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1.
The time-dependent problems of radiative transfer involve a coupling between radiation and material energy fields and are nonlinear because of proposed temperature dependence of the medium characteristics in semi-infinite medium with Rayleigh anisotropic scattering. By means of the limited flux, Chapman-Enskog and maximum entropy technique the time-dependent radiative transfer equation has been solved explicitly. The maximum entropy method is used to solve the resulting differential equation for radiative energy density. The calculations are carried out for temperature (normalized dimensionless) Θ(x,τ), radiative energy density and net flux with Rayleigh and anisotropic scattering for different space at different times.  相似文献   

2.
The Chapman-Enskog method of solution of the relativistic Boltzmann equation is generalized in order to admit a time-derivative term associated to a thermodynamic force in its first order solution. Both existence and uniqueness of such a solution are proved based on the standard theory of integral equations. The mathematical implications of the generalization introduced here are thoroughly discussed regarding the nature of heat as chaotic energy transfer in the context of relativity theory.  相似文献   

3.
4.
We study the diffusion of a particle on the sites of a triangular lattice of which half the sites are occupied by a background of other particles. No two particles may occupy the same site. We carry out Monte Carlo simulations for the following model: At each Monte Carlo step the tracer attempts to move to a neighboring site, which it does if the site is unoccupied. At each step, each background particle attempts to desorb with probability. If a background particle desorbs, it is replaced at a randomly chosen site on the lattice. We define R tr 2 (t)/t=D tr. For the case=0, we calculateD 0t k and findk=0.71±0.01, wheret is the number of Monte Carlo steps. When0, we calculateD tr ~ w 1 and findw ad=0.24±0.02. We compare this to the model in which the background particles are constrained to move to nearest neighbor sites and findD tr w 1 withw 1=0.28±0.03.  相似文献   

5.
测量电子气体的速度分布函数   总被引:2,自引:0,他引:2  
苏为宁  赵经武  袁文  孙理 《物理实验》2006,26(12):28-29
利用夫兰克-赫兹实验仪测量了电子气体的速度分布函数,并分析了电子与氩原子碰撞的动力学过程.  相似文献   

6.
In this paper a radioactive tracer technique based on sliding cell method developed in our laboratory for the study of diffusion in liquids is presented in detail. This method consists of radioactive and non-radioactive liquid columns of equal length and the radiation detector is placed in a vertical geometry over the diffusion column. Some liquid metals and aqueous electrolyte solutions were studied by this method. The data of liquid metals like mercury and gallium have been analyzed from the point of view of hard sphere model and those of electrolyte solutions from phenomenological theories. Onsager’s coefficientsL 11,L 12,L 22 have been calculated from the experimental data and the variation of diffusion with solute concentration has been explained from ion-ion interaction.  相似文献   

7.
It is well-known that the classical Chapman-Enskog procedure does not work at the level of Burnett equations (the next step after the Navier-Stokes equations). Roughly speaking, the reason is that the solutions of higher equations of hydrodynamics (Burnett's, etc.) become unstable with respect to short-wave perturbations. This problem was recently attacked by several authors who proposed different ways to deal with it. We present in this paper one of possible alternatives. First we deduce a criterion for hyperbolicity of Burnett equations for the general molecular model and show that this criterion is not fulfilled in most typical cases. Then we discuss in more detail the problem of truncation of the Chapman-Enskog expansion and show that the way of truncation is not unique. The general idea of changes of coordinates (based on analogy with the theory of dynamical systems) leads finally to nonlinear Hyperbolic Burnett Equations (HBEs) without using any information beyond the classical Burnett equations. It is proved that HBEs satisfy the linearized H-theorem. The linear version of the problem is studied in more detail, the complete Chapman-Enskog expansion is given for the linear case. A simplified proof of the Slemrod identity for Burnett coefficients is also given.  相似文献   

8.
Analytical results are derived for the effective dispersion of a passive scalar in a stochastic velocity field evolving in a fast time scale. These results are favorably compared with direct computer simulation of stochastic differential equations containing multiplicative space-time correlated noise.  相似文献   

9.
Hermite cubic splines and collocation are used to solve, in an efficient and accurate way, the Chapman-Enskog equations for viscosity and heat transfer and to compute the Burnett functions required for Poiseuille-flow problems based on rigid-sphere collisions and the linearized Boltzmann equation.  相似文献   

10.
The method of calculation of intense helical electron beams which allows to find the distribution function of electrons with respect to their transverse (oscillatory) and longitudinal velocities is developed. The initial velocity distribution function can be arbitrary. The data obtained in numerical simulation and experimental measurements for beams with various topologies are compared. The evolution of the transverse velocity distribution function with the beam current growth is traced. It is found that the transformation of the velocity distribution function may indicate a possible instability in a real beam.  相似文献   

11.
The earlier-developed statistical theory of diffusion in concentrated alloys based on the master equation approach is generalized to treat tracer diffusion in binary alloys. The theory developed is used to describe concentration dependencies of both tracer and intrinsic diffusion coefficients and to estimate microscopic parameters of diffusion in alloys CuNi, CuZn and AgCd for which necessary experimental data are available. We show that all main features of strong and peculiar concentration dependencies of diffusion coefficients observed in these alloys are naturally explained by the theory. Signs and scales of interatomic interactions important for diffusion in these alloys are found to strongly depend on the ratio of atomic sizes of alloy components, and types of these dependencies agree with simple physical considerations. We also discuss physical reasons for sharp concentration dependencies of diffusion coefficients characteristic of real alloys.  相似文献   

12.
The initial-value problem for the Boltzmann-Lorentz equation for hard spheres at zero temperature is shown to be ill defined, the general solution depending on an arbitrary function. The uniqueness of the solution can be obtained by imposing the conservation of the number of particles (Carleman's type of condition does not suffice). The linearized Boltzmann equation for hard spheres is then analyzed, as it occurs in Enskog's method for calculating transport coefficients. It is demonstrated that in the case of viscosity and diffusion it is necessary to add supplementary conditions to obtain the uniqueness of the solution. The nonuniform character of Enskog's expansion and violation of positivity in the large velocity region are exhibited.  相似文献   

13.
In this paper, a new formalism of a combined tracer and interdiffusion experiment for a binary interdiffusion couple is developed. The analysis requires an interdiffusion couple that initially contains a thin layer of tracers of one or both of the constituent elements at the original interface of the couple (sandwich interdiffusion experiment). This type of interdiffusion experiment was first performed in 1958 by J.R. Manning. The theoretical analysis presented in this paper is based on a newly developed phenomenological theory of isotopic interdiffusion combined with the Boltzmann–Matano formalism. This new analysis now provides the means to obtain the composition dependent interdiffusion coefficient and tracer diffusion coefficients simultaneously from analysis of the interdiffusion and tracer profiles in a single sandwich interdiffusion experiment. The new analysis is successfully applied to the results of Manning’s original ‘sandwich interdiffusion’ experiment in the Ag–Cd system (six couples in total) and is validated with an independent determination of the Ag and Cd tracer diffusion coefficients by Schoen using the conventional thin film technique. Suggestions for further development of the sandwich interdiffusion experiment and analysis to the case of multicomponent alloys are provided.  相似文献   

14.
唐莹  佘守宪 《大学物理》2001,20(11):16-19
从演示统计规律的装置-伽耳顿板实验出发,用初等微积分方法推导高斯误差函数,麦氏速率分布律,扩散方程,扩散系数。  相似文献   

15.
For an argon glow discharge in a 1 mm thick cell at room temperature, we have observed the absorption spectrum of the 1s3–2p2 (Paschen notation) line by using a diode laser. It is found that, with a decrease in the gas pressure below 0.1 Torr, the linewidth drastically decreases; at 0.02 Torr the velocity distribution of the metastable atoms in the surface normal direction has an apparent temperature of 144 K. The velocity distribution is also found to be anisotropic: the spectrum profile depends on the direction of observation with respect to the surface normal. These phenomena are explained by a model in which the velocity distribution of the metastable atoms is controlled by collisional quenching at the wall surface and velocity-changing collisions with ground state atoms.  相似文献   

16.
Pulsed field gradient (PFG) NMR is applied to investigate flow processes. In this case the NMR signal experiences phase modulation due to flow and signal attenuation due to the distribution of velocities. The velocity distribution consists of one part originating from diffusion and of a second part, the distribution of the directed motion. The usual PFG-experiment in which the gradient strength is incremented cannot distinguish between both. Incrementing velocity at constant gradient strength keeps the contribution from diffusion constant but changes the absolute width of the velocity distribution. So the signal is attenuated again, but only due to the distribution of the directed motion. The phase modulation as a signature of flow is not affected by this strategy, because velocity and gradient strength are Fourier conjugated. The key advantage of this approach is the possibility of measuring very low velocities, which only cause a very slight phase modulation that is easily covered by diffusion. The method is discussed here for very slow flow in a rheometer cell.  相似文献   

17.
Tracer diffusion of 18O in dense, polycrystalline La1−xSrxCoO3 for x = 0.1 has been measured in the temperature range 400 to 600 °C and at 500 °C for x = 0.2 at an oxygen partial pressure of 1 × 105 Pa. Depth profiles were obtained by secondary ion mass spectrometry. The diffusion coefficient for La0.9Sr0.1CoO3 is given by D = (17–247) exp[(−232 ± 8 kJ/mole)/RT] cm2/s. This value is several orders of magnitude lower than D extrapolated from the results for x = 0.2 measured in the 700–900 °C temperature range. One possible explanation for the discrepancy is that the two measurements reflect different diffusion paths. As expected, La0.8Sr0.2CoO3 exhibits a higher diffusivity at 500 °C than does La0.9Sr0.1CoO3.  相似文献   

18.
Based on two-level atomic density matrix movement equation and emitting operator, the physical model is established for laser induced moving atomic resonant fluores cence. Theoretically study showsthat the measurement of atomic velocity distribution by means of laser induced fluorescence is only valid when the physical factors, such as atomic natural line width, laser power, laser line width, is suitably selected.  相似文献   

19.
20.
采用蒙特-卡罗(Monte Carlo)模拟方法,研究了初始溅射粒子密度对其传输中的密度和速度分布以及环境气体密度分布的影响.结果表明,随着初始溅射粒子密度增大,烧蚀粒子和环境气体高密度峰的交叠区离开靶的最大距离减小,被衬底反弹后,距靶的最小距离减小,烧蚀粒子的速度分布随初始溅射粒子密度增大而变宽,当初始溅射粒子密度大于8.33×1025 m-3时,出现速度劈裂现象.所得结论为进一步定量研究纳米晶粒的成核机理提供了基础. 关键词: Monte Carlo模拟 烧蚀粒子 密度分布 速度分布  相似文献   

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