Stability of travelling wave solutions for coupled surface and grain boundary motion

We investigate the spectral stability of the travelling wave solution for the coupled motion of a free surface and grain boundary that arises in materials science. In this problem a grain boundary, which separates two materials that are identical except for their crystalline orientation, evolves according to mean curvature. At a triple junction, this boundary meets the free surfaces of the two crystals, which move according to surface diffusion. The model is known to possess a unique travelling wave solution. We study the linearization about the wave, which necessarily includes a free boundary at the location of the triple junction. This makes the analysis more complex than that of standard travelling waves, and we discuss how existing theory applies in this context. Furthermore, we compute numerically the associated point spectrum by restricting the problem to a finite computational domain with appropriate physical boundary conditions. Numerical results strongly suggest that the two-dimensional wave is stable with respect to both two- and three-dimensional perturbations.     

广义边界条件和概率流密度的连续性

以四参量族－广义边界条件代替有限深方势阱内粒子波函数的对数的一阶导数连续性条件，表明这种替换比用广义边界条件取代一盒子内自由粒子波函数在两壁处为零的边界条件显行更加合理些。我们发现，如对参量ρ和θ取任意值，则会导致概率流密度连续性被破坏。我们找到了约束ρ和θ取值的条件，并得到一组新的解析解。     

Transparent boundary conditions for the Helmholtz equation in some ramified domains with a fractal boundary

The paper addresses a class of boundary value problems in some self-similar ramified domains, with the Laplace or Helmholtz equations. Much stress is placed on transparent boundary conditions which allow the solutions to be computed in subdomains. A self similar finite element method is proposed and tested. It can be used for numerically computing the spectrum of the Laplace operator with Neumann boundary conditions, as well as the eigenmodes. The eigenmodes are normalized by means of a perturbation method and the spectral decomposition of a compactly supported function is carried out. Finally, a numerical method for the wave equation is addressed.     

Free vibration of an embedded single-walled carbon nanotube with various boundary conditions using the RMVT-based nonlocal Timoshenko beam theory and DQ method

The nonlocal Timoshenko beam theories (TBTs), based on the Reissner mixed variation theory (RMVT) and principle of virtual displacement (PVD), are derived for the free vibration analysis of a single-walled carbon nanotube (SWCNT) embedded in an elastic medium and with various boundary conditions. The strong formulations of the nonlocal TBTs are derived using Hamilton's principle, in which Eringen's nonlocal constitutive relations are used to account for the small-scale effect. The interaction between the SWCNT and its surrounding elastic medium is simulated using the Winkler and Pasternak foundation models. The frequency parameters of the embedded SWCNT are obtained using the differential quadrature (DQ) method. In the cases of the SWCNT without foundations, the results of RMVT- and PVD-based nonlocal TBTs converge rapidly, and their convergent solutions closely agree with the exact ones available in the literature. Because the highest order with regard to the derivatives of the field variables used in the RMVT-based nonlocal TBT is lower than that used in its PVD-based counterpart, the former is more efficient than the latter with regard to the execution time. The former is thus both faster and obtains more accurate solutions than the latter for the numerical analysis of the embedded SWCNT.     

Prediction of the absorption exponent in rectangular enclosures with a single absorbent boundary

It is known that the classical theory of room acoustics cannot be strictly applied to the study of the sound field in a rectangular enclosure with only five boundaries (i.e., with a single absorbent boundary), as the sound field in the enclosure is not diffuse. A theoretical method is developed for the prediction of the absorption exponent in a rectangular enclosure with a single absorbent boundary, and the absorption exponent is used to describe the exponential decay of the sound energy. The method is based on the radiosity-based theoretical/computer model and is used for diffusely reflecting boundaries. The predicted absorption exponent is compared with the Kuttruff values and the simulation results from Monte-Carlo computations. It is found that the predicted absorption exponent of the proposed method shows better agreement with the simulation results from Monte-Carlo computations than the Kuttruff values. With the more accurately predicted absorption exponent, the slope of the energy decay curve and other acoustic parameters in an enclosure with a single absorbent boundary can be obtained accurately.     

Simultaneous density and velocity measurements in a supersonic turbulent boundary layer

A novel technique for simultaneous measurements of instantaneous whole-field density and velocity fields of supersonic flows has been developed.The density measurement is performed based on the nano-tracer planar laser scattering(NPLS) technique,while the velocity measurement is carried out using particle image velocimetry(PIV).The present experimental technique has been applied to a flat-plate turbulent boundary layer at Mach 3,and the measurement accuracy of the density and velocity are discussed.Based on this new technique,the Reynolds stress distributions were also obtained,demonstrating that this is an effective means for measuring Reynolds stresses under compressible conditions.     

Hole with diluted density in the presence of self-generated magnetic fields

The collapse behavior of the fields and hole with diluted density described by the nonlinear coupling equations in laser-produced plasma are investigated in the condition of non-static limit. The results show that the nonlinear plasma currents give rise to intermittent magnetic fields, leading to collapsing hole with diluted density. The self-generated magnetic field is very important for the formation of hole with diluted density. The resulting density perturbation rate is very similar to that observed experimentally.     

在HT-7托卡马克上密度扫描实验中的边界湍流和输运

在HT-7托卡马克上密度扫描实验中使用一个快速扫描气动朗缪尔探针来研究边界湍流和输运。随着中心弦平均等离子体密度的增加，在等离子体边界观察到径向电场剪切增强，径向电场的增强能够解释边界输运的减小和全局粒子约束的改善。粒子约束时间的增加和垂直扩散系数的减小证明粒子输运降低了。在等离子体边界区域发现电离和辐射驱动湍流的特征，表明电离和辐射在湍流驱动过程中具有重要性。     

高能质子照相中面密度的测量和不确定性分析

 依据洛斯·阿拉莫斯国家实验室的质子照相概念,通过研究高能质子与物质的相互作用规律,给出了质子照相确定面密度的计算公式及其不确定性分析,阐述了质子照相鉴别材料组分的原理。相对于X光照相,质子通过面密度较大的物体后的通量明显增加,界面探测和密度重建更加准确。研究了多库仑散射和磁透镜系统的色散对质子照相空间分辨率的影响及解决途径。结果表明,高能质子照相在穿透能力、面密度测量、材料的组分识别、空间分辨率等方面都优于X光照相。     

Graphene/silicon photoelectrode with high and stable photoelectrochemical response in aqueous solution

The graphene (Gr)/Si electrodes were fabricated by electrophoresis method and then following an annealing process. The p-Si surface was found to be covered completely with successive and transparent Gr sheets, and thus the impairment of aqueous solution on the photoelectrochemical capability of silicon could be avoided. This annealing process was a key process for improving the adhesion of Gr/Si interface. After annealing at 400 °C, the Gr/Si electrodes displayed high photoresponse ability and high stability in aqueous solution. The carriers transfer between Gr and Si is discussed on the basis of the semiconductor energy band theory. The results demonstrated that the Gr/Si electrodes would be a promising candidate as solar energy materials using in aqueous solution.     

Revision of single atom local density and capture number varying with coverage in uniform depletion approximation and its effect on coalescence and number of stable clusters

In vapour deposition,single atoms (adatoms) on the substrate surface are the main source of growth.The change in its density plays a decisive role in the growth of thin films and quantum size islands.In the nucleation and cluster coalescence stages of vapour deposition,the growth of stable clusters occurs on the substrate surface covered by stable clusters.Nucleation occurs in the non-covered part,while the total area covered by stable clusters on the substrate surface will gradually increase.Carefully taking into account the coverage effect,a revised single atom density rate equation is given for the famous and widely used thin-film rate equation theory,but the work of solving the revised equation has not been done.In this paper,we solve the equation and obtain the single-atom density and capture number by using a uniform depletion approximation.We determine that the single atom density is much lower than that evaluated from the single atom density rate equation in the traditional rate equation theory when the stable cluster coverage fraction is large,and it goes down very fast with an increase in the coverage fraction.The revised equation gives a higher value for the ’average’ capture number than the present equation.It also increases with increasing coverage.That makes the preparation of single crystalline thin film materials difficult and the size control of quantum size islands complicated.We also discuss the effect of the revision on coalescence and the number of stable clusters in vapour deposition.     

New expressions for the surface roughness length and displacement height in the atmospheric boundary layer

An alternative model for the prediction of surface roughness length is developed. In the model a new factor is introduced to compensate for the effects of wake diffusion and interactions between the wake and roughness obstacles. The experiments are carried out by the use of the hot wire anemometry in the simulated atmospheric boundary layer in a wind tunnel. Based on the experimental data, a new expression for the zero-plane displacement height is proposed for the square arrays of roughness elements, which highlights the influence of free-stream speed on the roughness length. It appears that the displacement height increases with the wind speed while the surface roughness length decreases with Reynolds number increasing. It is shown that the calculation results based on the new expressions are in reasonable agreement with the experimental data.     

Assessment of the nature of interactions of cations with cycloheptatriene derivatives using change in the aromaticity: Comparison with electron density and NBO results

ABSTRACT

Interactions of cycloheptatriene derivatives, C₇H₆X, (X?=?NH, PH, AsH, O, S, Se) with the cations H⁺, CH₃⁺, Cu⁺, Al⁺, Li⁺, Na⁺, and K⁺ are studied using B3LYP functional and 6-311++G(d,p) basis set. The calculated gas-phase cation affinities (CA) and cation basicities (CB) for all molecules decrease as H⁺ > CH₃⁺ > Cu⁺ > Al⁺ > Li⁺ > Na⁺ > K⁺. We used the induced aromaticity in the 7-membered ring of C₇H₆X upon interaction with the cations, M⁺, as a measure of C₇H₆X/M⁺ interaction. Nucleus-independent chemical shift (NICS) and harmonic oscillator model of aromaticity (HOMA) were used as two indices of aromaticity. The highest and lowest induced aromaticities were observed for interactions of H⁺ and K⁺, respectively. Also, the aromaticity induced by interaction with a cation in C₇H₆AsH and C₇H₆PH was larger than that in C₇H₆NH and C₇H₆O. Hence, the aromaticity was considered as a measure of covalency for the C₇H₆X/M⁺ interactions showing a rational dependence on both the molecule and cation. The nature of the interactions was also assessed using electron density, charge distribution analysis and NBO calculations. The results of the aromaticity indices, NICS and HOMA, were compared with the electron density and NBO results.     

Critical current density behaviors across a grain boundary inclined to current with different angles in YBa_2Cu_3O_(7-δ) bicrystal junctions

The critical current density behaviors across a bicrystal grain boundary(GB) inclined to the current direction with different angles in YBa_2Cu_3O_(7-δ) bicrystal junctions in magnetic fields are investigated.There are two main reasons for the difference in critical current density in junctions at different GB inclined angles in the same magnetic field:(i) the GB plane area determines the current carrying cross section;(ii) the vortex motion dynamics at the GB affects the critical current value when the vortex starts to move along the GB by Lorentz force.Furthermore,the vortex motion in a bicrystal GB is studied by investigating transverse(Hall) and longitudinal current–voltage characteristics(I–V_(xx) and I–V_(xy)).It is found that the I–V_(xx) curve diverges from linearity at a high driving current,while the I–V_(xy) curve keeps nearly linear,which indicates the vortices inside the GB break out of the GB by Lorentz force.     

Ionic solvation and association in LiCl aqueous solution: a density functional theory,polarised continuum model and molecular dynamics investigation

In this work, the ionic solvation and association behaviours in the LiCl aqueous solution were investigated using density functional theory (DFT), a polarised continuum model and classical molecular dynamics simulations. DFT calculations of LiCl(H₂O)_1–6,8 clusters show that contact ion pair (CIP) and solvent-shared ion pair (SSIP) conformers of LiCl(H₂O)_n (n ≥ 4) clusters are generally energetic both in the gas phase and in the aqueous solution. Some SSIP conformers may be slightly more stable than their CIP isomers when at least eight water molecules are incorporated in the inner hydration shells of LiCl hydrates. The transformation between CIP and SSIP conformers is easy by overcoming a small energy barrier, which mainly results from the hydration shell reorganisation of Li⁺. Molecular dynamics simulations show that ion pairs or ion clusters can be found in the LiCl aqueous solution, and the probability of CIP conformers or ion clusters presented in the LiCl solution generally increases with rise in temperature. However, the presentation of ion pairs or ion clusters in the LiCl aqueous solution does not inevitably lead to the nucleation of LiCl crystallisation.     

Asymptotic Analysis of a Bingham Fluid in a Thin Domain with Fourier and Tresca Boundary Conditions

In this paper we prove first the existence and uniqueness results for the weak solution, to the stationary equations for Bingham fluid in a three dimensional bounded domain with Fourier and Tresca boundary condition; then we study the asymptotic analysis when one dimension of the fluid domain tends to zero. The strong convergence of the velocity is proved, and a specific Reynolds limit equation and the limit of Tresca free boundary conditions are obtained.     

Statistical second-order two-scale analysis and computation for heat conduction problem with radiation boundary condition in porous materials

This paper discusses a statistical second-order two-scale(SSOTS) analysis and computation for a heat conduction problem with a radiation boundary condition in random porous materials.Firstly,the microscopic configuration for the structure with random distribution is briefly characterized.Secondly,the SSOTS formulae for computing the heat transfer problem are derived successively by means of the construction way for each cell.Then,the statistical prediction algorithm based on the proposed two-scale model is described in detail.Finally,some numerical experiments are proposed,which show that the SSOTS method developed in this paper is effective for predicting the heat transfer performance of porous materials and demonstrating its significant applications in actual engineering computation.