Global axisymmetric solutions of 3D inhomogeneous incompressible Navier-Stokes Systems with nonzero swirl

In this paper, we investigate the global well-posedness for the 3-D inhomogeneous incompressible Navier-Stokes system with the axisymmetric initial data. We prove the global well-posedness provided that $$\|\frac{a_{0}}{r}\|_{\infty} \textrm{ and } \|u_{0}^{\theta}\|_{3} \textrm{ are sufficiently small}.$$ Furthermore, if $\mathbf{u}_0\in L^1$ and $ru^\theta_0\in L^1\cap L^2$, we have \begin{equation*} \|u^{\theta}(t)\|_{2}^{2}+\langle t\rangle \|\nabla (u^{\theta}\mathbf{e}_{\theta})(t)\|_{2}^{2}+t\langle t\rangle(\|u_{t}^{\theta}(t)\|_{2}^{2}+\|\Delta(u^{\theta}\mathbf{e}_{\theta})(t)\|_{2}^{2}) \leq C \langle t\rangle^{-\frac{5}{2}},\ \forall\ t>0. \end{equation*}Comment: 21 page

Directed diffraction without negative refraction

Using the FDTD method, we investigate the electromagnetic propagation in two-dimensional photonic crystals, formed by parallel air cylinders in a dielectric medium. The corresponding frequency band structure is computed using the standard plane-wave expansion method. It is shown that within partial bandgaps, waves tend to bend away from the forbidden directions. This phenomenon perhaps need not be explained in terms of negative refraction or `superlensing' behavior, contrast to what has been conjectured.Comment: 3 pages, 4 figure

Effects of detraining on functional fitness and lymphocyte subsets in postmenopausal females

Introduction: Aging leads to declines of functional fitness and regular exercise has been recognized to be beneficial for keeping health and preventing degenerative diseases in older adults. Limited evidences connect the relationships among detraining, functional fitness, immunosenescence, and vascular integrity in aged individuals. Thus, the aims of this study was to inspect: How training and detraining influence functional fitness, mobilization of circulating leukocytes and lymphocyte subsets? Method: Twenty-two female volunteers aged 50 to 65 years were recruited as participants in this study. Participants were assigned into training group (TG, n=13) and control group (CG, n=9). The participants in TG were asked to attend exercise program, including aerobic exercise at 70% HRR for 60 min twice per week and resistance training at 60-70% 1RM, 3 sets and 9 exercises for 60 min per week for 16 weeks and subsequently avoid exercise for 6 weeks to investigate detraining effects. CG were asked to stay in their regular lifestyles. A six-items measurement of functional fitness and resting (at fasting status) venous blood samples were collected at before training program (Pre-training), 8th week of training (Mid-training), after training program (Post-training), and 6th week of detraining 6 weeks (Detraining). Blood cell counts (WBC, RBC, HCT, LYM) were measured using an automated cell counter and lymphocyte subsets (CD4, CD8, CD19, CD56) were analyzed by flow cytometry. Data were analyzed by descriptive statistic, mixed two-factors (time × group) measures ANOVA or ACOVA and the significance was set at pResult: Functional fitness of TG was not significantly improved following the training program although it was significantly better than CG in Pre-training. Blood cell counts were not changed and all in normal range. A significant difference in CD19 counts were observed between TG and CG (71.23±32.05 vs. 116.45±67.95 103/mL) in Post-training. CD19 counts in TG were increased at Detraining compared with Mid-training and Post-training (138.08±50.22 vs. 74.92±31.20, 71.23±32.05 103/mL). No alterations in quantity and percentage of CD4, CD8, and CD56 were observed in this study. Conclusion: Findings of this study suggest that both a 16-week moderate exercise program and a 6-week detraining did not significantly change the functional fitness and lymphocyte subsets in postmenopausal females

Oriented Graphene Nanoribbons Embedded in Hexagonal Boron Nitride Trenches

Graphene nanoribbons (GNRs) are ultra-narrow strips of graphene that have the potential to be used in high-performance graphene-based semiconductor electronics. However, controlled growth of GNRs on dielectric substrates remains a challenge. Here, we report the successful growth of GNRs directly on hexagonal boron nitride substrates with smooth edges and controllable widths using chemical vapour deposition. The approach is based on a type of template growth that allows for the in-plane epitaxy of mono-layered GNRs in nano-trenches on hexagonal boron nitride with edges following a zigzag direction. The embedded GNR channels show excellent electronic properties, even at room temperature. Such in-plane hetero-integration of GNRs, which is compatible with integrated circuit processing, creates a gapped channel with a width of a few benzene rings, enabling the development of digital integrated circuitry based on GNRs.Comment: 32 pages, 4 figures, Supplementary informatio