The phase-field-crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field-crystal dynamics can be derived from the microscopic Smoluchowski equation via dynamical density-functional theory. The different underlying approximations are discussed. In particular, a variant of the phase-field-crystal model is proposed which involves less approximations than the standard phase-field-crystal model. We finally test the validity of these phase-field-crystal models against dynamical density-functional theory. In particular, the velocities of a linear crystal front from the undercooled melt are compared as a function of the undercooling for a two-dimensional colloidal suspension of parallel dipoles. Good agreement is only obtained by a drastic scaling of the free energies in the phase-field-crystal model in order to match the bulk freezing transition point.

Abstract. We extend previous work and present a general approach for solving partial differential equations in complex, stationary, or moving geometries with Dirichlet, Neumann, and Robin boundary conditions. Using an implicit representation of the geometry through an auxilliary phase field function, which replaces the sharp boundary of the domain with a diffuse layer (e.g. diffuse domain), the equation is reformulated on a larger regular domain. The resulting partial differential equation is of the same order as the original equation, with additional lower order terms to approximate the boundary conditions. The reformulated equation can be solved by standard numerical techniques. We use the method of matched asymptotic expansions to show that solutions of the reformulated equations converge to those of the original equations. We provide numerical simulations which confirm this analysis. We also present applications of the method to growing domains and complex three-dimensional structures and we discuss applications to cell biology and heteroepitaxy.Key words. Partial differential equations, phase field approximation, complex geometry, diffuse interface, adaptive finite element methods, adaptive finite difference methods, multigrid methods.

We present a new phase-field model for strongly anisotropic crystal and epitaxial growth using regularized, anisotropic Cahn–Hilliard-type equations. Such problems arise during the growth and coarsening of thin films. When the anisotropic surface energy is sufficiently strong, sharp corners form and unregularized anisotropic Cahn–Hilliard equations become ill-posed. Our models contain a high-order Willmore regularization, where the square of the mean curvature is added to the energy, to remove the ill-posedness. The regularized equations are sixth order in space. A key feature of our approach is the development of a new formulation in which the interface thickness is independent of crystallographic orientation. Using the method of matched asymptotic expansions, we show the convergence of our phase-field model to the general sharp-interface model. We present two- and three-dimensional numerical results using an adaptive, nonlinear multigrid finite-difference method. We find excellent agreement between the dynamics of the new phase-field model and the sharp-interface model. The computed equilibrium shapes using the new model also match a recently developed analytical sharp-interface theory that describes the rounding of the sharp corners by the Willmore regularization.

Springtails (Collembola) are wingless arthropods adapted to cutaneous respiration in temporarily rain-flooded habitats. They immediately form a plastron, protecting them against suffocation upon immersion into water and even low-surface-tension liquids such as alkanes. Recent experimental studies revealed a high-pressure resistance of such plastrons against collapse. In this work, skin sections of Orthonychiurus stachianus are studied by transmission electron microscopy. The micrographs reveal cavity side-wall profiles with characteristic overhangs. These were fitted by polynomials to allow access for analytical and numerical calculations of the breakthrough pressure, that is, the barrier against plastron collapse. Furthermore, model profiles with well-defined geometries were used to set the obtained results into context and to develop a general design principle for the most robust surface structures. Our results indicate the decisive role of the sectional profile of overhanging structures to form a robust heterogeneous wetting state for low-surface-tension liquids that enables the omniphobicity. Furthermore, the design principles of mushroom and serif T structures pave the way for omniphobic surfaces with a high-pressure resistance irrespective of solid surface chemistry.

Recent advances in cell biology enable precise molecular perturbations. The spatiotemporal organization of cells and organisms, however, also depends on physical processes such as diffusion or cytoplasmic flows, and strategies to perturb physical transport inside cells are not yet available. Here, we demonstrate focused-light-induced cytoplasmic streaming (FLUCS). FLUCS is local, directional, dynamic, probe-free, physiological, and is even applicable through rigid egg shells or cell walls. We explain FLUCS via time-dependent modelling of thermoviscous flows. Using FLUCS, we demonstrate that cytoplasmic flows drive partitioning-defective protein (PAR) polarization in Caenorhabditis elegans zygotes, and that cortical flows are sufficient to transport PAR domains and invert PAR polarity. In addition, we find that asymmetric cell division is a binary decision based on gradually varying PAR polarization states. Furthermore, the use of FLUCS for active microrheology revealed a metabolically induced fluid-to-solid transition of the yeast cytoplasm. Our findings establish how a wide range of transport-dependent models of cellular organization become testable by FLUCS.