一类海冰-海水耦合热力学系统参数辨识问题的最优性

针对一维的海冰-海水耦合热力学系统,以该系统中的物理参数为辨识量,以温度偏差为目标函数,建立了一个参数辨识模型,并证明了该问题最优解的存在性,从而为这类海冰-海水耦合热力学系统参数辨识问题的数值计算提供数学理论依据.     

Blow-up Sets to a Coupled Heat System

This paper deals with a heat system coupled via local and localized sources subject to null Dirichlet boundary conditions. In a previous paper of the authors, a complete result on the multiple blow-up rates was obtained. In the present paper, we continue to consider the blow-up sets to the system via a complete classification for the nonlinear parameters. That is the discussion on single point versus total blow-up of the solutions. It is mentioned that due to the influence of the localized sources, there is some substantial difficulty to be overcomed there to deal with the single point blow-up of the solutions.     

基于扩展有限元的页岩水力压裂数值模拟

考虑裂缝内流体流动和周围岩石应力变形,建立了页岩人工裂缝扩展的数学模型,分别采用有限元和扩展有限元求解裂缝流场和岩石应力场,并通过Picard迭代方法耦合求解,计算结果与经典模型结果吻合,验证了模型正确性.在此基础上,分析了岩石弹性模量、Poisson(泊松)比和注入速度对裂缝几何形态的影响以及水力裂缝任意角度逼近天然裂缝扩展动态.结果表明:弹性模量和注入速度对裂缝形态具有重要影响,而Poisson比对裂缝形态影响较小;随着页岩脆性增高,压裂裂缝趋于"长窄型"扩展;地应力差和逼近角越大,水力裂缝越易贯穿天然裂缝;水力裂缝与天然裂缝相交处裂缝宽度存在相对较大的降低;扩展有限元方法避免了计算过程中的网格重构与网格加密,减少了计算量,该模型可以为页岩压裂设计提供理论指导.     

考虑非傅立叶效应的瞬态导热过程的波动响应分析

瞬态导热分析需要考虑非傅立叶效应.通过对抛物型及双曲型热传导方程,以及耦合热传导方程后的波动方程的数值求解,研究了非傅立叶效应下导热过程中的波动响应.结果表明,双曲型热传导过程具有明显的波动特性,所引起的波动响应前沿值成倍提高,且呈现显著的跃变行为,而波动峰值外的部位围绕着初始值小幅波动.     

解析法确定含蜡原油热质耦合的蜡分子扩散速率

蜡分子扩散过程是在热和质的广义热力学"力"耦合驱动下产生广义热力学"流"的结果,其实质是传热和传质同时存在的复杂耦合不可逆过程.基于非平衡态热力学的基本原理,推导出含蜡原油管输过程蜡分子扩散热质传递的线性唯象方程组;依据质量和能量的守恒关系,得到蜡分子扩散的传热一传质微分方程组,利用拉普拉斯变换求解到其解析解,探讨促使蜡分子扩散的动力学原因,分析输量和季节变化的不同工况对扩散速率的影响.     

时间测度链上具正负系数的二阶阻尼动力方程的振动准则

研究了时间测度链上一类具正负系数和阻尼项及非线性中立项的二阶变时滞非线性动力方程的振荡性.利用时间测度链上的有关理论及广义Riccati变换,结合大量不等式技巧,建立了该方程若干新的振动准则,这些准则不仅推广和改进了一些已知的结果,而且在时间测度链上统一了二阶非线性时滞阻尼微分方程和二阶非线性时滞阻尼差分方程的振动性质.     

TWISTING STATICS AND DYNAMICS FOR CIRCULAR ELASTIC NANOSOLIDS BY NONLOCAL ELASTICITY THEORY

The torsional static and dynamic behaviors of circular nanosolids such as nanoshafts, nanorods and nanotubes are established based on a new nonlocal elastic stress field theory. Based on a new expression for strain energy with a nonlocal nanoscale parameter, new higher-order governing equations and the corresponding boundary conditions are first derived here via the variational principle because the classical equilibrium conditions and/or equations of motion can- not be directly applied to nonlocal nanostructures even if the stress and moment quantities are replaced by the corresponding nonlocal quantities. The static twist and torsional vibration of circular, nonlocal nanosolids are solved and discussed in detail. A comparison of the conventional and new nonlocal models is also presented for a fully fixed nanosolid, where a lower-order governing equation and reduced stiffness are found in the conventional model while the new model reports opposite solutions. Analytical solutions and numerical examples based on the new nonlocal stress theory demonstrate that nonlocal stress enhances stiffness of nanosolids, i.e. the angular displacement decreases with the increasing nonlocal nanoscale while the natural frequency increases with the increasing nonlocal nanoscale.     

电感耦合等离子体质谱仪同时测定地下水中的溴和碘

研究并建立了电感耦合等离子体质谱仪（ICP-MS）同时测定地下水中溴、碘元素的方法。使用0.025%NH3.H2O作为测定介质,该方法线性范围宽,检出限为：79Br为0.02μg/L;127I为0.4μg/L。加标回收率在94.0%—102.4%之间。     

热冲击下分区均质材料耦合热弹性问题的变分原理

针对分区均质材料，考虑了热冲击产生的惯性效果和较大的应变速率对温度场的影响，建立了描述热冲击问题的理论模型，证明了热冲击下分区均质材料耦合热弹性问题的变分原理．为热冲击下分区均质材料耦合热弹性问题的定量求解，提供了理论基础．     

振动机械起动过程中的迟滞共振原因分析

振动机械在起动过程中，有时会出现一种特殊的共振现象─—迟滞共振．本文通过解析分析和数值算法解释了产生该现象的原因．