Related papers: Geometrical modeling of dendritic structures
A phenomenological free energy model is proposed to describe the behavior of smectic liquid crystals, an intermediate phase that exhibits orientational order and layering at the molecular scale. Advantageous properties render the functional…
Defects are a ubiquitous feature of ordered media. They have certain universal features, independent of the underlying physical system, reflecting their topological origins. While the topological properties of defects are robust, they…
Spherical models of collisionless but quasi-relaxed stellar systems have long been studied as a natural framework for the description of globular clusters. Here we consider the construction of self-consistent models under the same physical…
We demonstrate that higher-order electric susceptibilities in crystals can be enhanced and understood through nontrivial topological invariants and quantum geometry, using one-dimensional $\pi$-conjugated chains as representative model…
Purely real space versions of the differential equations describing the kinematics of a dislocated crystalline medium are considered. The differential geometric structures associated with them are revealed.
We derive a course grained, continuum model of the 2D vertex model, applicable for different underlying geometries, and allowing for analytical analysis of an otherwise numerical model. Using a geometric approach and out--of--equilibrium…
This article reports the spherical coordinate form of three-dimensional generalized dynamics of soft-matter quasicrystals with 12-fold symmetry which provides a basis for solving initial-boundary value problems of the equations under some…
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…
Phase transition problems on curved surfaces can lead to a panopticon of fascinating patterns. In this paper we consider finite element approximations of phase field models with a spatially inhomogeneous and anisotropic surface energy…
A first-order transition is numerically found in a spherical surface model with skeletons, which are linked to each other at junctions. The shape of the triangulated surfaces is maintained by skeletons, which have a one-dimensional bending…
The possibility of obtaining an open set of regular cosmological models is discussed. Cylindrical stiff perfect fluid cosmologies are studied in detail. The condition for geodesic completeness is easy to check. A large family of…
The past decade has witnessed a surge of interest in exploring emergent particles in condensed matter systems. Novel particles, emerged as excitations around exotic band degeneracy points, continue to be reported in real materials and…
We investigate how thin structures change their shape in response to non-mechanical stimuli that can be interpreted as variations in the structure's natural curvature. Starting from the theory of non-Euclidean plates and shells, we derive…
The relation between the properties of a specific crystallographic site and the properties of the full crystal is discussed by using spherical tensors. The concept of spherical tensors is introduced and the way it transforms under the…
The recent discovery of topological insulators has revived interest in the topological properties of insulating band structures. In this work, we extend the topological classification of insulating band structures to include certain point…
In mathematical crystallography and computational materials science, it is important to infer flexibility properties of framework materials from their geometric representation. We study combinatorial, geometric and kinematic properties for…
Understanding the mechanical response and failure of solids is of obvious importance in their use as structural materials. The nature of plastic deformation leading to yielding of amorphous solids has been vigorously pursued in recent…
Elucidating the interplay of stress and geometry is a fundamental scientific question arising in multiple fields. In this work, we investigate the geometric frustration of crystalline caps confined on the sphere in both elastic and plastic…
Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure…
We study singularities obtained by the contraction of the maximal divisor in compact (non kaehlerian) surfaces which contain global spherical shells. These singularities are of genus 1 or 2, may be Q-Gorenstein, numerically Gorenstein or…