Unstable and Stable Galaxy Models

To determine the stability and instability of a given steady galaxy configuration is one of the fundamental problems in the Vlasov theory for galaxy dynamics. In this article, we study the stability of isotropic spherical symmetric galaxy models $f_{0}(E)$, for which the distribution function $f_{0}$ depends on the particle energy $E$ only. In the first part of the article, we derive the first sufficient criterion for linear instability of $f_{0}(E):$ $f_{0}(E)$ is linearly unstable if the second-order operator $$A_{0}\equiv-\Delta+4\pi\int f_{0}^{\prime}(E)\{I-\mathcal{P}\}dv$$ has a negative direction, where $\mathcal{P}$ is the projection onto the function space $\{g(E,L)\},$ $L$ being the angular momentum [see the explicit formula (\ref{A0-radial})]. In the second part of the article, we prove that for the important King model, the corresponding $A_{0}$ is positive definite. Such a positivity leads to the nonlinear stability of the King model under all spherically symmetric perturbations.Comment: to appear in Comm. Math. Phy

Unstable Galaxy Models

The dynamics of collisionless galaxy can be described by the Vlasov-Poisson system. By the Jean's theorem, all the spherically symmetric steady galaxy models are given by a distribution of {\Phi}(E,L), where E is the particle energy and L the angular momentum. In a celebrated Doremus-Feix-Baumann Theorem, the galaxy model {\Phi}(E,L) is stable if the distribution {\Phi} is monotonically decreasing with respect to the particle energy E. On the other hand, the stability of {\Phi}(E,L) remains largely open otherwise. Based on a recent abstract instability criterion of Guo-Lin, we constuct examples of unstable galaxy models of f(E,L) and f(E) in which f fails to be monotone in E

Flow field calculation and dynamic characteristic analysis of spherical hybrid gas bearings based on passive grid

In order to research the spherical spiral groove hybrid gas bearings, the Realizable k − ε turbulence model of gas film was established based on FLUENT. The simulation calculation method of 6-degrees of freedom passive grid was used, which can simulate the lubrication characteristics of the gas film transient flow field accurately. And the gas film pressure distribution and dynamic characteristic coefficients are numerically calculated. The dynamic and static pressure coupling effects of the gas flow field were analyzed, and the axis motion trajectory was simulated. The effect of rotation speed, gas supply pressure and tangential angle on the dynamic characteristic coefficients during bearing operation was analyzed. And the stability of the gas bearing was studied. The conclusion from the analysis shows that different rotation speed and gas supply pressure will change the pressure distribution of the gas bearing during the operation. The dynamic characteristics of the gas film can be changed by reasonably optimizing the operation parameters, which can change the whirl characteristics of the gas film and improve the stability. Through calculation and analysis, the tangential angle is selected between 55° and 60°, to ensure that the gas film has a high stiffness, while it also can obtain the larger damping. The simulation results and the experimental results are compared and analyzed to verify the correctness and effectiveness of the simulation method. At the same time, the research of this paper provided a theoretical basis for optimizing the bearing structure and operating parameters, improving the dynamic characteristics of gas bearings and improving the operation stability

A sharp stability criterion for the Vlasov-Maxwell system

We consider the linear stability problem for a 3D cylindrically symmetric equilibrium of the relativistic Vlasov-Maxwell system that describes a collisionless plasma. For an equilibrium whose distribution function decreases monotonically with the particle energy, we obtained a linear stability criterion in our previous paper. Here we prove that this criterion is sharp; that is, there would otherwise be an exponentially growing solution to the linearized system. Therefore for the class of symmetric Vlasov-Maxwell equilibria, we establish an energy principle for linear stability. We also treat the considerably simpler periodic 1.5D case. The new formulation introduced here is applicable as well to the nonrelativistic case, to other symmetries, and to general equilibria

On the design evolution of hip implants: A review

This manuscript reviews the development of femoral stem prostheses in the biomedical field. After a brief introduction on the development of these prostheses and the associated problems, we describe the standard design of these systems. We review the different materials, constructions, and surfaces used in the development of femoral stems, in order to solve and avoid various problems associated with their use. Femoral stem prostheses have undergone substantial changes and design optimizations since their introduction. Common materials include stainless steel, cobalt–chromium alloy, titanium alloy, and composites. The structural development of femoral stem prostheses, including their length, shape, porosity, and functional gradient construction, is also reviewed. The performance of these prostheses is affected not only by individual factors, but also by the synergistic combination of multiple effects; therefore, several aspects need to be optimized. The main purpose of this study is to summarize various strategies for the material and construction optimization of femoral stem prostheses, and to provide a reference for the combined optimization of their performance. Substantial research is still needed to develop prostheses emulating the behavior of a real human femoral stem

Small BGK waves and nonlinear Landau damping

Consider 1D Vlasov-poisson system with a fixed ion background and periodic condition on the space variable. First, we show that for general homogeneous equilibria, within any small neighborhood in the Sobolev space W^{s,p} (p>1,s<1+(1/p)) of the steady distribution function, there exist nontrivial travelling wave solutions (BGK waves) with arbitrary minimal period and traveling speed. This implies that nonlinear Landau damping is not true in W^{s,p}(s<1+(1/p)) space for any homogeneous equilibria and any spatial period. Indeed, in W^{s,p} (s<1+(1/p)) neighborhood of any homogeneous state, the long time dynamics is very rich, including travelling BGK waves, unstable homogeneous states and their possible invariant manifolds. Second, it is shown that for homogeneous equilibria satisfying Penrose's linear stability condition, there exist no nontrivial travelling BGK waves and unstable homogeneous states in some W^{s,p} (p>1,s>1+(1/p)) neighborhood. Furthermore, when p=2,we prove that there exist no nontrivial invariant structures in the H^{s} (s>(3/2)) neighborhood of stable homogeneous states. These results suggest the long time dynamics in the W^{s,p} (s>1+(1/p)) and particularly, in the H^{s} (s>(3/2)) neighborhoods of a stable homogeneous state might be relatively simple. We also demonstrate that linear damping holds for initial perturbations in very rough spaces, for linearly stable homogeneous state. This suggests that the contrasting dynamics in W^{s,p} spaces with the critical power s=1+(1/p) is a trully nonlinear phenomena which can not be traced back to the linear level

Fatal Community-acquired Pneumonia in Children Caused by Re-emergent Human Adenovirus 7d Associated with Higher Severity of Illness and Fatality Rate

Human adenoviruses (HAdVs) are highly contagious pathogens causing acute respiratory disease (ARD), such as community-acquired pneumonia. HAdV-7d, a re-emergent genomic variant, has been recently reported in Asia and the United States after a several-decade absence. However, whether HAdV-7d is associated with higher severity than other types is currently unclear. In this study, the clinical and epidemiological investigation showed that fever, cough, and sore throat were the three most common respiratory symptoms of HAdV infections. HAdV-7 caused longer duration of fever, higher morbidity of tachypnea/dyspnea, pleural effusion, diarrhea, hepatosplenomegaly, consciousness alteration, as well as higher rates of pneumonia, mechanical ventilation and higher fatality rate (28.6%) than other types, particularly HAdV-3 and HAdV-2. The genomes of seven HAdV-7d isolates from mild, severe, and fatal cases were sequenced and highly similar with each other. Surprisingly, two isolates (2011, 2012) had 100% identical genomes with an earlier strain from a fatal ARD outbreak in China (2009), which elucidates the virus origin and confirms the unexpected HAdV genomic conservation and stability. Phylogenetic analysis indicated that L1 52/55-kDa DNA packaging protein may be associated with the higher severity of illness and fatality rate of HAdV-7. Clinicians need to be aware of HAdVs in children with ARD

Anti-icing property of bio-inspired micro-structure superhydrophobic surfaces and heat transfer model

Ice accumulation is a thorny problem which may inflict serious damage even disasters in many areas, such as aircraft, power line maintenance, offshore oil platform and locators of ships. Recent researches have shed light on some promising bio-inspired anti-icing strategies to solve this problem. Inspired by typical plant surfaces with super-hydrophobic character such as lotus leaves and rose petals, structured superhydrophobic surface are prepared to discuss the anti-icing property. 7075 Al alloy, an extensively used materials in aircrafts and marine vessels, is employed as the substrates. As-prepared surfaces are acquired by laser processing after being modified by stearic acid for 1 h at room temperature. The surface morphology, chemical composition and wettability are characterized by means of SEM, XPS, Fourier transform infrared (FTIR) spectroscopy and contact angle measurements. The morphologies of structured as-prepared samples include round hump, square protuberance and mountain-range-like structure, and that the as-prepared structured surfaces shows an excellent superhydrophobic property with a WCA as high as 166 ± 2°. Furthermore, the anti-icing property of as-prepared surfaces was tested by a self-established apparatus, and the crystallization process of a cooling water on the sample was recorded. More importantly, we introduced a model to analyze heat transfer process between the droplet and the structured surfaces. This study offers an insight into understanding the heat transfer process of the superhydrophobic surface, so as to further research about its unique property against ice accumulation

Genomic mosaicism due to homoeologous exchange generates extensive phenotypic diversity in nascent allopolyploids

Allopolyploidy is an important process in plant speciation, yet newly formed allopolyploid species typically suffer from extreme genetic bottlenecks. One escape from this impasse might be homoeologous meiotic pairing, during which homoeologous exchanges (HEs) generate phenotypically variable progeny. However, the immediate genome-wide patterns and resulting phenotypic diversity generated by HEs remain largely unknown. Here, we analyzed the genome composition of 202 phenotyped euploid segmental allopolyploid individuals from the 4th selfed generation following chromosomal doubling of reciprocal F1 hybrids of crosses between rice subspecies, using whole genome sequencing. We describe rampant occurrence of HEs that, by overcoming incompatibility or conferring superiority of hetero-cytonuclear interactions, generate extensive and individualized genomic mosaicism across the analyzed tetraploids. We show that the resulting homoeolog copy number alteration in tetraploids affects known-function genes and their complex genetic interactions, in the process creating extraordinary phenotypic diversity at the population level following a single initial hybridization. Our results illuminate the immediate genomic landscapes possible in a tetraploid genomic environment, and underscore HE as an important mechanism that fuels rapid phenotypic diversification accompanying the initial stages of allopolyploid evolution