Solution of the Poisson-Boltzmann Equation for a Cylindrical Particle with a Limited Length: Functional Theoretical Approach

With the help of the method of separation of variables and the Debye-Hüchel approximation, the Poisson-Boltzmann equation that describes the distribution of the potential in the electrical double layer of a cylindrical particle with a limited length has been firstly solved under a very low potential condition. Then with the help of the functional analysis theory this equation has been further analytically solved under general potential conditions and consequently, the corresponding surface charge densities have been obtained. Both the potential and the surface charge densities cointide with those results obtained from the Debye-Hüchel approximation when the very low potential of zeψ〈〈kT is introduced.

Drivers of the differentiation between broad-leaved trees and shrubs in the shift from evergreen to deciduous leaf habit in forests of eastern Asian subtropics

In eastern Asian subtropical forests,leaf habit shifts from evergreen to deciduous broad-leaved woody plants toward higher latitudes.This shift has been largely explained by the greater capacity of deciduous broad-leaved plants to respond to harsh climatic conditions(e.g.,greater seasonality).The advantages of deciduous leaf habit over evergreen leaf habit in more seasonal climates have led us to hypothesize that leaf habits would shift in response to climate changes more conspicuously in forest canopy trees than in forest understory shrubs.Furthermore,we hypothesize that in the forests of the subtropics,plants at higher latitudes,regardless of growth form,would better tolerate seasonal harsh climates,and hence show less differentiation in leaf habit shift,compared to those at lower latitudes.To test these two hypotheses,we modelled the proportion of deciduous broad-leaved species and the incidence of deciduous and evergreen broad-leaved species in woody angiosperm species compositions of ten largesized forest plots distributed in the Chinese subtropics.We found that the rate of leaf habit shift along a latitudinal gradient was higher in forest trees than in forest shrubs.We also found that the differentiation in leaf habit shift between trees and shrubs is greater at lower latitudes(i.e.,warmer climates)than at higher latitudes(i.e.,colder climates).These findings indicate that specialized forest plants are differentially affected by climate in distinct forest strata in a manner dependent on latitudinal distribution.These differences in forest plant response to changes in climate suggest that global climate warming will alter growth forms and geographical distributions and ranges of forests.

Partition Functions for Diatomic Molecules in Plasmas out of Thermal Equilibrium

Two calculation methods on the partition functions for diatomic molecules in plas- mas out of thermal equilibrium are reported. A Boltzmann distribution for the electronic, vi- brational and rotational quantum levels is assumed in the two calculation methods. The results obtained by two methods are displayed for four sorts of diatomic molecules, 02, N2, OH and NO, that are present in humid air plasmas. The calculation method of density for the electronically excited states is developed. Finally, a method to calculate the partition functions for simulating the non-normalized diatomic spectra is discussed.

Theoretical design and experimental synthesis of counter electrode for dye-sensitized solar cells: Amino-functionalized graphene

For some specific catalytic reaction, how to construct active sites on two dimensional materials is of great scientific significance. Dye-sensitized solar cells（DSCs） can be viewed as one representative photovoltaics because in which liquid electrolyte with triiodide/iodide（I;/I;） as redox couples are involved. In this study, amino-functionalized graphene（AFG） has been designed according to theoretically analyzing iodine reduction reaction（IRR） processes and rationally screening the volcanic plot. Then, such AFG has been successfully synthesized by a simple hydrothermal method and shows high electrocatalytic activity towards IRR when serving as counter electrode in DSCs. Finally, a high conversion efficiency of 7.39% by AFG-based DSCs was obtained, which is close to that using Pt as counter electrode.

Green's function Monte Carlo method combined with restricted Boltzmann machine approach to the frustrated J_(1)–J_(2)Heisenberg model

Restricted Boltzmann machine(RBM)has been proposed as a powerful variational ansatz to represent the ground state of a given quantum many-body system.On the other hand,as a shallow neural network,it is found that the RBM is still hardly able to capture the characteristics of systems with large sizes or complicated interactions.In order to find a way out of the dilemma,here,we propose to adopt the Green's function Monte Carlo(GFMC)method for which the RBM is used as a guiding wave function.To demonstrate the implementation and effectiveness of the proposal,we have applied the proposal to study the frustrated J_(1)-J_(2)Heisenberg model on a square lattice,which is considered as a typical model with sign problem for quantum Monte Carlo simulations.The calculation results demonstrate that the GFMC method can significantly further reduce the relative error of the ground-state energy on the basis of the RBM variational results.This encourages to combine the GFMC method with other neural networks like convolutional neural networks for dealing with more models with sign problem in the future.

Technical efficiency and its determinants of the various cropping systems in the purple-soiled,hilly region of southwestern China

This study examines the technical efficiency(TE) differences among typical cropping systems of smallholder farmers in the purple-soiled hilly region of southwestern China.Household-,plot-,and crop-level data and community surveys were conducted to explore TE levels and determinants of typical cropping systems by using a translog stochastic frontier production function.Results indicate significant difference in TE and its determinants among cropping systems.The mean TEs of the rice cropping system(R),the rice-rape cropping system(RR),the rice-rape-potato cropping system(RRP),and the oil cropping system(O) are0.86,0.90,0.84,and 0.85,respectively,which are over 1.17 times higher than those of the maize-sweet potato-other crop cropping system(MSO) and the maize-sweet potato-wheat cropping system(MSW) at0.78 and 0.69,respectively.Moreover,Technical inefficiency(TIE) of different cropping systems is significantly affected by characteristics of the household as well as plot.However,the impact of land quality,mechanical cultivation conditions,crop structure,farming system,farm radius,household type,cultivated land area per capita,and annual household income per capitalon TIE vary by cropping system.Additionally,output elasticity of land,labor,and capital,as a group,is greater than the one of agricultural machinery and irrigation.Finally,when household-owned effective agricultural labor is at full farming capacity,optimal plot sizes for the R,RR,RRP,MSO,MSW,and 0 cropping systems are 1.12hm^2,0.35 hm^2,0.25 hm^2,2.82 hm^2,1.87 hm^2,and 1.17hm^2,respectively.

Semi-analytical method of calculating the electrostatic interaction of colloidal solutions

We present a semi-analytical method of calculating the electrostatic interaction of colloid solutions for confined and unconfined systems. We expand the electrostatic potential of the system in terms of some basis functions such as spherical harmonic function and cylinder function. The expansion coefficients can be obtained by solving the equations of the boundary conditions, combining an analytical translation transform of the coordinates and a numerical multipoint collection method. The precise electrostatic potential and the interaction energy are then obtained automatically. The method is available not only for the uniformly charged colloids but also for nonuniformly charged ones. We have successfully applied it to unconfined diluted colloid system and some confined systems such as the long cylinder wall confinement, the air–water interfacial confinement and porous membrane confinement. The consistence checks of our calculations with some known analytical cases have been made for all our applications. In theory, the method is applicable to any dilute colloid solutions with an arbitrary distribution of the surface charge on the colloidal particle under a regular solid confinement, such as spherical cavity confinement and lamellar confinement.

Theoretical investigation of the thermoelectric transport properties of BaSi_2

The full-potential linear augmented plane wave method based on density functional theory is employed to investigate the electronic structure of BaSi2. With the constant relaxation time and rigid band approximation, the electrical conductivity, Seebeck coefficient and figure of merit are calculated by using Boltzmann transport theory, further eval- uated as a function of carrier concentration. We find that the Seebeck coefficient is more anisotropic than electrical conductivity. The figure of merit of BaSi2 is predicted to be quite high at room temperature, implying that optimal doping may be an effective way to improve thermoelectric properties.

Maxwell-Boltzmann Distribution Mathematica Based Practitioner’s Approach

Utilizing Mathematica this report shows how from a practitioner’s point of view useful quantities some known, and some unknown and fresh properties about the Maxwell-Boltzmann distribution are calculated. We shortcut circling the usage of antiquated incomplete tabulated error functions given in the textbooks and professional literature replacing them with efficient upgrades. And, utilizing the animation features of Mathematica displaying the temperature-dependence of the distribution function assists in visualizing the character of the distribution.

Mathematica在函数作图中的应用

通过介绍Mathematica在函数作图中的应用,为数学教学、数学实验等提供了一个新的适用工具,在多媒体教 学中能直观,形象的描出各种函数的图形,使教学更加深动、形象.

交通网络β指数增长曲线的Boltzmann模型

从已被验证的城市化水平和交通网络的经验模型出发,提出交通网络β指数的数学模型。基于城市化水平的一次logistic函数,借助数学演绎法,推导出交通网络β指数增长曲线的Boltzmann方程;基于城市化水平的二次logistic函数,推导出交通网络β指数增长曲线的二次Boltzmann方程。前者适用于欧美国家和中国东南沿海地区,后者则适用于中国内地,特别是中国北方地区。该模型具有两个主要功能:1)解释和预测交通网络的发展;2)有助于交通网络增长过程的分段研究。

Configuration of propagator method for calculation of electron velocity distribution function in gas under crossed electric and magnetic fields

This paper presents a self-contained description on the configuration of propagator method(PM)to calculate the electron velocity distribution function(EVDF) of electron swarms in gases under DC electric and magnetic fields crossed at a right angle. Velocity space is divided into cells with respect to three polar coordinates v,θ and f. The number of electrons in each cell is stored in three-dimensional arrays. The changes of electron velocity due to acceleration by the electric and magnetic fields and scattering by gas molecules are treated as intercellular electron transfers on the basis of the Boltzmann equation and are represented using operators called the propagators or Green’s functions. The collision propagator, assuming isotropic scattering, is basically unchanged from conventional PMs performed under electric fields without magnetic fields. On the other hand, the acceleration propagator is customized for rotational acceleration under the action of the Lorentz force. The acceleration propagator specific to the present cell configuration is analytically derived. The mean electron energy and average electron velocity vector in a model gas and SF6 were derived from the EVDF as a demonstration of the PM under the Hall deflection and they were in a fine agreement with those obtained by Monte Carlo simulations. A strategy for fast relaxation is discussed, and extension of the PM for the EVDF under AC electric and DC/AC magnetic fields is outlined as well.

Lattice Boltzmann simulations of high-order statistics in isotropic turbulent flows

The lattice Boltzmann method （LBM） is coupled with the multiple-relaxation- time （MRT） collision model and the three-dimensional 19-discrete-velocity （D3Q19） model to resolve intermittent behaviors on small scales in isotropic turbulent flows. The high- order scaling exponents of the velocity structure functions, the probability distribution functions of Lagrangian accelerations, and the local energy dissipation rates are investi- gated. The self-similarity of the space-time velocity structure functions is explored using the extended self-similarity （ESS） method, which was originally developed for velocity spatial structure functions. The scaling exponents of spatial structure functions at up to ten orders are consistent with the experimental measurements and theoretical results, implying that the LBM can accurately resolve the intermittent behaviors. This valida~ tion provides a solid basis for using the LBM to study more complex processes that are sensitive to small scales in turbulent flows, such as the relative dispersion of pollutants and mesoscale structures of preferential concentration of heavy particles suspended in turbulent flows.

Mathematical Physics in Diffusion Problems

Using the divergence theorem and the coordinate transformation theory for the general Fickian second law, fundamental diffusion problems are investigated. As a result, the new findings are obtained as follows. The unified diffusion theory is reasonably established, including a self-diffusion theory and an N (N ≥ 2) elements system interdiffusion one. The Fickian first law is incomplete without a constant diffusion flux corresponding to the Brown motion in the localized space. The cause of Kirkendall effect and the nonexistence of intrinsic diffusion concept are theoretically revealed. In the parabolic space, an elegant analytical method of the diffusion equation is mathematically established, including a nonlinear diffusion equation. From the Schr?dinger equation and the diffusion equation, the universal expression of diffusivity proportional to the Planck constant is reasonably obtained. The material wave equation proposed by de Broglie is also derived in relation to the Brown motion. The fundamental diffusion theories discussed here will be highly useful as a standard theory for the basic study of actual interdiffusion problems such as an alloy, a compound semiconductor, a multilayer thin film, and a microstructure material.

铁北煤矿褐煤自燃预测函数模型研究

针对铁北煤矿褐煤自燃精准预测预报的难题,利用程序升温实验对煤样升温氧化过程中产生的气体进行分析,并选择Logistic函数、指数函数、Boltzmann函数以及四次多项式函数对气体数据进行拟合。研究结果表明:CO的初现温度约为50℃,且随温度的升高呈指数增长趋势,C2H4的初现温度约为140℃,可以作为煤进入加速氧化阶段的标志。依照指标气体优选原则,确定铁北煤矿褐煤自燃的单一指标气体为CO、C2H4,复合指标气体为CO/CO_(2)、C2H4/C2H6;Boltzmann函数模型对0~200℃温度范围内CO和CO/CO_(2)的拟合效果最好,拟合优度R2为分别为0.99995和0.99814,基于统计学特征确定了A_(1)、A_(2)、d_(x)、x_(0)等4个参数的数值并推导出指标气体浓度与煤温的函数公式,经过验证Boltzmann函数模型可以很好地运用到铁北煤矿煤自燃的预测中。

基于Boltzmann光谱法的焊接电弧温度场测量计算

电弧等离子体是非均匀等离子体,其内部进行着复杂的能量和质量输运过程,等离子体的温度测量具有重要意义。Boltzmann作图法测量温度较谱线绝对强度法、标准温度法等测温方法更为方便。基于Boltzmann作图法原理,对TIG电弧进行实时的空间扫描,分析了谱线的选取原则,测量计算出TIG焊电弧等离子体的温度场分布。

发射光谱Boltzmann法测量毛细管放电产生的电热高密度等离子体温度之误差分析

本文详细地分析了目前文献报道的 :采用发射光谱Boltzmann法 ,测量毛细管放电产生的电热高密度等离子体温度时 ,产生误差的原因。当正确地选择光谱参数———谱线上能级统计权重g、跃迁几率A和上能级能量Ei ———Boltzmann法测量毛细管放电产生的电热高密度等离子体温度时 ,实验可信度可高达 99%～ 99 5 % ,测量误差仅为± 6 5 %。