Pattern Formation

1. Formation of Soft-Matter Quasicrystals

Soft matter crystals  can be analyzed in terms of the interaction potential between two soft-core particles. Such interacting particles form a variety of patterns in the bulk. In addition to forming regular crystalline arrangements, they are also observed to form quasicrystalline patterns – patterns that have rotational symmetry but never repeat in any direction. We investigate the formation and stability of icosahedral quasicrystals using a dynamic phase field crystal model. We identify that appropriate ratio of two length scales and strong resonanting nonlinear interactions between them are the required conditions to make quasicrystalline patterns.


 – Alastair Rucklidge

 – Andrew J. Archer

 – Edgar Knobloch

Relevant Publications:

8. Three-dimensional Phase Field Quasicrystals, Physical Review Letters, 117, 075501, 2016.

9. Spatially Localized Quasicrystals, submitted for review to Physical Review Letters, 2017.

Public Outreach:

– Demonstrator for never-repeating patterns at the Big Draw 2016 Festival at the Royal Society, London on October 22nd, 2016.

Talk at the Leeds Cafe Scientifique on 13th December 2016.

2. Localization & Pattern Formation in Fluid Flows

Turbulence transition in shear flows is initiated by patches of turbulence that invade the surrounding laminar flow. Spatially localized exact invariant solutions for di fferent shear flow systems can be obtained efficiently using numerical continuation methods. Dynamically, the occurrence of such spatially localized states can be explained by homoclinic snaking behavior observed in Swift-Hohenberg equation, plane Couette flow, etc.

Emergence of spatio-temporal patterns in systems with linear instability can be eff ectively analyzed with tools such as amplitude equations. We aim to exploit this feature by selecting the inclined layer convection (ILC) system for analysis. A rich variety of patterns are observed in an ILC system where there is a smooth change from a linearly unstable (buoyancy-driven instabilities) to a linearly stable (shear-driven instabilities) system with variation of the inclination angle. Full DNS simulations of Oberbeck-Boussinesq equations allow us to quantitatively compare di fferent patterns between our numerical simulations and experimental results (see Publication 7). Exact solutions obtained from simulations for small inclinations can then be numerically continued smoothly into shear-dominated regimes.


 – Werner Pesch

 – Tobias M. Schneider

 – Karen M. Daniels

 – Eberhard Bodenschatz

 – Florian Reetz (nee Sprung)

Relevant Publications:

7. Spatiotemporal patterns in inclined layer convection, Journal of Fluid Mechanics, 794, 719-745, 2016.

Public Outreach:

– Talk at the Superposition on 13th April 2016 with title ‘Patterns in Inclined Layer Convection’