气-液分层流界面波的实验研究及统计分析

用电导探针测量了水平及微倾斜上升和下降管内气 -液分层流瞬态液膜厚度 ,得到了不同的波形图 .用统计分析的方法研究了界面波信号的频谱特性 ,得到了不同倾角时管内分层流界面波各特征参数 ,如界面波振幅、波长、波速 ,并给出了各参数随气液折算速度和管子倾角的变化特性     

Simulation of discontinuous population balance equation with integral constraint of growth rate expression

An effective method based on the concept of continuous characteristics is developed to solve the continuous population equation with integral constraint of growth rate expression. This method can also be extended to solve a general form of a first order partial differential equation. A typical example of a class II MSMPR crystallization process at transient state is modelled and analyzed. The system which possesses originally a discontinuous population density function is transformed into a continuous one by appropriate treatment of the initial condition. The partial differential equation of the continuous population density function is solved by the shifted Legendre polynomials approximation and moments method simultaneously. The original discontinuous population density function is then transformed back from the calculated continuous one by the system characteristics. Very satisfactory computational results are obtained.     

DC electric fields produce periodic bending of polyelectrolyte gels

The periodic bending of polyelectrolyte hydrogels made of polyacrylamide, polyacrylic and polymethacrylic acids with 10% ionization under the DC electric field was observed in 0.8 mM CaCl₂. When the field with intensity 13.5 V/cm was applied perpendicular to the longitudinal axis of the gel sample, the gel first bent to cathode, then more substantially to anode, then to cathode again and so on with damping amplitude. Within experimental error up to two periods of such oscillations were observed. The maximum amplitude of bending was approximately 30% of sample length. After 150-200 s, the gel sample finally reached a steady state slightly bent to anode. During these oscillations the volume of the sample gradually decreased by 10-30% depending on the gel. Kinetics of displacement of the free end of the gel sample could be fitted by a damped sine wave function, depending initial amplitude, final displacement, wave period, and decay time. All parameters except wave period depended on sample cross-section. The amplitude, wave period and decay time decrease with the increase of initial degree of gel swelling. The physical basis of the periodic bending is discussed based on the theoretical approach of Doi, Matsumoto and Hirose, although that theory can describe only initial cathodic and successive anodic displacement of gel.     

具有基质抑制的流加反应器计算机模拟和优化

以单位时间内获得尽可能多的细胞生物量为目标函数,建立了流加反应器最优化模型。通过引入哈密尔顿函数和庞特雅金最小值原理,求解了这个最优化模型。此外,以安德鲁方程为例,还对几种特殊的流加反应器进行了计算机模拟,并给出了最优化计算结果。     

Dissipative structures in a reaction-diffusion system

A transient analysis of reaction-diffusion equations associated with the model reaction of Prigogine and Lefever (Brusselator model), has been performed. For low system lengths and for fixed boundary conditions, steady state solutions with the low amplitude are unstable. For zero flux boundary conditions the multiplicity of symmetric solutions with the same wave number may exist and the majority of them are unstable. The diffusion of initial components induces relaxation oscillations in space for fixed as well as zero flux boundary conditions. The amplitude of the oscillations increases as the diffusion coefficient of the initial component decreases. For conditions of relaxation oscillations the spatial profiles result in single or multiple propagating fronts. High system lengths for both zero flux and periodic boundary conditions, may give rise to a multipeak incoherent wave pattern. For periodic boundary conditions the multiplicity of waves has been observed. Numerical simulation of two-dimensional spatial structures reveals the existence of certain similarities between the one- and two-dimensional cases.     

Statistical analysis of kinetics of an adiabatic thermal explosion

Stochastic phenomena in the kinetics of chemical reactions induced by a thermal explosion are studied. The statistical analysis is performed on the basis of nonlinear differential equations for gas temperature and concentration of reacting particles with random initial conditions, and also corresponding equations for the probability density function of the state variables of the system. The results of the numerical solution of these equations are presented in the graphical form as a statistical set of an ensemble of kinetic curves of concentration of reacting particles and gas temperature and as the time evolution of their probability density function. Small random fluctuations of gas temperature and particle concentration at the beginning of the reaction are demonstrated to induce significant fluctuations of the induction period. __________ Translated from Fizika Goreniya i Vzryva, Vol. 45, No. 3, pp. 44–48, May–June, 2009.     

Likelihood functions for state space models with diffuse initial conditions

State space models with non‐stationary processes and/or fixed regression effects require a state vector with diffuse initial conditions. Different likelihood functions can be adopted for the estimation of parameters in time‐series models with diffuse initial conditions. In this article, we consider profile, diffuse and marginal likelihood functions. The marginal likelihood function is defined as the likelihood function of a transformation of the data vector. The transformation is not unique. The diffuse likelihood is a marginal likelihood for a data transformation that may depend on parameters. Therefore, the diffuse likelihood cannot be used generally for parameter estimation. The marginal likelihood function is based on an orthonormal data transformation that does not depend on parameters. Here we develop a marginal likelihood function for state space models that can be evaluated by the Kalman filter. The so‐called diffuse Kalman filter is designed for computing the diffuse likelihood function. We show that a minor modification of the diffuse Kalman filter is needed for the evaluation of our marginal likelihood function. Diffuse and marginal likelihood functions have better small sample properties compared with the profile likelihood function for the estimation of parameters in linear time series models. The results in our article confirm the earlier findings and show that the diffuse likelihood function is not appropriate for a range of state space model specifications.     

Reliability analysis of ceramic cutting tools in continuous and interrupted hard turning

Reliability analysis was carried out for ceramic cutting tools used in continuous and interrupted hard turning. On the basis of micromechanics and damage mechanics, statistical characteristics of the original defects in the tool material microstructure were evaluated and analyzed. A new tool performance indicator was proposed considering the combined effects of the original damage of the tool material microstructure, the macro-mechanical properties of the tool material and the external loads on the cutting tool. Statistical analysis of the tool performance indicator was performed for continuous and interrupted turning. The relationship between tool reliability and the probability distribution of tool performance indicator was identified. It was found that the original damage of the ceramic tool material followed a weibull distribution. The probability density of the original damage decreased as the original damage increased. When interrupted turning was adopted, tool performance indicator was relatively low and the indicator decreased as cutting length ratio became smaller. The indicator followed a weibull distribution and this was invariable when turning condition changed. Relatively low shape parameter and scale parameter in probability density function of tool performance indicator appeared when the tool was tested in interrupted turning and relatively small cutting length ratio was applied. Similar to tool performance indicator, tool lives obtained under different cutting conditions also followed a weibull distribution. When turning condition varied, shape parameter and scale parameter in probability density function of tool life changed in a similar way to those parameters in probability density function of tool performance indicator. Both the probability density function of tool life and that of tool performance indicator first increased and then decreased as the independent variable increased. Shape parameter for tool performance indicator can be used in the calculation of tool reliability when the cutting length ratio in interrupted turning was relatively small.     

连续多级串联完全混合槽中固体颗粒反应产率计算方法

本文针对级内颗粒完全混合一级间无颗粒返混的多级反应器,探讨了按停留时间分布计算固体颗粒反应率的方法。首先分析了用δ（0）函数示踪法与多元独立随机变量和的分布密度函数法求颗粒停留时间分布的特点;应用后一种方法推得了计算颗粒反应产率的一般公式。从固体颗粒固相反应物浓度分布密度函数也可以推得此公式。在此基础上对一类特殊的反应速度方程,解析求出了直接计算任何一级反应产率的通式;对求解计算通式困难的反应速度方程,论证了两种逐级计算方法:以反应时间作计算参量及以颗粒固相反应物浓度作计算参量。     

Possibility of detonation wave propagation in the Chapman-Jouguet regime in inhomogeneous media

We consider detonation wave propagation in an inhomogeneous fuel gas mixture at rest, whose initial state is characterized by values of pressure and density that are in the general case, functions of the spatial and time coordinates. The distance form the plane, axis or center of symmetry can be used as the spatial coordinate. The sources of mass, pulse, and energy are assumed to be present behind the detonation front. The appropriate necessary conditions for the detonation wave to propagate in the Chapman-Jouguet regime are determined. The relations obtained are analyzed for some inhomogeneous media: media with variable density, media with heat release varying with distance, and media with burnout sources behind the detonation front.Moscow. Translated from Fizika Goreniya i Vzryva, Vol. 29, No. 2, pp. 98–109, March–April, 1993.     

基于压电效应的纤维高性能混凝土损伤监测研究

以纤维掺量为变量制作48个混凝土试件,压电陶瓷传感器作为信号激励器和信号接收器置于混凝土试件表面。基于压电效应对玄武岩-聚丙烯纤维增强高性能混凝土(BPHPC)的损伤进行实时监测。通过对单掺、混掺纤维混凝土的压电应力波信号进行分析,得到基于小波包分析法的损伤指数(DI),并拟合出纤维掺量-荷载-DI的函数关系。结果表明:通过外观损伤状态和压电应力波信号变化定性评价试件的健康状态,纤维的掺入能够降低混凝土的外观损伤程度;单掺纤维混凝土的试件应力波信号幅值比混掺纤维混凝土试件大;玄武岩纤维体积掺量为0.15%、聚丙烯纤维体积掺量为0.10%时试件的DI最小,当DI超过0.8时,可以认为试件被完全破坏;试验数据和试验现象吻合良好,通过压电陶瓷实时监测BPHPC损伤有较高的可行性。     

聚合物混合状态的超声检测及在线监控

针对聚合物挤出过程中混合状态的在线监控要求,利用超声检测系统对聚合物的超声波形的幅度进行采集和分析,研究了聚合物连续超声波形的幅值变化的波动性。结果表明:在挤出螺杆通道内,聚合物的混合状态连续波形幅值变化的波动性呈逐渐减小的趋势,符合理论上对聚合物在线监控的要求,实现了在螺杆通道内对聚合物混合状态的实时监控。     

基于最小充分统计量模式分析的故障检测方法

统计量模式分析（SPA）最近在故障检测领域取得了广泛应用,其实质是用数据的统计量矩阵来代替原始数据矩阵进行故障检测,然而其统计量的选取存在盲目性且各统计量之间存在复杂的非线性关联关系,难以满足后续应用主成分分析（PCA）完成故障检测所需的基本条件。为了解决这个问题,提出了基于最小充分统计量模式分析的故障检测方法（MSSPA）。该方法首先将原始数据矩阵进行正交变换以消除变量之间的关联性,然后估计出每个变量的概率密度函数或者多个变量的联合概率密度函数,进而求出原始数据的最小充分统计量,并用最小充分统计量来构造统计量矩阵。最小充分统计量的引入还能够有效应对数据的非高斯分布问题。最后,通过在TE过程上的仿真测试验证了该方法用于故障检测的可行性和有效性。     

Discovery of a general method of solving the schrödinger and dirac equations that opens a way to accurately predictive quantum chemistry

Just as Newtonian law governs classical physics, the Schr?dinger equation (SE) and the relativistic Dirac equation (DE) rule the world of chemistry. So, if we can solve these equations accurately, we can use computation to predict chemistry precisely. However, for approximately 80 years after the discovery of these equations, chemists believed that they could not solve SE and DE for atoms and molecules that included many electrons. This Account reviews ideas developed over the past decade to further the goal of predictive quantum chemistry. Between 2000 and 2005, I discovered a general method of solving the SE and DE accurately. As a first inspiration, I formulated the structure of the exact wave function of the SE in a compact mathematical form. The explicit inclusion of the exact wave function's structure within the variational space allows for the calculation of the exact wave function as a solution of the variational method. Although this process sounds almost impossible, it is indeed possible, and I have published several formulations and applied them to solve the full configuration interaction (CI) with a very small number of variables. However, when I examined analytical solutions for atoms and molecules, the Hamiltonian integrals in their secular equations diverged. This singularity problem occurred in all atoms and molecules because it originates from the singularity of the Coulomb potential in their Hamiltonians. To overcome this problem, I first introduced the inverse SE and then the scaled SE. The latter simpler idea led to immediate and surprisingly accurate solution for the SEs of the hydrogen atom, helium atom, and hydrogen molecule. The free complement (FC) method, also called the free iterative CI (free ICI) method, was efficient for solving the SEs. In the FC method, the basis functions that span the exact wave function are produced by the Hamiltonian of the system and the zeroth-order wave function. These basis functions are called complement functions because they are the elements of the complete functions for the system under consideration. We extended this idea to solve the relativistic DE and applied it to the hydrogen and helium atoms, without observing any problems such as variational collapse. Thereafter, we obtained very accurate solutions of the SE for the ground and excited states of the Born-Oppenheimer (BO) and non-BO states of very small systems like He, H(2)(+), H(2), and their analogues. For larger systems, however, the overlap and Hamiltonian integrals over the complement functions are not always known mathematically (integration difficulty); therefore we formulated the local SE (LSE) method as an integral-free method. Without any integration, the LSE method gave fairly accurate energies and wave functions for small atoms and molecules. We also calculated continuous potential curves of the ground and excited states of small diatomic molecules by introducing the transferable local sampling method. Although the FC-LSE method is simple, the achievement of chemical accuracy in the absolute energy of larger systems remains time-consuming. The development of more efficient methods for the calculations of ordinary molecules would allow researchers to make these calculations more easily.     

Studies on melt spinning. V. Draw resonance as a limit cycle

The exact wave form of draw resonance in isothermal spinning of Newtonian liquids was sought by solving numerically the simultaneous partial differential equations¹ of melt spinning in their original nonlinear form without recourse to perturbation. When the draw-down ration of spinning exceeded 20, solution of the equations became a limit cycle, a sustained oscillation having amplitude and period independent of initial conditions. As the draw down ratio was further increased, the amplitude of the limit cycle grew very rapidly, and the wave form became close to a pulse train predicting an extreme thinning of the thread at regular intervals along the thread. The above solution for Newtonian liquids agreed well with experiment with respect to oscillation period. Agreement, however, was poor in amplitude, indicating that possibly the amplitude of draw resonance is affected by deviations of polymer viscosity from Newtonian.     

JBO-9021炸药初始密度对爆轰波阵面曲率效应的影响

采用高速扫描相机及电探针,在室温环境下对不同初始密度(1.894~1.901g/cm3)、不同半径(5.0、7.5、15.0mm)的钝感炸药JBO-9021药柱开展了曲率效应实验,获取了拟定态爆轰波阵面形状及波速,分析了其随炸药柱密度及半径的变化。结果表明,随着炸药JBO-9021的初始密度由1.894g/cm3增至1.901g/cm3,3种不同半径JBO-9021药柱的爆轰波拟定态波速均增大,拟定态波阵面形状变得更为平坦,波阵面中心点与边界点之间的波到达时间差降低;在小曲率范围内(κ0.2mm-1),JBO-9021药柱爆轰波波阵面法向波速Dn与当地曲率κ的关系(Dn(κ)关系)不受药柱半径及密度的影响,当曲率κ0.2mm-1时,Dn(k)关系随药柱半径及炸药密度呈现离散趋势,药柱半径及初始密度共同影响爆轰波波阵面大曲率的Dn(κ)关系。     

Hydrodynamic characteristics of activated carbon in air- and water-fluidized beds

The hydrodynamic characteristics of small hydrophobic activated carbon particles were determined in air flowing through both fixed and fluidized bed layers and water flowing through an inverse fluidized bed. Based on experimental data the Ergun-equation was corrected. A new relationship is proposed to predict the pressure drop in a fixed bed with gas flowing by using the minimum fluidizing velocity (u _mf ) and particle terminal velocity (u _t ). Apparent density of oven-dried activated carbon increases with filling the internal pores by water. After the bed density reaches the density of water, the system switches from an inverse fluidized layer into the classical fluidized state. Finally, it has been demonstrated that the Reynolds number (Re _mf ) at u _mf associated with the original Archimedes number (Ar) for gas-solid fluidized system and the modified Ar numbers characterizing the inverse fluidized beds lie on identical curves.     

Selection and refinement of finite elements for optimal design and control: A Hamiltonian function approach

In this work, we propose a /methodology for the selection and refinement of finite elements for the integration of process design and control. The proposed methodology is based on the selection criteria of the Hamiltonian function through the implementation of the Pontryagin's minimum principle. The Hamiltonian function features to be continuous and constant over time for autonomous systems; nevertheless, the Hamiltonian function shows a nonconstant profile for underestimated discretization meshes, which is exploited in this work for the refinement of the discretization. Furthermore, the residuals at noncollocation points are evaluated to estimate the collocation error, this is used as a second refinement criterion in the proposed framework. The methodology is illustrated using two case studies featuring a reaction system with two CSTRs in series and the Williams–Otto reactor, respectively. The results showed that an accurate selection of the finite elements return economically attractive designs with fewer elements than those obtained with equidistributed finite element strategies.     

Normal Mode Solution for Frequency-Dependent Damping of a Free Particle

The normal mode transformation of the Hamiltonian equivalent of the Generalized Langevin Equation for the free particle is used to provide explicit solutions for the classical and quantum-mechanical diffusion of a free particle.     

Monte carlo simulation of a probability screen

The interaction of a probability screen with spherical particles was simulated in a computer model. Repeated runs were made using randomly selected, slightly differing initial conditions, from which the penetration probability was obtained at a particular particle size under given screen operating conditions. The calculations were then repeated with differing particle sizes and operating conditions, and the results were found to compare favourably with experimental data obtained in a previous study. It was shown that the stochastic model correctly predicts the effects of the principal operating variables (screen angle of inclination and aperture size, frequency and amplitude of vibration). Because of excessive computer time requirements of this model a second, semi-empirical non-stochastic model was developed whose results closely match those of the earlier model. The second model is suitable for incorporation into a plant simulation computer package.