Spectral methods for partial differential equations

Origins of spectral methods, especially their relation to the Method of Weighted Residuals, are surveyed. Basic Fourier, Chebyshev, and Legendre spectral concepts are reviewed, and demonstrated through application to simple model problems. Both collocation and tau methods are considered. These techniques are then applied to a number of difficult, nonlinear problems of hyperbolic, parabolic, elliptic, and mixed type. Fluid dynamical applications are emphasized

Spectral multigrid methods with applications to transonic potential flow

Spectral multigrid methods are demonstrated to be a competitive technique for solving the transonic potential flow equation. The spectral discretization, the relaxation scheme, and the multigrid techniques are described in detail. Significant departures from current approaches are first illustrated on several linear problems. The principal applications and examples, however, are for compressible potential flow. These examples include the relatively challenging case of supercritical flow over a lifting airfoil

Prediction and analysis of slab quality based on neural network combined with particle swarm optimization (PSO)

Based on the study of the mechanism of bloom crack, the main factors affecting the quality of bloom are determined. The intelligent optimization algorithm combining PSO and Back Propagation(BP) neural network is introduced to establish the prediction model based on typical defects. Collect on-site sample data, normalize it, and PSO is used to recalculate the weights and thresholds to accelerate the convergence and improve the accuracy and stability of the results. The experimental results show that the prediction accuracy of the optimized neural network model is high, and it is closer to the actual production of continuous casting

Application of a dynamic subgrid-scale model to turbulent recirculating flows

The dynamic subgrid-scale model of Germano et al. is implemented in a finite volume formulation and applied to the simulation of turbulent flow in a three-dimensional lid-driven cavity at Reynolds number of 7500. The filtering operation is carried out in physical space, and the model coefficient is calculated locally. The computed mean and rms velocities as well as the Reynolds stress are compared with experimental data. It is shown that backscatter from small to large scales is necessary to sustain turbulent fluctuations. The model is being applied to the simulation of turbulent flows in a stratified and rotating environment in complex geometries

Transient Sub-Poissonian Distribution for Single-Mode Lasers

In this paper, the transient photon statistics for single-mode lasers is investigated by making use of the theory of quantum electrodynamics. By taking into account of the transitive time l,we obtain the master equation for Jaynes-Cummings model. The relation between the Mandel factor and the time is obtained by directly solving the master equation. The result shows that a transient phenomenon from the transient super-Poissonian distribution to the transient sub-Poissonian distribution occurs for single-mode lasers. In addition, the influences of the thermal light field and the cavity loss on the transient sub-Poissonian distribution are also studied

Isolation and identification of active ingredients and biological activity of Dioscorea nipponica Makino.

This study reported the isolation and identification of bioactive compounds from Dioscorea nipponica Makino, a plant used in traditional medicine for various ailments. Nine compounds were isolated, including a new compound named as diosniposide E, which was elucidated by analyzing its 1H-NMR, 13C-NMR, DEPT, COSY, HMBC and MS data and comparing them with data available in literature. The other eight compounds were identified as known compounds. Theoretical calculations of energy and the generation of a molecular electrostatic potential surface map were employed to assess the antioxidant capacity of nine compounds, the calculation results exhibited that compounds 5 and 6 had strong antioxidant capacities. To further evaluate the antioxidant activities of the investigated compounds, the DPPH and ABTS assays were conducted. The results from the DPPH scavenging activity test revealed that compounds 4-6 exhibited enhanced scavenging activities compared to L-ascorbic acid, while displaying similar efficacy to trolox. Moreover, the ABTS scavenging activities of compounds 4-6 were found to surpass those of L-ascorbic acid and trolox. In terms of α-glucosidase inhibition, compounds 3 and 4 displayed remarkable inhibitory activities that surpassed the effects of acarbose. Additionally, compound 2 exhibited potent anticholinesterase activities, outperforming donepezil. This research provides insights into the potential bioactive compounds present in Dioscorea nipponica Makino and may contribute to its use in traditional medicine

Characterization of a New Wheat- 1M(1B) Substitution Line with Good Quality-associated HMW Glutenin Subunit

In this study, a new substitution line, 12-5-1, with 42 chromosomes that was derived from BC3F2 descendants of the hybridization between Triticum aestivum cv. CN19 and Aegilops biuncialis was created and reported. The 12-5-1 was immune to both powdery mildew and stripe rust and has stable fertility. Multi-color fluorescence in situ hybridization indicated that 12-5-1 was a substitution line 1Mb(1B). The seed storage protein electrophoresis showed that 12-5-1 presented high molecular weight glutenin subunits (2 + 12) of CN19 and a new subunit designated as M which apparently originated from parent Ae. biuncialis, and absent 7 + 8 subunits. Additionally, the flour quality parameters showed that the protein content, Zeleny sedimentation value, wet gluten content, and grain hardness and mixing time of 12-5-1 were signifiantly higher than those of its parent CN19. Moreover, 5 pairs of the chromosome 1Mb-specifi polymerase chain reaction-based landmark unique gene markers, TNAC1021, TNAC1026, TNAC1041, TNAC1-02 and TNAC1-04, were also obtained. The new substitution line 1Mb(1B) 12-5-1 could be a valuable source for wheat improvement, especially for wheat end product quality and resistance to disease

Effects of upregulated indoleamine 2, 3-dioxygenase 1 by interferon γ gene transfer on interferon γ-mediated antitumor activity.

Interferon γ (IFN-γ), an anticancer agent, is a strong inducer of indoleamine 2, 3-dioxygenase 1 (IDO1), which is a tryptophan-metabolizing enzyme involved in the induction of tumor immune tolerance. In this study, we investigated the IDO1 expression in organs after IFN-γ gene transfer to mice. IFN-γ gene transfer greatly increased the mRNA expression of IDO1 in many tissues with the highest in the liver. This upregulation was associated with reduced L-tryptophan levels and increased L-kynurenine levels in serum, indicating that IFN-γ gene transfer increased the IDO activity. Then, Lewis lung carcinoma (LLC) tumor-bearing wild-type and IDO1-knockout (IDO1 KO) mice were used to investigate the effects of IDO1 on the antitumor activity of IFN-γ. IFN-γ gene transfer significantly retarded the tumor growth in both strains without any significant difference in tumor size between the two groups. By contrast, the IDO1 activity was increased only in the wild-type mice by IFN-γ gene transfer, suggesting that cells other than LLC cells, such as tumor stromal cells, are the major contributors of IDO1 expression in LLC tumor. Taken together, these results imply that IFN-γ gene transfer mediated IDO1 upregulation in cells other than LLC cells has hardly any effect on the antitumor activity of IFN-γ