正交各向异性厚板的边界元解法

本文利用 Hormander 算子法和平面波分解法导出了计入剪切变形的正交各向异性厚板的基本解。建立了计入剪切变形的正交各向异性厚板的边界积分方程。文中详细地讨论了基本解的数值计算,并用边界元法分析了一些算例。     

微平行管道内Eyring流体的电渗滑移流动

研究了微平行管道内非牛顿流体––Eyring 流体在外加电场力和压力作用下的电渗流动. 在考虑微尺度效应, 电场作用, 非牛顿特性, 滑移边界等情况下, 建立Eyring流体在微平行管道内电渗流动的力学模型. 通过解线性Possion-Boltzmann方程和Cauchy动量方程, 给出Eyring 流体速度分布的精确解和近似解析解, 并探讨了上述因素对电渗流动的影响. 将电场力和压力对于Eyring流体电渗流动的速度分布的影响进行了比较分析, 得到有意义的结果.     

Nonlinear stability of traveling wave solutions for the compressible fluid models of Korteweg type

This paper is concerned with the existence and time-asymptotic nonlinear stability of traveling wave solutions to the Cauchy problem of the one-dimensional compressible fluid models of Korteweg type, which governs the motions of the compressible fluids with internal capillarity. The existence of traveling wave solutions is obtained by the phase plane analysis, then the traveling wave solution is shown to be asymptotically stable by the elementary L²$L^2$-energy method.     

Simultaneous spreading and evaporation: Recent developments

The recent progress in theoretical and experimental studies of simultaneous spreading and evaporation of liquid droplets on solid substrates is discussed for pure liquids including nanodroplets, nanosuspensions of inorganic particles (nanofluids) and surfactant solutions. Evaporation of both complete wetting and partial wetting liquids into a nonsaturated vapour atmosphere are considered. However, the main attention is paid to the case of partial wetting when the hysteresis of static contact angle takes place. In the case of complete wetting the spreading/evaporation process proceeds in two stages. A theory was suggested for this case and a good agreement with available experimental data was achieved. In the case of partial wetting the spreading/evaporation of a sessile droplet of pure liquid goes through four subsequent stages: (i) the initial stage, spreading, is relatively short (1–2 min) and therefore evaporation can be neglected during this stage; during the initial stage the contact angle reaches the value of advancing contact angle and the radius of the droplet base reaches its maximum value, (ii) the first stage of evaporation is characterised by the constant value of the radius of the droplet base; the value of the contact angle during the first stage decreases from static advancing to static receding contact angle; (iii) during the second stage of evaporation the contact angle remains constant and equal to its receding value, while the radius of the droplet base decreases; and (iv) at the third stage of evaporation both the contact angle and the radius of the droplet base decrease until the drop completely disappears. It has been shown theoretically and confirmed experimentally that during the first and second stages of evaporation the volume of droplet to power 2/3 decreases linearly with time. The universal dependence of the contact angle during the first stage and of the radius of the droplet base during the second stage on the reduced time has been derived theoretically and confirmed experimentally. The theory developed for pure liquids is applicable also to nanofluids, where a good agreement with the available experimental data has been found. However, in the case of evaporation of surfactant solutions the process deviates from the theoretical predictions for pure liquids at concentration below critical wetting concentration and is in agreement with the theoretical predictions at concentrations above it.     

Electrochemical assessment of water|ionic liquid biphasic systems towards cesium extraction from nuclear waste

A room temperature ionic liquid (IL) composed of a quaternary alkylphosphonium (trihexyltetradecylphosphonium, P₆₆₆₁₄⁺) and tetrakis(pentafluorophenyl)borate anion (TB⁻) was employed within a water|P₆₆₆₁₄TB (w|P₆₆₆₁₄TB or w|IL) biphasic system to evaluate cesium ion extraction in comparison to that with a traditional water|organic solvent (w|o) combination. ¹³⁷Cs is a major contributor to the radioactivity of spent nuclear fuel as it leaves the reactor, and its extraction efficiency is therefore of considerable importance. The extraction was facilitated by the ligand octyl(phenyl)-N,N′-diisobutylcarbamoylphosphine oxide (CMPO) used in TRans-Uranium EXtraction processes and investigated through well established liquid|liquid electrochemistry. This study gave access to the metal ion to ligand (1:n) stoichiometry and overall complexation constant, β, of the interfacial complexation reaction which were determined to be 1:3 and 1.6 × 10¹¹ at the w|P₆₆₆₁₄TB interface while the study at w|o elicited an n equal to 1 with β equal to 86.5. Through a straightforward relationship, these complexation constant values were converted to distribution coefficients, δ_α, with the ligand concentrations studied for comparison to other studies present in the literature; the w|o and w|IL systems gave δ_α of 2 and 8.2 × 10⁷, respectively, indicating a higher overall extraction efficiency for the latter. For the w|o system, the metal ion-ligand stoichiometries were confirmed through isotopic distribution analysis of mass spectra obtained by the direct injection of an emulsified water–organic solvent mixture into an electron spray ionization mass spectrometer.     

The complex synthesis and solid state chemistry of ceria-lanthana solid solutions prepared via a hexamethylenetetramine precipitation

Mixed oxide solid solutions are becoming ever more commercially important across a range of applications. However, their synthesis can be problematical. Here, we show that ceria-lanthana solid solutions can be readily prepared via simple precipitation using hexamethylenetetramine. However, the solution chemistry can be complex, which results in the precipitated particles having a complex structure and morphology. Great care must be taken in both the synthesis and characterisation to quantify the complexity of the product. Even very high heat treatments were not able to produce highly homogeneous materials and X-ray diffractions reveals the non-equilibrium form of particles prepared in this way. Unexpected crystal structures are revealed including a new metastable cubic La₂O₃ phase.     

Traveling waves for nonlinear cellular neural networks with distributed delays

In this paper, we will establish the existence and nonexistence of traveling waves for nonlinear cellular neural networks with finite or infinite distributed delays. The dynamics of each given cell depends on itself and its nearest m left or l right neighborhood cells where delays exist in self-feedback and left or right neighborhood interactions. Our approach is to use Schauder?s fixed point theorem coupled with upper and lower solutions of the integral equation in a suitable Banach space. Further, we obtain the exponential asymptotic behavior in the negative infinity and the existence of traveling waves for the minimal wave speed by the limiting argument. Our results improve and cover some previous works.     

On well-posedness of semilinear parabolic and elliptic problems in the hyperbolic space

We investigate existence and uniqueness of solutions to semilinear parabolic and elliptic equations in bounded domains of the n-dimensional hyperbolic space (n?3). Lp→Lq estimates for the semigroup generated by the Laplace-Beltrami operator are obtained and then used to prove existence and uniqueness results for parabolic problems. Moreover, under proper assumptions on the nonlinear function, we establish uniqueness of positive classical solutions and nonuniqueness of singular solutions of the elliptic problem; furthermore, for the corresponding semilinear parabolic problem, nonuniqueness of weak solutions is stated.     

The sharp threshold and limiting profile of blow-up solutions for a Davey-Stewartson system

The blow-up solutions of the Cauchy problem for the Davey-Stewartson system, which is a model equation in the theory of shallow water waves, are investigated. Firstly, the existence of the ground state for the system derives the best constant of a Gagliardo-Nirenberg type inequality and the variational character of the ground state. Secondly, the blow-up threshold of the Davey-Stewartson system is developed in R³. Thirdly, the mass concentration is established for all the blow-up solutions of the system in R². Finally, the existence of the minimal blow-up solutions in R² is constructed by using the pseudo-conformal invariance. The profile of the minimal blow-up solutions as t→T (blow-up time) is in detail investigated in terms of the ground state.