Related papers: Nonlinear Methods for Shape Optimization Problems …
We propose a numerical strategy to generate the anisotropic meshes and select the appropriate stabilized parameters simultaneously for two dimensional convection-dominated convection-diffusion equations by stabilized continuous linear…
The phase-field-crystal model for liquid crystals is solved numerically in two spatial dimensions. This model is formulated with three position-dependent order parameters, namely the reduced translational density, the local nematic order…
Shape optimization problems constrained by variational inequalities (VI) are non-smooth and non-convex optimization problems. The non-smoothness arises due to the variational inequality constraint, which makes it challenging to derive…
We investigate a complex system involving multiple shapes to be optimized in a domain, taking into account geometric constraints on the shapes and uncertainty appearing in the physics. We connect the differential geometry of product shape…
Achieving control and tunability of lyotropic materials has been a long-standing goal of liquid crystal research. Here we show that the elasticity of a liquid crystal system consisting of a dense suspension of semiflexible biopolymers can…
Chromonic nematics are lyotropic liquid crystals that have already been known for half a century, but have only recently raised interest for their potential applications in life sciences. Determining elastic constants and anchoring…
We derive a F\"{o}ppl-von K\'{a}rm\'{a}n-type constitutive model for solid liquid crystalline plates where the nematic director may or may not rotate freely relative to the elastic network. To obtain the reduced two-dimensional model, we…
We demonstrate scaffolding of plasmonic nanoparticles by topological defects induced by colloidal microspheres to match their surface boundary conditions with a uniform far-field alignment in a liquid crystal host. Displacing energetically…
The bent-core liquid crystals (LCs) are highly regarded as the next-generation materials for electro-optic devices. The nematic (N) phase of these LCs possesses highly ordered smectic-like cybotactic clusters which are promising in terms of…
We use lattice Boltzmann simulations of the Beris--Edwards formulation of nematodynamics to probe the response of a nematic liquid crystal with conflicting anchoring at the boundaries under shear and Poiseuille flow. The geometry we focus…
We show that nonlinear continuum elasticity can be effective in modeling plastic flows in crystals if it is viewed as Landau theory with an infinite number of equivalent energy wells whose configuration is dictated by the symmetry group…
In this work, we propose a disentangled latent optimization-based method for parameterizing grouped deforming 3D objects into shape and deformation factors in an unsupervised manner. Our approach involves the joint optimization of a…
A Landau-de Gennes model that integrates the nematic quadrupolar tensor order parameter and complex smectic-A order parameters is used to simulate the two-dimensional growth of an initially homogeneous smectic-A spherulite in an isotropic…
The interaction of electromagnetic waves with metallic nanostructures generates resonant oscillations of the conduction-band electrons at the metal surface. These resonances can lead to large enhancements of the incident field and to the…
The topology and the geometry of a surface play a fundamental role in determining the equilibrium configurations of thin films of liquid crystals. We propose here a theoretical analysis of a recently introduced surface Frank energy, in the…
We propose a simple surface potential favoring the planar degenerate anchoring of nematic liquid crystals, i.e., the tendency of the molecules to align parallel to one another along any direction parallel to the surface. We show that, at…
We introduce a new framework for analyzing (Quasi-}Newton type methods applied to non-smooth optimization problems. The source of randomness comes from the evaluation of the (approximation) of the Hessian. We derive, using a variant of…
Recent experiments report that the long looked for thermotropic biaxial nematic phase has been finally detected in some thermotropic liquid crystalline systems. Inspired by these experimental observations we concentrate on some elementary…
Nematic liquid-crystal devices are a powerful tool to structure light in different degrees of freedom, both in classical and quantum regimes. Most of these devices exploit either the possibility of introducing a position-dependent phase…
Fluid configurations in three-dimensions, displaying a plausible decay of regularity in a finite time, are suitably built and examined. Vortex rings are the primary ingredients in this study. The full Navier-Stokes system is converted into…