A comparison of high-order time integrators for thermal convection in rotating spherical shells

A numerical study of several time integration methods for solving the three-dimensional Boussinesq thermal convection equations in rotating spherical shells is presented. Implicit and semi-implicit time integration techniques based on backward differentiation and extrapolation formulae are considered. The use of Krylov techniques allows the implicit treatment of the Coriolis term with low storage requirements. The codes are validated with a known benchmark, and their efficiency is studied. The results show that the use of high-order methods, especially those with time step and order control, increase the efficiency of the time integration, and allows to obtain more accurate solutions.     

任意基数集上的拟阵的圈及连通性

通过研究任意基数集上的拟阵圈的性质,继而得出当此拟阵连通时,它可由含任一给定元素的圈集唯一确定的结论.     

Vibration analysis of truncated conical shells subjected to flowing fluid

A method to predict the dynamic behaviour of anisotropic truncated conical shells conveying fluid is presented in this paper. It is a combination of finite element method and classical shell theory. The displacement functions are derived from exact solutions of Sanders’ shell equilibrium equations of conical shells. The velocity potential, Bernoulli’s equation and impermeability condition have been applied to the shell–fluid interface to obtain an explicit expression for fluid pressure which yields three forces (inertial, centrifugal, Coriolis) of the moving fluid. To the best of the authors’ knowledge, this paper reports the first comparison made between two works which deal with conical shells subjected to internal flowing fluid effects. The results obtained by this method for conical shells with various boundary condition and geometries, in vacuum, fully-filled and when subjected to flowing fluid were compared with those of other experimental and numerical investigations and good agreement was obtained.     

Use of Crustacean Shells for Uptake and Removal of Metal Ions in Solution

Abstract

The use of crustacean shells, in particular crab shells, for the removal of metal ions in solution is described. Research studies found in the literature on the ability of the shells, effect of particle size, pH, competitive studies in mixtures of metals, application to real samples such as acid mine drainage, and use of the shells in a column are presented. The major component of the shells that allows uptake to occur is chitin. Several mechanisms are proposed for uptake. There are conflicting accounts in the literature on such areas as the effect of pH, flow rate, and particle size.     

有环壳过渡段的锥—柱组合壳的应力和稳定性

用解析方法计算了受静水外压载荷作用的有环壳过渡段的锥—柱组合壳中的应力值，并用瑞利法计算了其失稳临界载荷。计算结果说明，利用环壳过渡值锥—柱壳形成光滑连接，可使连接部位的局部应力值显著降低，并使失稳临界载荷有所提高     

On reducible matrix patterns

A tool to study the inertias of reducible nonzero (resp. sign) patterns is presented. Sumsets are used to obtain a list of inertias attainable by the pattern 𝒜 ⊕ ? dependent upon inertias attainable by patterns 𝒜 and ?. It is shown that if ? is a pattern of order n, and 𝒜 is an inertially arbitrary pattern of order at least 2(n ? 1), then 𝒜 ⊕ ? is inertially arbitrary if and only if ? allows the inertias (0, 0, n), (0, n, 0) and (n, 0, 0). We illustrate how to construct other reducible inertially (resp. spectrally) arbitrary patterns from an inertially (resp. spectrally) arbitrary pattern 𝒜 ⊕ ?, by replacing 𝒜 with an inertially (resp. spectrally) arbitrary pattern 𝒮. We identify reducible inertially (resp. spectrally) arbitrary patterns of the smallest orders that contain some irreducible components that are not inertially (resp. spectrally) arbitrary. It is shown there exist nonzero (resp. sign) patterns 𝒜 and ? of orders 4 and 5 (resp. 4 and 4) such that both 𝒜 and ? are non-inertially-arbitrary, and 𝒜 ⊕ ? is inertially arbitrary.     

Density matrix of a quantum field in a particle-creating background

We examine the time evolution of a quantized field in external backgrounds that violate the stability of vacuum (particle-creating backgrounds). Our purpose is to study the exact form of the final quantum state (the density operator at the final instant of time) that has emerged from a given arbitrary initial state (from a given arbitrary density operator at the initial time instant) in the course of evolution. We find a generating functional that allows one to obtain density operators for an arbitrary initial state. Averaging over states of the subsystem of antiparticles (particles), we obtain explicit forms of reduced density operators for the subsystem of particles (antiparticles). Analyzing one-particle correlation functions, we establish a one-to-one correspondence between these functions and the reduced density operators. It is shown that in the general case a presence of bosons (e.g., gluons) in the initial state increases the creation rate of the same type of bosons. We discuss the question (and its relation to the initial stage of quark–gluon plasma formation) whether a thermal form of one-particle distribution can appear even if the final state of the complete system is not in thermal equilibrium. In this respect, we discuss some cases when pair-creation by an electric-like field can mimic the one-particle thermal distribution. We apply our technics to some QFT problems in slowly varying electric-like backgrounds: electric, SU(3) chromoelectric, and metric. In particular, we analyze the time and temperature behavior of the mean numbers of created particles, provided that the effects of switching the external field on and off are negligible. It is demonstrated that at high temperatures and in slowly varying electric fields the rate of particle-creation is essentially time-dependent.     

Micro/Nanoengineered α-Fe2O3 Nanoaggregate Conformably Enclosed by Ultrathin N-Doped Carbon Shell for Ultrastable Lithium Storage and Insight into Phase Evolution Mechanism

The Fe-based transition metal oxides are promising anode candidates for lithium storage considering their high specific capacity, low cost, and environmental compatibility. However, the poor electron/ion conductivity and significant volume stress limit their cycle and rate performances. Furthermore, the phenomena of capacity rise and sudden decay for α-Fe₂O₃ have appeared in most reports. Here, a uniform micro/nano α-Fe₂O₃ nanoaggregate conformably enclosed in an ultrathin N-doped carbon network (denoted as M/N-α-Fe₂O₃@NC) is designed. The M/N porous balls combine the merits of secondary nanoparticles to shorten the Li⁺ transportation pathways as well as alleviating volume expansion, and primary microballs to stabilize the electrode/electrolyte interface. Furthermore, the ultrathin carbon shell favors fast electron transfer and protects the electrode from electrolyte corrosion. Therefore, the M/N-α-Fe₂O₃@NC electrode delivers an excellent reversible capacity of 901 mA h g⁻¹ with capacity retention up to 94.0 % after 200 cycles at 0.2 A g⁻¹. Notably, the capacity rise does not happen during cycling. Moreover, the lithium storage mechanism is elucidated by ex situ XRD and HRTEM experiments. It is verified that the reversible phase transformation of α↔γ occurs during the first cycle, whereas only the α-Fe₂O₃ phase is reversibly transformed during subsequent cycles. This study offers a simple and scalable strategy for the practical application of high-performance Fe₂O₃ electrodes.