Spatiotemporal Evolution of a Landslide: A Transition to Explosive Percolation
Abstract
:1. Introduction
2. Data
3. Methodology
3.1. Algorithm Input and Network Construction
3.2. Algorithm Outputs
4. Results
4.1. Prediction of Location of Failure for B1 and B2
4.2. Identification of Regime Change Point for B1 and B2
4.3. Prediction of Location of Failure for the Mine
4.4. Identification of Regime Change Point for the Mine
5. Discussion
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A. Glossary of Terms
Term | Definition |
---|---|
Physical state space (PSS) | The space defined by the geographical coordinates () of the pixels (grains). |
Network state space (NSS) | The space in which the network is constructed. |
Largest component | The component in the network that consists of the most number of nodes. |
System-spanning component | A component that spans the network (greater than of N). |
Feature state space | The space defined by some feature of the pixels/grains in the system. It is n-dimensional depending on the feature chosen. |
Displacement state space (DSS) | The space defined by the displacement of pixels (grains) in the system. |
Velocity state space (VSS) | The space defined by the velocity of pixels (grains) in the system. |
The minimum distance between a node in one component, and a node in another component, , in a feature state space. | |
The minimum inter-component distance of the component, , which measures the separation of the component in the feature state space. | |
The critical radius or maximum separation across all components in the network. | |
The maximally separated component, i.e., . | |
Regime change point or time of imminent failure. | |
Time of failure or onset of failure regime. | |
or | Similarity of failure pattern across consecutive time states using the same feature state space. The term is used if a secondary similarity measure () is considered. |
Similarity of failure pattern across two feature state spaces, e.g., DSS and VSS, at the same time state. | |
Shared boundary | A collection of pairs of points, one from each of two distinct groups, that are in contact with each other in the physical state space. |
A tuning parameter used to determine the minimum size for a component to be considered. | |
Discontinuous jump | A jump in the order parameter, characterised by the merger of a component to the current largest component in the network. We limit our attention to components that are of size greater than of N. |
Appendix B. Component Sizes
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Singh, K.; Tordesillas, A. Spatiotemporal Evolution of a Landslide: A Transition to Explosive Percolation. Entropy 2020, 22, 67. https://doi.org/10.3390/e22010067
Singh K, Tordesillas A. Spatiotemporal Evolution of a Landslide: A Transition to Explosive Percolation. Entropy. 2020; 22(1):67. https://doi.org/10.3390/e22010067
Chicago/Turabian StyleSingh, Kushwant, and Antoinette Tordesillas. 2020. "Spatiotemporal Evolution of a Landslide: A Transition to Explosive Percolation" Entropy 22, no. 1: 67. https://doi.org/10.3390/e22010067
APA StyleSingh, K., & Tordesillas, A. (2020). Spatiotemporal Evolution of a Landslide: A Transition to Explosive Percolation. Entropy, 22(1), 67. https://doi.org/10.3390/e22010067