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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…

Topology can manifest itself in colloids when quantified by invariants like Euler characteristics of nonzero-genus colloidal surfaces, albeit spherical colloidal particles are most often studied, and colloidal particles with complex…

Heusler compounds, in both cubic and hexagonal polymorphs, exhibit a remarkable range of electronic, magnetic, elastic, and topological properties, rivaling that of the transition metal oxides. To date, research on these quantum materials…

The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the…

The displacement of a fluid by another less viscous one in a quasi-two dimensional geometry typically leads to complex fingering patterns. In an isotropic system, dense-branching growth arises, which is characterized by repeated…

We demonstrate that multiple topological transitions can occur, with high-sensitivity, by continuous change of the geometry of a simple 2D dielectric-frame photonic crystal consisting of circular air-holes. By changing the radii of the…

For cellular functions like division and polarization, protein pattern formation driven by NTPase cycles is a central spatial control strategy. Operating far from equilibrium, no general theory links microscopic reaction networks and…

Open cell foams have diverse industrial applications e.g. heat exchangers, structured reactors, filtration due to their unique properties such as high porosity and high specific surface area. In order to theoretically determine the…

In this chapter, criteria for existence of propagating optical modes which are transversely bound at the interface of two materials are studied. In particular, quite general cases are considered, where the materials involved are assumed to…

We investigate the deformation of elastic microcapsules adsorbed at liquid-liquid interfaces. An initially spherical elastic capsule at a liquid-liquid interface undergoes circumferential stretching due to the liquid-liquid surface tension…

Liquid crystalline elastomers (LCEs) are shape-changing materials that exhibit large deformations in response to applied stimuli. Local control of the orientation of LCEs spatially directs the deformation of these materials to realize…

We develop a molecular model of non-uniform deformations within the framework of liquid crystal rubber elasticity. We show that, similarly to the uniform case, the theory is not sensitive to the molecular details of polymer liquid crystal…

Bonding between polymeric interfaces is encountered widely in several industrial applications. Many of these bonding processes rely on time-consuming and temperature-dependent classical mechanism of polymer interdiffusion via reptation in a…

We review and compare recent work on the properties of fluctuating interfaces between nematic and isotropic liquid-crystalline phases. Molecular dynamics and Monte Carlo simulations have been carried out for systems of ellipsoids and hard…

Liquid Crystalline Elastomers (LCEs) are active materials that are of interest due to their programmable response to various external stimuli such as light and heat. When exposed to these stimuli, the anisotropy in the response of the…

Dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open…

Topological insulators are materials that conduct on the surface and insulate in their interior due to non-trivial topological order. The edge states on the interface between topological (non-trivial) and conventional (trivial) insulators…

Polaritons in polar biaxial crystals with extreme anisotropy offer a promising route to manipulate nanoscale light-matter interactions. The dynamical modulation of their dispersion is great significance for future integrated nano-optics but…

Nonlocal crystals are systems with translational symmetry but arbitrary range couplings or interactions between degrees of freedom. We argue that the notion of topology in such systems does not collapse to that in zero dimensions, as one…

Topological interfaces of two-dimensional conformal field theories contain information about symmetries of the theory and exhibit striking spectral and entanglement characteristics. While lattice realizations of these interfaces have been…