Related Experiment Video
Updated: Feb 15, 2026
13:18
Understanding Cerebellar Pattern Formation
Published on: November 1, 2007
5.5K
Formation and evolution of target patterns in Cahn-Hilliard flows.
Xiang Fan1, P H Diamond1, L Chacón2
1Department of Physics, University of California at San Diego, La Jolla, California 92093, USA.
Physical Review. E
|January 20, 2018
Summary
This study reveals three stages of scalar mixing in a 2D Cahn-Hilliard system, leading to a metastable target pattern. This pattern exhibits concentric bands aligned with streamlines, crucial for understanding fluid dynamics.
Area of Science:
- Fluid Dynamics
- Materials Science
- Statistical Mechanics
Background:
- Investigates scalar mixing processes in two-dimensional (2D) systems.
- Extends classic studies on flux expulsion in 2D magnetohydrodynamics.
- Builds upon research into homogenization of potential vorticity in 2D fluids.
Purpose of the Study:
- To analyze the evolution of concentration fields within a single eddy.
- To elucidate scalar mixing mechanisms in the 2D Cahn-Hilliard system.
- To understand pattern formation and long-term dynamics.
Main Methods:
- Numerical simulations of the 2D Cahn-Hilliard equation.
- Analysis of concentration field evolution over time.
- Observation of isoconcentration contour topology changes.
Main Results:
- Identified three distinct evolutionary stages: 'jelly roll,' topological change, and 'target pattern.'
- Observed that in the target pattern stage, isoconcentration bands align with streamlines.
- Determined the target pattern to be a metastable state with exponentially long band merger timescales.
Conclusions:
- The Cahn-Hilliard system exhibits complex pattern evolution during scalar mixing.
- The target pattern represents a metastable state in this system.
- Long-time evolution shows similarities to step merger phenomena in other fluid systems.
More Related Videos
Related Concept Videos
02:55The Evidence for Evolution
48.5K
Genetic variations accumulating within populations over generations give rise to biological evolution. Evolutionary changes can result in the formation of novel varieties and entire new species. These changes are responsible for the diverse forms of life inhabiting the planet. The evidence for evolution suggests that all living organisms descended from common ancestors.
48.5K
01:54Convergent Evolution
33.1K
Evolution shapes the features of organisms over time, ensuring that they are suited for the environments in which they live. Sometimes, selection pressure leads to the rise of similar but unrelated adaptations in organisms with no recent common ancestors, a process known as convergent evolution.
33.1K
01:24Eukaryotic Evolution
42.5K
The endosymbiont theory is the most widely accepted theory of eukaryotic evolution; however, its progression is still somewhat debated. According to the nucleus-first hypothesis, the ancestral prokaryote first evolved a membrane to enclose DNA and form the nucleus. Conversely, the mitochondria-first hypothesis suggests that the nucleus was formed after endosymbiosis of mitochondria.
Contrary to the endosymbiont theory, the eukaryote-first hypothesis proposes that the simpler prokaryotic and...
Contrary to the endosymbiont theory, the eukaryote-first hypothesis proposes that the simpler prokaryotic and...
42.5K
02:31Synteny and Evolution
3.8K
John H. Renwick first coined the term “synteny” in 1971, which refers to the genes present on the same chromosomes, even if they are not genetically linked. The species with common ancestry tend to show conserved syntenic regions. Therefore, the concept of synteny is nowadays used to describe the evolutionary relationship between species.
Around 80 million years ago, the human and mice lineages diverged from the common ancestor. During the course of evolution, the ancestral...
Around 80 million years ago, the human and mice lineages diverged from the common ancestor. During the course of evolution, the ancestral...
3.8K
02:39Gene Flow
38.1K
Gene flow is the transfer of genes among populations, resulting from either the dispersal of gametes or from the migration of individuals.
38.1K
01:31Formation of Species
45.5K
Speciation describes the formation of one or more new species from one or sometimes multiple original species. The resulting species are discrete from the parent species, and barriers to reproduction will typically exist. There are two primary mechanisms, speciation with and without geographic isolation—allopatric and sympatric speciation, respectively.
45.5K