Hans Bruun Nielsen

Optimization of pipe networks

The paper treats a piping system, where the layout of the network is given but the diameters of the pipes should be chosen among a small number of different values. The cost of realizing the system should be minimized while keeping the energy heads at the nodes above some lower limits. A new algorithm using successive linear programming is presented. The performance of the algorithm is illustrated by optimizing a network with 201 pipes and 172 nodes. It is concluded that the new algorithm seems to be very efficient and stable, and that it always finds a solution with a cost near the best possible.

A Finite Smoothing Algorithm for Linear

In this paper a new method for solving the linear

l_1

l_1

Estimation

problem is described, analysed, and tested. The method is based on smoothing the nondifferentiable

Exponential Data Fitting and its Applications

l_1

Bifurcation of the stationary Ekman flow into a stable periodic flow

function. The smoothing can be done in a well-onditioned manner since the method has finite convergence. Extensive numerical tests demonstrate significant superiority to existing simplex-type codes. Furthermore, the tests show that the new algorithm is very well suited for vector processing.

A New Finite Continuation Algorithm for Linear Programming

Type Ia supernova light curves are characterized by a rapid rise from zero luminosity to a peak value, followed by a slower quasi-exponential decline. The rise and peak last for a few days, while the decline persists for many months. It is widely believed that the decline is powered by the radioactive decay chain 56Ni → 56Co → 56Fe, but the rates of decline in luminosity do not exactly match the decay rates of Ni and Co. In 1976, Rust, Leventhal, and McCall [19] presented evidence that the declining part of the light curve is well modelled by a linear combination of two exponentials whose decay rates were proportional to, but not exactly equal to, the decay rates for Ni and Co. The proposed reason for the lack of agreement between the rates was that the radioactive decays take place in the interior of a white dwarf star, at densities much higher than any encountered in a terrestrial environment, and that these higher densities accelerate the two decays by the same factor. This paper revisits this model, demonstrating that a variant of it provides excellent fits to observed luminosity data from 6 supernovae.

Bound constrained quadratic programming via piecewise quadratic functions

The two cases of stationary Ekman boundary layer flow of an incompressible fluid near i) a plane boundary and ii) a free surface with constant shear are considered. It is proven that a stable secondary flow in the form of traveling waves bifurcates from the stationary flow at a certain Reynolds number, and that the stationary flow is unstable above this number. The values of the critical Reynolds number and of the numbers that characterize the traveling wave are computed and compared with experimental values.

A Finite Continuation Algorithm for Bound Constrained Quadratic Programming

We describe a new finite continuation algorithm for linear programming. The dual of the linear programming problem with unit lower and upper bounds is formulated as an

Implementation of QR up- and downdating on a massively parallel computer

\ell_1