关于"实在气体压强与器壁性质无关"的简单证明

从宏观的角度对“实在气体压强与器壁性质无关”作了简单论证。     

Stochastic response of van der Pol oscillator with two kinds of fractional derivatives under Gaussian white noise excitation

This paper aims to investigate the stochastic response of the van der Pol(VDP) oscillator with two kinds of fractional derivatives under Gaussian white noise excitation.First,the fractional VDP oscillator is replaced by an equivalent VDP oscillator without fractional derivative terms by using the generalized harmonic balance technique.Then,the stochastic averaging method is applied to the equivalent VDP oscillator to obtain the analytical solution.Finally,the analytical solutions are validated by numerical results from the Monte Carlo simulation of the original fractional VDP oscillator.The numerical results not only demonstrate the accuracy of the proposed approach but also show that the fractional order,the fractional coefficient and the intensity of Gaussian white noise play important roles in the responses of the fractional VDP oscillator.An interesting phenomenon we found is that the effects of the fractional order of two kinds of fractional derivative items on the fractional stochastic systems are totally contrary.     

八面体的各晶面的夹角不是90°

编辑同志:文献[1]在讲述晶面角守恒时,对于岩盐晶体画出了图1所示的几种常见外形(在不同条件下,食盐结晶可有不同的形状):立方体、八面体和立方八面混合体.并指出晶面ａ、ｂ之间,ｂ、ｃ之间和ａ、ｃ之间的夹角总是90°.文献[2]也指出,不管外形是立方体、八面体、还是立方和八面混合体各晶面夹角都是90°.但由图可以直接看出八面体的各晶面之间的夹角不是(不可能是)90°.八面体中的晶面之间的夹角以及混合体中与八面体相应的那些晶面(图1(ｃ)中未标字母的那些面)之间的夹角相等,但不等于90°.实际上,八面体中的晶面ａ、ｂ之间和ｂ、ｃ之间的…     

关于分布函数极大值位置的讨论

将关于某个变量的连续分布函数进行变数变换,除非新老变数为线性关系,否则变换前后的分布函数的极大值之间的关系一般会不同于新老变数之间的关系。     

Sparse identification method of extracting hybrid energy harvesting system from observed data

Hybrid energy harvesters under external excitation have complex dynamical behavior and the superiority of promoting energy harvesting efficiency. Sometimes, it is difficult to model the governing equations of the hybrid energy harvesting system precisely, especially under external excitation. Accompanied with machine learning, data-driven methods play an important role in discovering the governing equations from massive datasets. Recently, there are many studies of data-driven models done in aspect of ordinary differential equations and stochastic differential equations (SDEs). However, few studies discover the governing equations for the hybrid energy harvesting system under harmonic excitation and Gaussian white noise (GWN). Thus, in this paper, a data-driven approach, with least square and sparse constraint, is devised to discover the governing equations of the systems from observed data. Firstly, the algorithm processing and pseudo code are given. Then, the effectiveness and accuracy of the method are verified by taking two examples with harmonic excitation and GWN, respectively. For harmonic excitation, all coefficients of the system can be simultaneously learned. For GWN, we approximate the drift term and diffusion term by using the Kramers-Moyal formulas, and separately learn the coefficients of the drift term and diffusion term. Cross-validation (CV) and mean-square error (MSE) are utilized to obtain the optimal number of iterations. Finally, the comparisons between true values and learned values are depicted to demonstrate that the approach is well utilized to obtain the governing equations for the hybrid energy harvester under harmonic excitation and GWN.     

纤维复合基石墨烯气凝胶在水处理中的应用

采用静电纺丝制备聚丙烯腈（PAN）纳米纤维,把PAN纳米纤维、氧化石墨烯（GO）和氨基三亚甲基膦酸（ATMP）交联剂采用水热法制备成PAN纤维含量不同的复合石墨烯气凝胶。用扫描电子显微镜（SEM）和傅里叶红外光谱（FT-IR）等表征气凝胶的结构和化学组成,用紫外分光光度计（Uv-vis）研究气凝胶的吸附性能。气凝胶对亚甲基蓝（MB）的吸附动力学和等温线模型分别符合准二阶动力学和Langmuir等温吸附。同时,复合气凝胶在50%压缩应变下的应力随着电纺纤维含量的增加而增加。当氧化石墨烯（GO）与纤维的重量比为1∶4时,50%压缩应变下的应力达到7.34 kPa,比没有纤维的气凝胶提高183%。     

焦耳定律实验的改进

焦耳定律实验是中学物理实验中探究电流的热效应与电流、电阻关系的重要实验,但是中学课本上所述焦耳定律实验方法存在一定的问题,如何能够直观明显将电流的热效应与电流、电阻之间的变化规律通过这一实验展示出来,且尽量缩短实验时间、提高实验教学的效率,让学生通过物理实验掌握物理知识,给出了几点实验改进的思路,希望能为广大师生提供一定的参考.     

为什么多孔塞实验容易得到与理想气体有差别的结果而焦耳实验却不容易得到这样的结果

对多孔塞实验容易得到与理想气体有差别的结果而焦耳实验却不容易得到这样的结果的原因进行了解释。