A Graduate Project Report On Percolation Theory
Mathematics Project Topics
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This project is about the formulation and main theorems of percolation theory. It was introduced by Broadbent and Hamersley as a model for the flow of fluids in porous media and it is primarily concerned with the existence of open paths called open clusters. The project mainly focuses on the bond percolation, which is defined on the d-dimensional lattice. In this project, percolation probability and critical threshold are defined and some basic tools such as the FKG Inequality, the BK Inequality and the Russo’s Formula are mentioned. In addition to this, the uniqueness of the infinite open cluster containing the origin and the exponential decay of the radius of the mean cluster size are also discussed.
Subsurface Intelligence & Critical Mineral Exploration
Modern Geology projects now focus on Machine Learning in Mineral Targeting, Carbon Capture & Storage (CCS) Geologic Modeling, and Critical Mineral Systems (Lithium, REEs). If your research involves Hydrogeological Connectivity, Seismic Inversion, or Geotechnical Site Characterization, ensure your analysis follows the JORC or NI 43-101 reporting standards and utilizes robust 3D Subsurface Visualization and Geochemical Fingerprinting frameworks.
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