The numerical solution of the thin film flow surrounding a horizontal cylinder resulting from a vertical cylindrical jet

The numerical solution of the thin film flow surrounding a horizontal cylinder resulting from a single vertical cylindrical jet is obtained. This is effected by transforming the domain of the flow, which contains a free surface, onto a rectangular parallelepiped and using a marching strategy to solve the ensuing parabolic equations. The flow terminates at a finite distance along the cylinder, its position depending on the velocity and mass flux of the jet. A comparison with the usual two-dimensional model in which the jet is replaced by a vertical sheet shows that such a representation is valid provided the overall width of the flow is not too large. In particular, the differences in heat transfer characteristics amount to a few per cent, thus validating the use of the two-dimensional model when applied to heat exchanger tubes. A comparison with the more usual multicolumn case is also considered.     

The numerical treatment of perturbed bifurcation problems in ordinary differential equations

A new numerical method is presented to analyze perturbations of bifurcations of the solutions of nonlinear boundary value problems. The perturbations may result from imperfections or other inhomogeneities in the corresponding scientific problem. The nonisolated solutions are calculated in dependence of the perturbation parameter. Therefore, it is possible to determine the singular solution as well as a solution branch through this nonisolated solution simultaneously. Standard procedures of numerical analysis are applicable.     

Critical exponents and large-order behavior of perturbation theory

The principles of the recent calculations of critical exponents from three- and two-dimensional field theory are reviewed. They rely on the Callan-Symanzik equations, diagram calculations, and on the characterization of the asymptotic behavior of perturbation series at large order. We then present new results concerning the normalization of the large-order behavior.On leave of absence from INFN, Frascati.     

Stochastic dynamics of two-dimensional infinite-particle systems

The time evolution of an open system of infinitely many two-dimensional classical particles is investigated. Particles are interacting by a singular pair potentialU, and each particle is connected to a heat bath of temperatureT. The heat baths are represented by independent white noise forces and Langevin damping terms. Existence of strong solutions to the corresponding infinite system of stochastic differential equations is proved for initial configurations with a logarithmic order of energy fluctuations. Gibbs states forU at temperatureT are invariant under time evolution.     

Global solutions of the Boltzmann equation on a lattice

The nonlinear Boltzmann equation with a discretized spatial variable is studied in a Banach space of absolutely integrable functions of the velocity variables. Conservation laws and positivity are utilized to extend weak local solutions to a global solution. This is shown to be a strong solution by analytic semigroup techniques.Supported by National Science Foundation Grant ENG-7515882.