A Program for Fractal and Multifractal Analysis of Two-Dimensional Binary Images. Computer Algorithms versus Mathematical Theory.

In this paper we present a tool to carry out the multifractal analysis of binary, two-dimensional images through the calculation of the Rényi D(q) dimensions and associated statistical regressions. The estimation of a (mono)fractal dimension corresponds to the special case where the moment order is q = 0

Multifractal analysis of the pore- and solid-phases in binary two-dimensional images of natural porous structures

We use multifractal analysis (MFA) to investigate how the Rényi dimensions of the solid mass and the pore space in porous structures are related to each other. To our knowledge, there is no investigation about the relationship of Rényi or generalized dimensions of two phases of the same structure

Biocolloid retention in partially saturated soils

Unsaturated soils are considered excellent filters for preventing the transport of pathogenic biocolloids to groundwater, but little is known about the actual mechanisms of biocolloid retention. To obtain a better understanding of these processes, a number of visualization experiments were performed and analyzed

Twenty-three unsolved problems in hydrology (UPH) – a community perspective

This paper is the outcome of a community initiative to identify major unsolved scientific problems in hydrology motivated by a need for stronger harmonisation of research efforts. The procedure involved a public consultation through on-line media, followed by two workshops through which a large number of potential science questions were collated, prioritised, and synthesised. In spite of the diversity of the participants (230 scientists in total), the process revealed much about community priorities and the state of our science: a preference for continuity in research questions rather than radical departures or redirections from past and current work. Questions remain focussed on process-based understanding of hydrological variability and causality at all space and time scales. Increased attention to environmental change drives a new emphasis on understanding how change propagates across interfaces within the hydrological system and across disciplinary boundaries. In particular, the expansion of the human footprint raises a new set of questions related to human interactions with nature and water cycle feedbacks in the context of complex water management problems. We hope that this reflection and synthesis of the 23 unsolved problems in hydrology will help guide research efforts for some years to come

Digital image analysis for measuring fractal properties of soil structure

Ein Boden besteht, vereinfacht betrachtet, aus Festsubstanz (Mineralkörnern) und Poren. Die Poren können mit Wasser oder Luft gefüllt sein und bilden ein hochgradig vernetztes System, das für Transportprozesse von großer Bedeutung ist. Diese Struktur kann innerhalb natürlicher Grenzen als selbstähnlich angesehen und ihre Dimension gemessen werden. Für die vorliegende Arbeit wurden Dünnschliffe aus dem Bt-Horizont einer Parabraunerde präpariert. Von ihnen wurden licht- und rasterelektronenmikroskopische Aufnahmen mit unterschiedlichen Vergrößerungen und Auflösungen angefertigt. Die bildanalytischen Messungen wurden mit dem System KS400 (ZeissVision), das die Entwicklung von benutzerdefinierten Anwendungen erlaubt, durchgeführt. An digitalen Bildern wurde die fraktale Dimension (DS) der Grenzlinie zwischen Poren und Matrix mit dem Boxcounting- und dem Dilatations-Verfahren gemessen. Die fraktale Dimension einer Linie, gemessen in einer Fläche, entspricht 1<DS<2. Je höher die Werte, desto höher ist die Komplexität des Bildes. Die beobachteten Werte sind sehr hoch und erreichen mit bis zu DS =1.935 fast die Euklidische Dimension 2. Mit zunehmender Vergrößerung bzw. feinerer Auflösung nimmt DS bis zu DS =1.563 ab. Dieses Ergebnis kann als der Unterschied zwischen Textur und Struktur angesehen werden. Die Anpassung von zwei Geraden im log-log Plot des kombinierten Daten-Pools aller Vergrößerungsstufen ergibt einen Schnittpunkt zwischen 5 und 17 µm Größe des Strukturelements. Dies entspricht den Porendurchmessern, die aus der Hauptkörnungsart Grobschluff (20-63 µm) abgeleitet werden können. Die Porengrößenverteilung (PGV) wurde mit dem morphologischen Opening-Verfahren gemessen. Sie wurde von 0.1-1000 µm erfasst und zeigt ein Maximum bei rund 1 µm Durchmesser. Von Parallelproben des gleichen Bodenhorizonts wurden im Labor Retentions- und Leitfähigkeitskurven aufgenommen und die Phasenanteile bestimmt. Die kumulierte PGV wurde mit der am selben Bodenhorizont erhobenen Retentionskurve verglichen. Für Poren kleiner als 20 µm zeigt die Retentionskurve eine deutliche Abweichung, indem sie höhere Anteile an Fein- und Mittelporen wiederspiegelt. Mögliche Ursachen für dieses Verhalten werden diskutiert, wie auch die Relevanz der bildanalytisch gemessenen Dimension für die Anpassungsparameter der Retentionskurve

Estimating the Permeability of Naturally Structured Soil From Percolation Theory and Pore Space Characteristics Imaged by X-Ray

The saturated hydraulic conductivity of soil, Ks, is a critical parameter in hydrological models that remains notoriously difficult to predict. In this study, we test the capability of a model based on percolation theory and critical path analysis to estimate Ks measured on 95 undisturbed soil cores collected from contrasting soil types. One parameter (the pore geometry factor) was derived by model fitting, while the remaining two parameters (the critical pore diameter, dc, and the effective porosity) were derived from X‐ray computed tomography measurements. The model gave a highly significant fit to the Ks measurements (p < 0.0001) although only ~47% of the variation was explained and the fitted pore geometry factor was approximately 1 to 2 orders of magnitude larger than various theoretical values obtained for idealized porous media and pore network models. Apart from assumptions in the model that might not hold in reality, this could also be attributed to experimental error induced by, for example, air entrapment and changes in the soil pore structure occurring during sample presaturation and the measurement of Ks. Variation in the critical pore diameter, dc, was the dominant source of variation in Ks, which suggests that dc is a suitable length scale for predicting soil permeability. Thus, from the point of view of pedotransfer functions, it could be worthwhile to direct future research toward exploring the correlations of dc with basic soil properties and site attributes.publishedVersio

Membrane Surface-Associated Helices Promote Lipid Interactions and Cellular Uptake of Human Calcitonin-Derived Cell Penetrating Peptides

hCT(9-32) is a human calcitonin (hCT)-derived cell-penetrating peptide that has been shown to translocate the plasma membrane of mammalian cells. It has been suggested as a cellular carrier for drugs, green fluorescent protein, and plasmid DNA. Because of its temperature-dependent cellular translocation resulting in punctuated cytoplasmatic distribution, its uptake is likely to follow an endocytic pathway. To gain insight into the molecular orientation of hCT(9-32) when interacting with lipid models, and to learn more about its mode of action, various biophysical techniques from liposome partitioning to high-resolution NMR spectroscopy were utilized. Moreover, to establish the role of individual residues for the topology of its association with the lipid membrane, two mutants of hCT(9-32), i.e., W30-hCT(9-32) and A23-hCT(9-32), were also investigated. Although unstructured in aqueous solution, hCT(9-32) adopted two short helical stretches when bound to dodecylphosphocholine micelles, extending from Thr(10) to Asn(17) and from Gln(24) to Val(29). A23-hCT(9-32), in which the helix-breaking Pro(23) was replaced by Ala, displayed a continuous α-helix extending from residue 12 to 26. Probing with the spin label 5-doxylstearate revealed that association with dodecylphosphocholine micelles was such that the helix engaged in parallel orientation to the micelle surface. Moreover, the Gly to Trp exchange in W30-hCT(9-32) resulted in a more stable anchoring of the C-terminal segment close to the interface, as reflected by a twofold increase in the partition coefficient in liposomes. Interestingly, tighter binding to model membranes was associated with an increase in the in vitro uptake in human cervix epithelial andenocarcinoma cell line cells. Liposome leakage studies excluded pore formation, and the punctuated fluorescence pattern of internalized peptide indicated vesicular localization and, in conclusion, strongly suggested an endocytic pathway of translocation