Coagulation of Charged Aerosols

We consider the coagulation of an aerosol embedded in a stationary atmosphere of bipolar ions. Particles respond to the ionic environment by developing an instantaneous charge the fluctuations of which may produce attraction or repulsion between the particles. The governing parameter is the charge asymmetry factor which quantifies the relative charging efficiency of positive and negative ions. We use a Monte Carlo method to solve the coagulation equation in the free-molecule regime. We perform simulations for conditions ranging from symmetric and nearly symmetric environments (e.g. flames, ionizers), which result in particles that are on the average neutral to highly asymmetric conditions (low-pressure plasmas), which produce a substantial non-zero net charge. In symmetric ionic atmospheres we find that electrostatic interactions are unimportant and particles grow as if in the absence of charging ions. In asymmetric bipolar atmospheres, electrostatic interactions between particles are repulsive, the mean particle size grows logarithmically in time and the resulting size distributions are significantly narrower than the classical self preserving distributions.     

冲击波加载下TNT的初始反应路径及产物光谱特征研究

本文首先通过量子分子动力学方法结合多尺度冲击技术研究固相TNT晶体在冲击波加载下的初始分解反应路径及其产物组分变化.通过综合分析键长变化、电子布居和中间产物的存在寿命三个要素给出了不同冲击波速(3-15 km/s)下2类可能的初始分解路径:在低速冲击下(≤7 km/s),TNT发生部分分解和聚合,分解主要源于C-NO₂键的断裂,初始分解产物以NO₂为主;在高速冲击下(≥9 km/s)则发生完全分解,分解主要始于六元环的形成,即NO₂基团上的O与相邻CH₃基团上的H相结合,然后六元环被打破,生成了OH自由基,初始分解产物以CN、CO、C₂和OH为主.另外,根据模拟数据我们从理论上给出了TNT(ρ₀=1.7 g/cm~3)冲击Hugoniot关系为U_s=3.377+1.363 u.随后以分子光谱理论为基础,采用含时密度泛函理论获取这些主要分解产物的紫外可见吸收谱、荧光发射谱及振动分辨的荧光发射谱.此项研究有助于我们深入认识TNT高温高压状...     

Study on some aspects of the “singer's formant” in north indian classical singing

This article deals with a spectrographic analysis of the singer's formant as occurred during singing of the vowels /a/, /i/, and /o/ in North Indian classical vocal music. The resonance balance, center frequency, and band-width are shown as a function of fundamental frequency for eight singers.Two new parameters have been defined viz. asymmetry parameter (A) and spectral energy balance (W). Their variation with fundamental frequency is shown.     

Vortex Spatial Solitons to a Nonlinear Schr\"{o}dinger Equation with Varying Coefficients

Based on homogeneous balance method, soliton solutions to a generalized nonlinear Schrödinger equation (NLSE) with varying coefficients have been gotten. Our results indicate that a new family of vortex or petal-like spatial solitons can be formed in the Kerr nonlinear media in the cylindrical symmetric geometry. It is shown by numerical simulation that these soliton profiles are stable.     

Period-doubling bifurcation in two-stage power factor correction converters using the method of incremental harmonic balance and Floquet theory

In this paper, period-doubling bifurcation in a two-stage power factor correction converter is analyzed by using the method of incremental harmonic balance (IHB) and Floquet theory. A two-stage power factor correction converter typically employs a cascade configuration of a pre-regulator boost power factor correction converter with average current mode control to achieve a near unity power factor and a tightly regulated post-regulator DC-DC Buck converter with voltage feedback control to regulate the output voltage. Based on the assumption that the tightly regulated post-regulator DC-DC Buck converter is represented as a constant power sink and some other assumptions, the simplified model of the two-stage power factor correction converter is derived and its approximate periodic solution is calculated by the method of IHB. And then, the stability of the system is investigated by using Floquet theory and the stable boundaries are presented on the selected parameter spaces. Finally, some experimental results are given to confirm the effectiveness of the theoretical analysis.     

Harmonic balancing approach to nonlinear oscillations of a punctual charge in the electric field of charged ring

The harmonic balance method is used to construct approximate frequency-amplitude relations and periodic solutions to an oscillating charge in the electric field of a ring. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic solutions for the oscillator. To solve the nonlinear differential equation, firstly we make a change of variable and secondly the differential equation is rewritten in a form that does not contain the square-root expression. The approximate frequencies obtained are valid for the complete range of oscillation amplitudes and excellent agreement of the approximate frequencies and periodic solutions with the exact ones are demonstrated and discussed.     

Baeicklund Transformation and Multiple Soliton Solutions for （3＋1）-Dimensional Potential-YTSF Equation

We study an approach to constructing multiple soliton solutions of the (3 1)-dimensional nonlinear evolution equation. We take the (3 1)-dimensional potential- YTSF equation as an example. Using the extended homogeneous balance method, one can find a Backlund transformation to decompose the (3 1)-dimensional potential-YTSF equation into a set of partial differential equations. Starting from these partial differential equations, some multiple soliton solutions for the (3 1)-dimensional potential-YTSF equation are obtained by introducing a class of formal solutions.     

约瑟夫森结中周期解及其稳定性的解析分析

针对交流激励下电阻-电容分路的约瑟夫森结,采用增量谐波平衡法推导了系统中周期解的解析表达式,并运用Floquet理论分析了周期解的稳定性.发现系统处于稳定周期状态的同时,还存在着丰富的不稳定周期解.通过计算Floquet乘数,得到了系统稳定周期解失稳时的临界参数值,并确定了系统发生的分岔类型,从理论上证明了系统随激励电流幅值的增加由倍周期分岔通向混沌.解析分析与数值计算结果具有很好的一致性. 关键词： 约瑟夫森结 增量谐波平衡法 周期解 分岔     

对FD-GLB-Ⅱ型新型焦利氏秤的改进

对FD-GLB-Ⅱ型新型焦利氏秤做了改进,改进后的振子质量可变,很好的满足了实验教学中对弹簧阵子简谐振动关系式的验证要求.     

Energy inconsistency of Galerkin approximationsfor plane Couette flow

For classical solutions of the incompressible Navier-Stokes equations (NSE) the energybalance between kinetic energy, work done by external forces, and viscous dissipation holds rigorously true. It is shown in this paper that standard Galerkin approximations violate energy balance in the case of plane Couette flow, whereas Poiseuille flow turns out to be energy consistent at any cutoff. The main reason for this discrepancy is seen in the different boundary conditions between the stationary linear shear flow and its disturbances. In our analysis, essentially, we introduce an auxiliary external force field which enforces the finite dimensional Galerkin approximation to fulfil the NSE. It is exemplarily demonstrated how the energy discrepancy decreases when the number of disturbed modes is increased which couple to the stationary shear flow.