The Two Dimensional Liquid Crystal Droplet Problem with Tangential Boundary Condition

This paper studies a shape optimization problem which reduces to a nonlocal free boundary problem involving perimeter. It is motivated by a study of liquid crystal droplets with a tangential anchoring boundary condition and a volume constraint. We establish in 2D the existence of an optimal shape that has two cusps on the boundary. We also prove the boundary of the droplet is a chord-arc curve with its normal vector field in the VMO space, and its arc-length parametrization belongs to the Sobolev space $H^{3/2}$. In fact, the boundary curves of such droplets closely resemble the so-called Weil-Petersson class of planar curves. In addition, the asymptotic behavior of the optimal shape when the volume becomes extremely large or small is also studied

A New Method for Riccati Differential Equations Based on Reproducing Kernel and Quasilinearization Methods

We introduce a new method for solving Riccati differential equations, which is based on reproducing kernel method and quasilinearization technique. The quasilinearization technique is used to reduce the Riccati differential equation to a sequence of linear problems. The resulting sets of differential equations are treated by using reproducing kernel method. The solutions of Riccati differential equations obtained using many existing methods give good approximations only in the neighborhood of the initial position. However, the solutions obtained using the present method give good approximations in a larger interval, rather than a local vicinity of the initial position. Numerical results compared with other methods show that the method is simple and effective

Genetic differentiation in Japanese flounder in the Yellow Sea and East China Sea by amplified fragment length polymorphism (AFLP) and mitochondrial DNA markers

The population structure of Japanese flounder (Paralichthys olivaceus) in the Yellow and East China Seas were analyzed using amplified fragment length polymorphism (AFLP) and cytochrome c oxidase subunit I (COI) gene sequencing. A total of 390 reproducible bands were generated by 10 AFLP primer combinations in two populations collected from the coasts of Qingdao (located at the Yellow Sea) and Zhoushan (located at the East China Sea). The percentage of polymorphic loci (P), Nei’s genetic diversity (H) and Shannon’s information index (I) values were higher in the Qingdao population (P = 72.85%, H = 0.243 and I = 0.364) than those in the Zhoushan population (P = 56.35%, H = 0.189 and I = 0.284). The genetic diversity reduction in the Zhoushan population may be attributed to fishing pressure and habitat loss in this area. Based on the COI sequencing analysis, a total of 25 polymorphic sites were examined, and 15 haplotypes were identified in the two populations. The haplotype diversity (h) and nucleotide diversity (π) values in the Qingdao population were 0.746 ± 0.0728 and 0.00334 ± 0.00103, respectively. The corresponding values in the Zhoushan population were 0.712 ± 0.0470 and 0.00318 ± 0.00049. Both the AFLP and mtDNA data revealed significant genetic differentiation between the two populations. The present study discussed the factors that may result in genetic differentiation between the populations in the Yellow and East China Seas.Keywords: Japanese flounder, amplified fragment length polymorphism (AFLP), cytochrome c oxidase subunit I (COI) gene, genetic diversity, population structur

Wrist movement detector for ROS based control of the robotic hand

Robotic hands are used in a wide range of applications. They have many different shapes, constructions and capabilities. This work presents a new design of a robotic hand using tailor-made as well as widely available sensors and actuators. The information transferred between the sensor and actuators is processed using the Robot Operating System (ROS) topic mechanism. The robotic hand movement is remotely controlled by a movement detector mounted on the wrist of a human hand controller. Based on this simple hardware setup we demonstrate that the robotic hand can be remotely opened and closed thereby allowing to grasp objects flexibly

Automatic Stack Velocity Picking Using an Unsupervised Ensemble Learning Method

Seismic velocity picking algorithms that are both accurate and efficient can greatly speed up seismic data processing, with the primary approach being the use of velocity spectra. Despite the development of some supervised deep learning-based approaches to automatically pick the velocity, they often come with costly manual labeling expenses or lack interpretability. In comparison, using physical knowledge to drive unsupervised learning techniques has the potential to solve this problem in an efficient manner. We suggest an Unsupervised Ensemble Learning (UEL) approach to achieving a balance between reliance on labeled data and picking accuracy, with the aim of determining the stack velocity. UEL makes use of the data from nearby velocity spectra and other known sources to help pick efficient and reasonable velocity points, which are acquired through a clustering technique. Testing on both the synthetic and field data sets shows that UEL is more reliable and precise in auto-picking than traditional clustering-based techniques and the widely used Convolutional Neural Network (CNN) method

Automatic Velocity Picking Using a Multi-Information Fusion Deep Semantic Segmentation Network

Velocity picking, a critical step in seismic data processing, has been studied for decades. Although manual picking can produce accurate normal moveout (NMO) velocities from the velocity spectra of prestack gathers, it is time-consuming and becomes infeasible with the emergence of large amount of seismic data. Numerous automatic velocity picking methods have thus been developed. In recent years, deep learning (DL) methods have produced good results on the seismic data with medium and high signal-to-noise ratios (SNR). Unfortunately, it still lacks a picking method to automatically generate accurate velocities in the situations of low SNR. In this paper, we propose a multi-information fusion network (MIFN) to estimate stacking velocity from the fusion information of velocity spectra and stack gather segments (SGS). In particular, we transform the velocity picking problem into a semantic segmentation problem based on the velocity spectrum images. Meanwhile, the information provided by SGS is used as a prior in the network to assist segmentation. The experimental results on two field datasets show that the picking results of MIFN are stable and accurate for the scenarios with medium and high SNR, and it also performs well in low SNR scenarios