Criticality and pattern formation in fracture by residual stresses

A Quantitative Graph-Based Approach to Monitoring Ice-Wedge Trough Dynamics in Polygonal Permafrost Landscapes

In response to increasing Arctic temperatures, ice-rich permafrost landscapes are undergoing rapid changes. In permafrost lowlands, polygonal ice wedges are especially prone to degradation. Melting of ice wedges results in deepening troughs and the transition from low-centered to high-centered ice-wedge polygons. This process has important implications for surface hydrology, as the connectivity of such troughs determines the rate of drainage for these lowland landscapes. In this study, we present a comprehensive, modular, and highly automated workflow to extract, to represent, and to analyze remotely sensed ice-wedge polygonal trough networks as a graph (i.e., network structure). With computer vision methods, we efficiently extract the trough locations as well as their geomorphometric information on trough depth and width from high-resolution digital elevation models and link these data within the graph. Further, we present and discuss the benefits of graph analysis algorithms for characterizing the erosional development of such thaw-affected landscapes. Based on our graph analysis, we show how thaw subsidence has progressed between 2009 and 2019 following burning at the Anaktuvuk River fire scar in northern Alaska, USA. We observed a considerable increase in the number of discernible troughs within the study area, while simultaneously the number of disconnected networks decreased from 54 small networks in 2009 to only six considerably larger disconnected networks in 2019. On average, the width of the troughs has increased by 13.86%, while the average depth has slightly decreased by 10.31%. Overall, our new automated approach allows for monitoring ice-wedge dynamics in unprecedented spatial detail, while simultaneously reducing the data to quantifiable geometric measures and spatial relationships.

Universal scaling of polygonal desiccation crack patterns

Polygonal desiccation crack patterns are commonly observed in natural systems. Despite their quotidian nature, it is unclear whether similar crack patterns which span orders of magnitude in length scales share the same underlying physics. In thin films, the characteristic length of polygonal cracks is known to monotonically increase with the film thickness; however, existing theories that consider the mechanical, thermodynamic, hydrodynamic, and statistical properties of cracking often lead to contradictory predictions. Here we experimentally investigate polygonal cracks in drying suspensions of micron-sized particles by varying film thickness, boundary adhesion, packing fraction, and solvent. Although polygonal cracks were observed in most systems above a critical film thickness, in cornstarch-water mixtures, multiscale crack patterns were observed due to two distinct desiccation mechanisms. Large-scale, primary polygons initially form due to capillary-induced film shrinkage, whereas small-scale, secondary polygons appear later due to the deswelling of the hygroscopic particles. In addition, we find that the characteristic area of the polygonal cracks, A_{p}, obeys a universal power law, A_{p}=αh^{4/3}, where h is the film thickness. By quantitatively linking α with the material properties during crack formation, we provide a robust framework for understanding multiscale polygonal crack patterns from microscopic to geologic scales.

Spring-block model reveals region-like structures

A mechanical spring-block model is used for realizing an objective space partition of settlements from a geographic territory in region-like structures. The method is based on the relaxation-dynamics of the spring-block system and reveals in a hierarchical manner region-like entities at different spatial scales. It takes into account in an elegant manner both the spatiality of the elements and the connectivity relations among them. Spatiality is taken into account by using the geographic coordinates of the settlements, and by detecting the neighbors with the help of a Delaunay triangulation. Connectivity between neighboring settlements are quantified using a Pearson-like correlation for the relative variation of a relevant socio-economic parameter (population size, GDP, tax payed per inhabitant, etc.). The method is implemented in an interactive JAVA application and it is applied with success for an artificially generated society and for the case of USA, Hungary and Transylvania.