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.     

Optimization of performance of monolithic capillary column in gas chromatographic separations

Dependence of monolithic column efficiency on column pressure was analyzed using modified Van Deemter relationship with incorporated inlet and outlet column pressures as independent variables. It was demonstrated that the highest column efficiency is observed at high pressures. Inlet and outlet pressure increase has to be controlled in such a way that the relative pressure approaches 1 and the pressure drop across the column is close to zero. Experimental results obtained for open and monolithic capillary columns confirm up to 50% higher column efficiency as compared to column efficiency under standard conditions found using conventional Van Deemter plot. Pressure increase also results in a decrease in the optimal carrier gas velocity and corresponding increase in the analysis time. This drawback can be compensated via an increase in the column temperature.     

An efficient approach to solving fractional Van der Pol–Duffing jerk oscillator

The motive behind the current work is to perform the solution of the Van der Pol–Duffing jerk oscillator, involving fractional-order by the simplest method. An effective procedure has been introduced for executing the fractional-order by utilizing a new method without the perturbative approach. The approach depends on converting the fractional nonlinear oscillator to a linear oscillator with an integer order. A detailed solving process is given for the obtained oscillator with the traditional system.     

Fluctuation–dissipation approach to van der Waals potentials between atoms and dielectric bodies

We consider the problem of an atom in its ground state located at some distance z from an infinite plane surface bordering a dielectric body. For this system the atom–dielectric interaction potential has been calculated by Mavroyannis in terms of the frequency-dependent dielectric constant ?(ω ) of the body. We rederive Mavroyannis’ result by defining a correlation function involving the virtual atomic dipole of the external atom and its image inside the dielectric and then evaluating it by means of the fluctuation–dissipation theorem. This approach does not depend on coupling with the vacuum field, it only takes into account cohesion forces, i.e. atomic interactions inside the solid since these are the only effects that determine both the dissipative and the absorptive part of ?(ω ).     

关于Van Der Corput不等式加强式的改进

运用数值计算和分析方法将Van Der Corput不等式的加强形式作进一步改进,通过强弱比较表明,所建立的不等式的强度优于以往文献的结果,并且所建立的不等式在形式上也较为简洁.     

Repulsive and bound parts of the interatomic potentials of the lowest singlet electronic energy states of the MeRg complexes (Me = Zn, Cd; Rg = He, Ne, Ar, Kr, Xe)

Laser-induced fluorescence excitation spectra of MeRg (Me = Zn, Cd; Rg = He, Ne, Ar, Kr, Xe) complexes were recorded using the D¹ ← X¹ free ← bound transition. The complexes were produced in their ground state in a free-jet expansion beam and excited with a dye-laser beam directly to the excited state. Analysis of free ← bound unstructured profiles provided a shape of the repulsive part of the D¹-state potentials. Valence ab initio calculations of the ZnRg and CdRg ground- and excited-state potentials and electronic transition dipole moments for the studied transition were performed, taking scalar relativistic and spin-orbit effects into account. Results of the calculations show regularities and correlations in the repulsive branches and bound wells of the X¹- and D¹-state potentials as well as provide information on the bonding character in both electronic energy states. The trends were compared with available experimental results for ZnRg and CdRg as well as for MgRg and HgRg.     

Properties of synchronization in the systems of non-identical coupled van der Pol and van der Pol-Duffing oscillators. Broadband synchronization

The particular properties of dynamics are discussed for dissipatively coupled van der Pol oscillators, non-identical in values of parameters controlling the Hopf bifurcation. Possibility of a special synchronization regime in an infinitively long band between oscillator death and quasiperiodic areas is shown for such system. Features of the bifurcation picture are discussed for different values of the control parameters and for the case of additional Duffing-type nonlinearity. Analysis of the slow-flow equations is presented.     

二维半导体材料纳米电子器件和光电器件

近年来,随着各领域对微电子器件集成度及性能要求的不断提高,发展基于二维半导体材料的新型高性能功能性器件成为了突破当前技术瓶颈的重要环节和关键方向。目前,作为新型二维半导体材料的代表,二维过渡金属二硫化物、二维黑磷以及范德瓦尔斯异质结凭借其在电学、热学、机械、光学等方面的优异性能已经成为了发展高性能纳米电子器件和光电器件的最具潜力的材料之一。在本综述中,首先概述了几种用于纳米器件的常见二维材料,分析了材料的结构、性能及其在纳米器件中的应用,其次重点对基于过渡金属二硫化物、黑磷以及由其衍生的范德瓦尔斯异质结的纳米电子器件和光电器件的最新研究进展进行讨论,最后对目前二维半导体纳米器件所面临的挑战以及未来的发展方向进行总结及分析,从而为未来发展高性能功能性纳米器件提供支持。     

First-principles study of metal-semiconductor contact between MX2 (M = Nb,Pt; X = S,Se) monolayers

First principles calculations are performed to investigate the structural and electronic properties of MX₂ (M = Nb, Pt; X = S, Se) monolayers and their van der Waals (vdW) heterostructures. The dynamical stability of monolayers and vdW heterostructures is confirmed by binding energy and phonon spectra. An indirect band gap nature is found for PtS₂ and PtSe₂ monolayers while NbS₂, NbSe₂ and all vdW heterostructures are metals. The intrinsic electronic properties of both NbX₂ and PtX₂ are well preserved due to weak vdW contact. It is demonstrated that a p-type Schottky contact with a small barrier height is formed at NbX₂-PtX₂ interface. The zero tunnel barrier and higher potential drop across the interface in these contacts imply large transfer of charge carriers across the interface, making them potential candidates in nanoelectronic device applications.