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Invasion percolation with long-range correlations: first-order phase transition and nonuniversal scaling properties
1Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT, Australia.
Summary
We simulated invasion percolation with trapping (TIP) and long-range correlations. The backbone structure and fractal dimensions differ significantly between site and bond TIP, revealing distinct universality classes.
Area of Science:
- Physics
- Geophysics
- Complex Systems
Background:
- Multiphase flow in porous media and rock fractures is crucial for resource extraction and environmental studies.
- Invasion percolation with trapping (TIP) models fluid flow, but long-range correlations require advanced simulation techniques.
- Understanding the geometry of flow paths, particularly the backbone and trapped clusters, is key to predicting macroscopic behavior.
Purpose of the Study:
- To investigate the impact of long-range correlations on the invasion percolation model with trapping (TIP).
- To characterize the fractal properties of the sample-spanning cluster (SSC), minimal paths, and backbones for both site and bond TIP.
- To identify universality classes of TIP with long-range correlations based on simulation results.
Main Methods:
- Extensive Monte Carlo simulations of the TIP model with long-range correlations generated by fractional Brownian motion (Hurst exponent H).
- Development and application of a highly efficient TIP simulation algorithm.
- Implementation of a novel method for identifying the backbone of TIP clusters, distinguishing between site and bond TIP.
Main Results:
- The backbone of bond TIP is loopless and structurally distinct from site TIP.
- Precise estimates for fractal dimensions of the SSC, minimal paths, and backbones were obtained for both site and bond TIP.
- For site TIP, H > 1/2 leads to compact SSC and backbone (first-order transition), while H < 1/2 results in fractal structures dependent on H.
- The fractal dimension of the bond TIP backbone is significantly lower than that of site TIP for all H.
Conclusions:
- TIP with long-range correlations exhibits distinct behaviors and universality classes depending on the Hurst exponent H and whether site or bond percolation is considered.
- The structural differences in backbones highlight the importance of considering percolation type in modeling flow in porous media.
- The findings provide a deeper understanding of multiphase flow dynamics in natural systems like oil reservoirs and aquifers.