The Artis Problem

The Artis aquarium has had difficulty maintaining a reasonable temperature in the recently install mammoth sea water tanks during the peak of summer. At this time the approximately 400 000 liters of water may be as much as 3 degrees Celsius too hot. This represents a considerable amount of energy to dissipate. Any solution to this problem must take into account the limited budget of the zoo, the heritage status of the building and the health of the fish in the tank. In this report, we analyse the major sources of energy entering and leaving the system. From this analysis, we find that the most effective method of reducing the water temperature is to increase the amount of evaporation from the system

Reconstruction of sea surface temperatures from the oxygen isotope composition of fossil planktic foraminifera.

Knowledge of the historic surface temperature of sea water is of importance for the calibration of climate models. The oxygen isotope composition of the shells of several species of planktic foraminifera can be used as a measure for this sea surface temperature. In this paper we investigate how mathematical models can contribute to the process of extracting information about the temperature at which the foraminifera lived from measurement of the oxygen isotope composition of their shells. A simple model is proposed which captures both the average and the variability of the temperature. Preliminary findings suggest that this model forms a solid basis for future research

The Euro Diffusion Project

From 1st January 2002 we have the unique possibility to follow the spread of national euro coins over the different European countries. We model and analyse this movement and estimate the time it will take before on average half the coins in our wallet will be foreign

Закономерности изменения коэффициента динамичности в линии привода прокатной клети в процессе её работы

Показано, что процессе работы клети коэффициент динамичности на шпиндельном и моторном участках периодически существенно изменяется за счет износа сочленяемых элементов и развития зазоров. Установленные закономерности позволяют прогнозировать максимальные динамические нагрузки в линии привода

Magma Design Automation: Component placement on chips; the "holey cheese" problem.

The costs of the fabrication of a chip is partly determined by the wire length needed by the transistors to respect the wiring scheme. The transistors have to be placed without overlap into a prescribed configuration of blockades, i.e. parts of the chipthat are beforehand excluded from positioning by for example some other functional component, and holes, i.e. the remaining free area on the chip. A method to minimize the wire length when the free area is a simply connected domain has already been implemented by Magma, but the placement problem becomes much more complex when the free area is not a simply connected domain anymore, forming a ``holey cheese''. One of the approaches of the problem in this case is to first cluster the transistors into so-called macro's in such a way that closely interconnected transistors stay together, and that the macro's can be fit into the holes. One way to carry out the clustering is to use a graph clustering algorithm, the so-called Markov Cluster algorithm. Another way is to combine the placement method of Magma on a rectangular area of the same size as the total size of the holes, and a min cut-max flow algorithm to divide that rectangle into more or less rectangular macro's in such a way that as little wires as possible are cut. It is now possible to formulate the Quadratic Assignment Problem that remains after clustering the original problem to one with 100 up to 1000 macros. There exists a lot of literature on finding the global minimum of the costs, but nowadays computational possibilities are still too restrictive to find an optimal solution within a reasonable amount of time and computational memory. however, we believe it is possible to find a solution that leads to a acceptable local minimum of the costs

Roses are unselfish: a greenhouse growth model to predict harvest rates.

We consider the question of how rose production in a greenhouse can be optimised. Based on realistic assumptions, a rose growth model is derived that can be used to predict the rose harvest. The model is made up of two constituent parts: (i) a local model that calculates the photosynthetic rate per area of leaf and (ii) a global model of the greenhouse that transforms the photosynthesis of the leaves into an increase in mass of the rose crop. The growth rate of the rose stems depends not only on the time-dependent ambient conditions within the greenhouse, which include temperature, relative humidity, CO$_2$ concentration and light intensity, but also on the location and age distribution of the leaves and the form of the underlying rose bush supporting the crop

Pulses in a complex Ginzburg-Landau system: Persistence under coupling with slow diffusion,

Abstract The Ginzburg-Landau (GL) equation is essential for understanding the dynamics of patterns in a wide variety of physical contexts. It governs the evolutions of small amplitude instabilities near criticality. If the instabilities are, however, driven by two coupled instability mechanisms, of which one corresponds with a neutrally stable mode, their evolution is described by a GL equation coupled to a diffusion equation. In this paper, we study the influence of an additional diffusion equation on the existence of pulse solutions in the complex GL equation. In light of recently developed insights into the effect of slow diffusion on the stability of pulses, we consider the case of slow diffusion, i.e., in which the additional diffusion equation acts on a long spatial scale. In previous work [A. Doelman, G. Hek, N. Valkhoff, Stabilization by slow diffusion in a real Ginzburg-Landau system, J. Nonlinear Sci. 14 (2004) 237-278; A. Doelman, G. Hek, N.J.M. Valkhoff, Algebraically decaying pulses in a Ginzburg-Landau system with a neutrally stable mode, Nonlinearity 20 (2007) 357-389], we restricted ourselves to a model with both real coefficients and, more importantly, a real amplitude A rather than the complex-valued A that is needed to completely describe the pattern formation near criticality. In this simpler setting, we proved that pulse solutions of the GL equation can both persist and be stabilized under coupling with a slow diffusion equation. In the current work, we no longer make these restrictions, so that the problem is higher-dimensional and intrinsically harder. By a combination of a geometrical approach and explicit perturbation analysis, we consider the persistence of the solitary pulse solution of the GL equation under coupling with the additional diffusion equation. In the two limiting situations of the nearly real GL equation and the near nonlinear Schrödinger equation, we show that the pulse solutions can indeed persist under this coupling. Keywords: Coupled Ginzburg-Landau equation; Pulse solution; Homoclinic orbi