Phase Diagram and Order Reconstruction Modeling for Nematics in Asymmetric π-Cells

Intense electric fields applied to an asymmetric π-cell containing a nematic liquid crystal subjected to strong mechanical stresses induce distortions that are relaxed through a fast-switching mechanism: the order reconstruction transition. Topologically different nematic textures are connected by such a mechanism that is spatially driven by the intensity of the applied electric fields and by the anchoring angles of the nematic molecules on the confining plates of the cell. Using the finite element method, we implemented the moving mesh partial differential equation numerical technique, and we simulated the nematic evolution inside the cell in the context of the Landau–de Gennes order tensor theory. The order dynamics have been well captured, putting in evidence the possible existence of a metastable biaxial state, and a phase diagram of the nematic texture has been built, therefore confirming the appropriateness of the used technique for the study of this type of problem.

TIEOF: Algorithm for Recovery of Missing Multidimensional Satellite Data on Water Bodies Based on Higher-Order Tensor Decompositions

Satellite research methods are [DCh]actively involvedfrequently used in observations of water bodies. One of the most important problems in satellite observations is the presence of missing data due to internal malfunction of satellite sensors and poor atmospheric conditions. We proceeded on the assumption that the use of data recovery methods based on spatial relationships in data can increase the recovery accuracy. In this paper, we present a method for missing data reconstruction from remote sensors. We refer our method to as Tensor Interpolating Empirical Orthogonal Functions (TIEOF). The method relies on the two-dimensional nature of sensor images and organizes the data into three-dimensional tensors. We use high-order tensor decomposition to interpolate missing data [ZN] on chlorophyll a concentration in lake Baikal (Russia, Siberia). Using MODIS and SeaWiFS satellite data of lake Baikal we show that the observed improvement of TIEOF was 69% on average compared to the current state-of-the-art DINEOF algorithm measured in various preprocessing data scenarios including thresholding and different interpolating schemes.

The Multipole Structure and Symmetry Classification of Even-Type Deviators Decomposed from the Material Tensor

The number of distinct components of a high-order material/physical tensor might be remarkably reduced if it has certain symmetry types due to the crystal structure of materials. An nth-order tensor could be decomposed into a direct sum of deviators where the order is not higher than n, then the symmetry classification of even-type deviators is the basis of the symmetry problem for arbitrary even-order physical tensors. Clearly, an nth-order deviator can be expressed as the traceless symmetric part of tensor product of n unit vectors multiplied by a positive scalar from Maxwell’s multipole representation. The set of these unit vectors shows the multipole structure of the deviator. Based on two steps of exclusion, the symmetry classifications of all even-type deviators are obtained by analyzing the geometric symmetry of the unit vector sets, and the general results are provided. Moreover, corresponding to each symmetry type of the even-type deviators up to sixth-order, the specific multipole structure of the unit vector set is given. This could help to identify the symmetry types of an unknown physical tensor and possible back-calculation of the involved physical coefficients.

Image Completion in Embedded Space Using Multistage Tensor Ring Decomposition

Tensor Completion is an important problem in big data processing. Usually, data acquired from different aspects of a multimodal phenomenon or different sensors are incomplete due to different reasons such as noise, low sampling rate or human mistake. In this situation, recovering the missing or uncertain elements of the incomplete dataset is an important step for efficient data processing. In this paper, a new completion approach using Tensor Ring (TR) decomposition in the embedded space has been proposed. In the proposed approach, the incomplete data tensor is first transformed into a higher order tensor using the block Hankelization method. Then the higher order tensor is completed using TR decomposition with rank incremental and multistage strategy. Simulation results show the effectiveness of the proposed approach compared to the state of the art completion algorithms, especially for very high missing ratios and noisy cases.