Niklas L.P. Lundström

Spatially Balanced Sampling through the Pivotal Method

A simple method to select a spatially balanced sample using equal or unequal inclusion probabilities is presented. For populations with spatial trends in the variables of interest, the estimation can be much improved by selecting samples that are well spread over the population. The method can be used for any number of dimensions and can hence also select spatially balanced samples in a space spanned by several auxiliary variables. Analysis and examples indicate that the suggested method achieves a high degree of spatial balance and is therefore efficient for populations with trends.

How to find simple nonlocal stability and resilience measures

Stability of dynamical systems is a central topic with applications in widespread areas such as economy, biology, physics and mechanical engineering. The dynamics of nonlinear systems may completely change due to perturbations forcing the solution to jump from a safe state into another, possibly dangerous, attractor. Such phenomena cannot be traced by the widespread local stability and resilience measures, based on linearizations, accounting only for arbitrary small perturbations. Using numerical estimates of the size and shape of the basin of attraction, as well as the systems returntime to the attractor after given a perturbation, we construct simple nonlocal stability and resilience measures that record a systems ability to tackle both large and small perturbations. We demonstrate our approach on the Solow–Swan model of economic growth, an electro-mechanical system, a stage-structured population model as well as on a high-dimensional system, and conclude that the suggested measures detect dynamic behavior, crucial for a systems stability and resilience, which can be completely missed by local measures. The presented measures are also easy to implement on a standard laptop computer. We believe that our approach will constitute an important step toward filling a current gap in the literature by putting forward and explaining simple ideas and methods, and by delivering explicit constructions of several promising nonlocal stability and resilience measures.

Constrained growth flips the direction of optimal phenological responses among annual plants

Phenological changes among plants due to climate change are well documented, but often hard to interpret. In order to assess the adaptive value of observed changes, we study how annual plants with and without growth constraints should optimize their flowering time when productivity and season length changes. We consider growth constraints that depend on the plants vegetative mass: self-shading, costs for nonphotosynthetic structural tissue and sibling competition. We derive the optimal flowering time from a dynamic energy allocation model using optimal control theory. We prove that an immediate switch (bang-bang control) from vegetative to reproductive growth is optimal with constrained growth and constant mortality. Increasing mean productivity, while keeping season length constant and growth unconstrained, delayed the optimal flowering time. When growth was constrained and productivity was relatively high, the optimal flowering time advanced instead. When the growth season was extended equally at both ends, the optimal flowering time was advanced under constrained growth and delayed under unconstrained growth. Our results suggests that growth constraints are key factors to consider when interpreting phenological flowering responses. It can help to explain phenological patterns along productivity gradients, and links empirical observations made on calendar scales with life-history theory.

Phragmén-Lindelöf theorems and p-harmonic measures for sets near low-dimensional hyperplanes

We prove estimates of a p-harmonic measure, p∈(n−m,∞], for sets in Rn which are close to an m-dimensional hyperplane Λ⊂Rn, m∈[0,n−1]. Using these estimates, we derive results of Phragmén-Lindelöf type in unbounded domains Ω⊂Rn∖Λ for p-subharmonic functions. Moreover, we give local and global growth estimates for p-harmonic functions, vanishing on sets in Rn, which are close to an m-dimensional hyperplane.

Developments in Rotor Dynamical Modeling of Hydropower units

During the last century the hydropower units have been developed from a few megawatts per unit, up to several hundreds megawatts per unit. Over the years the operating conditions have also been changed from the ones that the machines were originally designed. These changes will significantly affect the lifespan of the machines. The hydropower plants are in general old, and large-scale revisions will be performed in the coming years. This implies that new components with new materials and design will be installed to the old machines. To reduce the risk of failures it is essential that better methods for rotor dynamical simulations are developed. In this paper our research on electromagnetic-rotor interaction is summarized. Results are presented on new rotor models in connection with stability, excitation sources for backward/forward whirling and the occurrence of a tangential force.