Related papers: Facet shapes in a Wulff crystal

We prove discrete-to-continuum convergence of interaction energies defined on lattices in the Euclidean space (with interactions beyond nearest neighbours) to a crystalline perimeter, and we discuss the possible Wulff shapes obtainable in…

We consider nematic liquid crystals in a bounded, convex polyhedron described by a director field n(r) subject to tangent boundary conditions. We derive lower bounds for the one-constant elastic energy in terms of topological invariants.…

It is shown that the wake-mediated interactions between microparticles in a two-dimensional plasma crystal affect the shape of the monolayer, making it non-flat. The equilibrium shape is calculated for various distributions of the particle…

Topological defects are one of the most conspicuous features of liquid crystals. In two dimensional nematics, they have been shown to behave effectively as particles with both, charge and orientation, which dictate their interactions. Here,…

We study the equilibrium shape of a liquid drop resting on top of a liquid surface, i.e., a floating lens. We consider the surface tension forces in non--wetting situations (negative spreading factor), as well as the effects of gravity. We…

We use computer simulations to study the phase behaviour for hard, right rhombic prisms as a function of the angle of their rhombic face (the "slant" angle). More specifically, using a combination of event-driven molecular dynamics…

Understanding crystal shapes is a fundamental subject in surface science. It is now well studied how chemical bondings determine crystal shapes via dependence of surface energies on surface orientations. Meanwhile, discoveries of…

We develop a rigorous framework for modelling the geometry equilibration of crystalline defects. We formulate the equilibration of crystal defects as a variational problems on a discrete energy space and establish qualitatively sharp…

We propose diagrams representing the equilibrium morphologies of two immiscible liquid droplets brought into contact. We study the dependence of the shape of the droplets on the surface tensions and ratio of volumes. We study theoretically…

We use confocal microscopy to study an equilibrated crystal-liquid interface in a colloidal suspension. Capillary waves roughen the surface, but locally the intrinsic interface is sharply defined. We use local measurements of the structure…

A systematic search for multicomponent crystal structures is carried out for five different ternary systems of nuclei in a polarizable background of electrons, representative of accreted neutron star crusts and some white dwarfs. Candidate…

In this paper we extend the classical method of lattice dynamics to defective crystals with partial symmetries. We start by a nominal defect configuration and first relax it statically. Having the static equilibrium configuration, we use a…

A continuum theory is employed to numerically study the equilibrium orientation and defect structures of a circular cylindrical particle with flat ends under a homeotropic anchoring condition in a uniform nematic medium. Different aspect…

The interface of a cholesteric liquid crystal with an isotropic fluid can display a range of unusual properties, such as a layer of topological defects close to an undulated interface. These properties have been know for a long time and…

Given a positive function F on S n satisfying an appropriate con-vexity assumption, we consider hypersurfaces for which a linear combination of some higher order anisotropic curvatures is constant. We define the varia-tional problem for…

Crystal growth processes produce a diverse array of surface formations, primarily distinguished by their geometric shapes. While some structures strictly adhere to the underlying crystal symmetry, others exhibit universal circular or oval…

We present a new approach for predicting stable equilibrium shapes of crystalline islands on flat substrates, as commonly occur through solid-state dewetting of thin films. The new theory is a generalization of the widely used Winterbottom…

We study the homogenized energy densities of periodic ferromagnetic Ising systems. We prove that, for finite range interactions, the homogenized energy density, identifying the effective limit, is crystalline, i.e. its Wulff crystal is a…

We investigate theoretically the elliptical shapes of soft colloids in freely standing smectic C films, that have been reported recently. The colloids favour parallel alignment of the liquid crystal molecules at their surfaces and, for…

A key question in the interaction of droplets with lubricated and liquid-infused surfaces is what determines the apparent contact angle of droplets. Previous work has determined this using measured values of the geometry of the `skirt' --…