A refined invariant subspace method and applications to evolution equations

The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that evolution equations admit. A two-component nonlinear system of dissipative equations was analyzed to shed light on the resulting theory, and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differential equations and their corresponding exact solutions with generalized separated variables.Comment: 16 page

Fe-doping induced superconductivity in charge-density-wave system 1T-TaS2

We report the interplay between charge-density-wave (CDW) and superconductivity of 1$T$-Fe$_{x}$Ta$_{1-x}$S$_{2}$ ($0\leq x \leq 0.05$) single crystals. The CDW order is gradually suppressed by Fe-doping, accompanied by the disappearance of pseudogap/Mott-gap as shown by the density functional theory (DFT) calculations. The superconducting state develops at low temperatures within the CDW state for the samples with the moderate doping levels. The superconductivity strongly depends on $x$ within a narrow range, and the maximum superconducting transition temperature is 2.8 K as $x=0.02$. We propose that the induced superconductivity and CDW phases are separated in real space. For high doping level ($x>0.04$), the Anderson localization (AL) state appears, resulting in a large increase of resistivity. We present a complete electronic phase diagram of 1$T$-Fe$_{x}$Ta$_{1-x}$S$_{2}$ system that shows a dome-like $T_{c}(x)$

Push-out tests and bond strength of rectangular CFST columns

Push-out tests have been conducted on 18 rectangular concrete-filled steel tubular (CFST) columns with the aim of studying the bond behaviour between the steel tube and the concrete infill. The obtained load-slip response and the distribution of the interface bond stress along the member length and around the cross-section for various load levels, as derived from measured axial strain gradients in the steel tube, are reported. Concrete compressive strength, interface length, cross-sectional dimensions and different interface conditions were varied to assess their effect on the ultimate bond stress. The test results indicate that lubricating the steel-concrete interface always had a significant adverse effect on the interface bond strength. Among the other variables considered, concrete compressive strength and cross-section size were found to have a pronounced effect on the bond strength of non-lubricated specimens for the range of cross-section geometries considered, which is not reflected in the European structural design code for composite structures, EN 1994-1-1 (2004). Finally, based on nonlinear regression of the test data generated in the present study, supplemented by additional data obtained from the literature, an empirical equation has been proposed for predicting the average ultimate bond strength for SHS and RHS filled with normal strength concrete

Vortex Phase Diagram of Layered Superconductor Cu0.03TaS2 for H || c

The magnetization and anisotropic electrical transport properties have been measured in high quality Cu0.03TaS2 single crystal. A pronounced peak effect has been observed, indicating that the high quality and homogeneity are vital to peak effect. A kink has been observed in the magnetic field H dependence of the in-plane resistivity {\rho}ab for H || c, which corresponds to a transition from activated to diffusive behavior of vortex liquid phase. In the diffusive regime of the vortex liquid phase, the in-plane resistivity {\rho}ab shows {\rho}ab $\propto$ H0.3 relation, which does not follow the Bardeen-Stephen law for free flux flow. Finally, a simplified vortex phase diagram of Cu0.03TaS2 for H || c is given.Comment: 28 pages, 9 figure

Managing The Combination Of Nonalcoholic Fatty Liver Disease And Metabolic Syndrome With Chinese Herbal Extracts In High-fat-diet Fed Rats

Nonalcoholic fatty liver disease (NAFLD) is the hepatic manifestation of metabolic syndrome (MetS). The aim of the study was to evaluate the effects of Chinese herbal extracts from Salvia miltiorrhiza and Gardenia jasminoides (SGE) on the combination of NAFLD and MetS induced by a high-fat diet (HFD) in rats. After 6 weeks of HFD feeding, rats ( each group) were treated with saline, rosiglitazone (RSG), and SGE for 4 weeks. HFD rats were obese, hyperinsulinemic, hyperlipidemic and increased hepatic enzymes with the histological images of NAFLD. Treatment with SGE significantly reduced serum triglycerides (TG), nonesterified fatty acids and enhanced insulin sensitivity, and ameliorated the elevated serum hepatic enzymes compared with HFD-saline group. SGE treatment also attenuated hepatic TG by 18.5% (). Histological stains showed SGE decreased lipids droplets in hepatocytes () and normalized macrovesicular steatosis in HFD rats. Significant reduction of TNF-a and IL6 in adipose tissue was detected in SGE treated rats. The anti-inflammatory action may be, at least in part, the mechanism of SGE on MetS associated with NAFLD. This study discovered that SGE is capable of managing metabolic and histological abnormalities of NAFLD and MetS. SGE may be an optimal treatment for the combination of NAFLD and MetS

Electric field-induced phase transitions in (111)-, (110)-, and (100)-oriented Pb(Mg1∕3Nb2∕3)O3 single crystals

Electric field-induced phase transitions were investigated in (111), (110), and (100) thin platelets of relaxor ferroelectric Pb(Mg1∕3Nb2∕3)O3 single crystals with electric fields applied along the ⟨111⟩, ⟨110⟩, and ⟨100⟩ directions, respectively. Temperature dependences of complex dielectric permittivity, pyroelectric current and dielectric hysteresis loops were investigated. Electric field-temperature (E-T) phase diagrams were proposed for the different directions of the field. Alongside with the high-temperature ergodic relaxor phase and the low-temperature glassy nonergodic relaxor phase existing at E=0, the ferroelectric phase may appear in the diagram at the fields higher than the threshold field (Eth). The temperature of the first-order transition between ergodic relaxor and ferroelectric phases (TC) was located in field cooling and field heating after field-cooling regimes. For the ⟨111⟩ field direction, TC is higher and Eth is lower than for the other directions. For the ⟨100⟩ direction, TC is the lowest and Eth is the highest. The critical point bounding the TC(E) line when the field is applied in ⟨111⟩ direction [ Z. Kutnjak, J. Petzelt and R. Blinc Nature 441 956 (2006)] is not observed in the ⟨110⟩ and ⟨100⟩ directions up to the highest applied field of 7.5 kV∕cm. Extrapolation of experimental data suggests that the critical point for the ⟨110⟩ and ⟨100⟩ directions (if any) can be expected only at much higher fields. In the hysteresis loops experiments performed after zero-field cooling, the lower temperature limit is determined above which a ferroelectric phase can be induced from the frozen glassy state at a given field strength or the polarization of the induced ferroelectric phase can be reversed. This limit is located at much lower temperatures in the (100) platelet than in the (110) or (111) platelets. An additional ferroelectric rhombohedral to ferroelectric orthorhombic phase transition occurs in the (110) platelet at high electric fields (∼20 kV∕cm). The mechanisms of the field-induced transformation from the glassy nonergodic relaxor phase or the ergodic relaxor phase to the ferroelectric phase are discussed

The instability of diffusive convection and its implication for the thermohaline staircases in the deep Arctic Ocean

In the present study, the classical description of diffusive convection is updated to interpret the instability of diffusive interfaces and the dynamical evolution of the bottom layer in the deep Arctic Ocean. In the new consideration of convective instability, both the background salinity stratification and rotation are involved. The critical Rayleigh number of diffusive convection is found to vary from 10³ to 10¹¹ in the deep Arctic Ocean as well as in other oceans and lakes. In such a wide range of conditions, the interface-induced thermal Rayleigh number is shown to be consistent with the critical Rayleigh number of diffusive convection. In most regions, background salinity stratification is found to be the main hindrance to the occurrence of convecting layers. With the new parameterization, it is predicted that the maximum thickness of the bottom layer is 1051 m in the deep Arctic Ocean, which is close to the observed value of 929 m. The evolution time of the bottom layer is predicted to be ~ 100 yr, which is on the same order as that based on ¹⁴C isolation age estimation