Related Experiment Video
Updated: Mar 7, 2026
08:02
Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography
Published on: February 25, 2015
13.1K
Universality and asymptotic scaling in drilling percolation
1JSC, FZ Jülich, D-52425 Jülich, Germany.
Physical Review. E
|February 18, 2017
Summary
This study simulates a 3D percolation model with cylinders, confirming prior findings but suggesting results may not yet reflect true asymptotic behavior in percolation theory.
Area of Science:
- Physics
- Statistical Mechanics
- Materials Science
Background:
- Bernoulli percolation models are fundamental in statistical mechanics.
- Previous studies explored 3D percolation with anisotropic obstacles.
Purpose of the Study:
- To simulate a 3D percolation model with randomly oriented cylinders.
- To verify and extend previous findings using a more efficient algorithm.
- To investigate the asymptotic behavior of the percolation model.
Main Methods:
- Utilizing a new, efficient algorithm for three-dimensional simulations.
- Employing larger system sizes and higher statistical sampling.
- Comparing simulation results with prior theoretical and numerical studies.
Main Results:
- Most previously reported results were confirmed.
- Indications suggest that the current results may not yet represent true asymptotic behavior.
- The model involves replacing isotropic holes with axis-aligned cylinders.
Conclusions:
- The efficient algorithm allows for larger-scale simulations of this percolation model.
- Further simulations are needed to reach the true asymptotic regime.
- The study opens avenues for exploring generalizations of the model.
Related Concept Videos
01:09The Buckingham Pi Theorem
1.7K
The Buckingham Pi theorem provides a structured method to simplify fluid dynamics problems by reducing complex systems of variables to dimensionless terms.
1.7K
01:25Ostwald’s Dilution Law
36
Consider a binary electrolyte AB with a concentration ‘c’ that reversibly dissociates into its constituent ions. The degree of this dissociation is represented by ⍺. This means that the equilibrium concentration of each ionic species can be expressed as ⍺c. As well as this, the fraction of the electrolyte that remains undissociated at equilibrium is given by (1−⍺). The corresponding equilibrium concentration for this undissociated portion is then calculated...
36
01:06Divergence and Stokes' Theorems
4.0K
The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...
4.0K
01:12Theorems of Pappus and Guldinus: Problem Solving
1.1K
Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a...
1.1K
01:23Pore Size Distribution
534
In concrete, the pore size distribution significantly influences the material's properties. Capillary pores, markedly larger than gel pores, form a vast network within partially hydrated cement paste, reducing the concrete's strength and increasing its permeability. This heightened permeability leads to a greater risk of damage from environmental factors like freeze-thaw cycles and chemical attacks, with the extent of vulnerability also being tied to the water-to-cement ratio.
Adequate...
Adequate...
534
01:29Improper Integrals: Infinite Intervals
173
An integral is classified as improper due to an infinite interval when at least one of its limits of integration extends to positive or negative infinity. In such cases, the region under the curve is unbounded, and standard techniques for evaluating definite integrals are not directly applicable. Instead, the improper integral is defined through a limiting process that allows one to determine whether the accumulated area remains finite despite the infinite domain.Application to Exponential...
173