Standing sausage modes in coronal loops with plasma flow

Magnetohydrodynamic waves are important for diagnosing the physical parameters of coronal plasmas. Field-aligned flows appear frequently in coronal loops.We examine the effects of transverse density and plasma flow structuring on standing sausage modes trapped in coronal loops, and examine their observational implications. We model coronal loops as straight cold cylinders with plasma flow embedded in a static corona. An eigen-value problem governing propagating sausage waves is formulated, its solutions used to construct standing modes. Two transverse profiles are distinguished, one being the generalized Epstein distribution (profile E) and the other (N) proposed recently in Nakariakov et al.(2012). A parameter study is performed on the dependence of the maximum period $P_\mathrm{max}$ and cutoff length-to-radius ratio $(L/a)_{\mathrm{cutoff}}$ in the trapped regime on the density parameters ($\rho_0/\rho_\infty$ and profile steepness $p$) and flow parameters (magnitude $U_0$ and profile steepness $u$). For either profile, introducing a flow reduces $P_\mathrm{max}$ relative to the static case. $P_\mathrm{max}$ depends sensitively on $p$ for profile N but is insensitive to $p$ for profile E. By far the most important effect a flow introduces is to reduce the capability for loops to trap standing sausage modes: $(L/a)_{\mathrm{cutoff}}$ may be substantially reduced in the case with flow relative to the static one. If the density distribution can be described by profile N, then measuring the sausage mode period can help deduce the density profile steepness. However, this practice is not feasible if profile E better describes the density distribution. Furthermore, even field-aligned flows with magnitudes substantially smaller than the ambient Alfv\'en speed can make coronal loops considerably less likely to support trapped standing sausage modes.Comment: 11 pages, 9 figures, to appear in Astronomy & Astrophysic

Spatial damping of propagating sausage waves in coronal cylinders

Sausage modes are important in coronal seismology. Spatially damped propagating sausage waves were recently observed in the solar atmosphere. We examine how wave leakage influences the spatial damping of sausage waves propagating along coronal structures modeled by a cylindrical density enhancement embedded in a uniform magnetic field. Working in the framework of cold magnetohydrodynamics, we solve the dispersion relation (DR) governing sausage waves for complex-valued longitudinal wavenumber $k$ at given real angular frequencies $\omega$. For validation purposes, we also provide analytical approximations to the DR in the low-frequency limit and in the vicinity of $\omega_{\rm c}$, the critical angular frequency separating trapped from leaky waves. In contrast to the standing case, propagating sausage waves are allowed for $\omega$ much lower than $\omega_{\rm c}$. However, while able to direct their energy upwards, these low-frequency waves are subject to substantial spatial attenuation. The spatial damping length shows little dependence on the density contrast between the cylinder and its surroundings, and depends only weakly on frequency. This spatial damping length is of the order of the cylinder radius for $\omega \lesssim 1.5 v_{\rm Ai}/a$, where $a$ and $v_{\rm Ai}$ are the cylinder radius and the Alfv\'en speed in the cylinder, respectively. We conclude that if a coronal cylinder is perturbed by symmetric boundary drivers (e.g., granular motions) with a broadband spectrum, wave leakage efficiently filters out the low-frequency components.Comment: 6 pages, 2 figures, to appear in Astronomy & Astrophysic

Research on forming quality of poly-wedge pulley spinning

As an important power transmission part, pulleys are widely used in automobile industry, agricultural machinery, pumps and machines. A near-net forming process for six-wedge belt pulleys manufacturing was put forward. For this purpose, the required tooth shape and size can be formed directly by spinning without machining. The whole manufacturing procedures include blanking, drawing and spinning. The spinning procedure includes five processes, performing, drumming, thickening, toothing and finishing. The forming defects occurred during each forming processes of poly-wedge pulley spinning, such as the drumming failure, flanged opening-end, folded side-wall, insufficient bottom size, flashed opening-end, cutting-off bottom, are introduced, and the factors influencing the defects are analyzed. The corresponding preventive measures are put forward

Understanding the Joule-Heating Behaviours of Electrically-Heatable Carbon-Nanotube Aerogels

Cylindrical monolithic, electrically-heatable reduced carbon nanotube (rCNT) aerogels were synthesized to exploit their Joule-heating behaviours using two different arrangements (i.e. the top–bottom arrangement and the side–side arrangement) under different compressive strains. The top–bottom arrangement results in faster heating kinetics (up to 286 K min(−1)), higher heating efficiency (up to 80 °C W(−1)), a more uniform temperature distribution profile and higher electro-thermal conversion efficiency than the side–side arrangement. This study provides fundamental perspectives for exploiting the Joule-heating behaviours of geometrically complex nanocarbon aerogels, and thus will have important implications in strain-sensitive materials

Roles of TGFβ and FGF signals during growth and differentiation of mouse lens epithelial cell in vitro.

Transforming growth factor β (TGFβ) and fibroblast growth factor (FGF) signaling pathways play important roles in the proliferation and differentiation of lens epithelial cells (LECs) during development. Low dosage bFGF promotes cell proliferation while high dosage induces differentiation. TGFβ signaling regulates LEC proliferation and differentiation as well, but also promotes epithelial-mesenchymal transitions that lead to cataracts. Thus far, it has been difficult to recapitulate the features of germinative LECs in vitro. Here, we have established a LEC culture protocol that uses SB431542 (SB) compound to inhibit TGFβ/Smad activation, and found that SB treatment promoted mouse LEC proliferation, maintained LECs' morphology and distinct markers including N-cadherin, c-Maf, Prox1, and αA-, αB-, and β-crystallins. In contrast, low-dosage bFGF was unable to sustain those markers and, combined with SB, altered LECs' morphology and β-crystallin expression. We further found that Matrigel substrate coatings greatly increased cell proliferation and uniquely affected β-crystallin expression. Cultured LECs retained the ability to differentiate into γ-crystallin-positive lentoids by high-dosage bFGF treatment. Thus, a suppression of TGFβ/Smad signaling in vitro is critical to maintaining characteristic features of mouse LECs, especially expression of the key transcription factors c-Maf and Prox1

Optimal Clustering of Discrete Mixtures: Binomial, Poisson, Block Models, and Multi-layer Networks

In this paper, we first study the fundamental limit of clustering networks when a multi-layer network is present. Under the mixture multi-layer stochastic block model (MMSBM), we show that the minimax optimal network clustering error rate, which takes an exponential form and is characterized by the Renyi divergence between the edge probability distributions of the component networks. We propose a novel two-stage network clustering method including a tensor-based initialization algorithm involving both node and sample splitting and a refinement procedure by likelihood-based Lloyd algorithm. Network clustering must be accompanied by node community detection. Our proposed algorithm achieves the minimax optimal network clustering error rate and allows extreme network sparsity under MMSBM. Numerical simulations and real data experiments both validate that our method outperforms existing methods. Oftentimes, the edges of networks carry count-type weights. We then extend our methodology and analysis framework to study the minimax optimal clustering error rate for mixture of discrete distributions including Binomial, Poisson, and multi-layer Poisson networks. The minimax optimal clustering error rates in these discrete mixtures all take the same exponential form characterized by the Renyi divergences. These optimal clustering error rates in discrete mixtures can also be achieved by our proposed two-stage clustering algorithm