Related papers: Topological defects in two-dimensional crystals
By using stochastic calculus for two-parameter processes and chaos expansion into multiple Wiener-It\^o integrals, we define a 2D-stochastic current over the Brownian sheet. This concept comes from geometric measure theory. We also study…
Extended defects in crystals, such as dislocations, stacking faults and grain boundaries, play a crucial role in determining a wide variety of materials properties. Extended defects can also lead to novel electronic properties in…
In the context of current particle physics theories, it is quite likely that topological defects may be present in our universe. An observation of these fossils from the early universe would lead to invaluable insight into cosmology and…
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…
Integrable defects in two-dimensional integrable models are purely transmitting thus topological. By fusing them to integrable boundaries new integrable boundary conditions can be generated, and, from the comparison of the two solved…
Topological defects play a key role in nonequilibrium phase transitions, ranging from birth of the early universe to quantum critical behavior of ultracold atoms. In solids, transient defects are known to generate a variety of hidden orders…
Topological defects (TDs) in crystal lattices are elementary lattice imperfections that cannot be removed by local perturbations, due to their real space topology. We show that adding TDs into a valley photonic crystal generates a lattice…
We study a class of symmetric critical points in a variational $2D$ Landau - de Gennes model where the state of nematic liquid crystals is described by symmetric traceless $3\times 3$ matrices. These critical points play the role of…
Recent advances in classical density functional theory are combined with stochastic process theory and rare event techniques to formulate a theoretical description of nucleation, including crystallization, that can predict nonclassical…
Intriguing analogies were found between a model of plastic deformation in crystals and turbulence in fluids. A study of this model provides remarkable explanations of known experiments and predicts fractal dislocation pattern formation.…
Topological defects, which are singular points in a director field, play a major role in shaping active systems. Here, we experimentally study topological defects and the flow patterns around them, that are formed during the highly rapid…
Active emulsions and liquid crystalline shells are intriguing and experimentally realisable types of topological matter. Here we numerically study the morphology and spatiotemporal dynamics of a double emulsion, where one or two passive…
Zero- and two-dimensional crystal defects form in open statistical ensembles, such as the grand canonical, that are usually inaccessible with conventional simulation techniques. This longstanding challenge is overcome with a new Hamiltonian…
Structural defects in a crystal are responsible for the "two length-scale" behavior, in which a sharp central peak is superimposed over a broad peak in critical diffuse X-ray scattering. We have previously measured the scaling behavior of…
The topological characteristics of photonic crystals have been the subject of intense research in recent years. Despite this, the basic question of whether photonic band topology is rare or abundant -- i.e., its relative prevalence --…
The Materials Project crystal structure database has been searched for materials possessing layered motifs in their crystal structures using a topology-scaling algorithm. The algorithm identifies and measures the sizes of bonded atomic…
Field theories predict that phase transitions sequentially breaking continuous and discrete symmetries can generate hybrid topological structures in which defects of different dimensionalities merge. We report experimental and numerical…
We study the scaling properties of two-dimensional turbulence using dimensional analysis. In particular, we consider the energy spectrum both at large and small scales and in the "inertial ranges" for the cases of freely decaying and forced…
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…
A problem about the present structure of dimensional analysis, and another one about the differences between solids and fluids are suggested. Both problems appear to have certain foundational aspects.