Constrained large solutions to Leray's problem in a distorted strip with the Navier-slip boundary condition

In this paper, we will solve the Leray's problem for the stationary Navier-Stokes system in a 2D infinite distorted strip with the Navier-slip boundary condition. The existence, uniqueness, regularity and asymptotic behavior of the solution will be investigated. Moreover, we discuss how the friction coefficient affects the well-posedness of the solution. Due to the validity of the Korn's inequality, all constants in each a priori estimate are independent of the friction coefficient. The main novelty is the total flux of the velocity can be relatively large (proportional to the {\it slip length}) when the friction coefficient of the Navier-slip boundary condition is small, which is essentially different from the 3D case.Comment: 45 pages. arXiv admin note: text overlap with arXiv:2204.10578. A remark is added to state the independent accomplishment of solving the 2D Leray's problem with the Navier-slip boundary condition by our group and Professor Chunjing Xie's grou

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

Genetic Engineering of the Biosynthesis of Glycine Betaine Modulates Phosphate Homeostasis by Regulating Phosphate Acquisition in Tomato

Glycine betaine (GB), as a putative compatible substance, protects plants against the damaging effects of abiotic stresses. Phosphorus deficiency is one type of abiotic stress that is detrimental to plant growth. Maintenance of phosphate (Pi) homeostasis is crucial. This study demonstrates GB-regulated phosphate homeostasis in the tomato (Solanum lycopersicum cv. ‘Moneymaker’) transformed with the choline oxidase gene codA from Arthrobacter globiformis. The codA-transgenic lines displayed more resistance to low-phosphate stress. The data revealed that the wild-type plants were stunted and consistently retained less Pi than transgenic lines, especially when grown under low-phosphate conditions. This difference in Pi retention was attributable to the enhanced Pi uptake ability in the transgenic lines. The transgenic plants translocated more Pi into the plant cell due to the enhanced enzymatic activity of plasma membrane H+-ATPase and increased Pi/H+ co-transport, which improved Pi uptake. The differential expression of ‘PHO regulon’ genes further maintained intracellular Pi homeostasis. Furthermore, GB maintained a higher photosynthesis rate, thus increasing the production and translocation of sucrose via phloem loading to enhance plant response to low-phosphate stress. We conclude that GB mediates Pi uptake and translocation by regulating physiological and biochemical processes that promote adaptation to environmental changes in Pi availability. These processes eventually lead to better growth and development of the codA-transgenic lines. This finding will help to further elucidate the signaling mechanism of how GB perceives and transmits low-phosphate signals to alleviate Pi nutritional stress

On-Chip Super-Resolution Imaging with Fluorescent Polymer Films

Wide field of view (FOV), label-free super-resolution imaging is demonstrated using a specially designed waveguide chip that can illuminate a sample with multi-colour evanescent waves travelling along different directions. The method is enabled by a polymer fluorescent film which emits over a broad wavelength range. Its polygonal geometry ensures coverage over all illumination directions, enabling high fidelity image reconstruction whilst minimizing distortion and image blurring. By frequency shifting and iterative stitching of different spatial frequencies in Fourier space, the reconstruction of two dimensional samples is achieved without distortion over wide FOVs. The fabrication process is facile and compatible with conventional semiconductor-fabrication methods. The super-resolution chip (SRC) can thus be produced with high yield, offer opportunities for potential conjunction of super-resolution techniques integrated optical circuits or for the development of single-use diagnostic kits

Public involvement in setting a national research agenda

<p>(A) Graphical map of the BLAST results showing nucleotide identity between <i>A</i>. <i>fasciata</i> mitogenome and 15 related species listed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0136297#pone.0136297.t001" target="_blank">Table 1</a>, as generated by the CGView comparison tool (CCT). CCT arranges BLAST result in an order where sequence that is most similar to the reference (<i>A</i>. <i>fasciata</i>) is placed closer to the outer edge of the map. The rings labelled 1 to17 indicate BLAST results of <i>A</i>. <i>fasciata</i> mitogenome against <i>A</i>. <i>chrysaetos</i>, <i>N</i>. <i>nipalensis</i>, <i>N</i>. <i>alboniger</i>, <i>S</i>. <i>cheela</i>, <i>A</i>. <i>monachus</i>, <i>B</i>. <i>lagopus</i>, <i>B</i>. <i>buteo</i>, <i>B</i>. <i>buteo burmanicus</i>, <i>A</i>. <i>soloensis</i>, <i>A</i>. <i>virgatus</i>, <i>A</i>. <i>gentilis</i>, <i>A</i>. <i>nisus</i>, <i>P</i>. <i>haliaetus</i>, <i>S</i>. <i>serpentarius</i>, <i>C</i>. <i>aura</i>, <i>P</i>. <i>badius</i>, and <i>S</i>. <i>leptogrammica</i>, respectively. (B) Nucleotide-based phylogenetic tree of 16 Accipitriformes species, with two Strigiformes birds as outgroups. This analysis is based on 13PCGs. Both ML and Bayesian analyses produced identical tree topologies. The ML bootstrap and Bayesian posterior probability values for each node are indicated.</p

Study on Rural Stock Cooperatives Based on Tangyue Village Model

At present, the issues concerning agriculture, farmers and rural areas are increasingly prominent, and the demand of rural economic reform is increasing. In view of current development situation of rural areas, with reference to successful experience of Tangyue Village Model, this paper analyzed functions of rural stock cooperatives to agricultural development, farmers’ income increase, and rural prosperity. Finally, it came up with feasible recommendations for rural reform and the issues concerning agriculture, farmers and rural areas

Genetic Engineering of the Biosynthesis of Glycinebetaine Enhances Photosynthesis against High Temperature Stress in Transgenic Tobacco Plants

Genetically engineered tobacco (Nicotiana tabacum) with the ability to synthesis glycinebetaine was established by introducing the BADH gene for betaine aldehyde dehydrogenase from spinach (Spinacia oleracea). The genetic engineering enabled the plants to accumulate glycinebetaine mainly in chloroplasts and resulted in enhanced tolerance to high temperature stress during growth of young seedlings. Moreover, CO(2) assimilation of transgenic plants was significantly more tolerant to high temperatures than that of wild-type plants. The analyses of chlorophyll fluorescence and the activation of Rubisco indicated that the enhancement of photosynthesis to high temperatures was not related to the function of photosystem II but to the Rubisco activase-mediated activation of Rubisco. Western-blotting analyses showed that high temperature stress led to the association of Rubisco activase with the thylakoid membranes from the stroma fractions. However, such an association was much more pronounced in wild-type plants than in transgenic plants. The results in this study suggest that under high temperature stress, glycinebetaine maintains the activation of Rubisco by preventing the sequestration of Rubisco activase to the thylakoid membranes from the soluble stroma fractions and thus enhances the tolerance of CO(2) assimilation to high temperature stress. The results seem to suggest that engineering of the biosynthesis of glycinebetaine by transformation with the BADH gene might be an effective method for enhancing high temperature tolerance of plants