Van der Waals气体Euler方程的Riemann问题及基本波的相互作用

研究了修正的等熵Van der Waals气体动力学Euler方程Riemann问题及其基本波的相互作用.利用Maxwell提出的等面积法则,将Van der Waals气体状态方程修正为与实际相符,从而守恒律方程组从混合型转化为双曲型.利用广义特征线分析法,构造性地得到了Riemann问题的解是存在的.进一步,得到了基本波相互作用.     

Lp- and Sp,qrB-discrepancy of the symmetrized van der Corput sequence and modified Hammersley point sets in arbitrary bases

We study the local discrepancy of a symmetrized version of the well-known van der Corput sequence and of modified two-dimensional Hammersley point sets in arbitrary base $b$. We give upper bounds on the norm of the local discrepancy in Besov spaces of dominating mixed smoothness $S_{p,q}^{r}B\left({[0,1)}^s\right)$, which will also give us bounds on the $L_p$-discrepancy. Our sequence and point sets will achieve the known optimal order for the $L_p$- and $S_{p,q}^{r}B$-discrepancy. The results in this paper generalize several previous results on $L_p$- and $S_{p,q}^{r}B$-discrepancy estimates and provide a sharp upper bound on the $S_{p,q}^{r}B$-discrepancy of one-dimensional sequences for $r>0$. We will use the $b$-adic Haar function system in the proofs.     

基于范德瓦尔斯气体的迈耶公式修正

在近似真实情况下,对迈耶公式作了理论修正,并与实验值进行了比较.     

现代磁学奠基人——约翰·范弗累克

约翰.哈斯布鲁克.范弗累克是著名的美国理论物理学家,1977年诺贝尔物理学奖的获得者.本文介绍了他的生平,叙述他在科学研究中的重要贡献,以及他在培养学生上的成就.     

A new approach to the evaluation of Casimir and van der Waals forces in the transition region

This paper studies the incorporation of Casimir and van der Waals forces applied to a nanostructure with parallel configuration. The focus of this study is in a transition region in which Casimir force gradually transforms into van der Waals force. It is proposed that in the transition region, a proportion of both Casimir and van der Waals forces, as the interacting nanoscale forces, can be considered based on the separation distance between upper structure and substrate during deflection. Moreover, as the separation distance descends during deflection, the nanoscale forces could transform from Casimir to a proportion of both Casimir and van der Waals forces and so as to van der Waals. This is also extended to the entire surface of the nanostructure in such a way that any point of the structure may be subjected to Casimir, van der Waals or a proportion of both of them about its separation distance from the substrate. Therefore, a mathematical model is presented which calculate the incorporation of Casimir and van der Waals forces considering transition region and their own domination area. The mechanical behavior of a circular nano-plate has been investigated as a case study to illustrate how different approaches to nanoscale forces lead to different results. For this purpose, the pull-in phenomena and frequency response in terms of magnitude have been studied based on Eringen nonlocal elasticity theory. The results are presented using different values of the nonlocal parameter and indicated in comparison with those of the classical theory. These results also amplify the idea of studying the mechanical behavior of nanostructures using the nonlocal elasticity theory.     

Chaos synchronization of a fractional‐order modified Van der Pol–Duffing system via new linear control,backstepping control and Takagi–Sugeno fuzzy approaches

In this article, based on the stability theory of fractional‐order systems, chaos synchronization is achieved in the fractional‐order modified Van der Pol–Duffing system via a new linear control approach. A fractional backstepping controller is also designed to achieve chaos synchronization in the proposed system. Takagi‐Sugeno fuzzy models‐based are also presented to achieve chaos synchronization in the fractional‐order modified Van der Pol–Duffing system via linear control technique. Numerical simulations are used to verify the effectiveness of the synchronization schemes. © 2015 Wiley Periodicals, Inc. Complexity 21: 116–124, 2016     

相对湿度对材料表面粘附力影响的研究

利用自制微摩擦及粘附力测试装置考察了在微载荷条件下,相对湿度对Si(100)材料表面粘附力的影响,分析了在大气环境中水分子的毛细作用力和范德华力对粘附力的贡献,并以BET吸附模型为基础推导出考虑湿度影响的粘附力计算公式.结果表明:在微载荷条件下,相对湿度对材料表面的粘附力影响十分显著,随着相对湿度升高粘附力增加,特别是相对湿度RH在40%～80%之间时,粘附力变化最为显著;当相对湿度RH小于20%时,范德华力大于水的毛细作用力且占主导地位;当相对湿度RH大于20%后,水分子的毛细作用力不断增加,同时范德华力因水膜的存在而降低,水的毛细作用力占主导地位.     

Numerical simulations of sonochemical production and oriented aggregation of BaTiO3 nanocrystals

Numerical simulations of sonochemical production and oriented attachment of BaTiO₃ nanocrystals are performed in aqueous solution with pH 14. It is suggested that most significant effect of ultrasound is the dissolution of Ti-based gel in aqueous solution. It results in the dissolution-precipitation mechanism in the production of BaTiO₃ nanoparticles, while with mechanical stirring without ultrasound it is the in situ mechanism that BaTiO₃ is gradually formed on Ti-based gel. The oriented attachment of spherical BaTiO₃ nanocrystals occurs by van der Waals torque (Casimir torque). Large aggregates of nanocrystals do not attach with each other as the repulsive double layer interaction is stronger for larger aggregates. For smaller spherical nanocrystals, the alignment of the crystal axes is less accurate due to more significant rotational Brownian motion of the nanocrystals.     

对Van Der Corput不等式的加强

有别于研究Van Der Corput不等式的传统方法,利用作者已经证明的最值单调定理,得出了该不等式的又一个新的加强式.它不仅强于现有的许多结果,而且形式美观;同时表明最值单调定理在不等式研究中具有重要的作用。     

The solution of high-order nonlinear ordinary differential equations by Chebyshev Series

By the use of the Chebyshev series, a direct computational method for solving the higher order nonlinear differential equations has been developed in this paper. This method transforms the nonlinear differential equation into the matrix equation, which corresponds to a system of nonlinear algebraic equations with unknown Chebyshev coefficients, via Chebyshev collocation points. The solution of this system yields the Chebyshev coefficients of the solution function. An algorithm for this nonlinear system is also proposed in this paper. The method is valid for both initial-value and boundary-value problems. Several examples are presented to illustrate the accuracy and effectiveness of the method.