• Corpus ID: 250243841

A discrete time evolution model for fracture networks

@inproceedings{Domokos2022ADT,
  title={A discrete time evolution model for fracture networks},
  author={G{\'a}bor Domokos and Krisztina RegHos},
  year={2022}
}
We examine geophysical crack patterns using the mean field theory of convex mosaics. We assign the pair (𝑛 Μ… βˆ— , 𝑣 Μ… βˆ— ) of average corner degrees to each crack pattern and we define two local, random evolutionary steps R 0 and R 1 , corresponding to secondary fracture and rearrangement of cracks, respectively. Random sequences of these steps result in trajectories on the (𝑛 Μ… βˆ— , 𝑣 Μ… βˆ— ) plane. We prove the existence of limit points for several types of trajectories. Also, we prove that… 

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References

SHOWING 1-10 OF 16 REFERENCES

Evolving fracture patterns: columnar joints, mud cracks and polygonal terrain.

  • L. Goehring
  • Materials Science
    Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
  • 2013
TLDR
It is shown how both types of pattern can arise from identical forces, and how a rectilinear crack pattern can evolve towards a hexagonal one.

An automaton for fractal patterns of fragmentation

FRACTURES in the Earth's crust have a fractal structure over a wide range of length scales. A micromechanical model has been proposed1 for the formation of fractal patterns of fragmentation in fault…

Scaling of columnar joints in basalt

[1]Β We describe field work, analysis, and modeling of columnar joints from the Columbia River Basalt Group. This work is focused on the regions around the Grand Coulee, Snake River, and Columbia…

Desiccation Cracks and their Patterns: Formation and Modelling in Science and Nature

The ideal team of authors, combining experimental and theoretical backgrounds, and with experience in both physical and earth sciences, discuss how the study of cracks can lead to the design of…

Plato’s cube and the natural geometry of fragmentation

TLDR
This study uses mechanical and geometric models and the theory of convex mosaics to explain the ubiquity of Plato’s cube in fragmentation and to uniquely map distinct fragment patterns to their formative stress conditions.

On Some Average Properties of Convex Mosaics

Abstract In a convex mosaic in we denote the average number of vertices of a cell by and the average number of cells meeting at a node by Except for the d = 2 planar case, there is no known formula…

Networked configurations as an emergent property of transverse aeolian ridges on Mars

Transverse aeolian ridges – enigmatic Martian features without a proven terrestrial analog – are increasingly important to our understanding of Martian surface processes. However, it is not well…

An updated digital model of plate boundaries

A global set of present plate boundaries on the Earth is presented in digital form. Most come from sources in the literature. A few boundaries are newly interpreted from topography, volcanism, and/or…

Dynamics and stability of evolutionary optimal strategies in duopoly

TLDR
This paper proposes an evolutionary game theory, which is based on the adaption of the company to the behaviour of other players in a duopoly, which shows the changing tendencies towards the companies’ strategies that ensure payoffs above the average in the long run using a replicator dynamics concept.

Tilings and Patterns

"Remarkable...It will surely remain the unique reference in this area for many years to come." Roger Penrose , Nature "...an outstanding achievement in mathematical education." Bulletin of The London…