Closure modeling in bridging regions of variable-resolution (VR) turbulence computations

Optimal utilization of computational resources mandates spatio-temporal variation in resolution for computing complex engineering flows. Closure modeling in regions bridging between different resolutions is rendered difficult due to changing interactions between resolved and unresolved fields. We develop a closure model for the bridging region based on energy conservation principles. Then we proceed to provide a proof of concept in decaying isotropic turbulence with temporally varying resolution. The simplicity of the flow permits a thorough examination of various aspects of the proposed closure not feasible in more complex flows. The results demonstrate the potential promise of the approach, but more validation studies need to be performed.While the present development is in the context of partially averaged Navier–Stokes (PANS) method, the closure principle should apply for other variable-resolution (VR) approaches.     

Estimation of the total population moving into and out of the 20 km evacuation zone during the Fukushima NPP accident as calculated using “Auto-GPS” mobile phone data

The first objective data showing the geographical locations of people in Fukushima after the Fukushima Dai-ichi nuclear power plant accident, obtained by an analysis of GPS (Global Positioning System)-enabled mobile phone logs, are presented. The method of estimation is explained, and the flow of people into and out of the 20 km evacuation zone during the accident is visualized.     

On the domain of fractional Laplacians and related generators of Feller processes

In this paper we study the domain of the generator of stable processes, stable-like processes and more general pseudo- and integro-differential operators which naturally arise both in analysis and as infinitesimal generators of Lévy- and Lévy-type (Feller) processes. In particular we obtain conditions on the symbol of the operator ensuring that certain (variable order) Hölder and Hölder–Zygmund spaces are in the domain. We use tools from probability theory to investigate the small-time asymptotics of the generalized moments of a Lévy or Lévy-type process ${(X_t)}_{t\ge 0}$,

$\underset{t\to 0}{\lim }?\frac{1}{t}({\mathbb{E}}^{x}f(X_t)?f(x)),x\in {\mathbb{R}}^d,$

for functions f which are not necessarily bounded or differentiable. The pointwise limit exists for fixed $x\in {\mathbb{R}}^d$ if f satisfies a Hölder condition at x. Moreover, we give sufficient conditions which ensure that the limit exists uniformly in the space of continuous functions vanishing at infinity. As an application we prove that the domain of the generator of ${(X_t)}_{t\ge 0}$ contains certain Hölder spaces of variable order. Our results apply, in particular, to stable-like processes, relativistic stable-like processes, solutions of Lévy-driven SDEs and Lévy processes.     

Closed-form solutions of general second order linear recurrences and applications

Two closed-form solutions of a general second order linear recurrence with variable coefficients are established. The first form is combinatorial in nature and is derived through the use of a set which counts the number of elements which are two units apart. The second form is closely related to continued fractions and is derived through the use of continued fraction-like relation. Several applications including a number of verifications of conjectures produced from the Ramanujan Machine are worked out, which illustrate its versatility in this respect.     

考查变量控制能力的科学探究题的命题与思考*

以一道科学探究题的命题为例,从题目的研发、学生问题反馈、教学策略改进等角度研究科学探究问题,寻找学生困惑的根源,找到对应教学改进策略,帮助学生提升科学探究能力。     

The thermophysical properties of low‐temperature Pb plasma

The thermophysical properties of low‐temperature Pb plasma are calculated at temperatures 10–100 kK and densities below 0.2 of the solid‐state value. The thermodynamic values (pressure and internal energy) and transport coefficients (electrical conductivity, thermal conductivity, and thermal power) are considered. The plasma composition and thermodynamic parameters are obtained within the chemical approach, namely by means of the solution of the corresponding system of the coupled mass action law equations. Atom ionization up to +4 is taken into consideration. The electronic transport coefficients are calculated within the relaxation time approximation. The results obtained by means of the present model are compared with the available data of other models and experiments.     

Statistics of reaction progress variable and mixture fraction gradients of a pulverised coal jet flame using Direct Numerical Simulation data

The statistical behaviour of the variances, covariance and gradients of the reaction progress variable (c), and the mixture fraction (ξ) have been analysed in a pulverised coal jet flame using a three-dimensional carrier phase direct numerical simulation (DNS) dataset. It has been observed that the Favre-probability density functions (PDFs) of c and ξ can be parametrised by the standard β function. Furthermore, the log-normal distribution has been found to accurately represent |?c| and |?ξ|. It is also found that ?c and ?ξ remain aligned throughout the flame brush. Finally the joint PDF of |?c| and |?ξ| has been compared with the product of the PDF of |?c| and PDF of |?ξ| extracted from carrier phase DNS, and it has been found that |?c| and |?ξ| are not statistically independent in the case investigated.The bivariate log-normal distributions with and without correlation have also been considered, and the former is found to be in better agreement with the carrier phase DNS data.     

Internal plasticization of poly(vinyl) chloride using glutamic acid as a branched linker to incorporate four plasticizers per anchor point

Internal plasticization of polyvinyl chloride (PVC) using thermal azide‐alkyne Huisgen dipolar cycloaddition between azidized PVC and electron‐poor acetylenediamides incorporating a branched glutamic acid linker resulted in incorporation of four plasticizing moieties per attachment point on the polymer chain. A systematic study incorporating either alkyl or polyethylene glycol esters provided materials with varying degrees of plasticization, with depressed T_g values ranging from ?1 °C to 62 °C. Three interesting trends were observed. First, T_g values of PVC bearing various internal plasticizers were shown to decrease with increasing chain length of the plasticizing ester. Second, branched internal plasticizers bearing triethylene glycol chains had lower T_g values compared to those with similar length long‐chain alkyl groups. Finally, thermogravimetric analysis of these internally plasticized PVC samples revealed that these branched internal plasticizers bearing alkyl chains are more thermally stable than similarity branched plasticizers bearing triethylene glycol units. These internal tetra‐plasticizers were synthesized and attached to PVC‐azide in three simple synthetic steps. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 1821–1835     

Degradation of a polyester‐urethane coating: Physical properties

In this article we studied the evolution of thermomechanical properties of a polyester‐urethane coating during degradation under different degradation conditions, i.e., aerobic and anaerobic conditions with and without dry/wet cycling during degradation. Dynamic mechanical and thermal analyses show that under aerobic conditions the coatings become stiffer and more brittle in the glassy state. This stiffening is probably due to the increase in the amount of hydrogen bonding and the formation of oxidized groups which increase the polarity of the material and enhance the interactions of the polymer segments. However, oxidation reactions result in a considerable decrease in cross‐link density and stiffness in the rubbery state. Both changes, in the glassy and rubbery states, give rise to development of internal stresses. These stresses increase as the degradation process proceeds. Nevertheless, for samples exposed to anaerobic conditions, the stiffness remains constant in the glassy state and the cross‐link density slightly increases as a result of degradation. This reconfirms the dominance of the effect of oxidation reactions on the mechanical failure of the coatings. Oxygen permeation measurements show a more‐or‐less time‐independent diffusion coefficient and a gradual decrease in solubility of oxygen as a function of exposure time. This results in a slight decrease in oxygen permeation (mainly in the early stage of the degradation) as degradation proceeds. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 659–671     

若干高维可积和不可积模型的严格解

可积和不可积模型可以描述自然科学中的诸多现象, 寻找高维非线性模型的严格解已成为可积系统的一个重要研究内容. 结合达布变换法和多线性分离变量法, 可以得到多个(2+1)维非线性模型包含任意函数的严格解, 通过选取不同的任意函数, 构造这些非线性模型新的相互激发模式. 进一步推广了形变映射理论, 建立了变系数 场和sine-Gordon以及双sine-Gordon场的形变映射关系, 从而得到高维不可积模型包含任意函数的新严格解. 对任意函数的不同选择, 构造了sine-Gordon和双sine-Gordon可积模型丰富的局域解和周期解, 如多solitoff解及其周期波推广、周期形变的蛇形孤波解以及变模的拟周期解等.