Related papers: A Topological Framework for Local Structure Analys…
Topology and geometry of a sphere create constraints for particles that lie on its surface which they otherwise do not experience in Euclidean space. Notably, the number of particles and the size of the system can be varied separately,…
Disorder in crystals is rarely random, and instead involves local correlations whose presence and nature are hidden from conventional crystallographic probes. This hidden order can sometimes be controlled, but its importance for physical…
This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…
Networks generated from Voronoi tessellations of space are prototypes for topologically disordered systems. In order to assess the effects of random coordination on the statistical properties of energy spectra, we analyze tight-binding…
Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however so far only with flat hypersurfaces as cell-cell contact borders. In order to reproduce the experimentally…
Topological features - global properties not discernible locally - emerge in systems from liquid crystals to magnets to fractional quantum Hall systems. Deeper understanding of the role of topology in physics has led to a new class of…
We argue for a convergence of crystallography, materials science and biology, that will come about through asking materials questions about biology and biological questions about materials, illuminated by considerations of information. The…
We present a new variational model for computing the electronic first-order density matrix of a crystalline material in presence of a local defect. A natural way to obtain variational discretizations of this model is to expand the…
Spacetime is represented by ordered sequences of topologically closed Poincare sections of the primary space constructed of primary empty cells. These mappings are constrained to provide homeomorphic structures serving as frames of…
We introduce a new self-consistent structure finding algorithm that parses large scale cosmological structure into clusters, filaments and voids. This structure finding algorithm probes the cosmological structure at multiple scales and…
Based on classical statistical thermodynamics, we develop a theoretical approach that provides new insight into how macroscopic and microscopic physical properties are bridged via crystal lattice for condensed mat- ters. We find that in…
Due to its non-crystalline nature, the glassy state has remained one the most exciting scientific challenges. To study such materials, Molecular Dynamics (MD) simulations have been extensively used because they provide a direct view into…
The plastic deformation of crystalline materials can be understood by considering their structural defects such as disclinations and dislocations. Although glasses are also solids, their structure resembles closely the one of a liquid and…
In classical systems, we reexamine how macroscopic structures in equilibrium state connect with spatial con- straint on the systems: e.g., volume and density as the constraint for liquids in rigid box, and crystal lattice as the constraint…
Jamming is an emergent phenomenon wherein the local stability of individual particles percolates to form a globally rigid structure. However, the onset of rigidity does not imply that every particle becomes rigid, and indeed some remain…
Quantifying the correlation between the complex structures of amorphous materials and their physical properties has been a long-standing problem in materials science. In amorphous Si, a representative covalent amorphous solid, the presence…
Many materials, processes, and structures in science and engineering have important features at multiple scales of time and/or space; examples include biological tissues, active matter, oceans, networks, and images. Explicitly extracting,…
The language and methods of algebraic topology, particularly homotopy theory, have been extensively used in the study of the identification, the classification and the evolution of defects. Topological methods provide the means for the…
The discovery of topological insulators has reformed modern materials science, promising to be a platform for tabletop relativistic physics, electronic transport without scattering, and stable quantum computation. Topological invariants are…
Directional media, such as nematic liquid crystals and ferromagnets, are characterized by their topologically stabilized defects in directional order. In nematics, boundary conditions and surface-treated inclusions often create complex…