The Fokker-Planck equation in the second-order pitch angle approximation and its exact solution

The diffusive particle propagation and its pitch angle scattering is studied using kinetic equation of the Fokker-Planck form. The case is considered when charged particles preferable propagate along the strong mean magnetic field direction and undergo the pitch angle scattering with respect to it. The paper deals with solution of the equation for particle distribution function in the second-order approximation in the pitch angle. The exact analytical solution is obtained in an integral form. The well-known solution in the first-order pitch angle approximation can be restored performing the small time limit in the result. Unlike the first-order solution the obtained solution in the second approximation rightly shows that the pitch angle diffusion is closely connected with the particle transport along the mean magnetic field. The expression for particle density for the point instantaneous unidirectional source also has been obtained.     

Deposition of inertial particles from turbulent flow in channels at high Reynolds numbers

On the basis of the previously developed asymptotic theory of turbulent particle-laden flow with particle deposition in channels coupled with the transport model for the particle Reynolds stress, an asymptotic solution to the problem on the deposition of particles in the limit of high Reynolds numbers was obtained. The numerical calculations confirmed the presence, in the region of the transition from the diffusion-impaction regime of particle sedimentation to the inertia-moderated regime, bifurcation phenomenon of a solution found previously in earlier studies. Features of particle accumulation in the viscous sublayer are analyzed. On the basis of the numerical solution, correlations for particle deposition velocity were obtained. Boundary conditions of the wall-function type for particle concentration whose use allows widening the applicability limits of the equilibrium Eulerian models in terms of particle inertia are proposed.     

Slowing down approximations to the boltzmann equation: I. Applications to energy deposition and ion implantation

An approximale method for solving the Boltzmann equation for fast particles slowing down in homogeneous media is described. The Boltzmann equation is used in its straight ahead form and the method of Goertzel and Greuling, developed for neutron transport calculations, is extended to cover the problem of ion slowing down and energy deposition. Solutions are obtained in a simple analytical form and compared with exact calculations. We observe that the error passes through a maximum as the index of anisotropy, m, goes from zero to unity. The limitations of simple áge theory are discussed and it is shown how these solutions become exact in the Coulomb limit. The additional problem of electronic stopping is included and its effect on the solution is assessed. Numerical examples are given to support the general conclusions; namely that the Goertzel-Greuling method provides a convenient way to obtain useful estimates of ion implantation profiles and energy deposition.     

Counting translocations of strongly repelling particles through single channels: fluctuation theorem for membrane transport

Transport of strongly repelling particles through a single membrane channel is analyzed assuming that the channel cannot be occupied by more than one particle. An exact solution is found for the Laplace transform of the probability P_{n}(t) that n particles have been transported in time t. This transform is used to find the flux through the channel and to show that P_{n}(t) and P_{-n}(t) are related by the fluctuation theorem. The solution is obtained using an observation that P_{n}(t) is the propagator for a non-Markovian random walk, which can be found by solving a set of integral equations.     

雾霾粒子的紫外光散射特性研究

紫外光与雾霾粒子发生散射后,其散射信道特性能够反映雾霾粒子的相关物理信息,利用无线紫外光单次和多次散射信道模型,采用Mie散射和T矩阵理论分析了霾粒子在不同形态和浓度下的紫外光散射信道特性,以及散射角对散射光强的影响,并完成了紫外光在雾霾环境下的实测。通过理论及仿真分析,得到了不同霾粒子形态下的紫外光通信路径损耗以及光强分布。结果表明：紫外光直视通信方式下,路径损耗随着霾粒子浓度的增大而增大,且通信质量差于晴朗天。非直视通信方式中,在短距离通信时,高霾浓度下的路径损耗小于中低霾浓度,然而随着通信距离的继续增大,高雾霾浓度下的通信质量急剧下降,低霾浓度下通信质量最终达到最优,且距离为200 m时通信质量能优于晴朗环境。当通信距离相同时,三种雾霾浓度下的紫外光散射光强分布均随着散射角的增大而减小,当散射角继续增大并超过90°时,低霾浓度下的散射光强最大。主要原因是虽然散射角继续增大,但是有效散射体体积逐渐减小,因此低霾浓度下的散射光强较大。且当粒子粒径相同时,球形粒子的衰减较非球形粒子大。雾霾环境下实测结果与仿真结果相类似,证明了仿真结果的正确性,并在一定程度上证明了实际大气中雾霾非球形粒子多于球形粒子。     

Angular moment model for the Fokker-Planck equation

An accurate and rapid kinetic model describing the collisional transport of particles is presented. It is derived from the Fokker-Planck equation and involves an angular closure in the phase space leading to a set of hyperbolic equations for the moments of the distribution function evolving in time, space and energy. This method provides an alternative to the prohibitive cost of a direct solution to the full kinetic equation. Moreover, it is exact for the cases of collimated beams and the quasi-isotropic distributions. It can be approximated with the usual numerical schemes of the non-linear hyperbolic analysis. This model has features that are required to simulate the electron or ion transport for the inertial confinement fusion and the dose deposition for radiation therapy of cancers.     

The path length distribution function in a heterogeneous medium

The transport of fast particles in a heterogeneous substrate is studied using the path length approximation. With the power law scattering model, exact solutions are obtained for the energy deposition rate and the implanted ion density in two contiguous, but dissimilar, plane layers. A discontinuity in the particle density at the interface is observed which is consistent with the Monte Carlo results of Furukawa and Ishiwara and with some recent work of Winterbon. The method shows promise of predicting implanted ion distributions with some confidence.     

The Exact Solution,Berry's Phase and Coherent State for the Driven Generalized Time-Dependent Harmonic Oscillator

The Lewis'invariant and exact solution for the driven generalized time-dependent harmonic oscillator is found by making use of the Lewis-Riesenfeld quantum theory. Then, the adiabatic asymptotic limit of the exact solution is discussed and the Berry's phase for thirr system is obtained. We then proceed to use the exact solution to construct the coherent state and calculate the corresponding exact classical phase angle. This phase angle can give the Hannay's angle in the adiabatic limit. The relation between the exact Lewis'phase and the corresponding classical phase angle L'discusrred.     

Fluctuations of dielectric constant in a system of hard spheres

The correlation function for fluctuations of a dielectric constant in a latex-like suspension of spherical particles was calculated. An exact analytical expression was derived for the correlation function using the Percus-Yewick approximation for a system of hard spheres. The obtained results made it possible to calculate the indicatrix of single scattering, the extinction coefficient, and the transport mean path. It is shown that, starting with a volume content of about ten percent, the “gas” approximation becomes invalid, and optical parameters begin to depend on concentration in quite a complicated manner. In particular, the extinction length and the mean transport path, which are the basic parameters in describing the coherent effects in multiple scattering, vary nonmonotonically with concentration. It is found that there exists a range of sizes and concentrations of scattering particles in which an effect similar to the emergence of blue phase in liquid crystals can be observed.     

圆截面直流道中微粒黏弹性聚焦机理研究

微粒黏弹性聚焦技术近年来受到了广泛的研究重视, 但影响粒子聚焦特性的关键参数调控机理仍不清楚. 基于此目的, 本文量化研究了圆截面直流道中非牛顿流体诱导微粒黏弹性聚焦的行为, 给出了流速和流道长度对粒子聚焦特性的调控机理. 具体而言: 首先, 对比分析不同黏度牛顿流体(水和22 wt%甘油水溶液)和非牛顿流体(8 wt%聚乙烯吡咯烷酮水溶液)中粒子横向迁移行为, 发现非牛顿流体中粒子将在弹性力主导下聚焦至流道中心区域, 而牛顿流体中粒子则在惯性升力主导下迁移形成Segré-Silberberg圆环. 其次, 量化分析粒子尺寸和驱动流速对黏弹性聚焦效果的影响, 发现随着流速的增加, 粒子聚焦效果逐渐变好并最终趋于稳定, 且大粒子较小粒子具有更好的聚焦效果. 最后, 研究粒子沿流道长度的动态聚焦过程, 推导并验证了粒子聚焦所需安全流道长度的数学模型, 发现大粒子聚焦所需安全流道长度显著短于小粒子. 上述研究结果对于提升粒子黏弹性聚焦机理和过程的理解, 实现微粒聚焦特性的灵活控制具有非常重要的意义.     

Multiple monopole scattering of sound waves from spherical particles in liquid and elastic media

A solution to the problem of the mean sound field in liquid and elastic media with spherical particles causing monopole scattering of sound is proposed. The integral equation obtained for the field allows passage to the Helmholtz equation with an effective wave number. The characteristic features of the solution are the absence of radiation loss in the mean field wave and the absence of limitations on the particle concentration. The integral equation is used as the basis for solving the problem of the incidence of a plain sound wave at an arbitrary angle on a plane layer of a medium with particles.     

Comparison of exact and mean beam length results for a radiating hydrogen plasma

The purpose of this work is to investigate the accuracy of the mean beam length technique in high-temperature radiative heat transfer, combined with other modes of heat transfer. In order to study the validity of the mean beam length method, Nusselt numbers are presented for fully developed channel flow of a radiating nonisothermal hydrogen plasma. Black isothermal boundaries are considered. Numerical results obtained from the exact integrodifferential equation have been obtained previously for this problem. Linearized radiation and local thermodynamic equilibrium are assumed.The results show that the Nusselt numbers obtained by using the geometric mean beam length are in close agreement with results obtained by using the mean beam length. Therefore the complicated calculations needed to obtain the mean beam length are unnecessary.A comparison of the results obtained in the present work with previously reported work shows that the mean beam length technique is a better approximation to the exact solution than the optically-thick, or nongray differential approximation solutions.     

含灰湿空气外掠翅片管束积灰和阻力特性实验研究

本文针对以褐煤预干燥乏气为代表的含灰含湿气体余热回收问题,采用含灰湿空气模拟真实干燥乏气/烟气,搭建了混合气体外掠圆形翅片管束对流冷凝实验系统,获得了灰分浓度、水蒸气质量分数、主流气体入口温度等因素对其积灰和阻力特性的影响规律.实验结果表明,阻力系数随着灰分浓度和气体入口温度的增加而增加,随水蒸气质量分数的增加而减小,...     

Anti-function solution of uniaxial anisotropic Stoner-Wohlfarth model

The anti-trigonometric function is used to strictly solve the uniaxial anisotropic Stoner-Wohlfarth (SW) model, which can obtain the relation of the angle α (θ) between the magnetization (the anisotropy field) and the applied magnetic field. Using this analytic solution, the hysteresis loops of uniaxial anisotropic SW particles magnetized in typical directions could be numerically calculated. Then, the hysteresis loops are obtained in randomly distributed SW particle ensembles while ignoring the dipole interaction among them with the analytic solution. Finally, the correctness of the analytic solution is verified by the exact solutions of remanence, switching field, and coercivity from the SW model. The analytic solution provides an important reference for understanding the magnetizing and magnetization reversal processes of magnetic materials.     

Superdiffusion on a comb structure

We study specific properties of particles transport by exploring an exact solvable model, a so-called comb structure, where diffusive transport of particles leads to subdiffusion. A performance of the Lévy-like process enriches this transport phenomenon. It is shown that an inhomogeneous convection flow is a mechanism for the realization of the Lévy-like process. It leads to superdiffusion of particles on the comb structure. This superdiffusion is an enhanced one with an arbitrary large transport exponent, but all moments are finite. A frontier case of superdiffusion, where the transport exponent approaches infinity, is studied. The log-normal distribution with the exponentially fast superdiffusion is obtained for this case.     

溶液液滴蒸发变干的环状沉积

液体蒸发驱动的颗粒自组装现象在许多的工业技术中有重要应用. 本文利用显微镜观测含有颗粒物质的液滴变干后留在固体表面的颗粒形成的环状沉积图案. 采用微米粒径的SiO₂小球水溶液液滴蒸发变干模拟咖啡环的形成过程, 结果发现液滴蒸发过程中接触线的钉扎是环状沉积的必要条件. 在液滴蒸发过程中颗粒随着补偿流不断的向液滴边缘移动, 聚集在接触线处形成环. 液滴蒸发变干后残留在液滴内部的颗粒数随颗粒质量分数的增加而增加, 可以达到单层的颗粒排列. 而玻璃衬底上的颗粒环在颗粒质量分数很小时, 形成单层排列, 且一排一排地生长. 蒸发过程中颗粒环由于液滴边缘的尺寸限制向液滴中心缓慢移动. 这会导致液滴中不同大小颗粒的分离. 关键词： 液滴 接触线 蒸发 颗粒     

In‐Situ Measurement of Local Particle Flux Densities in a Complex Two‐Phase Flow

An optical measuring technique is presented allowing the exact in‐situ measurement of local particle flux densities in a confined channel flow by counting single particles penetrating an optically well defined measuring volume. This enables a precise flux determination up to the direct vicinity of planar walls. The measurement set‐up and its calibration as well as the whole test facility are described in detail. This measurement technique is used to study the particle transport in electrostatic precipitators. Exemplarily, results of particle flux profiles as well as precipitation, as gained from balances of parts of the precipitator channel, are presented. Furthermore, the possibility to determine particle velocity fluctuations is demonstrated.     

Development of the diffusion-inertia model of particle deposition in turbulent flows

There is presented a modification of the diffusion-inertia model that describes the distribution and deposition of low-inertia particles in turbulent near-wall flows. For the transport equation of the dispersed phase concentration, there is proposed a new wall function that takes into account the nonequilibrium effects and nonlocality of the turbulent transport of the dispersed phase in the near-wall zone caused by the particles’ inertia. This allowed widening the applicability limits of the diffusion-inertia model even for particles with a relaxation time with a magnitude of several hundred. The calculation results for the rate of the particles’ deposition from the turbulent flow to the walls in a round pipe are in good accord with the literature experimental data and the data of direct numerical simulation.     

微通道板电子输运特性的仿真研究

对微通道板(Micro-Channel Plate,MCP)的电子输运特性进行仿真研究.利用数值方法分析微光像增强器电子光学系统,得到电场分布.通过电场分布追踪MCP电子运动轨迹,确定电子在荧光屏像面上的落点分布.据此研究MCP电子输运,分析斜切角、通道直径及两端电压对电子输运、像增强器调制传递函数(Modulation Transfer Function,MTF)及分辨率的影响.结果显示,当MCP斜切角为14°、通道直径为5.0μm、两端电压为900 V时,MCP具有良好的电子输运特性,像增强器MTF特性好,分辨率高.     

Time history of diesel particle deposition in cylindrical dielectric barrier discharge reactors

Non-thermal plasma (NTP) treatment reactors have recently been developed for elimination of diesel particulate matter for reducing both the mass and number concentration of particles. The role of the plasma itself is obscured by the phenomenon of particle deposition on the reactor surface. Therefore, in this study, the Lagrangian particle transport model is used to simulate the dispersion and deposition of nano-particles in the range of 5 to 500 nm in a NTP reactor in the absence of an electric field. A conventional cylindrical dielectric barrier discharge reactor is selected for the analysis. Brownian diffusion, gravity and Saffman lift forces were included in the simulations, and the deposition efficiencies of different sized diesel particles were studied. The results show that for the studied particle diameters, the effect of Saffman lift is negligible and gravity only affects the motion of particles with a diameter of 500 nm or larger. Time histories of particle transport and deposition were evaluated for one-time injection and a continuous (multiple-time) injection. The results show that the number of deposited particles for one-time injection is identical to the number of deposited particles for multiple-time injections when adjusted with the shift in time. Furthermore, the maximum number of escaped particles occurs at 0.045 s after the injection for all particle diameters. The presented results show that some particle reduction previously ascribed to plasma treatment has ignored contributions from the surface deposition.