Related papers: Breaking the Rules for Topological Defects: Smecti…
We present recent Monte Carlo results on surfaces of bcc-structured binary alloys which undergo an order-disorder phase transformation in the bulk. In particular, we discuss surface order and surface induced disorder at the bulk transition…
We describe experimental investigations of the structure of two-dimensional spherical crystals. The crystals, formed by beads self-assembled on water droplets in oil, serve as model systems for exploring very general theories about the…
We consider binary liquid mixtures near their critical consolute points and exposed to geometrically flat but chemically structured substrates. The chemical contrast between the various substrate structures amounts to opposite local…
The effect of short chain grafting on the liquid crystalline (LC) ordering of nano-crystals is investigated using molecular dynamics simulations of a coarse-grained grafted nano-rod model. Monodisperse nano-rods, with aspect ratios typical…
We study filling sets of simple closed curves on punctured surfaces. In particular we study lower bounds on the cardinality of sets of curves that fill and that pairwise intersect at most k times on surfaces with given genus and number of…
Packing of particles in confined environments is a common problem in multiple fields. Here, based on the two-dimensional Hertzian particle model, we study the packing of deformable spherical particles under compression, and reveal the…
We point out a possible mechanism by which smooth surfaces can become spiky as the constant of curvature stiffness $\kappa$ falls below certain critical values. This happens either in a single first-order transition, or in a sequence of two…
A flux liquid can condense into a smectic crystal in a pure layered superconductor with the magnetic field oriented nearly parallel to the layers. Similar order can arise in low temperature $^4$He films with a highly anisotropic periodic…
We present a mesoscale description of deformations and defects in thin, flexible sheets with crystalline order, tackling the interplay between in-plane elasticity, out-of-plane deformation, as well as dislocation nucleation and motion. Our…
Recent transport experiments in the original cuprate high temperature superconductor, {La$_{2-x}$Ba$_x$CuO$_4$}, have revealed a remarkable sequence of transitions and crossovers which give rise to a form of dynamical dimensional reduction,…
Elastic theory of ring-(or cylinder-)shaped crystals is constructed and the generation of edge dislocations due to geometrical frustration caused by the bending is studied. The analogy to superconducting (or superfluid) vortex state is…
Identifying the regions responsible for plastic flow in amorphous solids remains an open problem, since structural disorder seems to prevent the direct application of concepts such as dislocations, topological defects that successfully…
Apparently conflicting phase-sensitive measurements of the order parameter symmetry in the high-T$_c$ superconductors may be explained by regions near surfaces in which the order parameter symmetry is different than in the bulk. These…
The energetically optimal position of lattice defects on intrinsically curved surfaces is a complex function of shape parameters. For open surfaces, a simple condition predicts the critical size for which a central disclination yields lower…
A modified phase field crystal model in which the free energy may be minimised by an order parameter profile having isolated bumps is investigated. The phase diagram is calculated in one and two dimensions and we locate the regions where…
We study the geometry and codes of quartic surfaces with many cusps. We apply Gr\"obner bases to find examples of various configurations of cusps on quartics.
As pointed out by Linus Pauling in his classic work on the relationship between crystal packing and ionic radius ratio, a difference in atomic size can be accommodated more readily by an ordered structure than by a disordered one. Because…
Confined samples of liquid crystals are characterized by a variety of topological defects and can be exposed to external constraints such as extreme confinements with nontrivial topology. Here we explore the intrinsic structure of smectic…
The stable magnetisation configurations of antiferromagnets on quasiperiodic tilings are investigated theoretically. The exchange coupling is assumed to decrease exponentially with the distance between magnetic moments. It is demonstrated…
We consider textures of biaxial nematics confined between two parallel plates. The boundary conformations at the bordering plates are supposed to be identical, the gradients of the order parameter being generally nonzero. We claim that for…