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In this work, the novel quadrilateral overlapping element incorporated with the harmonic trigonometric functions is presented to reduce the efforts in mesh division for modal analysis. The new partition of unity functions in the overlapping element are cubic polynomials. Therefore, low-order polynomials can be utilized to augment local approximation space without the linear dependence problem. Moreover, the original polynomial approximation spaces are further enriched by the harmonic trigonometric functions without introducing additional rank deficiencies in the system matrices. Thus, the presented enriched overlapping finite element method (EOFEM) provides very precise eigenfrequencies and eigenmodes by using a very coarse mesh. However, the shape functions in the presented EOFEM do not possess the Kronecker delta function property. Hence, a conforming method that modifies the shape functions rather than the variational principle is proposed to impose the essential boundary conditions. Several numerical examples in two dimensions are then investigated to elaborate on the performance of the presented EOFEM in modal analyses. Besides, a block-diagonal lumped mass matrix is presented and further extended to the structure vibration analysis by incorporating the explicit time integration method. It is proven that the enriched overlapping element is computationally more efficient than the quadratic finite element and the original overlapping element. [ABSTRACT FROM AUTHOR]

Glyphosate (GP) has given rise to concerns regarding its environmental impact and potential hazards to human health. Herein, a solvothermal approach was used for doping Co and Zr into Fe 3 O 4 , thereby endowing the adsorption and catalytic efficacy for GP elimination and phosphate recovery from aqueous solution. The magnetic nanoparticles achieved 100 % removal of 100 mg/L GP in 30 min with 0.5 mM peroxymonosulfate (PMS). Electron paramagnetic resonance (EPR) test verified that both radical and non-radical pathways were produced in the catalytic oxidation process. Density functional theory (DFT) investigations have demonstrated that Co and Zr co-doping led to an improved removal efficiency of GP. Moreover, the as-prepared material used in this integrated PMS activation and adsorption maintained a high stability towards GP degradation and phosphate recovery during five successive cycles. This study provides an efficient technique for the removal of GP and the simultaneous adsorption of secondary inorganic phosphorus from water. [Display omitted] • Co and Zr co-doped Fe3O4 nanoparticles were synthesized by a facile solvothermal method. • Synergism of adsorption and PMS-activation for glyphosate removal and phosphorus recovery from solution. • Both radical and non-radical pathways were responsible for glyphosate degradation. • The performance and mechanism were elucidated via characterizations and DFT calculations. [ABSTRACT FROM AUTHOR]

Intrinsic nonlinear elasticity deals with the deformations of elastic bodies as isometric immersions of Riemannian manifolds into the Euclidean spaces (see Ciarlet [9,10]). In this paper, we study the rigidity and continuity properties of elastic bodies for the intrinsic approach to nonlinear elasticity. We first establish a geometric rigidity estimate for mappings from Riemannian manifolds to spheres (in the spirit of Friesecke–James–Müller [23]), which is the first result of this type for the non-Euclidean case as far as we know. Then we prove the asymptotic rigidity of elastic membranes under suitable geometric conditions. Finally, we provide a simplified geometric proof of the continuous dependence of deformations of elastic bodies on the Cauchy–Green tensors and second fundamental forms, which extends the Ciarlet–Mardare theorem in [18] to arbitrary dimensions and co-dimensions. [ABSTRACT FROM AUTHOR]

• The enriched quadrilateral overlapping elements are proposed for analyses of time-harmonic acoustics. • Comparisons of different local approximations in overlapping elements for helmholtz problems are conducted. • Detailed dispersion error analyses are conducted. • The proposed EOFEM is computationally efficient and practically insensitive to mesh distortion. The pronounced numerical dispersions and numerical anisotropy make solutions from the finite element model using low-order elements unreliable for the time-harmonic acoustic problems with fairly large wavenumber. In this work we propose a novel enriched quadrilateral overlapping elements for Helmholtz problems. In this scheme, the original overlapping elements are strengthened by the harmonic trigonometric functions stemming from the spectral techniques. Since all additional degrees of freedom are aligned on the vertex node of every overlapping element, the proposed method can be directly applied to the original finite element model without changing the mesh topology. Because of the enriched approximation space, the proposed method can significantly suppress the numerical dispersions with practically negligible numerical anisotropy, and can be more computationally efficient in providing comparable solution accuracy compared to the original scheme and the classic finite element method. Besides, the linear dependence issue is completely avoided and these enriched overlapping elements are distortion-insensitive. In this work, the original variational formulation is perturbed using the penalty method to impose the essential boundary conditions. Numerical experiments show that the developed method can reduce user interventions in mesh creation and adjustment, and is promising in practical engineering applications for time-harmonic acoustics. [ABSTRACT FROM AUTHOR]

A theory for the evolution of a metric g driven by the equations of three-dimensional continuum mechanics is developed. This metric in turn allows for the local existence of an evolving three-dimensional Riemannian manifold immersed in the six-dimensional Euclidean space. The Nash–Kuiper theorem is then applied to this Riemannian manifold to produce a wild evolving C 1 manifold. The theory is applied to the incompressible Euler and Navier–Stokes equations. One practical outcome of the theory is a computation of critical profile initial data for what may be interpreted as the onset of turbulence for the classical incompressible Navier–Stokes equations. [ABSTRACT FROM AUTHOR]

This paper investigates the gas permeability and the electrical conductivity of structural concretes under different pore saturations. The gas permeability was measured by CemBureau device and the electrical conductivity by alternating current method. The pore structure was characterized by mercury intrusion porosimetry (MIP) and gravimetric methods. The Archie's law is used to interpret the tortuosity of the pore structure. The impact of pore saturation is evaluated through the Van Genuchten-Mualem (VGM) and Kozeny's models. The results show that (1) the global correlation between the gas permeability in dried state and the electrical conductivity in saturated sate is weak; (2) both VGM and Kozeny's models can describe the relative permeability/conductivity, but the VGM model gives more consistent exponents for permeability and conductivity; (3) as the pore gas and liquid phases are both percolated, the gas permeability is correlated to the electrical conductivity for arbitrary pore saturation. [ABSTRACT FROM AUTHOR]

In order to realize the wavelength division multiplexing (WDM) device with compact channels and high transmission, a novel three-channel WDM device based on a two-dimensional photonic crystal with a square lattice is proposed. Three parallel line defect waveguides are introduced in this structure to control the propagation of light. Elliptical and rectangular resonators are employed to carry out the selection of light wavelengths by the coupling resonant effects. The point defect cavity is placed at the end of the middle waveguide to further filter the wavelengths. We theoretically analyze the effects of the distances between the resonator and the micro-cavity and between asymmetrical resonators on the light propagation by the finite-difference time-domain (FDTD) method. Three different wavelengths (1560, 1580, and 1620 nm) in the communication window range with maximum transmission over 90% are obtained. The findings may provide potential applications in filters, WDM optical communication systems and other optoelectronics devices. [ABSTRACT FROM AUTHOR]

Abstract: Controlled disorder is artificially introduced in self-assembled three-dimensional photonic crystals by adding large fluorescent spheres of different concentrations in the host suspension of small PS spheres during the growth process. Structural characterizations reveal the increase of disorder with the increase of doping concentration. Transmission and reflection spectra demonstrate the pronounced changes in the bandgaps of photonic crystals with different degrees of controlled disorder. The stop band gradually vanishes with the increased disorder, especially for the completely disordered nanostructure, the transmission and reflection intensity in the stop band both decrease to almost zero. The measured emission spectra show significant modification on emission intensity and frequency band of fluorescent spheres in partially disordered photonic crystals as compared to those of the highly ordered and completely disordered nanostructures. The proposed structure could provide a new approach for random lasing and strong Anderson localization. [Copyright &y& Elsevier]

To improve the performance of the classical finite element method (FEM) in acoustic analyses, in this work the interpolation cover functions are incorporated into the standard linear nodal shape functions to give the finite element with cover functions (FEwC). Since the original linear approximation space of the standard FEM is significantly enriched, more accurate solutions can be obtained. However, this FEwC encounters the intractable linear dependence (LD) problem. In this paper the LD problem is studied systematically and then an effective method is given to completely avoid this problem. The imposition of Dirichlet boundary conditions in FEwC which is different from that in FEM is also illustrated. Besides, to handle the acoustic scattering problems in the unbounded domains, the Dirichlet-to-Neumann (DtN) map technique is employed as the non-reflecting boundary condition. The dispersion error analyses and several typical numerical experiments associated with the joint frequency-domain and time-domain analysis are performed to exhibit the high performance of the FEwC compared with the classic FEM and the edge-based smoothed FEM in solving underwater acoustic propagation problems. • An efficient approach to completely eliminate the linear dependence (LD) problems of the FEwC/GFEM is proposed. • The exact imposition of Dirichlet boundary conditions is illustrated. • A joint analysis in time-domain and frequency-domain is conducted for two-dimensional underwater acoustic problems. [ABSTRACT FROM AUTHOR]

Due to the pollution errors in acoustic analysis, the requirement of very refined meshes at high wavenumbers limits the practical application of the conventional finite element method (FEM). In this work, the three-node linear triangular element with linear interpolation cover functions (FEwC) is applied to solve acoustic radiation problems in two dimensions. The present FEwC has considerable generality since the polynomial interpolation cover functions can be easily implemented without changing the mesh topology. As the original linear approximation space is enriched by the cover functions, the FEwC can significantly alleviate the pollution errors and increase the convergence rate of the original low-order element in acoustic computation. We show the proper imposition of the Dirichlet boundary conditions in acoustic problems and illustrate an effective iterative algorithm to resolve the system equations with a singular coefficient matrix. The Dirichlet-to-Neumann mapping technique is used to truncate the infinite problem domain into a bounded computational domain for the exterior problems and the Sommerfeld radiation condition then can be satisfied at infinity. Several numerical experiments demonstrate that the present scheme is a promising numerical tool for acoustic radiation problems. [ABSTRACT FROM AUTHOR]

Abstract: We establish the existence, stability, and asymptotic behavior of transonic flows with a transonic shock for the steady, full Euler equations in two-dimensional infinite nozzles of slowly varying cross-sections. Given a smooth incoming flow that is close to a uniform supersonic state at the entrance, we prove that there exists a transonic flow whose infinite downstream smooth subsonic region is separated by a smooth transonic shock from the upstream supersonic flow. The solution is unique within the class of transonic solutions that are close to the background solution. This problem is approached by a free boundary problem in which the transonic shock is formulated as a free boundary. An iteration scheme for the free boundary is developed and its fixed point is shown to exist, which is a solution of the free boundary problem, by combining some delicate estimates for a second-order nonlinear elliptic equation on a Lipschitz domain. [Copyright &y& Elsevier]

[Display omitted] • NBR was fluorinated via radical graft polymerization of fluorinating monomer. • Gelation could be avoided completely in presence of NDM as chain transfer agent. • The graft polymerization mechanism was proposed from the 1H NMR analysis. Fluorination could efficiently improve the comprehensive performance of nitrile-butadiene rubber (NBR). However, severe gelation usually occurred in the radical graft polymerization onto the diene-based polymers. Here, a facile approach has been established for the facile fluorination of NBR without gelation via radical graft polymerization in presence of n -dodecylmercaptan (NDM) as chain transfer agent, with 2,2,3,4,4,4-hexafluorobutyl acrylate (F6) as the model fluorinating monomer. The gel content decreased with increasing the feeding ratio of NDM and reached 0 with a feeding ratio of NDM of 50 mol% of the initiator, with a fluorination degree of 0.50%. The graft polymerization mechanism was proposed with the 1H NMR analysis. The proposed strategy is expected to provide a promising approach for the functionalization of diene-based polymers. [ABSTRACT FROM AUTHOR]

Fluorination could efficiently improve the comprehensive performance of nitrile-butadiene rubber (NBR). Here, a facile approach has been established for the fluorination of NBR via olefin cross metathesis (OCM) technique, with 1H,1H,2H,2H-perfluorooctyl acrylate (F13) as the model fluorinating chain transfer agent (F-CTA). The effect of reaction conditions on the fluorination degree (defined as the mass content of F13 in the fluorinated nitrile-butadiene rubber (F-NBR)) has been optimized, such as feeding ratios of F13 and Hoveyda-Grubbs II (HG2) catalyst, and the reaction time. The liquid F-NBR was obtained with fluorination degree of 1.84% at the optimized condition. Additionally, the reaction process was also proposed from the variations in the fluorination degree and molecular weight of the F-NBR products. Image 1 • Nitrile-butadiene rubber (NBR) was fluorinated via olefin cross metathesis (OCM). • The fluorination condition was optimized with a fluorination degree of 1.84%. • The reaction process was proposed as two-stage competitive reactions. [ABSTRACT FROM AUTHOR]

The classical finite element approach cannot guarantee satisfactory accuracy for acoustic problems at large wavenumbers on account of the numerical pollution error effect. This negative effect stems from the fact that the approximate wavenumbers are usually in conflict with the real wavenumbers in many numerical methods. To suppress this effect, a radial point interpolation meshless technique with a modified scheme for selecting interpolation nodes is employed in this paper. One-dimensional dispersion analysis shows that this modified scheme can effectively reduce numerical errors compared with the original scheme. The results of several numerical examples have manifested that the present method can generate more accurate and reliable solutions than the standard finite element approach and the original radial point interpolation method in the acoustic analyses. • The radial point interpolation meshfree method is first extended into exterior acoustics with the Dirichlet-to-Neumann map. • The modified node selection scheme is proposed to increase the accuracy of the present method. • The present method is more accurate and reliable than the standard FEM and the original RPIM for acoustics. [ABSTRACT FROM AUTHOR]

Abstract: Partially disordered three-dimensional photonic crystals (PCs) were fabricated by self-assembly of small polystyrene spheres doped with large fluorescent spheres. Photoluminescence measurements show that the introduced disorder largely affects the spontaneous emission (SE) behaviors of the fluorescent spheres. Two pronounced emission peaks found at 565nm and 620nm gradually merge into one emission peak with the doping concentration increase from 0.02wt% to 0.20wt%, accompanied by the red-shift of the main emission peak. The dynamic modification of SE originates from the deterioration of stop band of PCs due to the disorder aggravated by increasing the doping concentration. The efficient modification on the emission intensity and frequency indicates potential applications in random lasing. [Copyright &y& Elsevier]