The individual time trial as an optimal control problem

In a cycling time trial, the rider needs to distribute his power output optimally to minimize the time between start and finish. Mathematically, this is an optimal control problem. Even for a straight and flat course, its solution is non-trivial and<br/>involves a singular control, which corresponds to a power that is slightly above the aerobic...

A variational approach to determine the optimal power distribution for cycling in a time trial

The optimal pacing strategy of a cyclist in an individual time-trial depends on terrain, weather conditions and the cyclists endurance capacity. Previous experimental and theoretical studies have shown that a suboptimal pacing strategy may have a substantial negative effect. In this paper we express the optimal pacing problem as a...

Flux-splitting schemes for improved monotonicity of discrete solutions of elliptic equations with highly anisotropic coefficients

: A family of flux-continuous, locally conservative, finite-volume schemes has been developed for solving the general tensor pressure equation of petroleum reservoir-simulation on structured and unstructured grids. These schemes are control-volume distributed. The schemes are applicable to diagonal and full tensor pressure equation with...

Higher order elliptic problems and positivity

The main subject of this thesis concerns positivity for fourth order elliptic problems. By positivity we mean that a positive source term in the differential equation leads to a positive solution. For second order elliptic partial differential equations such a result is known and referred to by the name maximum principle. It is also well known...