Qualitative analysis of thermal explosion of sodium droplet with variable thermophysical properties and thermal radiations

There are many coolants frequently used in the industry for controlling not only heat transfer, but also temperature distribution in a confined domain. However, little is known on the thermal properties of sodium droplets. The qualitative analysis of differential equations that model the thermal explosion, nonlinear dynamic of sodium droplet with variable thermophysical properties when thermal radiations are considered as suggested by Cogley et al, Sohrab et al, and P‐1 approximation Sazhin et al is deliberated upon in this study. The governing equations, first‐order nonlinear ordinary differential equations, are nondimensionalized using the appropriate similarity variables. The existence and uniqueness of the solutions, concavity, and convexity of the temperature distribution, and positivity nature of the solutions of the dimensionless governing equations are established. It is concluded that there exists a solution for a certain range of the admissible parameters and when the reduced activation energy is negative and temperature distribution fits concavity. More so, the major criteria to obtain a positive solution are outlined in this study.     

地基承载力的数值分析方法

介绍了边坡稳定的塑性力学上限解在计算地基承载力方面的推广。简要回顾了由Ｄｏｎａｌｄ和Ｃｈｅｎ提出的能量法的基本原理，说明该法可以得出与闭合解一样精确的解答，使用此数值方法来复核地基容重不为零时承载力计算的各种经验方法，发现这些经验方法在大多数情况下均低估了地基的承载力。计算基础有埋深和荷载偏心的经验公式也低估了地基承载力约５％～１０％。     

岩质边坡稳定塑性极限分析方法——斜分条法

基于塑性极限分析上限定理,依据岩质边坡沿某一滑裂面滑动破坏时,在其内部产生沿陡倾角结构面(断层、节理和层面)的剪切破坏现象,建立了岩质边坡极限分析斜分条法破坏模式。进一步根据滑体处于极限状态时的虚功率方程,推导得出了斜分条后岩质边坡的塑性极限分析稳定系数计算公式。采用超载系数的方法,将稳定系数表示在块体所受的极限荷载,避免了隐式出现,有效地简化了公式推导。以锦屏一级水电站右岸边坡为例进行了稳定性分析。计算表明,结论较为合理,对于具有倾斜界面的岩质边坡稳定性评价具有重要意义。     

珠江三角洲地区竖向排水体施工扰动初探

竖向排水体施工具有挤土效应，按照平面应力问题，应用圆柱孔扩张理论分析表明，竖向排水体周围土体孔隙水压力显著增大，应力变化明显，形成瓶状塑性区。地面以下一定深度Zo范围内，塑性区半径取决于土体初始应力和不排水强度，并随深度增大；Zo以下，塑性区半径不再变化，其大小与土体初始应力、不排水强度，割线模量、排水体类型、间距、长度、导管类型等有关。施工扰动以塑性区为主，塑性区地面发生隆起，珠江三角洲地区，在饱和软粘土基中施工竖向排水体时，实测表明土体强度显著降低，最终沉降增大。计算表明扰动区半径可取塑性区半径的1.2倍，扰动区半径约为竖向排水体导管半径的9倍。     

Cosserat理论的应变能定理及解的唯一性

Cosserat理论已广泛应用于岩土工程，求解Cosserat问题时，解析方法与数值方法都曾被采用，证明了Cosserat问题的能量原理及解的唯一性定理，进一步完善了该理论，并保证了数值及解析求解结果的正确性。     

Effect of seepage force on tunnel face stability reinforced with multi-step pipe grouting

Tunneling in difficult geological conditions is often inevitable especially in urban areas. Ground improvement and reinforcement techniques are required to guarantee safe tunnel excavations and/or to prevent damage to adjacent structures. The steel pipe-reinforced multi-step grouting method has been recently applied to tunnel sites as an auxiliary technique in Korea for impermeabilization in underwater tunnels as well as for reinforcement. However, this technique has been usually employed empirically without much understanding with regard to its effect on the tunnel safety. In this study, the face stability with steel pipe-reinforced multi-step grouting in underwater tunnels was evaluated by simultaneously considering two factors: one is the effective stress acting on the tunnel face calculated by limit theorem and limit equilibrium method; the other is the seepage force obtained by means of numerical analysis. This study revealed that the influence of the steel pipe-reinforced multi-step grouting on the support pressure required for the stability of the tunnel face in dry condition is not significant while there is relatively a significant reduction in seepage forces by adopting the technique in the underwater tunnel. The effect of permeability anisotropy on the seepage force acting on the tunnel face was also assessed by conducting a coupled analysis.     

黑体辐射逆问题方程解的唯一性与Riemann假设

黑体辐射反演是黑体辐射研究中提出的新课题.在实际应用中,许多物体的表面温度分布(a(T)),难以直接测量,但其温度辐射功率谱W(v)可以被测量,此文给出一个由功率谱W(v)获得表面温度分布a(T)的严格解并讨论其解的唯一性.     

异步电机基于MRAC的转子时间常数在线辨识算法的统一描述

应用于异步电机转子时间常数在线辨识的模型参考自适应控制器(MRAC),依据其参考模型设计的不同,有着不同的算法形式。在深入分析转子时间常数T_r偏差对电机间接磁场定向、输出电磁转矩、无功功率影响的基础上,运用李雅普诺夫稳定理论提出了T_r在线辨识的统一MRAC自适应律,通过自适应律中参数的不同配置,可以得到多种基于MRAC的T_r在线辨识算法。借助于统一自适应律理论,为多种辨识模型间的演化和对比提供了理论依据。同时,该文所提自适应律的统一描述也有助于基于MRAC的T_r辨识理论体系的完善,使得辨识模型的选择有章可循。仿真和实验结果验证了该文分析的有效性。     

Revisited generalized substitution theorem and its consequences for circuit analysis

The Substitution Theorem (ST) is generally perceived as a mere theoretical curiosity. In this paper, a formerly derived generalized ST (GST) is carefully revised, which leads to both a Weak Revisited GST (RGST) and a Strong RGST (characterized by noticeably relaxed hypotheses with respect to the GST). Then, despite the common opinion about the ST, such RGSTs are showed to be powerful analytical tools to generalize, make rigorous and rigorously prove several classic results of Circuit Theory, namely: the Substitution Theorem for Multiterminal Circuits, the Source‐Shift Theorem, the Thévenin–Norton Theorem, the Miller Theorem alongside its Dual, and the Augmentation Principle. More specifically, the Substitution Theorem for Multiterminal Circuits is extended to an arbitrary set of sources, possibly including nullors. The Source‐Shift Theorem is rigorously derived, and possible related ambiguities are removed. Also, all possible hybrid forms of the Thévenin–Norton Theorem for multiports are individuated, and a precise operative procedure for calculating the relevant entities is provided for all cases. Furthermore, the Miller Theorem and its Dual are extended to an arbitrary number of variables and to multiports. As to the Augmentation Principle, the constraint regarding the linearity of the augmenting resistors is removed. Finally, thoroughly worked examples are given in which the aforementioned noteworthy consequences of the RGSTs are proved to be efficient tools for analysis by inspection of linear and nonlinear circuits. Among the other things, systematic pencil‐and‐paper procedures for DC‐point and input‐output (or driving‐point) characteristic calculation in nonlinear networks are derived and applied to circuits with considerably complex topology. Copyright © 2016 John Wiley & Sons, Ltd.     

An improved under frequency load shedding strategy based on dynamic power flow tracing

Under frequency load shedding is an effective approach to maintain or restore the steady-state operation of the power system when frequency accidents occur. An improved under frequency load shedding strategy based on dynamic power flow tracking is proposed. The expression of the kinetic energy theorem in power system is derived and combined with the power flow tracing method to analyze the relation between system energy distribution and its frequency. The power system frequency influencing factors are then constructed and applied to find the reasons of frequency decline and to quantify the contributions of the mechanical power of the generators, the load power and the transmission losses for the frequency deviation. Finally, considering a variety of unbalanced power scenarios in the system, the modified load shedding strategy is designed. Based on the results of dynamic power flow tracing, the strategy can choose the suitable load node to control, and the defined load frequency contribution indicator is utilized to determine the load shedding amount which each control object undertakes. The proposed methodology is verified by the fault scenarios when the generator sets mistakenly cut off and the trip of important tie-lines in the IEEE 39-bus system. Compared with the conventional strategies, the proposed strategy is more selective, can reduce the blackout range, and improve the effect of stable frequency recovery.