Chapter 1 Introduction

Pattern Formation and Dynamics in Nonequilibrium Systems

Figures (some with related videos) in PNG and EPS formats:

• Fig-1.1-rayleigh-benard-convection   png   eps

• Fig-1.2-buoyancy-forces   png   eps

• Fig-1.3-2dF-galaxy-survey   png   eps
  This figure was obtained from this image. Many other related images, including fly-through animations, are available at the 2dF Galaxy Redshift Survey home page.

• Fig-1.4-m74-galaxy   png   eps
  This figure of the M74 spiral galaxy, was based on this image.

• Fig-1.5-surface-of-sun   png   eps
  The granulated surface structure of the Sun is even more apparent in this image. Other images and animations of the Sun's surface can be found on the SOHO (Solar and Heliospheric Observatory) website.

• Fig-1.6-jupiter   png   eps
  The Astronomy Picture of the Day has this better picture of Jupiter (take by the Hubble Space telescope) and this nice picture of the Great Red Spot. A sense of the dynamics can be obtained from this movie from the CICLOPS website (Cassini Imaging Central Laboratory for Operations).

• Fig-1.7-sand-dunes   png   eps

• Fig-1.8-three-snowflakes   png   eps
  Many other wonderful snowflake images can be found on Kenneth Libbrecht's website SnowCrystals.com.

• Fig-1.9-slime-mold-aggregation   png   eps
  This figure was taken from this movie (8 MB AVI file) of the aggregation of a starving slime mold (Dictyostelium discoideum), by Professor Florian Siegert .

• Fig-1.10-surface-potential-fibrillating-heart   png   eps
  The Virtual Heart webpage by Flavio Fenton and Elizabeth Cherry has related visualizations of experimental data and simulations related to cardiac dynamics. For example, on this webpage, click on the "Movies" icon in the left vertical column, then click on the "Experimental" tab near the top of the Movies page, then click on "Optical mapping in tissue" to observe electrical waves in cardiac tissue as revealed by a voltage sensitive dye.

• Fig-1.11-examples-of-Taylor-Couette-flow   png   eps
  YouTube has several videos of Taylor-Couette flow that complement Figures 1.11 and 1.12 in the book:
  • Onset of the stripe state from the uniform state, a nice example of a type-Is instability of a uniform state.
  • Wavy vortex flow, a periodic spatial state that arises from a Hopf bifurcation of the stripe state (Taylor vortex flow).

• Fig-1.12-Taylor-Couette-phase-diagram   png   eps

• Fig-1.13-shadowgraphy-method-for-convection-pattern   png   eps

• Fig-1.14-three-convection-patterns   png   eps

• Fig-1.15-spiral-defect-chaos-and-domain-chaos   png   eps
  The corresponding dynamics can be observed in this Spiral defect chaos movie (20 MB AVI file), see the information given in the description of the back cover figure. You can compare this simulation with this brief Youtube video, which shows spiral defect chaos from the first experiment to discover this phenomenon. The paper by Professor Stephen Morris and collaborators that describes the discovery of spiral defect chaos can be downloaded here.

  The dynamics of domain chaos can be observed from this simulation (13 MB AVI file) by Professor Janet Scheel. This calculation had the following parameters: aspect ratio Γ=40, Prandtl number σ=0.93, rotational Reynolds number (dimensionless rotation rate) Ω=40, Rayleigh number R=2400, conducting lateral boundaries, a time step Δt=0.005 t_v, spatial resolution Δx=0.11 measured in units of the depth of the fluid. Successive frames are separated by one vertical diffusion time t_v.

• Fig-1.16-three-fluid-crispation-patterns   png   eps

• Fig-1.17-six-granular-crispation-patterns   png   eps

  See this YouTube video of an hexagonal granular crispation pattern.

• Fig-1.18-three-chemical-patterns   png   eps
  There are several videos of experimental reaction-diffusion patterns available through YouTube, for example these two videos
  • pattern of targets (propagating circular waves). There is likely an impurity such as a dust particle at the center of each target wave, which initiates wave formation. Note how waves from different targets collide, they annihilate one another, a nonlinear phenomenon.
  • pair of spirals.
  of the Belousov-Zhabotinsky reaction which has excitable dynamics. Searching YouTube for "reaction diffusion" will bring up many computer simulations of reaction-diffusion systems, with many interesting patterns: labyrinthine patterns, spiral dynamics, self-replicating spots, and so on.

• Fig-1.19-thermosyphon-vs-convection-system   png   eps

• Fig-1.20-N-R-Gamma-space-of-nonequilibrium-systems   png   eps

• Fig-1.21-4000-dots   png   eps

• Fig-1.22-bottom-convection-plate-with-bump   png   eps