Conversion between kinetic energy and potential energy in the classical nonlocal Boltzmann equation

An important property of the classical Boltzmann equation is that kinetic energy is conserved. This is closely connected to the fact that the Boltzmann equation describes the nonequilibrium properties of an ideal gas. Generalizations of the Boltzmann equation to higher density involve, among other things, allowing the colliding particles to be at different positions. This spatial nonlocality is known to contribute to the density corrections of gas transport properties. For soft potentials such a spatial separation of the particles also leads to a conversion between kinetic and potential energy. In evaluating these effects the classical dynamics of the whole collision trajectory must be taken into account, involving also the time for the collision process. The resulting time nonlocality has usually been reinterpreted in terms of a spatial nonlocality. However, for a homogeneous system this is not possible and only the time nonlocality remains, this then being responsible for the conversion between kinetic and potential energy. This paper aims to clarify these properties of the nonlocal corrections to the classical mechanical Boltzmann collision term. Comments on the corresponding problem for the quantum Boltzmann equation are also made.     

Dirac方程的数值解法及其在原子总能量计算中的应用

中心势近似下径向Dirac方程的求解是相对论性原子(离子)结构计算的基础.本文通过相对论性方程中径向波函数大分量与非相对论方程径向波函数的类比,提出了径向Dirac方程的一种数值解法.为了验证数值解法的精度和可靠性,首先将数值结果与类氢势作用下的解析解进行比较.然后,将这种算法扩展到基于解析势的相对论性原子结构计算中,并将计算出的总能量与实验结果和其他方法得到的结果进行对比.     

Simultaneous solution of Kompaneets equation and radiative transfer equation in the photon energy range 1-125 keV

Radiative transfer equation in plane parallel geometry and Kompaneets equation is solved simultaneously to obtain theoretical spectrum of 1-125 keV photon energy range. Diffuse radiation field are calculated using time-independent radiative transfer equation in plane parallel geometry, which is developed using discrete space theory (DST) of radiative transfer in a homogeneous medium for different optical depths. We assumed free-free emission and absorption and emission due to electron gas to be operating in the medium. The three terms n, n² and (∂n/∂x_k) where n is photon phase density and x_k=(hν/kT_e), in Kompaneets equation and those due to free-free emission are utilized to calculate the change in the photon phase density in a hot electron gas. Two types of incident radiation are considered: (1) isotropic radiation with the modified black body radiation I^MB[1] and (2) anisotropic radiation which is angle dependent. The emergent radiation at τ=0 and reflected radiation τ=τ_max are calculated by using the diffuse radiation from the medium. The emergent and reflected radiation contain the free-free emission and emission from the hot electron gas. Kompaneets equation gives the changes in photon phase densities in different types of media. Although the initial spectrum is angle dependent, the Kompaneets equation gives a spectrum which is angle independent after several Compton scattering times.     

Intermittent Structures in the High Field Side Boundary of the HYBTOK-II Tokamak

The spatial and temporal characteristics of the turbulence in the inboard and outboard scrape-off layer (SOL) of tokamak HYBTOK-II have been studied using poloidal probe array. Bursty behaviour with intermittent bursts was observed for both outboard and inboard SOL. In the inboard (high field side), high level of density fluctuations has been observed. The fluctuations in the high field side and low field side are identical in statistics that is non-Gaussian one.     

Application of microscopic transport model in the study of nuclear equation of state from heavy ion collisions at intermediate energies

The equation of state (EOS) of nuclear matter, i.e., the thermodynamic relationship between the binding energy per nucleon, temperature, density, as well as the isospin asymmetry, has been a hot topic in nuclear physics and astrophysics for a long time. The knowledge of the nuclear EOS is essential for studying the properties of nuclei, the structure of neutron stars, the dynamics of heavy ion collision (HIC), as well as neutron star mergers. HIC offers a unique way to create nuclear matter with high density and isospin asymmetry in terrestrial laboratory, but the formed dense nuclear matter exists only for a very short period, one cannot measure the nuclear EOS directly in experiments. Practically, transport models which often incorporate phenomenological potentials as an input are utilized to deduce the EOS from the comparison with the observables measured in laboratory. The ultrarelativistic quantum molecular dynamics (UrQMD) model has been widely employed for investigating HIC from the Fermi energy (40 MeV per nucleon) up to the CERN Large Hadron Collider energies (TeV). With further improvement in the nuclear mean-field potential term, the collision term, and the cluster recognition term of the UrQMD model, the newly measured collective flow and nuclear stopping data of light charged particles by the FOPI Collaboration can be reproduced. In this article we highlight our recent results on the studies of the nuclear EOS and the nuclear symmetry energy with the UrQMD model. New opportunities and challenges in the extraction of the nuclear EOS from transport models and HIC experiments are discussed.     

Klein-Gordon方程Q球解中能量稳定性和扰动研究

本文研究了一种复标量场模型中的双层Q球解,在解析形式下计算了Q球荷和能量. 同时,分析了其能量稳定性质,通过Klein-Gordon 方程获得了Q球能量的扰动表达式. 另外,还讨论了Q球暗物质产生的物理效应. 关键词： Klein-Gordon方程 Q球解 能量稳定性与扰动 暗物质     

放射性束引起的重离子碰撞中敏感于对称能的几个观测量

利用同位旋与动量相关的强子输运模型，我们研究了放射性束引起的中能重离子碰撞中几个观测量的对称能效应。我们发现自由核子发射的非对称度的快度分布，中快度中－质比的横动量分布，的动能分布，以及同位旋相分化（fractionation）的时间演化都敏感于对称能。     

宏观交通流模型的能耗研究

本文在几种典型的宏观交通流模型的基础上,导出能量耗散的计算公式,宏观交通流模型能耗不同于元胞自动机交通模型,其能耗不仅考虑车流速度减少,而且还要计及通过路段的车流通量引起的能耗.通过对满足黎曼初始条件的道路能耗和道路交通瓶颈处能耗的计算和理论分析,表明交通拥堵处,能量耗散比较高,而且能量耗散的变化也能反映交通拥堵产生及消散的情况.     

Novel energy dissipative method on the adaptive spatial discretization for the Allen–Cahn equation

We propose a novel energy dissipative method for the Allen–Cahn equation on nonuniform grids. For spatial discretization, the classical central difference method is utilized, while the average vector field method is applied for time discretization. Compared with the average vector field method on the uniform mesh, the proposed method can involve fewer grid points and achieve better numerical performance over long time simulation. This is due to the moving mesh method, which can concentrate the grid points more densely where the solution changes drastically. Numerical experiments are provided to illustrate the advantages of the proposed concrete adaptive energy dissipative scheme under large time and space steps over a long time.     

弱电离大气等离子体电子能量分布函数的理论研究

使用球谐展开的方法求解玻尔兹曼方程,得到了弱电离大气等离子体(79％氮气和21％的氧气)的电子能量分布函数(EEDF).发现当约化电场较小时(E/N＜100 Td),EEDF在2-3 eV急剧下降,在此情况下,高能尾部比麦氏分布要小;当约化电场增加,E/N＞ 400 Td,分布函数趋近于麦氏分布;当约化电场进一步增加,E/N＞ 2000 Td,EEDF的高能尾部(超过200 eV)相对于麦氏分布增加,在高频场作用下,EEDF更倾向于麦氏分布.当ω》vm时,有效电子温度只依赖于E/ω,而与碰撞频率无关;当ω《vm时,有效电子温度只依赖于E/N,与微波频率无关.与一些单原子分子等离子体中电子-电子碰撞在电离度大于10-6时就会影响EEDF不同,空气等离子体中,只有当电离度大于0.1％时,电子-电子碰撞才会对EEDF有明显影响.     

Restricted scaling range models for turbulent velocity and scalar energy transfers in decaying turbulence

The effect of finite Reynolds numbers and/or internal intermittency on the total kinetic energy and scalar energy transfers is examined in detail. For this purpose, two distinct models for velocity and scalar energy transfer are proposed in the specific context of freely decaying isotropic turbulence. The first one extends the already existing dynamical models (hereafter DYM, i.e. based on transport equations originated in Navier–Stokes and advection-diffusion transport equations). The second one relies on the characteristic time of the strain at a specific scale (hereafter SBM). Both models account for the Reynolds number dependence of the scaling exponent of the second-order structure functions, over a range of scales where such exponents may be defined, i.e. a restricted scaling range (RSR). Therefore, the models developed aim at reproducing the energy transfer over the RSR. The predicted energy transfer is very sensible to variations of the scaling exponent, especially at low Reynolds numbers. The approach towards the asymptotic 4/3 law is closely reproduced by the two models. The dynamical model reproduces the experimental results accurately especially in the vicinity of the Taylor microscale, while the SBM agrees almost perfectly with measurements at nearly all scales.     

Analytical solution of the Boltzmann--Poisson equation and its application to MIS tunneling junctions

In order to consider quantum transport under the influence of an electron--electron (e--e) interaction in a mesoscopic conductor, the Boltzmann equation and Poisson equation are investigated jointly. The analytical expressions of the distribution function for the Boltzmann equation and the self-consistent average potential concerned with e--e interaction are obtained, and the dielectric function appearing in the self-consistent average potential is naturally generalized beyond the Thomas--Fermi approximation. Then we apply these results to the tunneling junctions of a metal--insulator--semiconductor (MIS) in which the electrons are accumulated near the interface of the semiconductor, and we find that the e--e interaction plays an important role in the transport procedure of this system. The electronic density, electric current as well as screening Coulombic potential in this case are studied, and we reveal the time and position dependence of these physical quantities explicitly affected by the e--e interaction.     

On the advanced integral equation theory description of dense Yukawa one-component plasma liquids

Different advanced bridge function closures are utilized to investigate the structural and thermodynamic properties of dense Yukawa one-component plasma liquids within the framework of integral equation theory. The isomorph-based empirically modified hypernetted-chain, the variational modified hypernetted-chain, the Rogers–Young, and the Ballone–Pastore–Galli–Gazzillo approaches are compared at the level of thermodynamic properties, radial distribution functions, and bridge functions. The comparison, based on accuracy and computational speed, concludes that the two modified hypernetted-chain approaches are superior and singles out the isomorph-based variant as the most promising alternative to computer simulations of structural properties of dense Yukawa liquids. The possibility of further improvement through artificial crossover to exact asymptotic limits is studied.     

脉冲高能量密度等离子体材料表面改性及其应用

脉冲高能量密度等离子体（pulsed high energy density plasma, PHEDP）是一项新的材料表面改性技术.它集高电子温度、高能量密度、高定向速度于一身,在制备薄膜时具有沉积薄膜的温度低、沉积效率高、能量利用率高的优点,并兼具表面溅射、离子注入、冲击波和强淬火效应等综合效应;它可以制备纳米晶或非晶硬质薄膜,提高基底材料的表面硬度和耐磨、耐蚀性能;能够实现非金属材料表面金属化,所制备薄膜与基底之间存在很宽的混合过渡区,因此膜/基结合良好.文章主要介绍了作者近年来在该领域的部分研究成果,简要介绍了脉冲高能量密度等离子体的原理、特点及应用.分析了脉冲等离子体与材料相互作用的基本物理现象.     

The quantum Kirchhoff equation and quantum current and energy spectrum of a homogeneous mesoscopic dissipation transmission line

On the basis of quantization of charge, the loop equations of quantum circuits are investigated by using the Heisenberg motion equation for a mesoscopic dissipation transmission line. On the supposition that the system has a symmetry under translation in charge space, the quantum current and the quantum energy spectrum in the mesoscopic transmission line are given by solving their eigenvalue equations. Results show that the quantum current and the quantum energy spectrum are not only related to the parameters of the transmission line, but also dependent on the quantized character of the charge obviously.     

Effect of dark energy models on the energy content of charged and rotating black holes

The energy content of the charged-Kerr(CK)spacetime surrounded by dark energy(DE)is investigated using approximate Lie symmetry methods for the differential equations.For this,we consider three different DE scenarios:cosmological constant with an equation of state parameter$ω_q=-2/3,quintessence DE with an equation of state parameterω_c=-1,and a frustrated network of cosmic strings with an equation of state parameterω_n=-1/3.To study the gravitational energy of the CK black hole surrounded by the DE,we explore the symmetries of the 2nd-order perturbed geodesic equations.It is noticed,for all the values ofω,the exact symmetries are recovered as 2nd-order approximate trivial symmetries.These trivial approximate symmetries give the rescaling of arc length parameter s in this spacetime which indicates that the energy in the underlying spacetime has to be rescaled by a factor that depends on the black hole parameters and the DE parameter.This rescaling factor is compared with the factor of the CK spacetime found in[Hussain et al.Gen.Relativ.Gravit.(2009)]and the effects of the DE on it are discussed.It is observed that for all the three values of the equation of state parameterω,the effect of DE results in decreased energy content of the black hole spacetime,regardless of values of the charge Q,spin a and the DE parameterα.This reduction in the energy content due to the involvement of the DE favours the idea of mass reduction of black holes by accretion of DE given by[Babichev et al.Phys.Rev.Lett.(2004)].     

国际热核实验反应堆计划及其对中国核能发展战略的影响

随着世界人口增长和经济持续发展,能源短缺问题变得越来越严峻,世界各国都在努力寻找煤、石油、天然气等化石能源的替代能源.核聚变能具有清洁、高效、资源丰富等优点,是最有希望解决人类能源问题的途径之一.文章指出了发展核聚变能的重要性,回顾了磁约束聚变研究的历程,简述了国际热核实验反应堆（ITER）计划的进展及中国的相关研究情况,最后对中国核能发展战略作出展望.     

国际热核实验反应堆计划及其对中国核能发展战略的影响

随着世界人口增长和经济持续发展,能源短缺问题变得越来越严峻,世界各国都在努力寻找煤、石油、天然气等化石能源的替代能源.核聚变能具有清洁、高效、资源丰富等优点,是最有希望解决人类能源问题的途径之一.文章指出了发展核聚变能的重要性,回顾了磁约束聚变研究的历程,简述了国际热核实验反应堆(ITER)计划的进展及中国的相关研究情况,最后对中国核能发展战略作出展望.     

等离子体屏蔽效应对类氢离子能级结构和辐射跃迁性质的影响

在Debye-Hückel屏蔽近似下,基于相对论Dirac-Fock方法,发展了包括等离子体屏蔽效应的自洽场计算程序.使用该程序研究了等离子体屏蔽效应对类氢离子能级结构和辐射跃迁性质的影响.结果表明,当原子处于等离子体环境中,所有束缚态能级向连续态移动, 移动量随着屏蔽长度的减小而增大.振子强度随屏蔽长度的变化也表现出了相同的规律.进一步分析了相对论效应和等离子体屏蔽效应的耦合,发现对于中Z元素,相对论效应和等离子体屏蔽效应存在较强的耦合.讨论了等离子体屏蔽效应对原子精细结构能级的影响.计算发现,由于等离子体屏蔽效应,原子的能级次序发生了变化,κ简并被消除. 关键词： 等离子体屏蔽 Debye-Hückel 模型 能级结构 跃迁概率     

Adjustment of the ion energy distribution in double plasma and other synthesized plasma devices

The parallel ion energy distribution of a synthesized plasma can be readily controlled via plasma potential gradients in the ion source chamber(s). Alternatively, layers of electrically biased metal filaments can introduce an isotropic ion heating.