Related papers: Geometric theory of topological defects: methodolo…
Active colloids and liquid crystals are capable of locally converting the macroscopically-supplied energy into directional motion and promise a host of new applications, ranging from drug delivery to cargo transport at the mesoscale. Here…
A general theory of topological classification of defects is introduced. We illustrate the application of tools from algebraic topology, including homotopy and cohomology groups, to classify defects including several explicit calculations…
Many physical systems involve two types of orientational order, which are coupled together. For example, ferroelectric nematic liquid crystals have coupled polar and nematic order, and tilted hexatic phases have coupled polar and hexatic…
Liquid crystals have proven to provide a versatile experimental and theoretical platform for studying topological objects such as vortices, skyrmions, and hopfions. In parallel, in hard condensed matter physics, the concept of topological…
The interplay of nonlinearity and topology results in many novel and emergent properties across a number of physical systems such as chiral magnets, nematic liquid crystals, Bose-Einstein condensates, photonics, high energy physics, etc. It…
Defects in liquid crystals are of great practical importance and theoretical interest. Despite tremendous efforts, predicting the location and transition of defects under various topological constraint and external field remains to be a…
The transport of many kinds of singular structures in a medium, such as vortex points/lines/sheets in fluids, dislocation loops in crystalline plastic solids, or topological singularities in magnetism, can be expressed in terms of the…
Colloidal particles in a liquid crystal (LC) behave very differently from their counterparts in isotropic fluids. Elastic nature of the orientational order and surface anchoring of the director cause long-range anisotropic interactions and…
Abundant in nature, colloids also find increasingly important applications in science and technology, ranging from direct probing of kinetics in crystals and glasses to fabrication of third-generation quantum-dot solar cells. Because…
The topology of space is usually assumed simply connected, but could be multi-connected. We review in the latter case the possibility that topological defects arising at high energy phase transitions might still be present and find that…
Topological defects, such as disclination lines in nematic liquid crystals, are fundamental to many physical systems and applications. In this work, we study the behavior of nematic disclinations in thin parallel-plate geometries with…
Disclinations lines play a key role in many physical processes, from the fracture of materials to the formation of the early universe. Achieving versatile control over disclinations is key to developing novel electro-optical devices,…
The continuum mechanics of line defects representing singularities due to terminating discontinuities of the elastic displacement and its gradient field is developed. The development is intended for application to coupled phase…
Extended objects (defects) in Quantum Field Theory exhibit rich, nontrivial dynamics describing a variety of physical phenomena. These systems often involve strong coupling at long distances, where the bulk and defects interact, making…
We describe the flows and morphological dynamics of topological defect lines and loops in three-dimensional active nematics and show, using theory and numerical modelling, that they are governed by the local profile of the orientational…
Topological phenomena typically govern the behavior of delocalized waves, giving rise to robust transport in electronic, photonic, and mechanical systems. Whether similar principles can directly control the motion of a localized particle,…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
We propose a general formalism to characterize orientational frustration of smectic liquid crystals in confinement by interpreting the emerging networks of grain boundaries as objects with a topological charge. In a formal idealization,…
These lectures review certain topological defects and aspects of their cosmology. Unconventional material includes brief descriptions of electroweak defects, the structure of domain walls in non-Abelian theories, and the spectrum of…
Crystallography typically studies collections of point particles whose interaction forces are the gradient of a potential. Lifting this assumption generically gives rise in the continuum limit to a form of elasticity with additional moduli…