Related Experiment Video
Updated: May 3, 2026

Analyzing Dendritic Morphology in Columns and Layers
Published on: March 23, 2017
Hierarchical coarse-graining transform
Vera Pancaldi1, Peter R King, Kim Christensen
1Earth Science & Engineering, Imperial College London, Prince Consort Road, London SW7 2BP, United Kingdom. vera.pancaldi00@imperial.ac.uk
Abstract:
We present a hierarchical transform that can be applied to Laplace-like differential equations such as Darcy's equation for single-phase flow in a porous medium. A finite-difference discretization scheme is used to set the equation in the form of an eigenvalue problem. Within the formalism suggested, the pressure field is decomposed into an average value and fluctuations of different kinds and at different scales. The application of the transform to the equation allows us to calculate the unknown pressure with a varying level of detail. A procedure is suggested to localize important features in the pressure field based only on the fine-scale permeability, and hence we develop a form of adaptive coarse graining. The formalism and method are described and demonstrated using two synthetic toy problems.
More Related Videos
09:00Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography
Published on: September 29, 2019
09:19Measuring the Structure, Composition, and Change of Underwater Environments with Large-area Imaging
Published on: April 18, 2025
Related Concept Videos
Computed Tomography
The technique was invented in the 1970s and is based on the principle that as X-rays pass through the body, they are absorbed or reflected at different levels. In the technique, a patient lies on a motorized platform while a computerized axial tomography (CAT) scanner rotates...
Transformation of Plane Strain
Under plane strain conditions, typical for members where one dimension significantly exceeds the others, deformations and resultant strains are...
Shape and Texture of Coarse Aggregate
Types of Aggregate Grading
Well-graded aggregates include a complete range of necessary size fractions that fit together to create a dense matrix with minimal voids, represented by a smooth, continuous gradation curve. This type of grading ensures good...
Design Example: Aggregate Gradation
The grading, or particle-size distribution, of sand is determined using sieve analysis, with standard sizes ranging from 150 μm to 10 mm (ASTM No. 100 sieve to 3⁄8 in. sieve). Sand is...
Methods of Obtaining Topography