Asymptotic Solutions for Mean-Field Slab Dynamos

We discuss asymptotic solutions of the kinematic $\alpha\omega$-dynamo in a thin disc (slab). Focusing upon the strong dynamo regime, in which the dynamo number $D$ satisfies $|D|\gg1$, we resolve uncertainties in the earlier treatments and conclude that some of the simplifications that have been made in previous studies are questionable. Comparing numerical solutions with asymptotic results obtained for $|D|\gg1$ and $|D|\ll1$ we find that the asymptotic solutions give a reasonably accurate description of the dynamo even far beyond their formal ranges of applicability. Indeed, our results suggest a simple analytical expression for the growth rate of the mean magnetic field that remains accurate in the range $-200< D< -10$ (which is appropriate for dynamos in spiral galaxies and accretion discs). Finally, we analyse the role of various terms in the dynamo equations to clarify the fine details of the dynamo process.Comment: "This is an Author's Original Manuscript of an article submitted for consideration in Geophysical and Astrophysical Fluid Dynamics [copyright Taylor & Francis]; Geophysical and Astrophysical Fluid Dynamics is available online at http://www.tandfonline.com/gafd

Harmonic analysis, Hecke algebra and cohomology on groups of trees and buildings

PhD ThesisThe PhD project consists of two parts. The first part is about finite trees, realizations and random walks. The second part is about the Hecke algebras of infinite trees and buildings and the cohomology groups. We note that some examples of finite trees can be generalized to the infinite cases. The words of finite length in the example of ultrametric rooted trees with finite depth can be extended to doubly infinite chains in the infinite homogeneous trees thus defining a Banach algebra. As the background of the project, we study the topics of finite phylogenetic trees by understanding the combinatorial and geometrical structure of rooted and unrooted discrete BHV tree space of n taxa. Certain types of random walks on the space of trees can be used to model the evolution process. As a method to improve the computation of such random walks, we realize some tree spaces into polytopes in Euclidean space where the vertices, edges and faces indicate trees of different degenerate levels. In particular, we study the links between the permuto-associahedra and the BHV tree-space. One specific realization is called the secondary polytope, which is used to construct the associahedra, and we will generalize this construction into more complicated examples and compare with the BME polytopes of the BHV trees. In order to study the random walks on tree space, we apply several classic methods such as the eigensolutions of Markov chains, Gelfand pairs and spherical functions to decompose the functions on tree space. We present some classic examples where these methods solve the random walk explicitly. We consider biinvariant subalgebras of group algebra which are commutative under convolution. These arise from Gelfand pairs where spherical functions can be used to produce the eigenvectors of the transition matrix of the random walk. We note that an example of the q-homogeneous rooted tree of a finite depth is a good link to generalize the study from finite to infinite cases where the space is still discrete. The first example in the second part of the thesis is the infinite homogeneous trees and we study the invariant subalgebra under the ` 1 norm. The space can be discretized to Z+ and we show that it is isomorphic to a Hecke algebra with single generator, the Hecke operator which corresponds to the random walk generator. It is natural to consider some key properties of the algebra, i.e. the spherical functions, character space, derivations and b.a.i.. The main example we study is the Gelfand pair given by projective general linear groups over p-adic numbers and the subgroup corresponding to the the p-adic integers, where the example of the smallest dimension corresponds to infinite homogeneous trees and examples of higher dimensions correspond to the Bruhat-Tits buildings of type A˜. We claim that the Hecke algebras of these Gelfand pairs are isomorphic to the invariant subalgebras of functions on the A˜ lattice subject to weight conditions determined by p. Based on the isomorphic algebras on the type A˜ lattices, we consider the examples of types A˜ and B˜, with and without the invariance conditions under the Weyl group action on the lattices. We show that the above examples are all finitely generated and the number of generators in each case are equal to the dimension of the lattice in the Euclidean space. We then compute cohomology groups of the algebras of functions on the weighted lattices. We build up from the methods introduced in the examples of those similar to Z+ and Z k + . The general idea is to calculate the approximate formulae from the precise ones in Z+ and Z k + and iterate the process with an induction by reducing the degree of the leading terms. We also expect this method can be generalized to the Hecke algebras of other Gelfand pairs with corresponding weighted lattices

STUDY ON STEADY-STATE TEMPERATURE FIELD OF THE MESHING PAIR OF TWO-TOOTH DIFFERENCE SWING-ROD MOVABLE TOOTH DRIVE

Based on the basic theory of heat transfer and tribology,the calculation formulas of the friction heat flux density of meshing pair,the meshing tooth surface and the end face convective heat transfer coefficient with two-tooth difference swing-rod movable tooth drive are derived under the slip condition.A finite element model of the thermal analysis of the gear meshing pair is established,and the steady-state temperature field of the meshing pair under thermal balance state is calculated and analyzed by using the ANSYS finite element software.Combined with numerical simulation results,the influence of tooth profile design parameters on the temperature field is revealed.The result shows that:the steady-state temperature field of the meshing pair is determined collectively by the heat flux of the contact zone and the convection heat transfer coefficient of each surface.Because the temperature rise of sliding friction is larger,the maximum temperature appears in the center of the gear meshing face width of the center,the radius of the base circle radius has a great influence on the body temperature of the meshing surface,and the swing rod length is less affected.The research results lay the foundation for the study of the thermal deformation and thermal mechanical coupling characteristics of the meshing pair,so as to guide the dynamic design of the two-tooth difference swing-rod movable tooth drive

Attention boosted bilinear pooling for remote sensing image retrieval

Remote sensing image retrieval is to find the most identical or similar images to a query image in the vast archive of remote sensing images. A key process is to extract the most distinctive features. In this study, we introduce a second-order pooling named compact bilinear pooling (CBP) into convolutional neural networks (CNNs) for remote sensing image retrieval. The retrieval algorithm has three stages, pretraining, fine-tuning and retrieval. In the pretraining stage, two classic CNN structures, VGG16 and ResNet34, are pretrained respectively with the ImageNet consisting of close-range images. A CBP layer is introduced before the fully connected layers in the two networks. To extract globally consistent representations, a channel and spatial integrated attention mechanism is proposed to refine features from the last convolution layer and the features are used as the input of the CBP. In the fine-tuning stage, the new network is fine-tuned on a remote sensing dataset to train discriminable features. In the retrieval stage, the network, with fully connected layers being replaced by a PCA (principal component analysis) module, is applied to new remote sensing datasets. Our retrieval algorithm with the combination of CBP and PCA obtained the best performance and outperformed several mainstream pooling or encoding methods such as full-connected layer, IFK (Improved Fisher Kernel), BoW (Bag-of-Words) and maxpooling, etc. The channel and spatial attention mechanism contributes to the CBP based retrieval method and obtained the best performance on all the datasets, as well as outperformed several recent attention methods. Source code is available at http://study.rsgis/whu.edu.cn/pages/download

Elevated Temperature Tensile Creep Behavior of Aluminum Borate Whisker-Reinforced Aluminum Alloy Composites (ABOw/Al–12Si)

In order to evaluate the elevated temperature creep performance of the ABOw/Al–12Si composite as a prospective piston crown material, the tensile creep behaviors and creep fracture mechanisms have been investigated in the temperatures range from 250 to 400 °C and the stress range from 50 to 230 MPa using a uniaxial tensile creep test. The creep experimental data can be explained by the creep constitutive equation with stress exponents of 4.03–6.02 and an apparent activation energy of 148.75 kJ/mol. The creep resistance of the ABOw/Al–12Si composite is immensely improved by three orders of magnitude, compared with the unreinforced alloy. The analysis of the ABOw/Al–12Si composite creep data revealed that dislocation climb is the main creep deformation mechanism. The values of the threshold stresses are 37.41, 25.85, and 17.36 at elevated temperatures of 300, 350 and 400 °C, respectively. A load transfer model was introduced to interpret the effect of whiskers on the creep rate of this composite. The creep test data are very close to the predicted values of the model. Finally, the fractographs of the specimens were analyzed by Scanning Electron Microscope (SEM), the fracture mechanisms of the composites at different temperatures were investigated. The results showed that the fracture characteristic of the ABOw/Al–12Si composite exhibited a macroscale brittle feature range from 300 to 400 °C, but a microscopically ductile fracture was observed at 400 °C. Additionally, at a low tensile creep temperature (300 °C), the plastic flow capacity of the matrix was poor, and the whisker was easy to crack and fracture. However, during tensile creep at a higher temperature (400 °C), the matrix was so softened that the whiskers were easily pulled out and interfacial debonding appeared

Study on Two Typical Progressive Motions in Tai Chi (Bafa Wubu) Promoting Lower Extremity Exercise

Background: By comparatively investigating the joints, muscles and bones of the lower extremity during two progressive motions in Bafa Wubu and normal walking, this paper aims to enrich the diversity of walking exercise and scientifically provide theoretical guidance for primary practitioners. The scientific training methods and technical characteristics of Bafa Wubu, as well as its contribution to comprehensive exercise of the lower extremities, are further explored. Methods: A total of eight professional athletes of Tai Chi at the national level were recruited. The kinetic parameters of the lower extremity were calculated using AnyBody 7.2 musculoskeletal modeling. Stress analysis of the iliac bone was performed using an ANSYS 19.2 workbench. Results: In Bafa Wubu, the ground reaction force during two progressive motions was significantly smaller than that noted during normal walking. During warding off with steps forward and laying with steps forward, the load at the three joints of the lower extremity was significantly smaller than that during normal walking in the frontal plane, but significantly greater than that noted during normal walking in the vertical axis. In addition, the lower limb joint torque was higher than that of normal walking in both progressive movements, and lower limb muscle activation was higher. The iliac bone loads during the two progressive motions were larger than those during normal walking, and the maximum loading point differed. Conclusions: This is the first study to demonstrate the biomechanical performance of Bafa Wubu in professional athletes of Tai Chi. Two progressive motions of Bafa Wubu require the lower extremity to be slowly controlled, thereby resulting in a smaller ground reaction force. In addition, the loads of the three joints at the lower extremity all increase in the vertical direction and decrease in the lateral direction, reducing the possibility of lateral injury to the joints. In addition, the two progressive motions significantly enhance the muscle strength of the plantar flexion muscles, dorsiflexor, and muscles around the thigh, and effectively stimulate the bones of the lower extremity. Therefore, progressive motion training contributes to improving the controlling and supporting capabilities of the lower extremities during normal walking

Discrete element modelling of rubber-protected ballast performance subjected to direct shear test and cyclic loading

The rubber-protected ballast (RPB) is made from natural ballast particles and crumb rubber particles. The crumb rubber is shredded waste tires. RPB was chosen to replace the ballast as it has higher resistance to breakage and abrasion. However, the static and dynamic performance of the RPB has not been confirmed yet. Towards this end, experimental tests and numerical simulations were utilized to study the feasibility of RPB application. Direct shear tests (DSTs) were performed and a DST model and three-sleeper track model with the discrete element method (DEM) were built. The shear strength, settlement, displacement, and acceleration of the RPB were studied. The results show that the RPB has the advantage of increasing the force (stress) distribution and that the smaller crumb rubber size was more suitable for replacing the ballast particles.Railway Engineerin

Attention boosted bilinear pooling for remote sensing image retrieval

Remote sensing image retrieval is to find the most identical or similar images to a query image in the vast archive of remote sensing images. A key process is to extract the most distinctive features. In this study, we introduce a second-order pooling named compact bilinear pooling (CBP) into convolutional neural networks (CNNs) for remote sensing image retrieval. The retrieval algorithm has three stages, pretraining, fine-tuning and retrieval. In the pretraining stage, two classic CNN structures, VGG16 and ResNet34, are pretrained respectively with the ImageNet consisting of close-range images. A CBP layer is introduced before the fully connected layers in the two networks. To extract globally consistent representations, a channel and spatial integrated attention mechanism is proposed to refine features from the last convolution layer and the features are used as the input of the CBP. In the fine-tuning stage, the new network is fine-tuned on a remote sensing dataset to train discriminable features. In the retrieval stage, the network, with fully connected layers being replaced by a PCA (principal component analysis) module, is applied to new remote sensing datasets. Our retrieval algorithm with the combination of CBP and PCA obtained the best performance and outperformed several mainstream pooling or encoding methods such as full-connected layer, IFK (Improved Fisher Kernel), BoW (Bag-of-Words) and maxpooling, etc. The channel and spatial attention mechanism contributes to the CBP based retrieval method and obtained the best performance on all the datasets, as well as outperformed several recent attention methods. Source code is available at http://study.rsgis/whu.edu.cn/pages/download

miR-409 Inhibits Human Non-Small-Cell Lung Cancer Progression by Directly Targeting SPIN1

Lung cancers, the leading cause of cancer mortality worldwide, are characterized by a high metastatic potential. Growing evidence reveals that Spindlin 1 (SPIN1) is involved in tumor progression and carcinogenesis. However, the role of SPIN1 in non-small-cell lung cancer (NSCLC) and the molecular mechanisms underlying SPIN1 in human NSCLC remain undetermined. Here we examined the function of SPIN1 in human NSCLC and found that the expression of SPIN1 was closely correlated with the overall survival and poor prognosis of NSCLC patients. Aberrant regulation of microRNAs (miRNAs) has an important role in cancer progression. We revealed that miR-409 inhibits the expression of SPIN1 by binding directly to the 3′ UTR of SPIN1 using dual-luciferase reporter assays. Overexpression of miR-409 significantly suppressed cell migration, growth, and proliferation by inhibiting SPIN1 in vitro and in vivo. SPIN1 overexpression in miR-409-transfected NSCLC cells effectively rescued the suppression of cell migration, growth, and proliferation regulated by miR-409. miR-409 regulates the PI3K/AKT (protein kinase B) pathway in NSCLC. Moreover, clinical data showed that NSCLC patients with high levels of miR-409 experienced significantly better survival. miR-409 expression was also negatively associated with SPIN1 expression. Taken together, these findings highlight that the miR-409/SPIN1 axis is a useful pleiotropic regulatory network and could predict the metastatic potential in NSCLC patients early, indicating the possibility that miR-409 and SPIN1 might be attractive prognostic markers for treating NSCLC patients. Keywords: non-small lung cancer, NSCLC, miR-409, SPIN1, therap