Decoupled energy‐law preserving numerical schemes for the Cahn–Hilliard–Darcy system

We study two novel decoupled energy‐law preserving and mass‐conservative numerical schemes for solving the Cahn‐Hilliard‐Darcy system which models two‐phase flow in porous medium or in a Hele–Shaw cell. In the first scheme, the velocity in the Cahn–Hilliard equation is treated explicitly so that the Darcy equation is completely decoupled from the Cahn–Hilliard equation. In the second scheme, an intermediate velocity is used in the Cahn–Hilliard equation which allows for the decoupling. We show that the first scheme preserves a discrete energy law with a time‐step constraint, while the second scheme satisfies an energy law without any constraint and is unconditionally stable. Ample numerical experiments are performed to gauge the efficiency and robustness of our scheme. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 936–954, 2016     

Influence of Metal Oxides on Platinum Activity towards Methanol Oxidation in H2SO4 solution

Pt–CeO₂/C, Pt–TiO₂/C, and Pt–ZrO₂/C electrocatalysts were prepared by using a modified microwave‐assisted polyol process. Physical characterization was performed by using XRD, TEM, and EDX analyses. The incorporation of different metal oxides increased the dispersion degree of Pt nanoparticles and reduced their diameter to 2.50 and 2.33 nm when TiO₂ and ZrO₂ were introduced to Pt/C, respectively. The electrocatalytic activity of various electrocatalysts was examined towards methanol oxidation in H₂SO₄ solution by using cyclic voltammetry, chronoamperometry, and electrochemical impedance spectroscopy. Among the studied composites, Pt–ZrO₂/C was selected to be a candidate electrocatalyst for better electrochemical performance in direct methanol fuel cells.     

激发介质相对不应态对螺旋波动力学行为的影响

采用元胞自动机模型研究激发介质相对不应态对螺旋波动力学行为的影响。数值模拟表明：元胞激发阈值存在一临界区间,该区间的螺旋波周期会突然增加,并存在一最大周期,在合适的系统尺寸和状态数下,螺旋波周期不再受相对不应态的影响而只取决于系统的激发阈值;相对不应态导致螺旋波“Z”型漫游、小范围无规律漫游、花瓣状漫游、锯齿状漫游、风车状漫游等复杂的波头运动。观察到稳定螺旋波、漫游螺旋波和螺旋波消失,并对产生这些现象的机制作简要的解释。     

聚合物载体中水杨酸晶体的太赫兹极化率测定

极化率作为材料的重要微观属性,与其呈现出的多种宏观属性等紧密相关,在新型药物及功能材料的设计中扮演着关键角色。对于微观结构存在复杂分子间作用的物质体系,获取其太赫兹波段的动态极化率具有重要意义。极化率的实验测定建立在其本征介电常数的准确测定之上,太赫兹时域光谱系统凭借其相干探测属性,可直接提供太赫兹波在穿透样品后的相位变化信息,用于精确测定样品的介电常数。当样品由待测物纯物质组成时,实验测得的介电常数可直接用于计算极化率。但对于大多数的有机晶体,其自身对太赫兹波的特征吸收以及与颗粒尺寸与波长相当造成的散射,使其纯样品的太赫兹时域光谱表征受到系统信噪比的限制,通常需要将待测物均匀分布于对太赫兹波透明且可塑性极强的聚合物载体中。聚合物载体的使用导致实验直接测定的混合物介电常数中也包含了聚合物的介电影响,无法直接用于计算待测物质的极化率。针对这一问题,将嵌于聚合物载体中的有机晶体整体等效为聚合物、空气气隙和待测样品三组份混合介质模型,结合各组份体积占比以Landau, Lifshitz and Looyenga有效介质模型从实验测得的混合物介电常数中移除聚合物和空气气隙的影响,获取待测物的太赫兹本征介电常数,从而进一步结合Clausius-Mossotti关系式计算其太赫兹极化率。选取水杨酸晶体为研究对象,利用所提出的理论方案,从聚乙烯和聚四氟乙烯两种聚合物载体三种浓度混合物的原始介电常数中,提取出了具有高度一致性的本征介电常数和太赫兹极化率,验证了方法的有效性,并利用实验结果首次报道了水杨酸晶体的太赫兹极化率,在聚乙烯和聚四氟乙烯载体中的测定值分别为(17.2±0.2)和(17.6±1.0)Å3。     

Magnetic line source diffraction by a conductive half-plane in an anisotropic plasma

An integral theory that is associated with the scattered fields is considered for the solution of H-polarized line source diffraction by a conductive half-plane, which is surrounded by an anisotropic plasma. As the anisotropy does not affect an E-polarized incident wave, only one polarization case is considered. The cold plasma medium is characterized by the dielectric tensor. The constant external magnetic field producing the anisotropy in a cold plasma is applied parallel to the edge of the half-plane. The total, scattered, and diffracted waves are derived in terms of the Fresnel functions. Therefore, finite magnitude values at the transition boundaries are obtained. The wave behaviours are investigated numerically for different quantities of the medium.     

Parametric study of plasma active medium and gain saturation region in a Ne-like soft X-ray laser

Plasmas created by the interaction of high power optical laser with a target surface can be used as a source of soft X-ray lasers. Plasma and pump laser characteristics play significant role in achieving high gain coefficient for such plasma based on soft X-ray lasers. In the present work, the plasma active medium parameters for germanium element at a wavelength of 19.6 nm irradiated by a double-pulse pump laser have been studied using MED103 hydrodynamic code. For this purpose, first, the effects of laser intensity, pulse width and delay time of two pulses on the gain coefficient have been investigated and the optimum conditions for the maximum gain extent of Ne-like germanium soft X-ray laser are obtained. Then, in order to calculate the intensity of such high gain lasers in which Linford equation is invalid, we have adopted the general formula of amplified spontaneous emission intensity, which is valid in all range of intensities even at much higher intensities than saturation intensity. Finally, the soft X-ray laser intensities in the saturated areas for different plasma lengths have been calculated. The results show that the output of soft X-ray laser intensity with 294 cm⁻¹ gain coefficient can reach to about several times saturated intensity by applying a 1–2 mm plasma length as the active medium.     

Magnetohydrodynamic flow and heat transfer of a hybrid nanofluid over a rotating disk by considering Arrhenius energy

This research work explores the effect of hybrid nanoparticles on the flow over a rotating disk by using an activation energy model. Here, we considered molybdenum disulfide and ferro sulfate as nanoparticles suspended in base fluid water. The magnetic field is pragmatic normal to the hybrid nanofluid flow direction. The derived nonlinear ordinary differential equations are nondimensionalized and worked out numerically with the help of Maple software by the RKF-45method. The scientific results for a non-dimensionalized equation are presented for both nanoparticle and hybrid nanoparticle case. Accoutrements of various predominant restrictions on flow and thermal fields are scanned. Computation estimation for friction factor, local Nusselt number and Sherwood number are also executed. Results reveal that the reduction of the heat transfer rate is greater in hybrid nanoparticles when compared to nanoparticles for increasing values of Eckert Number and the thermal field enhances for the enhanced values of volume fraction.     

脉冲激光在板状介质中的爆轰破坏

本文从激光作用时间内介质存在“假膨胀”的假设出发，采用圆柱模型研究了脉冲激光在板状介质内部产生的爆轰破坏机理。文中认为，当固体介质为各向同性且为板状时，可采用圆柱轴对称模型，并将激光作用点置于圆柱坐标系的原点。脉冲激光作用时，介质吸收光能导致圆柱体内压力增大，但在激光作用时间内体积不变，从而得到介质产生的压力脉冲的迁移效应。对位移波方程应用Ｌａｐｌａｃｅ变换和Ｆａｒｔｏｎｇｅｎ定理得到了位移波的解析解。     

Darcy's laws for non‐stationary viscous fluid flow in a thin porous medium

We consider a non‐stationary Stokes system in a thin porous medium Ω_? of thickness ? which is perforated by periodically solid cylinders of size a _? . We are interested here to give the limit behavior when ? goes to zero. To do so, we apply an adaptation of the unfolding method. Time‐dependent Darcy's laws are rigorously derived from this model depending on the comparison between a _? and ? . Copyright © 2016 John Wiley & Sons, Ltd.     

Porous Medium Flow with Both a Fractional Potential Pressure and Fractional Time Derivative

The authors study a porous medium equation with a right-hand side. The operator has nonlocal diffusion effects given by an inverse fractional Laplacian operator.The derivative in time is also fractional and is of Caputo-type, which takes into account"memory". The precise model isD_t~αu- div(u(-Δ)~(-σ)u) = f, 0 σ 1/2.This paper poses the problem over {t ∈ R~+, x ∈ R~n} with nonnegative initial data u(0, x) ≥0 as well as the right-hand side f ≥ 0. The existence for weak solutions when f, u(0, x)have exponential decay at infinity is proved. The main result is H¨older continuity for such weak solutions.