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Metal sulfides have been universally studied as anode materials for lithium ion batteries (LIBs). Herein, we studied the lithiation storage behavior of a novel metal sulfide PbTiS3 (PTS), which is one of misfit layer compounds (MLCs) including intercalation-type TiS2 layer and conversion-alloying-type PbS layer. In-situ powder X-ray diffraction measurement reveals that the final lithiated product Li22Pb5 can be restored, indicating a reversible conversion-alloying mechanism in PTS. Theoretical calculation indicates the soft PbS interlayers of rock salt structure can hinder the distortion of TiS2 layers upon lithiation, resulting in a high structural integration of PTS anodes as well as a high concentration of intercalated Li ions. Moreover, with the assistance of the strong interfacial C–O–Pb/Ti interaction between PTS and graphene oxide (GO), PTS can be embedded in the conductive GO network which could stabilize PTS structure during long term cycling. Consequently, the fabricated LIBs anode delivers a relatively high reversible capacity (569 mA h g−1 at 2.0 A g−1 after 1000 cycles) and an outstanding high-rate capability. Besides, the assembled lithium ion full battery maintains a capacity retention of 70% after 100 cycles at 0.1 A g−1. This work provides insights into the design of MLCs as next-generation secondary batteries.

To explore the semantic computed tomography (CT) features associated with BRCA1-associated protein 1 (BAP1) and/or tumor protein p53 (TP53) mutation in clear cell renal cell carcinoma (ccRCC).Clinical characteristics and gene mutation information of 336 ccRCC patients were retrieved from The Cancer Genome Atlas-Kidney Renal Clear Cell Carcinoma database (TCGA-KIRC). Kaplan-Meier analysis was performed to examine prognosis by gene mutation. CT imaging data and gene mutation information of 156 ccRCC patients treated between January 2019 to January 2021 (the training cohort) were retrospectively analyzed. CT imaging information and gene mutation data of 123 patients with ccRCC were downloaded from The Cancer Imaging Archive and The Cancer Genome Atlas database (the external validation cohort). Univariate Chi-square test and multivariate binary logistic regression analysis were performed to determine predictors of gene mutation; a nomogram was developed using these predictors. Receiver operating characteristic curve analysis and the Hosmer-Lemeshow test were performed to evaluate the performance of the nomogram.Kaplan-Meier analysis showed that BAP1 and/or TP53 mutation was significantly correlated with worse survival outcome. Multivariate binary logistic regression analysis indicated ill-defined margin (P=0.001), spiculated margin (P= 0.018), renal vein invasion (P=0.002), and renal pelvis invasion (P=0.001) were independent predictors of BAP1 and/or TP53 mutation. A nomogram containing these four semantic CT features was constructed; the area under the receiver operating characteristic curves was 0.872 (95% CI, 0.809-0.920). The Hosmer-Lemeshow test showed acceptable goodness-of-fit for the nomogram (XSemantic CT feature is a potential and promising method for predicting BAP1 and/or TP53 mutation status in ccRCC patients.

AIM Pulmonary hypertension (PH) is a pathophysiological syndrome with functional abnormalities of the pulmonary artery and heart, eventually becoming life threatening to the patients. Autophagy-related gene 7 (ATG)-7 is involved in many cardiovascular diseases, but little is known about the specific role of ATG-7 in the development of PH. We aimed to examine the expression of ATG-7 in PH patients and PH mice, specifically investigate pulmonary physiological responses in a mouse model with conditional deletion of ATG-7 in smooth muscle cells (SMCs) and further clarify the mechanism of PH caused by ATG-7 deficiency. METHODS AND RESULTS SMC-ATG-7-/- mice underwent echocardiography and subsequent pulmonary arterial pressure (PAP) checks. The PAP was lower in wild-type (WT) mice (22.6 ± 2.0 mmHg) than knockout (KO) mice (34.0 ± 2.5 mmHg; p

Samples of Ni0.6Zn0.3Co0.1NdxFe2-xO4 (0.00 ≤ x ≤ 0.10) ferrites were synthesized by the sol-gel auto-combustion method and microwave sintering technology. The effects of Nd substitution on the crystal structure, magnetic, and electrical properties have been investigated. The XRD results showed that the main phase of sintered samples was a standard spinel structure. When x > 0.02, the second phase appeared in the sintered samples, which led to the phenomenon that the lattice constant of the sample increased and then decreased. Overall, the saturation magnetization of the samples showed a downward trend, and the value of coercivity increased with the amount of substitution. In terms of electrical performance, the dielectric constant of the samples showed an overall increasing trend with the amount of substitution after a sharp drop in the low frequency band and tended to be stable in the high frequency band. At x = 0.02, the ferrite sample exhibited the lowest dielectric constant (e', 41.63), the highest dc resistivity (ρ, 4.973 × 106 Ω∙m), relatively small coercivity (Hc, 20.878 Oe) and relatively high saturation magnetization (Ms, 79.214 emu/g).

Ni06Zn0.3Co0.1YxFe2-xO4 ferrites (0 ≤ x ≤ 0.1) were fabricated by a sol–gel autocombustion method using Microwave Sintering Technology (MST) and Conventional Sintering Technology (CST). With increased Y3+ ions, the structure and electromagnetic performance of all MST samples were better than those of CST. In addition, the MST and CST samples formed a second phase (YFeO3) when x > 0.025 because the radius of the Y3+ ion is larger than that of the Fe3+ ion. Compared with the CST samples, the MST samples showed increased densification and average grain size. Meanwhile, excellent electromagnetic performance of MST was achieved when the amount of Y substitution was 0.025, with high saturation magnetization (Ms, 154.19 emu/g), the lowest coercivity (Hc, 20.21 Oe), the lowest dielectric constant (e′, 10.82@1 MHz), lower dielectric loss (tanδ, 0.0093@1 MHz) and the highest direct-current resistivity (ρ, 2.706 × 106 Ω⋅m). These excellent results also confirm the good prospects of microwave sintering, which can better meet the needs of modern electronic devices for high frequency and low loss.

A strategy of doping chalcogen-heteroatom in red phosphorus (RP) nanoparticles is adopted to improve the electrochemical performance of RP based composites as lithium storage materials. RP nanoparticles embedded in porous carbon with chalcogen-doping (S-, Se- and Te–P@PC) composites are synthesized via a facile evaporation-condensation approach. The large volume expansion of RP upon cycling is well mitigated by nanoscale feature and buffered by pore-closed carbon matrix. The extra fillings of chalcogen dopants lessen the specific surface areas of the doped composites, minimizing parasitic surface reactions of anode materials with electrolyte that can lead to high initial coulombic efficiencies. The high conductivity of Se dopant and the formed conductive Li–Se/Li–Se–P confer the Se–P@PC anode with improved electron/ion transport properties to deliver a superior fast-charging capability over 900 cycles. Moreover, a high-rate capacity of 908.5 mA h g−1 at 5.0 A g−1 and an impressive reversible capacity of 848.2 mA h g−1 even after 1800 cycles at 1.0 A g−1 of Se–P@PC surpass most of reported RP-based anode materials.

Ni0.6Zn0.4Co0.2Fe1.8O4 ferrites doped with x wt.% K0.5Na0.5NbO3 (0.00≤x≤1.00) were successfully prepared by solid-state reaction method. The lattice parameters a decreased and the diffraction peak of (311) shifted to higher angle with the increase of K0.5Na0.5NbO3 (KNN) content. The grain size D initially increased to 3.12 μm (x = 0.50) and then reduced to 2.66 μm (x=1.00). The study also showed the addition of KNN effectively improved magnetic and electrical properties of NiZnCo ferrites. The saturation magnetization Ms decreased from 60.59 to 46.11 emu/g and the coercivity Hc overall showed a decreasing trend from 84.64–67.00 Oe. The dielectric constant e´ of prepared samples increased when x≤0.75, then decreased when x>0.75, and all prepared samples had low loss tangent tanδ at high frequency. In addition, all samples exhibited high resistivity ρ and activation energy Eρ.

In this paper, we are concerned with output tracking for a one-dimensional heat equation where both disturbance and performance output are non-collocated to the controller. The method of trajectory planning is used to overcome the difficulties caused by these non-collocated configurations. An observer based output feedback law is designed by using only the tracking error between performance output and reference signal. Exponential convergence of tracking error and uniform boundedness of state of the whole closed-loop system are obtained. These theoretical results are validated by numerical simulations.

HfO2 doped NiZnCo bulk ferrites, Ni0.5Zn0.3Co0.2Fe2O4 with different HfO2 dopant content (0 ≤ x ≤ 0.1 wt%), were fabricated by the solid states reaction method. We investigated the influence of HfO2 doping on structure and electromagnetic properties. The XRD pattern shows that as the doping of HfO2 increases, the lattice parameter decreases and the X-ray density increases. There is an extra peak in each sample due to generation of NiCo2O4 impurity phase. The SEM images demonstrate the grain size slightly decreases with increasing HfO2 content. As the amount of HfO2 doping increases, the saturation magnetization increases linearly and the coercivity decreases. The polarization of all ferrite samples is due to the fact that the electronic hopping frequency between Fe2+ and Fe3+ ions can't keep up with external applied frequency. As the amount of HfO2 doping increases, the dielectric constant increases when x

Two ternary lanthanide complexes [Ln(2-Br-5-MOBA)3(5,5′-DM-2,2′-DIPY)]2 (Ln = Sm(1), Eu(2); 2-Br-5-MOBA = 2-bromo-5-methoxybenzoate; 5,5′-DM-2,2′-DIPY = 5,5′-dimethyl-2,2′-bipyridine) with 2-bromo-5-methoxybenzoic acid and 5,5′-dimethyl-2,2′-bipyridine have been synthesized and characterized. The Single-crystal X-ray diffraction date show that complexes 1 and 2 are isostructural in the triclinic system, space group P 1 ¯ . Infrared spectra (IR) and X-ray powder diffraction (PXRD) further confirm that complexes 1 and 2 are isostructural. The basic structural unit forms a 1D chain through the weak C H⋯Br hydrogen bond interaction along the b-axis, and forms a 2D sheet through the π–π stacking interactions along the a-axis. The 2D sheets are further interconnected by the C H⋯O hydrogen bond interaction to assembled into a 3D supramolecular network along the c-axis. In addition, the simultaneous thermal analysis (TG, DTG and DSC) of the complexes and the FTIR spectra of the escaped gas were measured. The heat capacities of the complexes were determined by DSC in the temperature region of 258.15–393.15 K. Furthermore, the luminescence spectrum of the complexes 1 and 2 and luminescence lifetime of complex 2 were also measured.

Ni0.55Zn0.3Co0.15GdxFe2-xO4 (x = 0, 0.05, 0.10, 0.15, 0.20) ferrite materials with spinel structure were successfully synthesized by sol–gel self-propagation and microwave sintering technique. The structure and electromagnetic properties of NiZnCo ferrite with Gd substitution are systematically studied. The results show that the substitution of Gd3+ for Fe3+ at the B site changes the electromagnetic properties of NiZnCo ferrite. Among them, the resonant frequency increased from 637 MHz (x = 0.00) to more than 1.5 GHz (x = 0.20), which is 2.5 times higher than that of pure NiZnCo ferrite. Moreover, when the doping amount x = 0.05, the dielectric constant of ferrite is the lowest (e′, 37.735), the DC resistivity is the highest (ρ, 3.64 × 106 Ω·m), and the dielectric loss is the lowest (tanδ, 3.03). In general, the substitution of Gd can make NiZnCo ferrite obtain excellent electromagnetic properties, which provides a reference for high-frequency microwave device materials.

Shear transfer at concrete-to-concrete interfaces under direct shear is of great significance to the performance of concrete structures. In this study, a series of direct shear specimens with concrete-to-concrete interfaces were designed by considering the normal pressure, longitudinal reinforcement, and coupling effects. Adding reinforcement or normal pressure increased the interface cracking stress, ultimate shear strength, and residual shear strength, and changed the brittle behavior of the bonding interface to a gradual strength degradation mode. However, an increase in the normal pressure from 4 to 8 MPa only slightly improved the elastic stiffness and plastic ductility of the direct shear specimens. Furthermore, comparing the observed ultimate strengths with the calculated ultimate strengths of three models in main codes, it was shown that all calculated strengths were conservative. During the shear-slip process, among cohesion, friction, and dowel action, the friction was the most affected property during the direct shear process. In the final residual stage, the ratios of cohesion, friction, and dowel action were found to be similar, and no significant relationship was observed between the longitudinal reinforcement and normal pressure before the ultimate shear stress was reached. However, after the ultimate shear stress was reached, the interaction was found to improve the shear resistance at the concrete-to-concrete interface, thereby improving the ductility and interface shear performance.

Misfit layer SnTiS3 (STS) crystal as a bulk van der Waals (vdW) heterostructure SnS/TiS2 is developed as a superior anode material for lithium-ion batteries (LIBs). STS can combine the advantages of metallic character of TiS2 layers and high lithium-storage of SnS layers. Moreover, graphene oxide (GO) is adopted to support STS via a hand-grinding route. A strong binding between STS and GO is conducive to decreasing the crystalline domain size of STS. Besides, the in-situ electrochemical reduction of GO nanosheets during the first cycling could offer a conductive network for both ions and electrons. Consequently, the electrochemical performance of STS/GO is superior than that of pristine STS and STS/rGO (rGO = reduced GO), and outstanding among the latest reports of SnS- or TiS2-based on LIBs anodes. Specifically, STS/GO anode delivers a capacity of 614 mA h g−1 at 2.0 A g−1 after 1000 cycles, as well as a high rate capability due to the dominated surface-capacitive contribution. Furthermore, the combination of in-situ and ex-situ powder X-ray diffraction patterns unequivocally reveals a conversion-alloy mechanism in STS anode upon lithiation/delithiation.

Two novel lanthanide complexes with the general formula [Ln(2-Br-5-MOBA) 3 (2,2′-DIPY)] 2 (Ln = Pr(1), Dy(2); 2-Br-5-MOBA = 2-bromine-5-methoxybenzoate; 2,2′-DIPY = 2,2′-bipyridine) have been successfully synthesized and characterized. The complexes 1 and 2 are isostructural and nine-coordinated with distorted monocapped square antiprismatic coordination geometry by the single-crystal X-ray diffraction analyses. Two complexes are all assembled into the 1D, 2D, 3D supramolecular structures by C H⋯O hydrogen bonding and π–π stacking interactions. The thermal decomposition mechanism for title complexes were obtained by TG/DSC-FTIR technology. The molar heat capacities of the complexes 1 and 2 are measured by a DSC instrument over the temperature range from 263.15 K to 365.15 K. On the basis of the fitted polynomial and thermodynamic equations, the smoothed values of heat capacities and thermodynamic functions ( H T - H 298.15K ), and ( S T - S 298.15K ) of the two complexes are calculated. In addition, the fluorescence spectra indicate that the complex 2 exhibits the characteristic emission of Dy(III) ion ( 4 F 9/2 → 6 H 13/2–15/2 ).

A phytochemical study on the rhizomes of Smilax riparia led to the isolation of 16 saponin compounds, including nine furostanol steroidal saponins (1–4, 6, 7, 10, 12, 14), six spirostanol steroidal saponins (5, 8, 9, 11, 13, 15) and one 20-carboxylic acid γ-lactone steroidal saponin (16). The structures of these compounds were identified by spectroscopic methods and comparison of their data with those reported in the literature. This is the first report of compounds 1, 4, 5, 8, 9, 11–16 from the genus Smilax . The chemotaxonomic significance of the isolated compounds has also been summarized.

CoFe2O4 is mainly used in magnetic strain sensor, magnetic resonance imaging, supercapacitor, cryogen, high density magnetic recording medium and magneto-optical devices and so on. In this study, SixCo1-xFe2O4 (where x = 0, 0.05, 0.10, 0.15, 0.30, 0.40, 0.50) ferrites were prepared by sol-gel self-propagating method, and the effects of different amount of silicon substitution on the properties of cobalt ferrite were studied. The X-ray diffraction spectrums demonstrate that the secondary phase Fe2O3, Fe2·56Si0·44O4 and FeO appear when x ≥ 0.15. The SEM images of the samples show that with the increase of silicon ion content, the porosity of cobalt ferrite increases and the sintering density decreases. The substitution of silicon significantly changed the electromagnetic properties of Co ferrite samples. Fortunately, the coercive force (Hc) increased. Moreover, the dielectric constant raised initially when 0 ≤ x ≤ 0.30 and then reduced when 0.30

In this paper, we consider exponential stabilization for a 1-D wave equation with variable coefficients and Neumann boundary actuation. A novel transformation is constructed to convert the wave equation into an equation of the same type with constant coefficient and low order term. By using the backstepping approach, we design a state observer via non-collocated boundary displacement and velocity measurement. An observer based output feedback is then designed using the backstepping gain to stabilize the system exponentially. The well-posedness and the exponential stability of the closed-loop system are proved. As an illustration, some numerical simulations are presented.

Allopurinol is a commonly used medication to treat hyperuricemia and its complications. Pallidifloside D, a saponin glycoside constituent from the total saponins of Smilax riparia, had been proved to enhanced hypouricemic effect of allopurinol based on uric acid metabolism enzyme XOD. In this study, we evaluated whether Pallidifloside D (5mg/kg) enhanced hypouricemic effect of allopurinol (5mg/kg) related to others uric acid metabolism enzymes such as PRPS, HGPRT and PRPPAT. We found that, compared with allopurinol alone, the combination of allopurinol and Pallidifloside D significantly up-regulated HGPRT mRNA expression and down-regulated the mRNA expression of PRPS and PRPPAT in PC12 cells (all P

Pallidifloside D, a saponin glycoside constituent from the total saponins of Smilax riparia, had been proved to be effective in hyperuricemic control. Allopurinol is a commonly used medication to treat hyperuricemia and its complications. In this study, we evaluated whether Pallidifloside D could enhance allopurinol's effects by decreasing the serum uric acid level in a hyperuricemic mouse model induced by potassium oxonate. We found that, compared with allopurinol alone, the combination of allopurinol and Pallidifloside D significantly decreased the serum uric acid level and increased the urine uric acid level (both P0.05), leading to the normalized serum and urine uric acid concentrations. Data on serum, urine creatinine and BUN supported these observations. Our results showed that the synergistic effects of allopurinol combined with Pallidifloside D were linked to the inhibition of both serum and hepatic xanthine oxidase (XOD), the down-regulation of renal mURAT1 and mGLUT9, and the up-regulation of mOAT1. Our data may have a potential value in clinical practice in the treatment of gout and other hyperuricemic conditions.

Background: Colorectal cancer (CRC) is a leading cause of death worldwide. Chronic gut inflammation is recognized as a risk factor for tumor development, including CRC. American ginseng is a very commonly used ginseng species in the West. Methods: A genetically engineered ApcMin/+ mouse model was used in this study. We analyzed the saponin composition of American ginseng used in this project, and evaluated its effects on the progression of high-fat-diet-enhanced CRC carcinogenesis. Results: After oral ginseng administration (10–20 mg/kg/d for up to 32 wk), experimental data showed that, compared with the untreated mice, ginseng very significantly reduced tumor initiation and progression in both the small intestine (including the proximal end, middle end, and distal end) and the colon (all p

The roots and rhizomes of Smilax riparia are called "Niu-Wei-Cai" in traditional Chinese medicine (TCM). This botanical has been used in treating the symptoms of gout and other hyperuricemic-related conditions in TCM. Allopurinol is a commonly used medication to treat hyperuricemia and its complications. In this study, we evaluated whether Smilax riparia could enhance allopurinol׳s effects by decreasing the serum uric acid level in a hyperuricemic mouse model induced by potassium oxonate.We examined the effects of allopurinol (5mg/kg) administration alone or in combination with Smilax riparia saponins (SRS, 500 mg/kg) on the serum uric acid (SUA), serum creatinine (SCr) and blood urea nitrogen (BUN) levels in a hyperuricemic mouse model. The effects of allopurinol alone or those of allopurinol plus SRS on the XOD activities were measured. Western blot analysis was used to measure the levels of mURAT1, mGLUT9 and mOTA1 in the mice.Compared with allopurinol alone, the combination of allopurinol and SRS significantly decreased the serum uric acid level and increased the urine uric acid level (both P0.05), leading to the normalized serum and urine uric acid concentrations. Data on serum and urine creatinine and BUN supported these observations. The attenuation of hyperuricemia-induced renal dysfunction was linked to the inhibition of both serum and hepatic xanthine oxidase (XOD), the down-regulation of renal mURAT1 and mGLUT9, and the up-regulation of mOAT1.The anti-hyperuricemia effects of allopurinol are improved by Smilax riparia co-administration. The results were supported by the measurement of uric acid, creatinine, BUN, XOD, mURAT1, mGLUT9 and mOAT1. Our data may have a potential value in clinical practice in the treatment of gout and other hyperuricemic conditions.

In this paper, a novel ruthenium(II) complex of emodin, Ru(bpy)2Emodin(RBL17, bpy = 2,2'-bipyridine; Eomdin = 1,3,8-trihydroxy-6-methyl-anthraquinone), has been synthesized and characterized by ESI-MS, 1H NMR, 1H–1H COSY and electronic spectra. The binding behavior of RBL17 with c-myc G4 DNA has been further investigated by ITC (isothermal titration calorimetry), FRET (fluorescence resonance energy transfer) and 1H NMR spectra, as well as spectroscopic methods. Those results showed that this complex has the ability to bind and stabilize the conformation of c-myc G-quadruplex via groove binding mode. Taken together, ruthenium(II) complex of emodin can act as a potential inhibitor in chemotherapy by targeting to c-myc G4 DNA.

The metabolism of traditional Chinese medicine is very complicated and has been a great challenge. In the present paper, a new strategy was established to study the metabolism of crude extract from Ganoderma lucidum using the highly separative and sensitive ultra-performance liquid chromatography/quadrupole time-of-flight mass spectrometry. Based on the investigation of the metabolism of five representative single compounds (ganoderic acid), a total of 90 metabolites were identified from the bile sample after oral administration of the crude extract. Among them, 21 compounds were identified by comparison with the reference standards, the other unknown metabolites were tentatively characterized by interpretation of the high resolution low collision energy and high collision energy mass spectra using the fragmentation rules. The metabolic characteristics and "soft spots" of the ganoderic acids were revealed. After being absorbed, the ganoderic acids from the extract could undergo extensive phases I and II metabolism in rat before excreted into the bile. The main ganoderic acids could transform from one to another through reduction, oxidation, deacetylation and desaturation reactions. Other metabolic transformation included hydroxylation, sulfation and glucuronidation. The total tendency was that the low polar ganoderic acids were transformed into the high polar metabolites to eliminate from the organism. The metabolic "soft spots" of the ganoderic acids were 3,7,15,23-carbonyl groups (or hydroxyl groups), angular methyl groups, 20(22)-double bond, 12-acetoxyl group and 26-carboxylic acid moiety. These results are considered to be important for the further investigation of G. lucidum.

In this paper we study multiscale finite element methods (MsFEMs) using spectral multiscale basis functions that are designed for high-contrast problems. Multiscale basis functions are constructed using eigenvectors of a carefully selected local spectral problem. This local spectral problem strongly depends on the choice of initial partition of unity functions. The resulting space enriches the initial multiscale space using eigenvectors of local spectral problem. The eigenvectors corresponding to small, asymptotically vanishing, eigenvalues detect important features of the solutions that are not captured by initial multiscale basis functions. Multiscale basis functions are constructed such that they span these eigenfunctions that correspond to small, asymptotically vanishing, eigenvalues. We present a convergence study that shows that the convergence rate (in energy norm) is proportional to (H/??)1/2, where ?? is proportional to the minimum of the eigenvalues that the corresponding eigenvectors are not included in the coarse space. Thus, we would like to reach to a larger eigenvalue with a smaller coarse space. This is accomplished with a careful choice of initial multiscale basis functions and the setup of the eigenvalue problems. Numerical results are presented to back-up our theoretical results and to show higher accuracy of MsFEMs with spectral multiscale basis functions. We also present a hierarchical construction of the eigenvectors that provides CPU savings.

An ionic liquid was synthesized with anhydrous aluminum chloride and amine hydrochloride with the mole ratio of 2:1. The isomerization of n-hexane catalyzed by the ionic liquid was investigated. The results indicate that the ionic liquid can catalyze the isomerization of n-hexane, but it requires long reaction time. The influence of initiators including n-butanol, i-butene, i-butane and i-pentane on the isomerization of n-hexane was investigated. The conversion of n-hexane, the yield of liquid components and the selectivity of isoparaffins are 84.54%, 80.08% and 94.74%, respectively, when i-pentane is used as the initiator. This shows that i-pentane is a good initiator for the isomerization of n-hexane. The dosage of i-pentane shows great influence on the isomerization of n-hexane, and the suitable dosage is 30%. The initiator i-pentane can greatly accelerate the rate of the isomerization of n-hexane. The reaction time can be shortened from 6 h to 45 min to achieve the similar reaction extent.

In this paper, we study a multiscale finite element method for solving a class of elliptic problems arising from composite materials and flows in porous media, which contain many spatial scales. The method is designed to efficiently capture the large scale behavior of the solution without resolving all the small scale features. This is accomplished by constructing the multiscale finite element base functions that are adaptive to the local property of the differential operator. Our method is applicable to general multiple-scale problems without restrictive assumptions. The construction of the base functions is fully decoupled from element to element; thus, the method is perfectly parallel and is naturally adapted to massively parallel computers. For the same reason, the method has the ability to handle extremely large degrees of freedom due to highly heterogeneous media, which are intractable by conventional finite element (difference) methods. In contrast to some empirical numerical upscaling methods, the multiscale method is systematic and self- consistent, which makes it easier to analyze. We give a brief analysis of the method, with emphasis on the “resonant sampling” effect. Then, we propose an oversampling technique to remove the resonance effect. We demonstrate the accuracy and efficiency of our method through extensive numerical experiments, which include problems with random coefficients and problems with continuous scales. Parallel implementation and performance of the method are also addressed.

The vorticity-velocity formulation for incompressible viscous flows is studied. The main concern is effective numerical solution of the kinematic Cauchy-Riemann equations for velocity, especially when the divergence-free condition of vorticity is violated due to numerical error. The mathematical formulation of a differential and an integral approaches are revisited. A novel projection of vorticity onto the divergence-free space and its application to the two approaches are studied. As an illustration of the differential approach, the 3D lid-driven cavity problem is solved. The projection scheme is justified through numerical tests by comparing it to a new fully divergence-free scheme. Numerical tests indicate that keeping vorticity divergence-free is important for obtaining correct and accurate solutions. The theory and methods apply to other divergence-free fields of physical interest as well, such as that in electro-magnetic dynamics.