Finite speed axially symmetric Navier-Stokes flows passing a cone

Let $D$ be the exterior of a cone inside a ball, with its altitude angle at most $\pi/6$ in $\mathbb{R}^3$, which touches the $x_3$ axis at the origin. For any initial value $v_0 = v_{0,r}e_{r} + v_{0,\theta} e_{\theta} + v_{0,3} e_{3}$ in a $C^2(\overline{D})$ class, which has the usual even-odd-odd symmetry in the $x_3$ variable and has the partial smallness only in the swirl direction: $| r v_{0, \theta} | \leq \frac{1}{100}$, the axially symmetric Navier-Stokes equations (ASNS) with Navier-Hodge-Lions slip boundary condition has a finite-energy solution that stays bounded for all time. In particular, no finite-time blowup of the fluid velocity occurs. Compared with standard smallness assumptions on the initial velocity, no size restriction is made on the components $v_{0,r}$ and $v_{0,3}$. In a broad sense, this result appears to solve $2/3$ of the regularity problem of ASNS in such domains in the class of solutions with the above symmetry. Equivalently, this result is connected to the general open question which asks that if an absolute smallness of one component of the initial velocity implies the global smoothness, see e.g. page 873 in \cite{CZZ17}. Our result seems to give a positive answer in a special setting. As a byproduct, we also construct an unbounded solution of the forced Navier Stokes equation in a special cusp domain that has finite energy. The forcing term, with the scaling factor of $-1$, is in the standard regularity class. This result confirms the intuition that if the channel of a fluid is very thin, arbitrarily high speed in the classical sense can be attained under a mildly singular force which is physically reasonable in view that Newtonian gravity and Coulomb force have scaling factor $-2$.Comment: 85 pages. A blow up solution in a special cusp domain, two references and a few sentences adde

Impacts of crystal orientation of GaAs on the interfacial structures and electrical properties of Hf0.6La0.4Ox films

One of the major challenges in realizing the GaAs channel in the metal oxide semiconductor field effect transistor is the degrading in electron transport properties at the interface between GaAs and the gate oxide. In this study, Hf0.6La0.4Ox gate oxide films were deposited at a low temperature (200 °C) on GaAs(111)A and GaAs(100) substrates by plasma enhanced atomic layer deposition. Microstructure analysis indicates that residuals of gallium oxide, arsenic oxide, and As element remained at the interface of Hf0.6La0.4Ox/GaAs(100). On contrast, a smoother interface is observed between Hf0.6La0.4Ox thin film and GaAs(111)A substrate. Furthermore, a reduction of interfacial layer is observed in Hf0.6La0.4Ox/GaAs(111)A. Electrical characterization of the metal-insulator-semiconductor Pt/Hf0.6La0.4Ox/n-GaAs(111)A capacitor indicated a reduction of Dit and leakage current compared with the capacitor fabricated on GaAs(100)

An NmrA-Like Protein, Lws1, Is Important for Pathogenesis in the Woody Plant Pathogen Lasiodiplodia theobromae

The NmrA-like proteins have been reported to be important nitrogen metabolism regulators and virulence factors in herbaceous plant pathogens. However, their role in the woody plant pathogen Lasiodiplodia theobromae is less clear. In the current study, we identified a putative NmrA-like protein, Lws1, in L. theobromae and investigated its pathogenic role via gene silencing and overexpression experiments. We also evaluated the effects of external carbon and nitrogen sources on Lws1 gene expression via qRT-PCR assays. Moreover, we analyzed the molecular interaction between Lws1 and its target protein via the yeast two-hybrid system. The results show that Lws1 contained a canonical glycine-rich motif shared by the short-chain dehydrogenase/reductase (SDR) superfamily proteins and functioned as a negative regulator during disease development. Transcription profiling revealed that the transcription of Lws1 was affected by external nitrogen and carbon sources. Interaction analyses demonstrated that Lws1 interacted with a putative GATA family transcription factor, LtAreA. In conclusion, these results suggest that Lws1 serves as a critical regulator in nutrition metabolism and disease development during infection