Soft Matter
Concepts, Phenomena, and Applications
8. Pattern Formation
The additional material is organized according to book sections and it includes links to (review) papers mentioned in the book, videos of different phenomena we discuss (experiments and simulations), as well as links to online lectures that address certain topics in more details.
8.0 Introductory lectures by Wim van Saarloos on pattern formation
- Lectures on “Non-equilibrium Pattern Formation” by Wim van Saarloos given at the Summer School on Soft Solids and Complex Fluids at UMass Amherst in 2021. These four lectures very much inspired the presentation in chapter 8. Slides are available via the school’s website.
Lecture 1: introduction to pattern formation, keleidoscope of systems, experimental examples, leading to relevant questions.
Lecture 2: patterns arising from instabilities, instability analysis, start with amplitude description.
Lecture 3: amplitude equation description, part II.
Lecture 4: patterns in chemical systems and biology.
8.2 Gearing up for patterns in spatially extended system
Short introductory lecture by Shane Ross on pitchfork and supercritical bifurcations.
From Shane Ross.
A more mathematical lecture on pitchfork bifurcations.
From FacultyofKhan.
Examples of the simulation of the SH equation in two dimensions with symmetry breaking term.
From Richters Finger.
8.3 Rayleigh-Bénard convection and Turing patterns
- On the webpage of Steinberg lab you can find many images of pattern forming systems.
- Some of the images used in the book come from Michael Schatz at Georgia Tech
A lecture by Arup Kumar Das on the derivation of the Boussinesq equations for RB convection. From Convective Heat Transfer.
Simulation of RB convection at high Rayleigh number.
From TurbulenceTeam (left) and Physics of Fluids group Twente (right).
- Transcribed lecture of Alan Turing can be found here.
An introduction to reaction-diffusion Turing models.
From TheShapeofMath.
Lectures by Philip Maini on Turing and developmental pattern formation.
From Kings College Cambridge (left) and University of Edinburgh (right).
- On this website you can play with the Turing models yourself by changing the parameters.
- A talk general talk on emergence and self-organization in biological systems.
8.7 Amplitude equations for oscillatory Type I instabilities
Example of the Belousov Zhabotinsky reaction in a petri dish. From meyavuz.
A whole lecture by Walter Lewin on these concepts. From Lectures by Walter Lewin.
Illustration of the chaotic regime dominated by coherent structures in the 1d CGL; the image moves up in the timewise direction, the horizontal direction is space. From UltraProQQQ.
Simulations of the complex ginzburg landau equation in 2d. Left and right: spatiotemporal chaos; middle: transient chaos.
From Richters Finger (left and middle) and Alex Halavanau.
A short lecture by Hermann Riecke on the 2d CGL.
From Hermann Riecke.
8.10 Excitable media
Simulation showing the behavior of an excitable medium in the core of a spiral.
From HeartKOR Leuven.
Video of the Belousov Zhabotinsky reaction.
From Tim Kench.
A video on recreating the original BZ reaction experiment. From Nile Red.
Problems
Coding Problems
Below you can find links to several coding problems formatted as jupyter notebooks that can be easily opened for example in Google Colaboratory. These notebooks have embedded images. If these do not appear when you open the file, you can use the link from the markdown cell directly in your browser to view them.
1. Swift-Hohenberg equation in 2d Download jupyter notebook
2. Belousov-Zhabotinsky reaction Download jupyter notebook
3. Turing patterns Download jupyter notebook