高斯型空间光孤子相互作用的数值研究

 通过数值模拟的方法,对高斯孤子在对数型饱和非线性介质中的相互作用进行了研究,考查了两光束间的相对振幅和相对相位对其相互作用的影响。结果表明：高斯孤子之间的相互作用敏感地依赖于两光束间的相对振幅和相对相位。在不同的振幅差异范围内,光束间的主要作用交替地表现为相互排斥和相互吸引,并由于高斯孤子的不稳定性,导致了光束在碰撞后以一种尺寸周期性变化的呼吸模式传输。随着相对相位的增大,两光束间始终持续地表现出强烈的排斥作用,直到相对相位增加到一个2π周期之后。而且碰撞之后,光束也都以呼吸模式进行传输,其分离的角度越大,呼吸就越明显。     

Numerical Study on an RBF-FD Tangent Plane Based Method for Convection–Diffusion Equations on Anisotropic Evolving Surfaces

In this paper, we present a fully Lagrangian method based on the radial basis function (RBF) finite difference (FD) method for solving convection–diffusion partial differential equations (PDEs) on evolving surfaces. Surface differential operators are discretized by the tangent plane approach using Gaussian RBFs augmented with two-dimensional (2D) polynomials. The main advantage of our method is the simplicity of calculating differentiation weights. Additionally, we couple the method with anisotropic RBFs (ARBFs) to obtain more accurate numerical solutions for the anisotropic growth of surfaces. In the ARBF interpolation, the Euclidean distance is replaced with a suitable metric that matches the anisotropic surface geometry. Therefore, it will lead to a good result on the aspects of stability and accuracy of the RBF-FD method for this type of problem. The performance of this method is shown for various convection–diffusion equations on evolving surfaces, which include the anisotropic growth of surfaces and growth coupled with the solutions of PDEs.     

Velocity overshoot of start-up flow for a Maxwellfluid in a porous half-space

Stokes' first problem has been investigated for a Maxwell fluid in a porous half-space for gaining insight into the effect of viscoelasticity on the start-up flow in a porous medium. An exact solution was obtained by using the Fourier sine transform. It was found that at large values of the relaxation time the velocity overshoot occurs obviously and the system exhibits viscoelastic behaviours. On the other hand, for short relaxation time the velocity overshoot disappears and the system exhibits viscous behaviours. A critical value of the relaxation time was obtained for the emergence of the velocity overshoot. Furthermore, it was found that the velocity overshoot is caused by both the viscoelasticity of the Maxwell fluid and the Darcy resistance resulting from the structure of the micropore in the porous medium.     

变形双重介质分形油藏非达西流动分析

考虑与实际生产相符的介质的双重特性和分形特征,并考虑介质的变形,引入双重分形介质渗透率模数,建立应力敏感地层双重分形介质系统的流动方程.采用Douglas-Jones预估-校正法获得无限大地层定产量生产时变形双重分形介质模型的数值解和无限大地层定压生产时分形介质双孔模型的数值解,作出了典型的压力曲线图版.     

气体和气溶胶在多孔介质中迁移的数值模拟

为了研究多孔介质对气体和气溶胶的封闭能力,用数值方法模拟了气体和气溶胶在多孔介质中的迁移.考虑了渗透、吸附过滤、扩散、热传导等因素,在柱对称坐标下用双孔双渗模型进行了数值模拟,并与实验结果进行了比较.计算结果显示,多孔介质对气溶胶有较强的阻挡作用,模拟实验结果也证明了这一点.     

Keller–Osserman estimates and removability result for the anisotropic porous medium equation with gradient absorption term

We study “large” nonnegative solutions for a class of quasilinear equations model of which is We give a sufficient condition on the exponents and for the removability of isolated singularities.     

Investigation of different liquid media and ablation times on pulsed laser ablation synthesis of aluminum nanoparticles

Aluminum nanoparticles were synthesized by pulsed laser ablation of Al targets in ethanol, acetone, and ethylene glycol. Transmission Electron Microscope (TEM) and Scanning Electron Microscope (SEM) images, Particle size distribution diagram from Laser Particle Size Analyzer (LPSA), UV-visible absorption spectra, and weight changes of targets were used for the characterization and comparison of products. The experiments demonstrated that ablation efficiency in ethylene glycol is too low, in ethanol is higher, and in acetone is highest. Comparison between ethanol and acetone clarified that acetone medium leads to finer nanoparticles (mean diameter of 30 nm) with narrower size distribution (from 10 to 100 nm). However, thin carbon layer coats some of them, which was not observed in ethanol medium. It was also revealed that higher ablation time resulted in higher ablated mass, but lower ablation rate. Finer nanoparticles, moreover, were synthesized in higher ablation times.     

A comparison of numerical and analytical radiative-transfer solutions for plane albedo of natural waters

Several numerical and analytical solutions of the radiative transfer equation (RTE) were compared for plane albedo in a problem of solar light reflection by sea water. The study incorporated the simplest case—a semi-infinite one-dimensional plane—parallel absorbing and scattering homogeneous layer illuminated by a monodirectional light beam. Inelastic processes (such as Raman scattering and fluorescence), polarization and air-water surface refraction-reflection effects, were not considered. Algorithms were based on the invariant imbedding method and two different variants of the discrete ordinate method (DOM). Calculations were performed using parameters across all possible ranges (single-scattering albedo ω₀ and refracted solar zenith angle θ₁), but with a special emphasis on natural waters. All computations were made for two scattering phase functions, which included an almost isotropic Rayleigh phase function and strongly anisotropic double-peaked Fournier-Forand-Mobley phase function. Models were validated using quasi-single-scattering (QSSA) and exponential approximations, which represent the extreme cases of ω₀→0 and ω₀→1, respectively. All methods yielded relative differences within 1.8% for modeled natural waters. An analysis of plane albedo behavior resulted in the development of a new extended QSSA approximation, which when applied in conjunction with the extended Hapke approximation developed earlier, resulted in a maximum relative error of 2.7%. The study results demonstrated that for practical applications, the estimation of inherent optical properties from observed reflectance can best be achieved using an extended Hapke approximation.     

Heavy-Ion Collisions: Experimental Highlights

Lattice QCD predicts a phase transition between hadronic matter and a system of deconfined quarks and gluons (the Quark Gluon Plasma) at high energy densities. Our current understanding of this new state of matter will be discussed with two key results from the Relativistic Heavy Ion Collider (RHIC).     

A novel route to prepare highly surface active nanogel particles based on nonaqueous emulsion polymerization

The motivation of the current work has stemmed from the fact that the selection of suitable stabilizers for nonaqueous emulsions is still challenging because of lack of general knowledge about the underlying stabilization mechanisms. The preparation and surface activity of new amphiphilic gel nanoparticles in organic solvents were investigated. A new bifunctional surfmer was prepared by reacting polyoxyethylene 4‐nonyl‐2‐propylene‐phenol nonionic reactive surfactant with maleic anhydride followed by esterification with poly(ethylene glycol). This surfmer was used as stabilizer to prepare amphiphilic crosslinked N‐isopropylacrylamide (NIPAm) and 2‐acrylamido‐2‐methylpropane sulfonic acid (AMPS) copolymer nanogel on the basis of nonaqueous radical copolymerization temperature modified method in the presence of toluene and formamide (FA) as solvents and N, N‐methylene bisacrylamide as a crosslinker. The chemical structure of the prepared nanogels was determined by Fourier transform infrared spectroscopy analyses. The morphologies of the prepared nanogels were detected by transmission electron microscopy and scanning electron microscopy techniques. The surface tension of colloidal NIPAm/AMPS dispersions was measured in FA as functions of surface age (time), temperature, and the morphology of the NIPAm/AMPS nanogels. The NIPAm/AMPS nanogels reduced the surface tension of FA from 58.2 to about 30.2 mN/m at 25°C, and a little increase in the surface tension was observed at 40°C. The prepared nanogels show great reduction in interfacial tension values between FA and styrene. The NIPAm/AMPS dispersions exhibited high surface activity and used as stabilizers to prepare crosslinked styrene‐co‐AMPS microgel in the presence of divinylbenzene and FA as organic solvents based on nonaqueous emulsion crosslinking polymerization technique. Copyright © 2013 John Wiley & Sons, Ltd.