Related papers: Forming a cube from a sphere with tetratic order
We report on a construction for smectic blue phases, which have quasi-long range smectic translational order as well as three dimensional crystalline order. Our proposed structures fill space by adding layers on top of a minimal surface,…
Smectic orders on curved substrates can be described by differential forms of rank one (1-forms), whose geometric meaning is the differential of the local phase field of density modulation. The exterior derivative of 1-form is the local…
Topological electric quadrupole is a recently proposed concept that extends the theory of electric polarization of crystals to higher orders. Such a quadrupole phase supports topological states localized on both edges and corners. In this…
Pattern formation in uniaxial polymeric liquid crystals is studied for different dynamic closure approximations. Using the principles of mesoscopic non-equilibrium thermodynamics in a mean-field approach, we derive a Fokker-Planck equation…
We describe the linear and nonlinear stability and instability of certain symmetric configurations of point vortices on the sphere forming relative equilibria. These configurations consist of one or two rings, and a ring with one or two…
We calculate the phase behavior of hard spheres with size polydispersity, using accurate free energy expressions for the fluid and solid phases. Cloud and shadow curves, which determine the onset of phase coexistence, are found exactly by…
We study a two-dimensional fluid of particles interacting through a spherically-symmetric and marginally soft two-body repulsion. This model can exist in three different crystal phases, one of them with square symmetry and the other two…
We report the formation of a binary crystal of hard polyhedra due solely to entropic forces. Although the alternating arrangement of octahedra and tetrahedra is a known space-tessellation, it had not previously been observed in…
General topological principles how to transfer the planar orders onto a sphere are considered. Formation of extended topological defects (ETDs), which have a reconstructed inner structure surrounded by perfect initial order, is discussed.…
Covariant density functional theory is solved in 3D lattice space by implementing the preconditioned conjugate gradient method with a filtering function (PCG-F). It considerably improves the computational efficiency compared to the previous…
A 10-dimensional symplectic moduli space of torsion sheaves on the cubic 4-fold is constructed. It parametrizes the stable rank 2 vector bundles on the hypeplane sections of the cubic 4-fold which are obtained by Serre's construction from…
All hard, convex shapes are conjectured by Ulam to pack more densely than spheres, which have a maximum packing fraction of {\phi} = {\pi}/\sqrt18 ~ 0.7405. For many shapes, simple lattice packings easily surpass this packing fraction. For…
We use a series of molecular dynamics simulations, and analytical theory, to demonstrate that a system of hard spheres confined to a narrow cylindrical channel exhibits a continuous phase transition from an isotropic fluid at low densities,…
We study the quadratic invariants of the elasticity tensor in the framework of its unique irreducible decomposition. The key point is that this decomposition generates the direct sum reduction of the elasticity tensor space. The…
The aim of this paper is two-fold. First, via a phenomenological consideration I show that, equally with the conventional phases (body-centred cubic, hexagonal planar and lamellar), such non-conventional phases as simple cubic,…
We investigate the motions of a bar structure consisting of two congruent tetrahedra, whose edges in their basic position form the face diagonals of a rectangular parallelepiped. The constraint of the motion is that the originally…
Numerical simulations of phase ordering under dissipative dynamics in a (2+1)-dimensional 3-vector model with O(3) symmetry are reported. The energy functional includes terms which stabilize the size of extended topological defects. They…
A model describing the three-dimensional folding of the triangular lattice on the face-centered cubic lattice is generalized allowing the presence of defects corresponding to cuts in the two-dimensional network. The model can be expressed…
Previous Monte Carlo investigations by Wojciechowski \emph{et al.} have found two unusual phases in two-dimensional systems of anisotropic hard particles: a tetratic phase of four-fold symmetry for hard squares [Comp. Methods in Science and…
The best-understood crystal ordering transition is that of two-dimensional freezing, which proceeds by the rapid eradication of lattice defects as the temperature is lowered below a critical threshold. But crystals that assemble on closed…