AN ANALYTICAL SOLUTION FOR THREE-DIMENSIONAL DIFFRACTION OF PLANE P-WAVES BY A HEMISPHERICAL ALLUVIAL VALLEY WITH SATURATED SOIL DEPOSITS

An analytical solution for the three-dimensional scattering and diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits is developed by employing Fourier-Bessel series expansion technique. Unlike previous studies, in which the saturated soil deposits were simulated with the single-phase elastic theory, in this paper, they are simulated with Biot＇s dynamic theory for saturated porous media, and the half space is assumed as a single-phase elastic medium. The effects of the dimensionless frequency, the incidence angle of P-wave and the porosity of soil deposits on the surface displacement magnifications of the hemispherical alluvial valley are investigated. Numerical results show that the existence of a saturated hemispherical alluvial valley has much influence on the surface displacement magnifications. It is more reasonable to simulate soil deposits with Biot＇s dynamic theory when evaluating the displacement responses of a hemispherical alluvial valley with an incidence of P-waves.

Analytical solutions for constant-rate test in bounded confined aquifers with non-Darcian effect

This paper proposes a simplified analytical solution considering non-Darcian and wellbore storage effect to investigate the pumping flow in a confined aquifer with barrier and recharge boundaries.The mathematical modelling for the pumping-induced flow in aquifers with different boundaries is developed by employing image-well theory with the superposition principle,of which the non-Darcian effect is characterized by Izbash’s equation.The solutions are derived by Boltzmann and dimensionless transformations.Then,the non-Darcian effect and wellbore storage are especially investigated according to the proposed solution.The results show that the aquifer boundaries have non-negligible effects on pumping,and ignoring the wellbore storage can lead to an over-estimation of the drawdown in the first 10 minutes of pumping.The higher the degree of non-Darcian,the smaller the drawdown.

Exact analytical solution to three-dimensional phase change heat transfer problems in biological tissues subject to freezing

Analytically solving a three-dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.

Analytical solutions for the slow neutron capture process of heavy element nucleosynthesis

In this paper, the network equation for the slow neutron capture process （s-process） of heavy element nucleosynthesis is investigated. Dividing the s-process network reaction chains into two standard forms and using the technique of matrix decomposition, a group of analytical solutions for the network equation are obtained. With the analytical solutions, a calculation for heavy element abundance of the solar system is carried out and the results are in good agreement with the astrophysical measurements.

Local Analytic Solutions of Complete Equations for Mixed Fluid

With the straification theory we have proved the transversal layer s 0 3,k (D) of complete equations for mixed fluid is not an empty set: s 0 3,k (D) ≠ for all k(k≥1) . Based on this conclusion and the “secondary equation” of s 0 3,k (D), this paper fully presents the expressions of coefficients in all local analytic solutions of the equations. Therefore we provide the calculation formulas by which we can get the numerical solutions to any desired accuracy.

Green's function solution for transient heat conduction in annular fin during solidification of phase change material

The Green＇s function method is applied for the transient temperature of an annular fin when a phase change material （PCM） solidifies on it. The solidification of the PCMs takes place in a cylindrical shell storage. The thickness of the solid PCM on the fin varies with time and is obtained by the Megerlin method. The models are found with the Bessel equation to form an analytical solution. Three different kinds of boundary conditions are investigated. The comparison between analytical and numerical solutions is given. The results demonstrate that the significant accuracy is obtained for the temperature distribution for the fin in all cases.

Casson hybrid nanofluid flow over a Riga plate for drug deliveryapplications with double diffusion

Casson fluid-mediated hybrid nanofluids are more effective at transferring heat than traditional heat transfer fluids in terms of thermal conductivity.Heat exchangers,cooling systems and other thermal management systems are ideal for use with Casson fluids.Precise control of the flow and release of medication is necessary when using Casson fluids in drug delivery systems because of their unique rheological properties.Nanotechnology involves the creation of nanoparticles that are loaded with drugs and distributed in Casson fluid-based carriers for targeted delivery.In this study,to create a hybrid nanofluid,both single-walled carbon nanotubes(SWCNTs)and multi-walled carbon nanotubes(MWCNTs)are dispersed in a Casson fluid with Fourier’s and Fick’s laws assumptions.The Casson fluid is suitable for various engineering and medical applications due to the enhancement of heat transfer and thermal conductivity by the carbon nanotubes.Our objective is to understand how SWCNTs and MWCNTs impact the flow field by studying the flow behavior of the Casson hybrid nanofluid when it is stretched against a Riga plate.The Darcy-Forchheimer model is also used to account for the impact of the porous medium near the stretching plate.Both linear and quadratic drag terms are taken into account in this model to accurately predict the flow behavior of the nanofluid.In addition,the homotopy analysis method is utilized to address the model problem.The outcomes are discussed and deliberated based on drug delivery applications.These findings shed valuable light on the flow characteristics of a Casson hybrid nanofluid comprising SWCNTs and MWCNTs.It is observed that the incorporation of carbon nanotubes makes the nanofluid a promising candidate for medical applications due to its improved heat transfer properties.

竖向入射S波作用下单桩水平地震响应简化解析方法

基于连续介质模型并考虑桩-土运动相互作用,将单桩视为一维线弹性梁,研究了竖向入射S波作用下的单桩水平地震响应问题。将竖向入射S波模拟为基岩水平位移,基于平面应变模型建立的土体控制方程,推导出地震作用下土体水平动力阻抗函数表达式。将土体阻抗代入单桩控制方程并联立桩-土接触条件及桩顶和桩底的边界条件,得出了竖向入射S波作用下单桩的地震响应解析解。通过将所得解与已有文献理论解和有限元结果进行对比,验证了该方法的合理性。基于所得理论解进行参数分析得出:桩-土模量比的增加可以明显降低桩-土运动相互作用因子的最小值,而较大桩身长径比以及土体滞回阻尼对桩-土运动相互作用因子的影响较小;对于桩顶水平地震放大因子来说,桩-土模量比的增加仅在高共振频率处抑制其幅值,较大桩身长径比对其影响较小,而滞回阻尼比的增加会显著抑制共振频率处的幅值;桩身地震响应仅在较小桩径比时受桩-土模量比的影响明显,并随桩-土模量比的增加而降低。

Analytical solutions of three-dimensional contaminant transport in uniform flow field in porous media:A library

The purpose of this study is to present a library of analytical solutions for the three-dimensional contaminant transport in uniform flow field in porous media with the first-order decay,linear sorption,and zero-order production.The library is constructed using Green's function method(GFM)in combination with available solutions.The library covers a wide range of solutions for various conditions.The aquifer can be vertically finite,semi-infinitive or infinitive,and laterally semi-infinitive or infinitive.The geometry of the sources can be of point,line,plane or volumetric body;and the source release can be continuous,instantaneous,or by following a given function over time.Dimensionless forms of the solutions are also proposed.A computer code FlowCAS is developed to calculate the solutions.Calculated results demonstrate the correctness of the presented solutions.The library is widely applicable to solve contaminant transport problems of one-or multiple-dimensions in uniform flow fields.

Analytical Solution for Waves Propagation in Heterogeneous Acoustic/Porous Media. Part II: The 3D Case

We are interested in the modeling of wave propagation in an infinite bilayered acoustic/poroelastic media. We consider the biphasic Biot’s model in the poroelastic layer. The first part was devoted to the calculation of analytical solution in twodimensions, thanks to Cagniard de Hoop method. In the first part (Diaz and Ezziani,Commun. Comput. Phys., Vol. 7, pp. 171-194) solution to the two-dimensional problem is considered. In this second part we consider the 3D case.

深海S-lay铺设大直径薄壁管道的奇异摄动分析

文中利用奇异摄动理论得到了深海管道S-lay铺设过程中的构型解析解,并研究了不同张紧力、水深以及海流力对管道构型及弯矩的影响.同时,采用有限元法对深海大直径管道铺设过程进行了数值仿真,并与奇异摄动解进行了对比和验证.理论结果表明:其他参数相同时,适当增大张紧力可使管道构型更平缓,对铺管有利;海水越深,管道的构型越陡,靠近海底处管道的弯矩峰值越大,对铺管不利;当管道受到与铺设方向相反的海流力时,海流力越大,靠近海底部管道弯矩的峰值越大,对铺管越不利.

有机/无机杂化钙钛矿太阳能电池S形电流扭结的集总参数等效电路模型

提出一种改进的太阳能电池集总参数等效电路模型,可以实现对S形电流电压曲线的准确拟合。该改进模型使用四个二极管,采用分区和Lambert W函数方法建立结点电压显式算法,获得电流-电压显式方程。与具有多个子电路的电路模型比较,改进模型中加入分流电阻,结构上更加完整。此外,该模型可以描述S形曲线,对较大正向电压下I-V特性第一象限的指数型曲线可实现良好拟合。基于该模型解析求解算法,可避免长时间数值迭代计算,获得满足误差要求的计算结果,利于仿真电路和模型参数提取。

An improved method to assess the required strength of cemented backfill in underground stopes with an open face

Backfill is increasingly used in underground mines to reduce the surface impact from the wastes produced by the mining operations. But the main objectives of backfilling are to improve ground stability and reduce ore dilution. To this end, the backfill in a stope must possess a minimum strength to remain self-standing during mining of an adjacent stope. This required strength is often estimated using a solution proposed by Mitchell and co-workers, which was based on a limit equilibrium analysis of a wedge exposed by the open face. In this paper, three dimensional numerical simulations have been performed to assess the behavior of the wedge model. A new limit equilibrium solution is proposed, based on the backfill displacements obtained from the simulations. Comparisons are made between the proposed solution and experimental and numerical modeling results. Compared with the previous solution, a better agreement is obtained between the new solution and experimental results for the required cohesion and factor of safety. For large scale(field) conditions, the results also show that the required strength obtained from the proposed solution corresponds quite well to the simulated backfill response.

Periodic solitons in dispersion decreasing fibers with a cosine profile

Periodic solitons are studied in dispersion decreasing fibers with a cosine profile. The variable-coefficient nonlinear Schrrdinger equation, which can be used to describe the propagation of solitons, is investigated analytically. Analytic soli- ton solutions for this equation are derived with the Hirota＇s bilinear method. Using the soliton solutions, we obtain periodic solitons, and analyze the soliton characteristics. Influences of physical parameters on periodic solitons are discussed. The presented results can be used in optical communication systems and fiber lasers.

Dynamic response of electromagnetic launcher's rail subjected to harmonic magnetic pressure

In order to extend the rail life and improve the firing accuracy,the electromagnetic launcher's rail can be modeled as a beam on elastic foundation with simply supported beam with moving load.Euler beam theory is applied to build the mechanical model and the analytical solution of the equation subjected to harmonic magnetic pressure is derived in details,which has successfully avoided the errors caused by using the uniform pressure to approximately replace the variable force.Numerical analysis of the dynamic response on rail by using the MATLAB software shows that the peak values of maximal deflection and vibration velocity increase gradually as the exciting frequency increases.Taking the same speed of load into account,the dynamic response of rail is obviously smaller than that under constant force.Therefore the reliable theory basis is provided for the design and control of rail to promote the practical application of electromagnetic launcher.

Oxidation Kinetics of Aluminum Powders in a Gas Fluidized Bed Reactor in the Potential Application of Surge Arresting Materials

In this technical paper, the oxidation mechanism and kinetics of aluminum powders are discussed in great details. The potential applications of spherical aluminum powders after oxidation to be part of the surging arresting materials are discussed. Theoretical calculations of oxidation of spherical aluminum powders in a typical gas fluidization bed are demonstrated. Computer software written by the author is used to carry out the basic calculations of important parameters of a gas fluidization bed at different temperatures. A mathematical model of the dynamic system in a gas fluidization bed is developed and the analytical solution is obtained. The mathematical model can be used to estimate aluminum oxide thickness at a defined temperature. The mathematical model created in this study is evaluated and confirmed consistently with the experimental results on a gas fluidization bed. Detail technical discussion of the oxidation mechanism of aluminum is carried out. The mathematical deviations of the mathematical modeling have demonstrated in great details. This mathematical model developed in this study and validated with experimental results can bring a great value for the quantitative analysis of a gas fluidization bed in general from a theoretical point of view. It can be applied for the oxidation not only for aluminum spherical powders, but also for other spherical metal powders. The mathematical model developed can further enhance the applications of gas fluidization technology. In addition to the development of mathematical modeling of a gas fluidization bed reactor, the formation of oxide film through diffusion on both planar and spherical aluminum surfaces is analyzed through a thorough mathematical deviation using diffusion theory and Laplace transformation. The dominant defects and their impact to oxidation of aluminum are also discussed in detail. The well-controlled oxidation film on spherical metal powders such as aluminum and other metal spherical powders can potentially become an important part of switch devices of surge arresting materials, in general.

圆柱外表面受热冲击问题的广义热弹性分析

基于L-S广义热弹性理论,针对实心圆柱体在外表面受均匀热冲击作用下的一维广义热弹性问题进行研究分析.利用热冲击的瞬时特征,借助于Laplace正、反变换技术及柱函数的渐近性质,推导了热冲击作用周期内温度场、位移场和应力场的渐近表达式.通过计算,得到了热冲击条件下各物理场的分布规律以及延迟效应和耦合效应对热弹性响应的影响规律.结果表明:当考虑延迟效应和耦合效应时,热扰动将以两组速度不同的波的形式向前传播,延迟效应和耦合效应对各物理场的建立时间,阶跃间隔和阶跃峰值均产生影响,且延迟效应和耦合效应均在一定程度上削弱了热冲击的作用效果.

有限厚度圆柱壳热冲击问题的广义热弹性解

针对包含有界边界的轴对称结构受热冲击作用的广义热弹性问题进行了研究分析.基于Lord-Shulman广义热弹性理论(L-S理论),构建了热冲击下有限厚度圆柱壳热弹性响应的广义热弹性模型.借助Laplace(拉普拉斯)变换技术以及Bessel函数的渐进特性,推导了温变载荷作用下,圆柱壳内部位移、温度以及应力场的解析表达式.该表达式不仅可以清楚地揭示热冲击下热波、热弹性波在壳体内部的传播、反射以及叠加的作用过程,更可准确地捕捉到热波、热弹性波波前位置处的阶跃现象,并对热冲击诱发的动态热应力峰值进行有效预测.

矩形封闭空间内非饱和多孔介质自然对流的近似分析解

从合湿多孔封闭腔内流体流动与传热特征出发，提出了一种线性近似假设法，并用该法对矩形封闭腔内含湿多孔介质的自然对流行为进行了近似分析求解，得到了其温度分布、速度分布与传热数表达式．

非饱和土粘弹性地基一维固结特性分析

基于Fredlund的非饱和土一维固结理论,采用李氏比拟法,研究有限厚度粘弹性非饱和土层在大面积均布瞬时加荷时的一维固结问题.针对Merchant粘弹性模型,采用Laplace变换及Cayley-Hamilton等数学方法,引入边界及初始条件,得到Laplace变换域内顶面排气不排水、底面不渗透情况下粘弹性非饱和土地基一维固结时的超孔隙水压力、超孔隙气压力以及土层沉降的解,采用Crump及Durbin方法实现Laplace逆变换,获得半解析解;分析在不同气、水渗透系数比ka/kw下,Merchant粘弹性模型的Kelvin体中弹性模量E1和粘滞系数η等对粘弹性非饱和土地基一维固结特性的影响,揭示粘弹性非饱和土地基的固结特性;最后通过与弹性解析解的对比,验证了半解析解方法的正确性.