An analytical study of space-dependent evolution problems in particle transport theory

Summary Space-dependent evolution problems arising in particle transport theory are analytically studied via a systematic application of the Boltzmann equation. Some explicit solutions, that can improve our knowledge of the spatial effects in such a class of problems, are constructed and briefly commented on a physical ground.

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Riassunto Problemi spaziali di evoluzione che si incontrano nella teoria del trasporto di particelle sono studiati analiticamente per mezzo di una sistematica applicazione dell'equazione di Boltzmann. Alcune soluzioni esplicite, che possono migliorare la nostra conoscenza degli effetti spaziali in tale classe di problemi, sono costruite e commentate brevemente su base fisica.

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Резюме Аналитически, используя уравнение Больцмана, исследуются проблемы пространственной эволюции, зозниакющие в теории переноса частиц. Конструируются некоторые точные решения, которые могут уточнить наше понимание пространственных эффектов в таком классе проблем. Проводится обсуждение этих решений.

     

An enhanced beam model for constrained layer damping and a parameter study of damping contribution

An enhanced analytical model is presented based on an extension of previous models for constrained layer damping (CLD) in beam-like structures. Most existing CLD models are based on the assumption that shear deformation in the core layer is the only source of damping in the structure. However, previous research has shown that other types of deformation in the core layer, such as deformations from longitudinal extension and transverse compression, can also be important. In the enhanced analytical model developed here, shear, extension, and compression deformations are all included. This model can be used to predict the natural frequencies and modal loss factors. The numerical study shows that compared to other models, this enhanced model is accurate in predicting the dynamic characteristics. As a result, the model can be accepted as a general computation model. With all three types of damping included and the formulation used here, it is possible to study the impact of the structure's geometry and boundary conditions on the relative contribution of each type of damping. To that end, the relative contributions in the frequency domain for a few sample cases are presented.     

Effects of damping on the low-frequency acoustics of listening rooms based on an analytical model

A study of the effects of damping on the low-frequency acoustics of listening rooms has been undertaken. The study was carried out using a new numerical implementation of an analytical solution based on a model developed by Bistafa and Morrissey. The model was designed to simulate the sound field in rectangular enclosures below the Schroeder cut-off frequency. Four hypothetical rooms were studied, a lightly damped room, a well damped room, a statistically compliant European Broadcast Union control room and a compliant European Broadcast Union control room. The most important result from the study using the proposed model was the influence of modes above the Schroeder cut-off frequency on reverberation time. This was caused by the variations in damping between mode types and variations in the modal coupling between the source and receiver. The research suggests that Schroeder's 1954 cut-off frequency for the influence of modes was more correct for highly damped rooms, in comparison with the Schroeder's 1964 relation.     

量子阻尼振子的两种解析解法

应用u变换与不变量理论，求解一维量子阻尼振子，两种解法的不同仅在于交换了u变换与相因子的顺序。     

An analytical excitation model for an ionizing plasma

From an analytical model for the population of high-lying excited levels in ionizing plasmas it appears that the distribution is a superposition of the equilibrium (Saha) value and an overpopulation. This overpopulation takes the form of a Maxwell distribution for free electrons. Experiments for He II, Na I and Ar I confirm the general validity of the model.     

An analytical model for evaporative cooling of atoms

Evaporative cooling of trapped atoms is described as a sequence of truncation of the high-energy tail of the thermal distribution followed by collisional relaxation. This model is solved analytically for arbitrary power-law potentials. The threshold density for accelerated evaporation is. found to be lowest in a three-dimensional linear potential.Dedicated to H. Walther on the occasion of his 60th birthday     

纳米MOSFET迁移率解析模型

从玻尔兹曼方程出发，重新计算了纳米MOSFET沟道内的载流子所服从的分布函数，特别是考虑了纳米MOSFET横向电场和纵向电场之间的相互作用，并且以得到的非平衡状态下的分布函数为基础，考虑载流子寿命和速度的统计分布，给出了纳米MOSFET载流子迁移率的解析表达式.通过与数值模拟结果进行比较和分析，该迁移率解析模型形式简洁、物理概念清晰，且具有相当精度. 关键词： 玻尔兹曼方程 纳米MOSFET 迁移率 沟道有效电场     

An analytical model for total absorption of a band

A theoretical model for total absorption of a band is developed based on the Elsasser band model and considering the effects of spectral band contour and low-intensity lines in the spectral band. This model yields a simple and analytical expression and has the correct asymptotic forms. Comparisons with other models are presented.     

An analytical threshold voltage model for dual-strained channel PMOSFET

Based on the analysis of vertical electric potential distribution across the dual-channel strained p-type Si/strained Si 1-x Ge x /relaxd Si 1-y Ge y (s-Si/s-SiGe/Si 1-y Ge y) metal-oxide-semiconductor field-effect transistor (PMOSFET),an-alytical expressions of the threshold voltages for buried channel and surface channel are presented.And the maximum allowed thickness of s-Si is given,which can ensure that the strong inversion appears earlier in the buried channel (compressive strained SiGe) than in the surface channel (tensile strained Si),because the hole mobility in the buried channel is higher than that in the surface channel.Thus they offer a good accuracy as compared with the results of device simulator ISE.With this model,the variations of threshold voltage and maximum allowed thickness of s-Si with design parameters can be predicted,such as Ge fraction,layer thickness,and doping concentration.This model can serve as a useful tool for p-channel s-Si/s-SiGe/Si 1-y Ge y metal-oxide-semiconductor field-effect transistor (MOSFET) designs.     

An analytical model for evaluating the metal-metal surface energy

Metal-metal surface energies are calculated as a function of the electron density at the interface. Their contribution to the adhesion energy is shown to be small.     

An interacting particle model with compact hierarchical structure

We present a model interacting particle system with a population of fixed size in which particles wander randomly in space, and pairs interact at a rate determined by a reaction kernel with finite range. The pairwise interaction randomly selects one of the particles (the victim) and instantly transfers it to the position of the other (the killer), thus maintaining the total number. The special feature of the model is that it possesses a closed hierarchical structure in which the statistical moments of the governing master equation lead to closed equations for the reduced distribution functions (the concentration, pair correlation function, and so on). In one spatial dimension, we show that persistent spatial correlations (clusters) arise in this model and we characterize the dynamics in terms of analytical properties of the pair correlation function. As the range of the reaction kernel is increased, the dynamics varies from an ensemble of largely independent random walkers at small range to tightly bound clusters with longer-range reaction kernels.     

A second-order implicit particle mover with adjustable damping

A new algorithm for the calculation of particle trajectories is introduced. The algorithm combines second-order accuracy in the real frequency with third-order user-adjustable attenuation. It requires little storage of data from previous time levels. The method was designed for use in implicit particle-in-cell plasma simulation codes, and this application is treated in detail. It may also prove useful in other applications where one seeks to preserve the accuracy of low-frequency oscillations while rapidly damping under-resolved high frequency motions, e.g., solution of the field equations in electromagnetic particle codes. An explicit variation, wherein future quantities are obtained by extrapolation, can provide attenuation but not large-timestep stability.     

Soft hollow particle damping identification in honeycomb structures

The aim of this study is to provide a structural damping solution for space applications to enhance mission performance of honeycomb structures. Classical particle dampers are enclosures partially filled with small metallic or glass spheres, attached to a vibrating structure. The induced damping mechanism is mainly due to frictional losses and collision effects. This paper deals with replacing classical hard particles with soft hollow ones. This study is oriented toward experimental investigations and theoretical validation in order to distinguish dissipation phenomena. The experimental approach first relies on identifying the damping in small honeycomb samples filled with particles. Instead of dissipation by friction and impact, the elliptical shape of the measured hysteresis loops highlights that visco-elastic behavior is dominant with these specific soft particle dampers. Then, experimental and numerical validations are performed on aluminum honeycomb cantilever beams filled with particles. To take into account the effect of the particles, equivalent oscillators, based on the previous experimental damping identification, are added to a finite element model. These kinds of particle dampers are highly nonlinear as a function of excitation frequency and amplitude. It is shown that good damping efficiency is achieved across a large frequency range with low impact on structure stiffness. This paper suggests a convenient method to model the structural damping induced by soft hollow particles.     

An analytical model of gas transport in the human lung

Summary A simple physico-mathematical model of gas transport in the human lung is developed. Care is taken to obtain an analytical concordance with the bronchial-tree geometry as given by the Weibel’s morphometric data. The dynamics of diffusion is modelled according to the Taylor and Aris model. The simplest boundary conditions are assumed. An approximate analytical solution is derived with applications to some simple breathing washout experiments. A satisfactory agreement confirms the validity of the model. This work was partially supported by Ministero della Pubblica Istruzione.     

An analytical dispersion model for sources in the surface layer

Summary A two-dimensional model, based on an analytical solution of the diffusion equation in a shear flow, is validated by comparison with cross-wind integrated concentrations of Prairie-Grass experiment. The wind velocity and eddy diffusivity power law profiles, defined respectively by exponent α and β, are determined by fitting log-linear profiles using both Businger and Dyer flux-profile relationships. They result to depend on the vertical plume spread which is a function both of the stability and of the distance from the source. The model, with Dyer's parametrization, fits the data quite well, except for very unstable conditions. Paper presented at the 1^o Congresso del Gruppo Nazionale per la Fisica dell'Atmosfera e dell'Oceano, June 19–22, 1984, Rome.     

An analytical study of the Curie temperature in the D-vector model

The successive analytical expressions up to fifth order for the Curie temperature, T_c(D,d), of the D-vector model on d-dimensional hypercubic lattices are evaluated by the Ginzburg-Landau theory based on cumulant expansion. The results by substituting d = 3 and D = 1, 2, 3 into the expressions approach order by order those of the Ising, XY, and Heisenberg models by Monte Carlo simulation (MC). The differences between ours and the other models are about 5.52, 6.86, and 7.94 percent, respectively.