Related papers: Dendrites with corners
A continuum density-field formulation with particle-scale resolution is constructed to simultaneously incorporate the orientation dependence of interparticle interactions and the rotational invariance of the system, a fundamental but…
We apply a simple dynamical density functional theory, the phase-field crystal (PFC) model of overdamped conservative dynamics, to address polymorphism, crystal nucleation, and crystal growth in the diffusion-controlled limit. We refine the…
Dendrites are one of the most widely observed patterns in nature and occur across a wide spectrum of physical phenomena. In solidification and growth patterns in metals and crystals, the multi-level branching structures of dendrites pose a…
The anisotropic phase-field crystal model recently proposed and used by Prieler et al. [J. Phys.: Condens. Matter 21, 464110 (2009)] is derived from microscopic density functional theory for anisotropic particles with fixed orientation.…
Polar ice develops anisotropic crystal orientation fabrics under deformation, yet ice is most often modelled as an isotropic fluid. We present three-dimensional simulations of the crystal orientation fabric of Derwael Ice Rise including the…
Extending previous work [T. Pusztai, L. R\'atkai, A. Sz\'all\'as, and L. Gr\'an\'asy, Phys. Rev. E {\bf 87}, 032402 (2013)], we have studied the formation of eutectic dendrites in a model ternary system within the framework of the…
Dendritic growth patterns exhibiting four-fold anisotropy are observed when polyethylene oxide undergoes phase segregation from a solution phase to a solid phase. When this phase transition occurs on a substrate that has patterns of…
We develop a description of diffusion limited growth in solid-solid transformations, which are strongly influenced by elastic effects. Density differences and structural transformations provoke stresses at interfaces, which affect the phase…
We have studied the conformational and scaling behaviors of a flexible dendrimer immersed in athermal or good solvents. A self-consistent field theory combined with a pre-averaged excluded volume potential representing the two-body…
We extend the phase-field approach to model the solidification of faceted materials. Our approach consists of using an approximate gamma-plot with rounded cusps that can approach arbitrarily closely the true gamma-plot with sharp cusps that…
We study the evolution of solidification microstructures using a phase-field model computed on an adaptive, finite element grid. We discuss the details of our algorithm and show that it greatly reduces the computational cost of solving the…
A thin shell finite element approach based on Loop's subdivision surfaces is proposed, capable of dealing with large deformations and anisotropic growth. To this end, the Kirchhoff-Love theory of thin shells is derived and extended to allow…
Understanding crystal growth and morphology is a fundamental issue in condensed matter physics. While crystal morphology due to the distribution and dynamics of the diffusion field has been intensively studied, how the intrinsic material…
A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here…
Dendritic growth, and the formation of material microstructure in general, necessarily involves a wide range of length scales from the atomic up to sample dimensions. The phase field approach of Langer, enhanced by optimal asymptotic…
Eutectic dendrites forming in a model ternary system have been studied using the phase-field theory. The eutectic and one-phase dendrites have similar forms, and the tip radius scales with the interface free energy as for one-phase…
Large-scale 3D martensitic microstructure evolution problems are studied using a finite-element discretization of a finite-strain phase-field model. The model admits an arbitrary crystallography of transformation and arbitrary elastic…
A phase field theory of polycrystalline solidification is presented that is able to describe the nucleation and growth of anisotropic particles with different crystallographic orientation in three dimensions. As opposed with the…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
Facetted growth of snow crystals leads to a rich diversity of forms, and exhibits a remarkable sixfold symmetry. Snow crystal structures result from diffusion limited crystal growth in the presence of anisotropic surface energy and…