A reduced simulation applied to the viscoelastic fatigue of polymers

The paper extends the use of the PGD method to viscoelastic evolution problems described by a large number of internal variables and with a large spectrum of relaxation times. The internal variables evolution is described by a set of linear differential equations that involve many time scales. The feasibility and the robustness of the method are discussed in the case of a polymer in a non-equilibrium state under creep and cyclic loading. The relationships between different time scales (loading and internal variables) are also discussed.     

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.     

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。     

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.     

Complete NMR assignments of bioactive rotameric (3 → 8) biflavonoids from the bark of Garcinia hombroniana

The genus Garcinia is reported to possess antimicrobial, anti‐inflammatory, anticancer, hepatoprotective and anti‐HIV activities. Garcinia hombroniana in Malaysia is used to treat itching and as a protective medicine after child birth. This study was aimed to isolate the chemical constituents from the bark of G. hombroniana and explore their possible pharmacological potential. Ethyl acetate extract afforded one new (1) and six (2–7) known 3 → 8 rotameric biflavonoids. Their structures were elucidated by UV, IR and NMR (1D and 2D) spectroscopy together with electron ionization/ESI mass spectrometric techniques and were identified as (2R, 3S) volkensiflavone‐7‐O‐rhamnopyranoside (1), volkensiflavone (2), 4″‐O‐methyl‐volkensiflavone (3), volkensiflavone‐7‐O‐glucopyranoside (4), morelloflavone (5), 3″‐O‐methyl‐morelloflavone (6) and morelloflavone‐7‐O‐glucopyranoside (7). The absolute configuration of compound 1 was assigned by circular dichroism spectroscopy as 2R, 3S. The coexistence of conformers of isolated biflavonoids in solution at 25 °C in different solvents was confirmed by variable temperature NMR studies. At room temperature (25 °C), compounds 1–7 exhibited duplicate NMR signals, while at elevated temperature (90 °C), a single set of signals was obtained. Compound 5 showed significant in vitro antioxidant activities against 1,1‐diphenyl‐2‐picrylhydrazyl and 2,2′‐azino‐bis‐3‐ethyl benzthiazoline‐6‐sulfonic acid radicals. The antibacterial studies showed that compounds 5 and 6 are the most active against Staphylococcus aureus, Bacillus subtilis and Escherichia coli. Compounds 3 and 6 also showed moderate antituberculosis activity against H₃₈Rv. Based on the research findings, G. hombroniana could be concluded as a rich source of flavanone–flavone (3 → 8) biflavonoids that exhibit rotameric behaviour at room temperature and display significant antioxidant and antibacterial activities. Copyright © 2014 John Wiley & Sons, Ltd.     

Relaxation oscillations in a slow–fast modified Leslie–Gower model

In this paper, we prove the existence and uniqueness of relaxation oscillation cycle of a slow–fast modified Leslie–Gower model via the entry–exit function and geometric singular perturbation theory. Numerical simulations are also carried out to illustrate our theoretical result.     

Acetate anion-selective encapsulation in the ellipsoidal cavity of symmetrical α,α′,δ,δ′-tetramethyl-cucurbit[6]uril

Four symmetrical α,α′,δ,δ′-tetramethyl-cucurbit[6]uril-based compounds have been prepared and characterised by X-ray crystallography. Their crystal structures displayed the acetate anion-selective encapsulating capability of symmetrical α,α′,δ,δ′-tetramethyl-cucurbit[6]uril. The host–guest interaction between the symmetrical α,α′,δ,δ′-tetramethyl-cucurbit[6]uril and the acetate anion in aqueous solution has also been observed by variable temperature ¹H NMR spectroscopy.     

变限积分的求导方法

结合实例归纳总结不同类型变限积分的求导方法．