Space Saving by Dynamic Algebraization

Dynamic programming is widely used for exact computations based on tree decompositions of graphs. However, the space complexity is usually exponential in the treewidth. We study the problem of designing efficient dynamic programming algorithm based on tree decompositions in polynomial space. We show how to construct a tree decomposition and extend the algebraic techniques of Lokshtanov and Nederlof such that the dynamic programming algorithm runs in time $O^*(2^h)$, where $h$ is the maximum number of vertices in the union of bags on the root to leaf paths on a given tree decomposition, which is a parameter closely related to the tree-depth of a graph. We apply our algorithm to the problem of counting perfect matchings on grids and show that it outperforms other polynomial-space solutions. We also apply the algorithm to other set covering and partitioning problems.Comment: 14 pages, 1 figur

Measuring very negative water potentials with polymer tensiometers: principles, performance and applications

In recent years, a polymer tensiometer (POT) was developed and tested to directly measure matric potentials in dry soils. By extending the measurement range to wilting point (a 20-fold increase compared to conventional, water-filled tensiometers), a myriad of previously unapproachable research questions are now open to experimental exploration. Furthermore, the instrument may well allow the development of more water-efficient irrigation strategies by recording water potential rather than soil water content. The principle of the sensor is to fill it with a polymer solution instead of water, thereby building up osmotic pressure inside the sensor. A high-quality ceramic allows the exchange of water with the soil while retaining the polymer. The ceramic has pores sufficiently small to remain saturated even under very negative matric potentials. Installing the sensor in an unsaturated soil causes the high pressure of the polymer solution to drop as the water potentials in the soil and in the POT equilibrate. As long as the pressure inside the polymer chamber remains sufficiently large to prevent cavitation, the sensor will function properly. If the osmotic potential in the polymer chamber can produce a pressure of approximately 2.0 MPa when the sensor is placed in water, proper readings down to wilting point are secured. Various tests in disturbed soil, including an experiment with root water uptake, demonstrate the operation and performance of the new polymer tensiometer and illustrate how processes such as root water uptake can be studied in more detail than before. The paper discusses the available data and explores the long term perspectives offered by the instrument

Stability criteria for a pyramidal shaped asperity ploughing through a plastically deforming substrate

In two body abrasion processes hard asperities plough through a soft surface. If the asperities can resist the forces that act on it, scratches will develop in the soft material. If the asperities cannot withstand these forces, they will break off and not cause direct abrasion damage. The same is the case for galling, where lumps develop on one of the surfaces because of material transfer. These lumps will abrade the counter surface, if the lumps are strong enough to withstand the forces that act on it. In order to describe these phenomena, simple criteria are desired to describe the mechanical stability of asperities and lumps.\ud \ud In this work, an analytical model is presented for the mechanical stability of asperities. In the analysis, a pyramidal asperity shape will be assumed. Given the pyramidal asperity shape, several cases will be studied: the load is carried by a pyramid with a triangular base, a pyramid with a triangular base and an extended backside and the case where a crack has developed. Based on these models stability criteria of ploughing pyramidal asperities will be developed. Important results of the model will be discussed in the context of abrasion and adhesive wear processes

Plasma-based CO2 conversion

The conversion of CO2 to chemicals and consumables is a pioneering approach to utilize undesired CO2 emissions and simultaneously create new products out of sustainable feedstock. Volume 1 gives an introduction to CO2 chemistry, utilisation and sustainability and further discusses its capture and separation. Volume 2 describes several routes to transform CO2 into various compounds by catalytic and electrochemical as well as photo- and plasma induced reactions. The set combines fundamentals of CO2 chemistry, its capture and separation as well transformative reactions. Both volumes are available individually: Vol1: ISBN 978-3-11-056309-2 and Vol2: 978-3-11-066503-1. Both volumes are also included in a set ISBN 978-3-11-066549-9. Vol2, Part VI: Photo- and plasma induced reactions of CO, Chapter 28.</p