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The purpose of this investigation is to study the dynamic hardness of MCrAlY abradable coatings under different strain rates. A dynamic indentation device based on the split Hopkinson pressure bar system (SHPB) was used. The results show that the hardness of MCrAlY coating increased with the increase of the strain rate, which has a positive strain rate effect. In addition, the difference of the static hardness of MCrAlY coating prepared by HVOF and LPPS was only 4%, while the difference in dynamic hardness was 16%.

The third-generation vortex identification method of Liutex (previously called Rortex) was introduced by the team led by Prof. Chaoqun Liu from University of Texas at Arlington to mathematically extract the rigid rotation part from the fluid motion, and thus to define and visualize vortices. Unlike the vorticity-based first generation and the scalar-valued second generation, Q, λ2, Δ and λci methods for example, the Liutex vector provides a unique, mathematical and systematic way to define vortices and visualize vortical structures from multiple perspectives without ambiguity. In this article, we summarize the recent developments of the Liutex framework and discuss the Liutex theoretical system including its existence, uniqueness, stability, Galilean invariance, locality and globality, decomposition in tensor and vector forms, Liutex similarity in turbulence, and multiple Liutex-based vortex visualization methods including Liutex lines, Liutex magnitude iso-surfaces, Liutex-Ω method, and Liutex core line method, etc.. Thereafter, the six core elements of vortex identification, including (1) absolute strength, (2) relative strength, (3) local rotational axis, (4) vortex rotation axes, (5) vortex core size, (6) vortex boundary, are used as touchstones against which the Liutex vortex identification system is examined. It is demonstrated with illustrative examples that the Liutex system is able to give complete and precise information of all six core elements in contrast to the failure and inaccuracy of the first and second-generation methods. The important concept that vorticity cannot represent vortex and the superiority of the Liutex system over previous methods are reiterated and stated in appropriate places throughout the paper. Finally, the article concludes with future perspectives, especially the application of the Liutex system in studying turbulence mechanisms encouraged by the discovery of Liutex similarity law. As a newly defined physical quantity, Liutex may open a door for quantified vortex and turbulence research including Liutex (vortex) dynamics and lead the community out of the shadow of turbulence research which traditionally relies on observations, graphics, assumptions, hypotheses, and other qualitative analyses. An optimistic projection is that the Liutex system could be critical to investigation of the vortex dynamics in applications from hydrodynamics, aerodynamics, oceanography, meteorology, etc. and to research of the generation, sustenance, modelling and controlling of turbulence.

Kolmogorov’s 1941 theory (K41) of similarity hypotheses and the −5/3 law for energy spectrum are considered as the most important theoretical achievement in turbulence research and the success of the modern turbulence theory. The assumptions of sufficient high Reynolds number and isotropy of turbulence that K41 based upon, however, cannot generally be met in practice, and thus discrepancy is often observed between the κ−5/3 law and direct numerical simulation (DNS) results of boundary layers in wall bounded turbulence, especially for moderate to low Reynolds number flows. Liutex vector is a recently defined new physical quantity which is extracted from turbulent flow to represent the rigid rotation part of fluid motion. Actually, Liutex is free from viscous dissipation and thus independent of Reynolds number, relaxing the very high Reynold number assumption of K41. Liutex similarity has been solidly demonstrated by DNS for a moderate Reynolds number turbulent boundary layer (Reθ ≈1 000), both the frequency and wavenumber spectrum of Liutex accurately matches the −5/3 law, which is obviously much better than the turbulence energy spectrum, while vorticity and other popular vortex identification methods, Q criterion for example, do not possess such a distinguished feature due to stretching and shearing contamination.

This study investigated a magnetically recycled modified polishing powder (CMIO@PP) as an adsorbent of phosphate; the CMIO@PP was synthesized by combining the modified La/Ce-containing waste polishing powder with CaO2-modified Fe3O4 (CMIO). Results indicate that the CMIO@PP nanocomposite presents a crystal structure comprising La (OH)3, Ce (OH)3, and Fe3O4, and that CMIO is uniformly dispersed in the modified polishing powder. The CMIO@PP (1:3) is a suitable choice considering its magnetism and adsorption capacity. The magnetic adsorbent exhibits a high adsorption capacity of 53.72 mg/g, a short equilibrium time of 60 min, and superior selectivity for phosphate. Moreover, the adsorbent strongly depends on the pH during the adsorption process and maintains a large adsorption capacity when the pH level is between 2 and 6. The adsorption of phosphate by the CMIO@PP (1:3) accords with the Langmuir isotherm model, and the adsorption process follows the pseudo-second order model. Meanwhile, adsorption–desorption experiments show that the adsorbent could be recycled a few times and that a high removal efficiency of phosphate from civil wastewater was achieved. Finally, mechanisms show that the adsorption of phosphate by the CMIO@PP (1:3) is mainly caused by electrostatic attraction and ligand exchange.

Nine novel copper(I) complexes with diphosphine and diimine ligands, namely [Cu(dpq)(xantphos)]BF4 (1), [Cu(dpq)(xantphos)]I (2), [Cu(dpq)(dppp)]BF4 (3), [Cu(dppz)(dppp)]BF4 (4), [Cu(dppz)(dppp)]I (5), [Cu(dppz)(pop)]I (6), [Cu(dpq)(pop)]I (7), [Cu(dpq)(pop)]Br (8), [Cu(dpq)(pop)]SCN (9) (dpq = pyrazino[2,3-f][1,10]phenanthroline, dppz = dipyrido[3,2-a:2′,3′-c]phenazine, xantphos = 9,9-dimethyl-4,5-bis(diphenylphosphanyl)xanthene, dppp = 1,3-bis(diphenylphosphino)propane, pop = 1,1′-[(Oxydi-2,1-phenylene)]bis[1,1-diphenylphosphine]), were characterized by single crystal X-ray diffraction, IR, elemental analysis, 1H NMR, 31P NMR, fluorescence spectra and terahertz time domain spectroscopy (THz-TDS). These nine complexes were synthesized by the reactions of copper salts, diimine ligands and various of P-donor ligands through one-pot method. Single crystal X-ray diffraction reveals that complex 9 is of a simple mono-nuclear structure while complexes 6 and 7 are of dimer structures. For complex 8, hydrogen bonds and C H⋯π interactions lead to the formation of a 1D infinite chain structure. Interestingly, complexes 1–5 show novel 2D or 3D network structures through C H⋯π interactions. In addition, complexes 1–3 and 6–9 exhibit interesting fluorescence in the solid state at room temperature. Among the nine complexes, complex 1 shows the highest quantum yield up to 37% and the lifetime of 1 is 6.0 μs. The terahertz (THz) time-domain spectra of these complexes were also studied.

Vortices have been regarded as the building blocks and muscles of turbulence for a long time. To better describe and analyze vortices or vortical structures, recently a new physical quantity called Liutex (previously named Rortex) is introduced to present the rigid rotation part of fluid motion (Liu et al. 2018). Since turbulence is closely related to the vortex, it can be postulated that there exists no turbulence without Liutex. According to direct numerical simulations (DNS) and experiments, forest of hairpin vortices has been found in transitional and low Reynolds number turbulent flows, while one-leg vortices are predominant in full developed turbulent flows. This paper demonstrates that the hairpin vortex is unstable. The hairpin vortex will be weakened or lose one leg by the shear and Liutex interaction, based on the Liutex definition and mathematical analysis without any physical assumptions. The asymmetry of the vortex is caused by the interaction of symmetric shear and symmetric Liutex since the smaller element of a pair of vorticity elements determines the rotational strength. For a 2-D fluid rotation, if a disturbance shear effects the larger element, the rotation strength will not be changed, but if the disturbance shear effects the smaller element, the rotation strength will be immediately changed due to the definition of the Liutex strength. For a rigid rotation, if the shearing part of the vorticity and Liutex present the same directions, e.g., clockwise, the Liutex strength will not be changed. If the shearing part of the vorticity and Liutex present different directions, e.g., one clockwise and another counterclockwise, the Liutex strength will be weakened. Consequently, the hairpin vortex could lose the symmetry and even deform to a one-leg vortex. The one-leg vortex cannot keep balance, and the chaotic motion and flow fluctuation are doomed. This is considered as the mathematical foundation of turbulence formation. The DNS results of boundary layer transition are used to justify this theory.

Six core issues for vortex definition and identification concern with (1) the absolute strength, (2) the relative strength, (3) the rotational axis, (4) the vortex core center, (5) the vortex core size, and (6) the vortex boundary (Liu C. 2019). However, most of the currently popular vortex identification methods, including the Q criterion, the λ2 criterion and the λci criterion et al, are Eulerian local region-type vortex identification criteria and can only approximately identify the vortex boundary by somewhat arbitrary threshold. On the other hand, the existing Eulerian local line-type methods, which seek to extract line-type features such as vortex core line, are not entirely satisfactory since most of these methods are based on vorticity or pressure minimum that will fail in many cases. The key issue is the lack of a reasonable mathematical definition for vortex core center. To address this issue, a Liutex (previously named Rortex) based definition of vortex core center is proposed in this paper. The vortex core center, also called vortex rotation axis line here, is defined as a line where the Liutex magnitude gradient vector is aligned with the Liutex vector, which mathematically implies that the cross product of the Liutex magnitude gradient vector and the Liutex vector on the line is equal to zero. Based on this definition, a novel three-step method for extracting vortex rotation axis lines is presented. Two test cases, namely the Burgers vortex and hairpin vortices, are examined to justify the proposed method. The results demonstrate that the proposed method can successfully identify vortex rotation axis lines without any user-specified threshold, so that the proposed method is very straightforward, robust and efficient.

In the present study, the physical meaning of vorticity is revisited based on the Liutex-Shear (RS) decomposition proposed by Liu et al. in the framework of Liutex (previously called Rortex), a vortex vector field with information of both rotation axis and swirling strength (Liu et al. 2018). It is demonstrated that the vorticity in the direction of rotational axis is twice the spatial mean angular velocity in the small neighborhood around the considered point while the imaginary part of the complex eigenvalue (λci) of the velocity gradient tensor (if exist) is the pseudo-time average angular velocity of a trajectory moving circularly or spirally around the axis. In addition, an explicit expression of the Liutex vector in terms of the eigenvalues and eigenvectors of velocity gradient is obtained for the first time from above understanding, which can further, though mildly, accelerate the calculation and give more physical comprehension of the Liutex vector.

A new vortex identification method (Liu et al. 2016) was proposed to represent the rotation relative strength and capture and visualize the vortices in our previous study. The basic idea of the Ω method is that a ratio of the vorticity squared over the summation of the vorticity squared and the deformation squared should be used to measure the relative rotation strength. However, the vorticity tensor norm is not objective. Thus, a moving observer will observe different vortex structures in a moving reference frame, which will make people confused with the real vortex structures. In the present study, by the definitions of the net spin tensor and net vorticity vector, an objective omega vortex identification method is presented and the examples are presented to verify the vortex structures will still retain in a moving reference frame.

In the new vortex identification method (Liu et al. 2016) to represent the rotation level and capture and visualize the vortices, proposed in our previous study, the independence of the reference frame and the Galilean invariant were not proved. In the present study, the Galilean invariance of the omega vortex identification method is proved and several examples are presented to verify the conclusion.

A vortex is intuitively recognized as the rotational/swirling motion of fluids, but a rigorous and universally-accepted definition is still not available. Vorticity tube/filament has been regarded equivalent to a vortex since Helmholtz proposed the concepts of vorticity tube/filament in 1858 and the vorticity-based methods can be categorized as the first generation of vortex identification methods. During the last three decades, a lot of vortex identification methods, including Q, Δ, λ2 and λci criteria, have been proposed to overcome the problems associated with the vorticity-based methods. Most of these criteria are based on the Cauchy-Stokes decomposition and/or eigenvalues of the velocity gradient tensor and can be considered as the second generation of vortex identification methods. Starting from 2014, the Vortex and Turbulence Research Team at the University of Texas at Arlington (the UTA team) focus on the development of a new generation of vortex identification methods. The first fruit of this effort, a new omega (Ω) vortex identification method, which defined a vortex as a connected region where the vorticity overtakes the deformation, was published in 2016. In 2017 and 2018, a Liutex (previously called Rortex) vector was proposed to provide a mathematical definition of the local rigid rotation part of the fluid motion, including both the local rotational axis and the rotational strength. Liutex/Rortex is a new physical quantity with scalar, vector and tensor forms exactly representing the local rigid rotation of fluids. Meanwhile, a decomposition of the vorticity to a rotational part namely Liutex/Rortex and an anti-symmetric shear part (RS decomposition) was introduced in 2018, and a universal decomposition of the velocity gradient tensor to a rotation part (R) and a non-rotation part (NR) was also given in 2018 as a counterpart of the traditional Cauchy-Stokes decomposition. Later in early 2019, a Liutex/Rortex based Omega method called Omega-Liutex, which combines the respective advantages of both Liutex/Rortex and Omega methods, was developed. And a latest objective Omega method, which is still under development, is also briefly introduced. These advances are classified as the third generation of vortex identification methods in the current paper. To elaborate the advantages of the third-generation methods, six core issues for vortex definition and identification have been raised, including: (1) the absolute strength, (2) the relative strength, (3) the rotational axis, (4) the vortex core center location, (5) the vortex core size, (6) the vortex boundary. The new third generation of vortex identification methods can provide reasonable answers to these questions, while other vortex identification methods fail to answer all questions except for the approximation of vortex boundaries. The purpose of the current paper is to summarize the main ideas and methods of the third generation of vortex identification methods rather than to conduct a comprehensive review on the historical development of vortex identification methods.

Good application of metal-organic frameworks (MOFs) on uranium adsorption has attracted increasing attention recently. MIL-53(Al)-AO, synthesized by introducing amidoxime groups to MIL-53(Al)-NH2 aimed to adsorb U(VI), was characterized by scanning electron microscopy, X-ray diffraction, thermogravimetric analysis and fourier transformed infrared spectroscopy. The sorption capacity of MIL-53(Al)-AO for U(VI) in aqueous solutions has been enhanced to 2.36 times compared with MIL-53(Al)-NH2 at pH 6.0 under the same conditions according to the experimental results, possibly due to the strong chelation of amidoxime. Effects of contact time, pH, interfering ions, and U(VI) concentration on the sorption of U(VI) for MIL-53(Al)-AO were also investigated. The sorption was strongly dependent on pH and independent of coexist ions. Result of this study shows that the MIL-53(Al)-AO was a kind of potential material to enrich U(VI) from aqueous solutions, and amidoxime could be introduced to MOFs sorbent by transforming the grafted amino groups on MIL-53(Al)-NH2.

C61H52Ag2N2O6P2, orthorhombic, P212121 (no. 19), a = 14.4634(11) Å, b = 17.7866(18) Å, c = 20.5509(19) Å, V = 5286.8(8) Å3, Z = 4, R gt(F) = 0.0424, wR ref(F 2) = 0.0997, T = 298(2) K.

We extend the ordinary binomial theorem to the case which involves two-variable Hermite polynomials in the context of quantum optics, and analytically obtain several new generalized binomial theorems whose results exactly equal the single- or two-mode Hermite polynomials. As their applications in the field of quantum optics, we analytically prove that the multiple-photon-subtracted squeezed state ambnesa†b†+ra†+tb† |00⟩ is equivalent to the Hermite-polynomial-weighted quantum state serving as an easily produced non-Gaussian entangled information resource, and the Wigner functions of spin coherent states and their marginal distributions are respectively the Laguerre polynomials and the Hermite polynomials.

UIO-66 and UIO-66-NH2 were synthesized by a solvent thermal method, and their textures were characterized. The adsorption selectivity, kinetics, isotherms, and mechanism of the two MOFs in a single solute system for phenol, 4-nitrophenol, 2,4-dinitrophenol, and 2,4,6-trinitrophenol were studied. At pH 4.0, the two MOFs exhibited a greater adsorption capacity for 2,4-dinitrophenol than for other nitrophenols; however, at lower substrate concentrations (C0 < 100 mg/L), the adsorption capacity of UiO-66-NH2 for 2,4-dinitrophenol was greater than that of UiO-66. The study of the adsorption mechanism showed that the electrostatic attraction is the main way in which UIO-66 and UiO-66-NH2 adsorb nitrophenols. Moreover, there was π-electron accumulation at a certain angle between the benzene ring of the adsorbents and the benzene ring of nitrophenols, whereas UiO-66-NH2 could also combine the nitrophenols through the hydrogen bonds originating from the amino groups. The fitting results of adsorption data showed t...

The Triassic eclogite-bearing central Qiangtang metamorphic belt (CQMB) in the northern Tibetan Plateau has been debated whether it is a metamorphic core complex underthrust from the Jinsha Paleo-Tethys or an in-situ Shuanghu suture. The CQMB is thus a key issue to elucidate the crustal architecture of the northern Tibetan Plateau, the tectonics of the eastern Tethys, and the petrogenesis of Cenozoic high-K magmatism. We here report the newly discovered Baqing eclogite along the eastern extension of the CQMB near the Baqing town, central Tibet. These eclogites are characterized by the garnet + omphacite + rutile + phengite + quartz assemblages. Primary eclogite-facies metamorphic pressure–temperature estimates yield consistent minimum pressure of 25 ± 1 kbar at 730 ± 60 °C. U–Pb dating on zircons that contain inclusions (garnet + omphacite + rutile + phengite) gave eclogite-facies metamorphic ages of 223 Ma. The geochemical continental crustal signature and the presence of Paleozoic cores in the zircons indicate that the Baqing eclogite formed by continental subduction and marks an eastward-younging anticlockwise West–East Qiangtang collision along the Shuanghu suture from the Middle to Late Triassic.

The introduction of Rortex provides a new perspective to investigate the local properties of vortical structures in transitional and turbulent flows, as Rortex offers a new and systematic description of the local fluid rotation, including scalar, vector and tensor forms. Unfortunately, the previous definition of Rortex is not straightforward, which requires the explicit calculation of somewhat cumbersome coordinate rotation. In this letter, a new explicit tensor form of Rortex and the relevant explicit velocity gradient tensor decomposition are presented, based on an explicit formula of the Rortex vector. The explicit tensor form represents the real local rotational part of the velocity gradient tensor in the original coordinate system. The explicit calculation of coordinate rotations can be totally avoided, which indicates an important improvement of Rortex based velocity gradient tensor decomposition.The introduction of Rortex provides a new perspective to investigate the local properties of vortical structures in transitional and turbulent flows, as Rortex offers a new and systematic description of the local fluid rotation, including scalar, vector and tensor forms. Unfortunately, the previous definition of Rortex is not straightforward, which requires the explicit calculation of somewhat cumbersome coordinate rotation. In this letter, a new explicit tensor form of Rortex and the relevant explicit velocity gradient tensor decomposition are presented, based on an explicit formula of the Rortex vector. The explicit tensor form represents the real local rotational part of the velocity gradient tensor in the original coordinate system. The explicit calculation of coordinate rotations can be totally avoided, which indicates an important improvement of Rortex based velocity gradient tensor decomposition.

In this paper, a modified normalized Rortex/vortex identification method named ΩR is presented to improve the original ΩR method and resolve the bulging phenomenon on the isosurfaces, which is caused by the original ΩR method. Mathematical explanations and the relationship between the Q criterion and ΩR are described in detail. In addition, the new developed formula does not require two original coordinate rotations, and the calculation of ΩR is greatly simplified. The numerical results demonstrate the effectiveness of the new modified normalized Rortex/vortex identification method.In this paper, a modified normalized Rortex/vortex identification method named ΩR is presented to improve the original ΩR method and resolve the bulging phenomenon on the isosurfaces, which is caused by the original ΩR method. Mathematical explanations and the relationship between the Q criterion and ΩR are described in detail. In addition, the new developed formula does not require two original coordinate rotations, and the calculation of ΩR is greatly simplified. The numerical results demonstrate the effectiveness of the new modified normalized Rortex/vortex identification method.

Zeolitic imidazole frameworks (ZIFs), a new adsorbent with a high chemical and thermal stability and a high adsorption capacity, are used for adsorptive removal of azo dyes. The synthesized ZIF-67 was characterized with Fourier transform infrared spectroscopy (FTIR), thermogravimetric–differential thermal analysis (TG–DTA) and zeta potential instrument. The adsorption of some azo dyes on ZIF-67 in the single dye systems showed that the removal efficiencies are congo red > methyl orange > methyl red > methyl blue. The highest adsorption capacity of congo red and methyl orange were 3900 and 1340 mg/g, respectively. In a binary dye system the adsorption capacity of congo red decreased, while the removal efficiency of methyl orange increased in comparison with the single systems, indicating that a competitive adsorption of congo red and methyl orange over the ZIF-67 occurred. The experimental data indicate that the electrostatic attraction between ZIF-67 and congo red is the major driving force and the π–π stacking is also responsible for dye adsorption. After 5 cycles of ZIF-67 adsorption and desorption, the congo red removal efficiency maintained more than 95%.