Global Stability and Non-Vanishing Vacuum States of 3D Compressible Navier-Stokes Equations

We investigate the global stability and non-vanishing vacuum states of large solutions to the compressible Navier-Stokes equations on the torus $\mathbb{T}^3$, and the main novelty of this work is three-fold: First, under the assumption that the density $\rho({\bf{x}}, t)$ verifies $\sup_{t\geq 0}\|\rho(t)\|_{L^\infty}\leq M$, it is shown that the solutions converge to equilibrium state exponentially in $L^2$-norm. Second, by employing some new thoughts, we also show that the density converges to its equilibrium state exponentially in $L^\infty$-norm if additionally the initial density $\rho_0({\bf{x}})$ satisfies $\inf_{{\bf{x}}\in\mathbb{T}^3}\rho_0({\bf{x}})\geq c_0>0$. Finally, we prove that the vacuum states will not vanish for any time provided that the vacuum states are present initially. This phenomenon is totally new and somewhat surprising, and particularly is in contrast to the previous work of [H. L. Li et al., Commun. Math. Phys., 281 (2008), 401-444], where the authors showed that the vacuum states must vanish within finite time for the 1D compressible Navier-Stokes equations with density-dependent viscosity $\mu(\rho)=\rho^\alpha$ with $\alpha>1/2$.Comment: 17 page

On instability of a generic compressible two-fluid model in R3\mathbb R^3

We are concerned with the instability of a generic compressible two-fluid model in the whole space $\mathbb{R}^3$, where the capillary pressure $f(\alpha^-\rho^-)=P^+-P^-\neq 0$ is taken into account. For the case that the capillary pressure is a strictly decreasing function near the equilibrium, namely, $f'(1)<0$, Evje-Wang-Wen established global stability of the constant equilibrium state for the three-dimensional Cauchy problem under some smallness assumptions. Recently, Wu-Yao-Zhang proved global stability of the constant equilibrium state for the case $P^+=P^-$ (corresponding to $f'(1)=0$). In this work, we investigate the instability of the constant equilibrium state for the case that the capillary pressure is a strictly increasing function near the equilibrium, namely, $f'(1)>0$. First, by employing Hodge decomposition technique and making detailed analysis of the Green's function for the corresponding linearized system, we construct solutions of the linearized problem that grow exponentially in time in the Sobolev space $H^k$, thus leading to a global instability result for the linearized problem. Moreover, with the help of the global linear instability result and a local existence theorem of classical solutions to the original nonlinear system, we can then show the instability of the nonlinear problem in the sense of Hadamard by making a delicate analysis on the properties of the semigroup. Therefore, our result shows that for the case $f'(1)>0$, the constant equilibrium state of the two-fluid model is linearly globally unstable and nonlinearly locally unstable in the sense of Hadamard, which is in contrast to the cases $f'(1)<0$ and $P^+=P^-$ (corresponding to $f'(1)=0$) where the constant equilibrium state of the two--fluid model is nonlinearly globally stable.Comment: 17. arXiv admin note: substantial text overlap with arXiv:2204.10706, arXiv:2108.06974, arXiv:2010.1150

Bioleaching of Sphalerite by the Native Mesophilic Iron-oxidizing Bacteria from a Lead-Zinc Tailing

AbstractAn isolated native mesophilic iron-oxidizing bacteria, acidithiobacillus ferrooxidans, was used to extract zinc by the bioleaching method from a typical lead-zinc tailing. Experiments were carried out by mixed culture of the mesophilic strain in the shake flasks and the different influencing factors such as pH, temperature, inoculation cell number, as well as slurry concentration on the process of bioleaching were investigated. The results indicated that the extraction efficiency of zinc was relevant with these variables and more than 70% of sphalerite was dissolved on the condition of with pH 2.0, initial ferrous concentration of 10g/L and slurry concentration of 10wt.% during 25 d, while without bacteria, 22% of Zn was merely extracted

Ginsenosides are novel naturally-occurring aryl hydrocarbon receptor ligands.

The aryl hydrocarbon receptor (AHR) is a ligand-dependent transcription factor that mediates many of the biological and toxicological actions of structurally diverse chemicals. In this study, we examined the ability of a series of ginsenosides extracted from ginseng, a traditional Chinese medicine, to bind to and activate/inhibit the AHR and AHR signal transduction. Utilizing a combination of ligand and DNA binding assays, molecular docking and reporter gene analysis, we demonstrated the ability of selected ginsenosides to directly bind to and activate the guinea pig cytosolic AHR, and to stimulate/inhibit AHR-dependent luciferase gene expression in a recombinant guinea pig cell line. Comparative studies revealed significant species differences in the ability of ginsenosides to stimulate AHR-dependent gene expression in guinea pig, rat, mouse and human cell lines. Not only did selected ginsenosides preferentially activate the AHR from one species and not others, mouse cell line was also significantly less responsive to these chemicals than rat and guinea pig cell lines, but the endogenous gene CYP1A1 could still be inducted in mouse cell line. Overall, the ability of these compounds to stimulate AHR signal transduction demonstrated that these ginsenosides are a new class of naturally occurring AHR agonists

Development of a Vacuum Ultra-Violet Laser-Based Angle-Resolved Photoemission System with a Super-High Energy Resolution Better Than 1 meV

The design and performance of the first vacuum ultra-violet (VUV) laser-based angle-resolved photoemission (ARPES) system are described. The VUV laser with a photon energy of 6.994 eV and bandwidth of 0.26 meV is achieved from the second harmonic generation using a novel non-linear optical crystal KBe2BO3F2 (KBBF). The new VUV laser-based ARPES system exhibits superior performance, including super-high energy resolution better than 1 meV, high momentum resolution, super-high photon flux and much enhanced bulk sensitivity, which are demonstrated from measurements on a typical Bi2Sr2CaCu2O8 high temperature superconductor. Issues and further development related to the VUV laser-based photoemission technique are discussed.Comment: 29 pages, 10 figures, submitted to Review of Scientific Instrument

Mechanism of breast cancer centrosome regulatory protein SEC23B on tumor invasion and metastasis

Background and purpose: The novel centrosomal regulatory protein Sec23 homolog B (SEC23B) regulates autophagy in cells, thereby providing energy and nutrients that contribute to tumor growth and distant metastasis. However, whether this role is involved in the mechanism of infiltrative metastasis in breast cancer is unclear. The aim of this study was to investigate the molecular mechanism by which SEC23B promotes breast cancer infiltration and metastasis. Methods: The association between SEC23B expression and breast cancer prognosis and metastasis was analyzed using Kaplan-Meier Plotter database and HCMDB database. MCF-7 cells were divided into vector group (control) and SEC23B overexpression plasmid group (SEC23B), and MDA231-LM2 cells were divided into SEC23B knockdown group (sh-SEC23B) and control group (sh-NC). Western blot was used to detect the expressions of SEC23B, autophagy-associated proteins [dead bone fragment 1 (SQSTM1, p62), microtubule-associated-protein light-chain-3 (LC3)] and extracellular-regulated protein kinases (ERK)/mammalian target of rapamycin (mTOR) pathway proteins in breast cancer cells. Cell migration was assessed by transwell assay and wound healing assay, and autophagic granules in cells were detected by immunofluorescence staining. In addition, an in vivo intraperitoneal tumor model was constructed to study the effect of SEC23B on breast cancer cell metastasis in vivo. Results: The overall survival of breast cancer patients with high SEC23B expression was significantly shorter than that of patients with low SEC23B expression. The expression of SEC23B in metastatic breast cancer was significantly higher than that in breast cancer without metastasis. SEC23B protein levels were lower in primary breast cancer cells (MCF-7, BT-549, MDA-MB-468 and MDA-MB-453) than in metastatic breast cancer cells (MDA231-LM2 and ZR-75-30). Compared with the control group, the SEC23B group significantly accelerated cell migration (P&lt;0.001). Compared with the sh-NC group, the sh-SEC23B group significantly reduced cell migration (P&lt;0.001). Compared with the control group, the expression level of LC3A/B and the formation of autophagy particles in the SEC23B group were significantly increased, while the expression of p62 protein and the phosphorylation levels of mTOR and ERK were decreased. Compared with the sh-NC group, the LC3A/B expression level and the formation of autophagy particles were significantly decreased in the sh-SEC23B group, and the phosphorylation levels of mTOR and ERK were increased, especially under starvation conditions. In in vivo experiments, tumor weight was significantly lower in the sh-SEC23B group compared with the sh-NC group (P&lt;0.01), and there was an increase in necrotic tissue and a decrease in tumor metastasis in lung tissue in mice. sh-SEC23B group mice had a significantly lower number of lung metastatic tumors and LC3 immunohistochemical staining than the sh-NC group (P&lt;0.01). Conclusions: SEC23B induces breast cancer autophagy and promotes cancer cell metastasis by inhibiting ERK/mTOR signaling pathway

Superconductivity in Li8Au electride

Located at crystal voids, interstitial anion electrons (IAEs) have diverse topologies, which may be tuned to achieve new properties. Elucidating the role of IAEs in electron-phonon coupling (EPC), and using it to design new electride superconductors, leads to the current prediction of superconducting Li8Au at high pressure. We suggest that the occurence of high-temperature superconductivity in electrides requires high-symmetry structures with hydrogen-like cages, an electron acceptor element to balance charges, and isolated IAEs coupled with medium-frequency vibrations. The uniquely designed Li8Au electride has a NaCl-type (B1) lattice, with atomic Au and cubic Li8 cages as bases. Isolated IAEs are formed at the cage centers, with extra charges taken up by Au. These octahedrally coordinated IAEs have a p-orbital-like attribute and are strongly coupled with atomic vibrations in the Li8 cages. The strong EPC in Li8Au results in a calculated Tc of 73.1 K at 250 GPa, which is the highest Tc reported to date for all the electrides. A slight substitutional Pt doping can enhance the Tc of Li8Au to exceed liquid nitrogen temperature.Comment: 7 Pages, 3 Figure