相关论文: On one dimensional inverse problems arising from p…

The ability to manipulate polar entities with multiple external fields opens exciting possibilities for emerging functionalities and novel applications in spin systems, photonics, metamaterials, and soft matter. Liquid crystals (LCs),…

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…

We propose the fast semi-analytical method of modelling the polarization curves in the voltammetric experiment. The method is based on usage of the special func- tions and shows a big calculation speed and a high accuracy and stability. Low…

Statistical theory of the dielectric susceptibility of polar liquid crystals is proposed. The molecules are not uniaxial but similar to cones. It is assumed that the permanent dipole moment of a molecule is parallel to the axis of the…

We consider a strongly damped wave equation on compact manifolds, both with and without boundaries, and formulate the corresponding inverse problems. For closed manifolds, we prove that the metric can be uniquely determined, up to an…

We are concerned with inverse boundary problems for first order perturbations of the Laplacian, which arise as model operators in the acoustic tomography of a moving fluid. We show that the knowledge of the Dirichlet--to--Neumann map on the…

In this study, we address the inverse problem of recovering the Lam\'e parameters ($\lambda, \mu$) and the density $\rho$ of a medium from the Neumann-to-Dirichlet map for any dimension $d\geq 2$. This inverse problem finds its motivation…

Polar nematic liquid crystals are new classes of condensed-matter states where the inversion symmetry common to the traditional apolar nematics is broken. Establishing theoretical descriptions for the novel phase states is an urgent task.…

The polarization state of light is a key parameter in many imaging systems. For example, it can image mechanical stress and other physical properties that are not seen with conventional imaging, and can also play a central role in quantum…

We consider the inverse problem of determining the Lam\'{e} parameters and the density of a three-dimensional elastic body from the local time-harmonic Dirichlet-to-Neumann map. We prove uniqueness and Lipschitz stability of this inverse…

We summarise some recent results on solution landscapes for two-dimensional (2D) problems in the Landau--de Gennes theory for nematic liquid crystals. We study energy-minimizing and non energy-minimizing solutions of the Euler--Lagrange…

Using Landau theory, it is shown that eight phenomenological parameters are needed to describe and distinguish the twelve viscosity coefficients of a biaxial nematic phase, or the five viscosity coefficients of a uniaxial nematic phase. The…

We provide experimental evidence that photoalignment at the nematic liquid crystal (NLC) - polymer interface can not be simply considered as a two-dimensional process. Moreover, our experiments clearly indicate that the photoaligning…

Instabilities are discussed which take place when a nematic liquid crystal (LC) layer, enclosed between a planar reference plate and a photosensitive substrate, is illuminated with polarized light from the reference side ({\it reverse}…

We show that development of polar order may spontaneously destroy the lamellar structure of a liquid crystal. This results in an unusual sequence of phases with the ferroelectric nematic phase appearing below a non-polar smectic phase. The…

In uniaxial soft matter with a reorientational nonlinearity, such as nematic liquid crystals, a light beam in the extraordinary polarization walks off its wavevector due to birefringence, while it undergoes self-focusing via an increase in…

We study an inverse problem for fractional elasticity. In analogy to the classical problem of linear elasticity, we consider the unique recovery of the Lam\'e parameters associated to a linear, isotropic fractional elasticity operator from…

So-called polar liquid crystals possess spontaneous long-range mutual orientation of their electric dipole moments, conferring bulk polarity to fluid phases of matter. The combination of polarity and fluidity leads to complex phase…

Liquid crystals consisting of biaxial particles can exhibit a much richer phase behavior than their uniaxial counterparts. Usually, one has to rely on simulation results to understand the phase diagram of these systems, since very few…

The influence of controlable parameters like temperature and wavelength on the trajectories of light in a nematic liquid crystal with topological defects is studied through a geometric model. The model incorporates phenomenological details…