Formation and Spatial Localization of Phase Field Quasicrystals

The event is taking part on the Tuesday, Jun 13th 2017 at 15.30
Theme/s: Pure and Applied Colloquia
Location of Event: Room 306, Alan Turing
This event is a: Public Seminar

The dynamics of many physical systems often evolve to asymptotic states that exhibit spatial and temporal variations in their properties such as density, temperature, etc. Regular patterns such as graph paper and honeycombs look the same when moved by a basic unit and/or rotated by certain special angles. They possess both translational and rotational symmetries giving rise to discrete spatial Fourier transforms. In contrast, an aperiodic crystal displays long range order but no periodicity. Such quasicrystals lack the lattice symmetries of regular crystals, yet have discrete Fourier spectra. We look to understand the minimal mechanism which promotes the formation of such quasicrystalline structures arising in diverse soft matter systems such as dendritic-, star-, and block co-polymers using a phase field crystal model. Direct numerical simulations combined with weakly nonlinear analysis highlight the parameter values where the quasicrystals are the global minimum energy state and help determine the phase diagram. By locating parameter values where multiple patterned states possess the same free energy (Maxwell points), we obtain states where a patch of one type of pattern (for example, a quasicrystal) is present in the background of another (for example, the homogeneous liquid state). In a bifurcation diagram such localized states fall on solution branches that undergo homoclinic snaking and they can be obtained through numerical continuation.

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External Speakers

Priya Subramanian (University of Leeds)