Related papers: Curvature penalization of strongly anisotropic int…
In this work, we consider the three-dimensional solid-state dewetting with strongly anisotropic surface energy, assuming an axisymmetric morphology of the thin film. However, when surface energy exhibits strong anisotropy, certain…
The quantitative knowledge of interface anisotropy in lattice models is a major issue, both for the parametrization of continuum interface models, and for the analysis of experimental observations. In this paper, we focus on the anisotropy…
This article is concerned with the problem of minimising the Willmore energy in the class of \emph{connected} surfaces with prescribed area which are confined to a small container. We propose a phase field approximation based on De Giorgi's…
This paper gives a theoretical analysis for the fundamental problem of anisotropy induced by shear forces onan adhesive contact, discussing the experimental data of the companion Letter. We present a fracture mechanicsmodel where two…
By adjusting the interface energy, curvature, and velocity, the anisotropy plays an important role in the interaction between interfacial processes and transport processes, determining the solidification structures. In this paper, through…
We present a diffuse-interface model for the solid-state dewetting problem with anisotropic surface energies in ${\mathbb R}^d$ for $d\in\{2,3\}$. The introduced model consists of the anisotropic Cahn--Hilliard equation, with either a…
We propose a sharp interface model for simulating solid-state dewetting where the surface energy is (weakly) anisotropic. The morphology evolution of thin films is governed by surface diffusion and contact line migration. The mathematical…
True contact between randomly rough solids consists of myriad individual micro-junctions. While their total area controls the adhesive friction force of the interface, other macroscopic features, including viscoelastic friction, wear,…
Coherency misfit stresses and their related anisotropies are known to influence the equilibrium shapes of precipitates. Additionally, mechanical properties of the alloys are also dependent on the shapes of the precipitates. Therefore, in…
The elastic deformation of a soft solid induced by capillary forces crucially relies on the excess stress inside the solid-liquid interface. While for a liquid-liquid interface this "surface stress" is strictly identical to the "surface…
We explore the pressure of active particles on curved surfaces and its relation to other interfacial properties. We use both direct simulations of the active systems as well as simulations of an equilibrium system with effective (pair)…
The purpose of this paper is to derive anisotropic mean curvature flow as the limit of the anisotropic Allen-Cahn equation. We rely on distributional solution concepts for both the diffuse and sharp interface models, and prove convergence…
The interface stresses at of the solid-melt interface are, in general, anisotropic. The anisotropy in the interfacial stress can be evaluated using molecular dynamics (MD) and phase field crystal (PFC) models. In this paper, we report our…
An anisotropic surface energy is the integral of an energy density that depends on the normal at each point over the considered surface, and it is a generalization of surface area. The minimizer of such an energy among all closed surfaces…
Two benchmark problems for quantitative assessment of anisotropic curvature driving force in phase field method were developed and introduced. Both benchmarks contained an anisotropically shrinking grain in homogeneous matrix. The first…
Standard diffuse approximations of the Willmore flow often lead to intersecting phase boundaries that in many cases do not correspond to the intended sharp interface evolution. Here we introduce a new two-variable diffuse approximation that…
A new phase field model of microstructural evolution is presented that includes the effects of elastic strain energy. The model's thin interface behavior is investigated by mapping it onto a recent model developed by Echebarria et al (Phys…
We study the effects of anisotropic hopping amplitudes on quantum phases of ultracold fermions in optical lattices described by the repulsive Fermi-Hubbard model. In particular, using dynamical mean-field theory (DMFT) we investigate the…
We develop an approach to treat magnetic energy of a ferromagnet for arbitrary curved wires and shells on the assumption that the anisotropy contribution much exceeds the dipolar and other weak interactions. We show that the curvature…
A model describing cell membranes as optimal shapes with regard to the $L^2$-deficit of their mean curvature to a given constant called spontaneous curvature is considered. It is shown that the corresponding energy functional is lower…