Smoothing analysis of two-color distributive relaxation for solving 2D Stokes flow by multigrid method

Smoothing properties of two-color distributive relaxation for solving a two-dimensional (2D) Stokes flow by multigrid method are theoretically investigated by using the local Fourier analysis (LFA) method. The governing equation of the 2D Stokes flow in consideration is discretized with the non-staggered grid and an added pressure stabilization term with stabilized parameters to be determined is introduced into the discretization system in order to enhance the smoothing effectiveness in the analysis. So, an important problem caused by the added pressure stabilization term is how to determine a suitable zone of parameters in the added term. To that end, theoretically, a two-color distributive relaxation, developed on the two-color Jacobi point relaxation, is established for the 2D Stokes flow. Firstly, a mathematical constitution based on the Fourier modes with various frequency components is constructed as a base of the two-color smoothing analysis, in which the related Fourier representation is presented by the form of two-color Jacobi point relaxation. Then, an optimal one-stage relaxation parameter and related smoothing factor for the two-color distributive relaxation are applied to the discretization system, and an analytical expression of the parameter zone on the added pressure stabilization term is established by LFA. The obtained analytical results show that numerical schemes for solving 2D Stokes flow by multigrid method on the two-color distributive relaxation have a specific convergence zone on the parameters of the added pressure stabilization term, and the property of convergence is independent of mesh size, but depends on the parameters of the pressure stabilization term

A Smoothing Process of Multicolor Relaxation for Solving Partial Differential Equation by Multigrid Method

This paper is concerned with a novel methodology of smoothing analysis process of multicolor point relaxation by multigrid method for solving elliptically partial differential equations (PDEs). The objective was firstly focused on the two-color relaxation technique on the local Fourier analysis (LFA) and then generalized to the multicolor problem. As a key starting point of the problems under consideration, the mathematical constitutions among Fourier modes with various frequencies were constructed as a base to expand two-color to multicolor smoothing analyses. Two different invariant subspaces based on the 2h-harmonics for the two-color relaxation with two and four Fourier modes were constructed and successfully used in smoothing analysis process of Poisson’s equation for the two-color point Jacobi relaxation. Finally, the two-color smoothing analysis was generalized to the multicolor smoothing analysis problems by multigrid method based on the invariant subspaces constructed

A Deep Neural Network/Meshfree Method for Solving Dynamic Two-phase Interface Problems

In this paper, a meshfree method using the deep neural network (DNN) approach is developed for solving two kinds of dynamic two-phase interface problems governed by different dynamic partial differential equations on either side of the stationary interface with the jump and high-contrast coefficients. The first type of two-phase interface problem to be studied is the fluid-fluid (two-phase flow) interface problem modeled by Navier-Stokes equations with high-contrast physical parameters across the interface. The second one belongs to fluid-structure interaction (FSI) problems modeled by Navier-Stokes equations on one side of the interface and the structural equation on the other side of the interface, both the fluid and the structure interact with each other via the kinematic- and the dynamic interface conditions across the interface. The DNN/meshfree method is respectively developed for the above two-phase interface problems by representing solutions of PDEs using the DNNs' structure and reformulating the dynamic interface problem as a least-squares minimization problem based upon a space-time sampling point set. Approximation error analyses are also carried out for each kind of interface problem, which reveals an intrinsic strategy about how to efficiently build a sampling-point training dataset to obtain a more accurate DNNs' approximation. In addition, compared with traditional discretization approaches, the proposed DNN/meshfree method and its error analysis technique can be smoothly extended to many other dynamic interface problems with fixed interfaces. Numerical experiments are conducted to illustrate the accuracies of the proposed DNN/meshfree method for the presented two-phase interface problems. Theoretical results are validated to some extent through three numerical examples

Over 300-km Transmission of 25 Gb/s Optical SSB NPAM-4 Signal with Electronic Dispersion Pre-compensation and Interference Mitigation

We experimentally demonstrate the interference mitigation in direct-detection of optical SSB signals with Nyquist-PAM-4. At 25 Gb/s, we achieve over 300-km and 500-km SSMF with an average BER of 2.7×10-3 (<HD-FEC) and 9.4×10-3 (<SD-FEC), respectively

Smoothing Analysis of Distributive Red-Black Jacobi Relaxation for Solving 2D Stokes Flow by Multigrid Method

Smoothing analysis process of distributive red-black Jacobi relaxation in multigrid method for solving 2D Stokes flow is mainly investigated on the nonstaggered grid by using local Fourier analysis (LFA). For multigrid relaxation, the nonstaggered discretizing scheme of Stokes flow is generally stabilized by adding an artificial pressure term. Therefore, an important problem is how to determine the zone of parameter in adding artificial pressure term in order to make stabilization of the algorithm for multigrid relaxation. To end that, a distributive red-black Jacobi relaxation technique for the 2D Stokes flow is established. According to the 2h-harmonics invariant subspaces in LFA, the Fourier representation of the distributive red-black Jacobi relaxation for discretizing Stokes flow is given by the form of square matrix, whose eigenvalues are meanwhile analytically computed. Based on optimal onestage relaxation, a mathematical relation of the parameter in artificial pressure term between the optimal relaxation parameter and related smoothing factor is well yielded. The analysis results show that the numerical schemes for solving 2D Stokes flow by multigrid method on the distributive red-black Jacobi relaxation have a specified convergence parameter zone of the added artificial pressure term

De novo Assembly of the Camellia nitidissima Transcriptome Reveals Key Genes of Flower Pigment Biosynthesis

The golden camellia, Camellia nitidissima Chi., is a well-known ornamental plant that is known as “the queen of camellias” because of its golden yellow flowers. The principal pigments in the flowers are carotenoids and flavonol glycosides. Understanding the biosynthesis of the golden color and its regulation is important in camellia breeding. To obtain a comprehensive understanding of flower development in C. nitidissima, a number of cDNA libraries were independently constructed during flower development. Using the Illumina Hiseq2500 platform, approximately 71.8 million raw reads (about 10.8 gigabase pairs) were obtained and assembled into 583,194 transcripts and 466, 594 unigenes. A differentially expressed genes (DEGs) and co-expression network was constructed to identify unigenes correlated with flower color. The analysis of DEGs and co-expressed network involved in the carotenoid pathway indicated that the biosynthesis of carotenoids is regulated mainly at the transcript level and that phytoene synthase (PSY), β -carotene 3-hydroxylase (CrtZ), and capsanthin synthase (CCS1) exert synergistic effects in carotenoid biosynthesis. The analysis of DEGs and co-expressed network involved in the flavonoid pathway indicated that chalcone synthase (CHS), naringenin 3-dioxygenase (F3H), leucoanthocyanidin dioxygenase(ANS), and flavonol synthase (FLS) play critical roles in regulating the formation of flavonols and anthocyanidin. Based on the gene expression analysis of the carotenoid and flavonoid pathways, and determinations of the pigments, we speculate that the high expression of PSY and CrtZ ensures the production of adequate levels of carotenoids, while the expression of CHS, FLS ensures the production of flavonols. The golden yellow color is then the result of the accumulation of carotenoids and flavonol glucosides in the petals. This study of the mechanism of color formation in golden camellia points the way to breeding strategies that exploit gene technology approaches to increase the content of carotenoids and flavonol glucosides and to decrease anthocyanidin synthesis

Evaluation of Himawari-8 for live fuel moisture content retrieval

Near-real-time monitoring live fuel moisture content (LFMC) from remote sensing is paramount to wildfire early management at a large scale since LFMC is a critical variable in affecting fire ignition and fire spread rate. The geostationary satellite Himawari-8 observes the land surface every 10 minutes, making near-real-time LFMC retrieval achievable. To this end, the potential of Himawari-8 data for LFMC retrieval using the radiative transfer model was explored in this study. The performance of retrieved LFMC was validated using 16 LFMC samplings located in Australia involving two land cover types: croplands and tree cover lands. Additionally, the MODIS data was also applied and compared for the LFMC retrieval. The results showed that Himawati-8 data performed poor accuracy level with R-2 and RMSE of 0.26 and 42.16%, respectively. Whereas better accuracy level was found for MODIS data, R-2 and RMSE were 0.67 and 29.17%, respectively. This result indicated that the LFMC estimated from Himawari-8 is challenged. Detailed fieldwork and methodology improvements adopted for this data are needed for improving the LFMC estimate in the future