic solutions of a non-linear differential equation and the Fredholm integral equation.     

Artificial Intelligence Approaches to Simulation

Recent years have seen a number of attempts to apply both AI methods and AI software tools to the development of both simulations and simulation packages. This paper discusses the motivation behind such work: the increasing need for AI researchers to include simulation in AI systems and use simulation in research, and the need to model intelligent behaviour in OR simulation models. The current research and development effort is reviewed. A system called PROSS (the PROlog Simulation System), constructed to allow the integration of AI methods with traditional discrete simulation, is then briefly presented. It is concluded that AI software tools, and some of the novel approaches to simulation being taken by AI researchers, will have a considerable impact on simulation.     

Turbulent transport in tokamak plasmas with rotational shear

Nonlinear gyrokinetic simulations are conducted to investigate turbulent transport in tokamak plasmas with rotational shear. At sufficiently large flow shears, linear instabilities are suppressed, but transiently growing modes drive subcritical turbulence whose amplitude increases with flow shear. This leads to a local minimum in the heat flux, indicating an optimal E×B shear value for plasma confinement. Local maxima in the momentum fluxes are observed, implying the possibility of bifurcations in the E×B shear. The critical temperature gradient for the onset of turbulence increases with flow shear at low flow shears; at higher flow shears, the dependence of heat flux on temperature gradient becomes less stiff. The turbulent Prandtl number is found to be largely independent of temperature and flow gradients, with a value close to unity.