Related papers: Inverse Design of Parameter-Controlled Disclinatio…
The present paper studies non-uniform plastic deformations of crystals undergoing anti-plane constrained shear. The asymptotically exact energy density of crystals containing a moderately large density of excess dislocations is found by the…
We investigate the emergence of orientational order among +1/2 disclinations in active nematic liquid crystals. Using a combination of theoretical and experimental methods, we show that +1/2 disclinations have short-range antiferromagnetic…
Compared to isotropic liquids, orientational order of nematic liquid crystals makes their rheological properties more involved, and thus requires fine control of the flow parameters to govern the orientational patterns. In microfluidic…
In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the domain. In some…
The note focuses on the differential geometric approach to the study of nonlinear systems that are affine in control. We first develop normal forms for nonlinear system affine in control. Based on these normal forms, we then address the…
Thin nematic elastomers, composite hydrogels and plant tissues are among many systems that display uniform anisotropic deformation upon external actuation. In these materials, the spatial orientation variation of a local director field…
Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate…
Accurate control of light polarization represents a core building block in polarization metrology, imaging, and optical and quantum communications. Voltage-controlled liquid crystals offer an efficient way of polarization transformation.…
Topological defects are distinctive signatures of liquid crystals. They profoundly affect the viscoelastic behavior of the fluid by constraining the orientational structure in a way that inevitably requires global changes not achievable…
We propose a learning paradigm for the numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework…
Monte Carlo simulation, experiment and continuum theory are used to examine the anchoring exhibited by a nematic liquid crystal at a patterned substrate comprising a periodic array of rectangles that, respectively, promote vertical and…
Photonic crystals create dramatic new possibilities for nonlinear optics. Line defects are shown to support modes suitable for the production of pairs of photons by the material's second order nonlinearity even if the phase-matching…
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be…
In two dimensional nematics, topological defects are point like singularities with both a charge and a phase. We study topological defects within curved nematic textures on the surface of a cylinder. This allows us to isolate the effect of…
We study stability and distortions of liquid crystal nematic order in a cell with a random heterogeneous substrate. Modeling this system as a bulk xy model with quenched disorder confined to a surface, we find that nematic order is…
We use path integrals to calculate perturbative corrections to the correlation function of a particle under the action of nonlinear optical tweezers, both in the overdamped and underdamped regimes. In both cases, it is found that to leading…
Self-assembly of colloidal particles due to elastic interactions in nematic liquid crystals promises tunable composite materials and can be guided by exploiting surface functionalization, geometric shape and topology, though these means of…
Nonlinear metamaterials with tailored mechanical properties have applications in engineering, medicine, robotics, and beyond. While modeling their macromechanical behavior is challenging in itself, finding structure parameters that lead to…
Anisotropic fluids, such as nematic liquid crystals, can form non-spherical equilibrium shapes known as tactoids. Predicting the shape of these structures as a function of material parameters is challenging and paradigmatic of a broader…
A theoretical analysis is presented of a nematic liquid crystal confined between substrates pat- terned with squares that promote vertical and planar alignment. Two approaches are used to eluci- date the behavior across a wide range of…