Related papers: Stability of Two-Dimensional Soft Quasicrystals
Based on simplifications of previous numerical calculations [Graf and L\"{o}wen, Phys. Rev. E \textbf{59}, 1932 (1999)], we propose algebraic free energy expressions for the smectic-A liquid crystal phase and the crystal phases of hard…
Using fully minimized fundamental measure functionals, we investigate free energies, vacancy concentrations and density distributions for bcc, fcc and hcp hard-sphere crystals. Results are complemented by an approach due to Stillinger which…
The discovery of quasicrystals with crystallographically forbidden rotational symmetries has changed the notion of the ordering in materials, yet little is known about the dynamical emergence of such exotic forms of order. Here we…
Three-dimensional icosahedral random tilings with rhombohedral cells are studied in the semi-entropic model. We introduce a global energy measure defined by the variance of the quasilattice points in the orthogonal space. The internal…
We consider a two dimensional model of non-interacting chains of spinless fermions weakly coupled via a small inter-chain hopping and a repulsive inter-chain interaction. The phase diagram of this model has a surprising feature: an abrupt…
Molecular crystals often exist in multiple competing polymorphs, showing significantly different physico-chemical properties. Computational crystal structure prediction is key to interpret and guide the search for the most stable or useful…
In the following we consider a 2-dimensional system of ODE's containing quasiperiodic terms. The system is proposed as an extension of Mathieu-type equations to higher dimensions, with emphasis on how resonance between the internal…
For the first time the persistent current in a 2D free-electron system has been calculated analytically. The tight binding model is considered on a square lattice with filling factor 1/2. The array has a shape of rectangle with boundary…
Quasipatterns have been found in dissipative systems ranging from Faraday waves in vertically vibrated fluid layers to nonlinear optics. We describe the dynamics of octagonal, decagonal and dodecagonal quasipatterns by means of coupled…
Hyperuniform systems, which include crystals, quasicrystals and special disordered systems, have attracted considerable recent attention, but rigorous analyses of the hyperuniformity of quasicrystals have been lacking because the support of…
Anisotropies of Young's modulus E, the shear modulus G, and Poisson's ratio of all 2D symmetry systems are studied. Simple necessary and sufficient conditions on their elastic compliances are derived to identify if any of these crystals are…
The multidimensional energy surface of a cholesteric liquid crystal in a planar cell is investigated as a function of spherical coordinates determining the director orientation. Minima on the energy surface correspond to the stable states…
Elastic description of planar quasicrystals can be formulated as an interplay between two Goldstone fields corresponding to phonon and phason degrees of freedom. We reformulate this description as a gauge theory with one gauge field that is…
Stable vortices with topological charge of 3 and 4 are examined numerically and analytically in photonic quasicrystals created by interference of 5 as well as 8 beams, in the cases of cubic as well as saturable nonlinearities. These…
The description of the early stage of microfracture growth in a quasibrittle solid with thermodynamic positions is considered. From the most general thermodynamic performances the "principle" of minimization of free energy is received. The…
We investigate the stability, the dynamical properties and melting of a two-dimensional (2D) Wigner crystal (WC) of classical Coulombic particles in a bi-layer structure. Compared to the single-layer WC, this system shows a rich phase…
The self-assembly of two-dimensional dodecagonal quasicrystal (DDQC) from patchy particles are investigated by Brownian dynamics simulations. The patchy particle has a five-fold rotational symmetry pattern described by the spherical…
The phase diagram of colloidal hard superballs, of which the shape interpolates between cubes and octahedra via spheres, is determined by free-energy calculations in Monte Carlo simulations. We discover not only a stable face-centered cubic…
The Projected Shell Model is a shell model theory built up over a deformed BCS mean field. Ground state and excited bands in even-even nuclei are obtained through diagonalization of a pairing plus quadrupole Hamiltonian in an angular…
We investigate the phase behavior of a single-component system in 3 dimensions with spherically-symmetric, pairwise-additive, soft-core interactions with an attractive well at a long distance, a repulsive soft-core shoulder at an…