Related papers: Frameworks with crystallographic symmetry
The Euclidean dynamical symmetry hidden in the critical region of nuclear shape phase transitions is revealed by a novel algebraic F(5) description. With a nonlinear projection, it is shown that the dynamics in the critical region of the…
We give a combinatorial characterization of generic minimal rigidity for planar periodic frameworks. The characterization is a true analogue of the Maxwell-Laman Theorem from rigidity theory: it is stated in terms of a finite combinatorial…
Many compliant shell mechanisms are periodically corrugated or creased. Being thin, their preferred deformation modes are inextensional, i.e., isometric. Here, we report on a recent characterization of the isometric deformations of periodic…
We describe here in detail the recently introduced methodology for simulation of structural transitions in crystals. The applications of the new scheme are illustrated on various kinds of crystals and the advantages with respect to previous…
A random matrix model to describe the coupling of m-fold symmetry in constructed. The particular threefold case is used to analyze data on eigenfrequencies of elastomechanical vibration of an anisotropic quartz block. It is suggested that…
Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define…
A theory for surface transitions in the presence of a disordered pinning potential is presented. Arbitrary disorder correlations are treated in the framework of a dynamical functional renormalization group. The roughening transition, where…
This paper is devoted to the mathematical analysis of a time-domain electromagnetic scattering by periodic structures which are known as diffraction gratings. The scattering problem is reduced equivalently into an initial-boundary value…
The fact that a disordered material is not constrained in its properties in the same way as a crystal presents significant and yet largely untapped potential for novel material design. However, unlike their crystalline counterparts,…
Systems as diverse as mechanical structures assembled from elastic components, and photonic metamaterials enjoy a common geometrical feature: a sublattice symmetry. This property realizes a chiral symmetry first introduced to characterize a…
In this work, phase diagrams of a modified two-mode phase-field crystal (PFC) that show two-dimensional (2D) and three-dimensional (3D) crystallographic structures were determined by utilizing a free energy minimization method. In this…
Using the spectral approach, we analyze the effective properties of a composite which deviates slightly from periodicity. We find that, when the inclusions are randomly displaced from their equilibrium positions, the sharp resonances seen…
The use of machine learning methods for accelerating the design of crystalline materials usually requires manually constructed feature vectors or complex transformation of atom coordinates to input the crystal structure, which either…
The topological invariants of a periodic system can be used to define the topological phase of each band and determine the existence of topological interface states within a certain bandgap. Here, we propose a scheme based on the full phase…
Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…
Skeletal polyhedra and polygonal complexes are finite or infinite periodic structures in 3-space with interesting geometric, combinatorial, and algebraic properties. These structures can be viewed as finite or infinite periodic graphs…
Continuous time crystals, i.e., nonequilibrium phases with a spontaneously broken continuous time-translational symmetry, have been studied and recently observed in the long-time dynamics of open quantum systems. Here, we investigate a…
Graph maps that are homotopic to the identity and that permute the vertices are studied. Given a periodic point for such a map, a {\em rotation element} is defined in terms of the fundamental group. A number of results are proved about the…
We study parametric interactions in a new type of nonlinear photonic structures, which is realized in the vicinity of a pair of nonlinear crystals. In this kind of structure, which we call binary, multiple nonlinear optical processes can be…
We consider the crystallization problem for a finite one-dimensional collection of identical hard spheres in a periodic energy landscape. This issue arises in connection with the investigation of crystalline states of ionic dimers, as well…